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Eroica
2003-Dec-04, 08:25 AM
Peter and Paul are twins. Peter is on the Earth, to which our stationary frame of reference is attached. Paul is sitting at the controls of his spaceship out in space, far away from any gravitational fields. Paul is also at rest in the stationary frame. Peter’s clock and Paul’s clock are synchronized.

Paul now switches on the rockets on his spaceship and accelerates away into deep space at an acceleration of 1g (≈ 9.8 m/s^2). After 1 year he is travelling close to the speed of light and is benefiting from relativity’s time dilation effects.

5 years after the start of his journey (as measured by his own clock) Paul turns his ship around, but keeps his rockets firing. He is now slowing down at 1g relative to the Earth.

After another 5 years Paul’s ship comes to rest relative to the Earth. However, he keeps his rockets firing and now starts to accelerate back towards the Earth.

After another 5 years Paul’s ship is halfway back to Earth. Paul turns the ship around again, but once again he keeps his rockets firing. He is now slowing down at 1g.

After another 5 years Paul’s ship comes to rest relative to the Earth and Paul now switches off his rockets. He is now back where he began. But when he compares his clock with Peter’s he discovers that while he has aged only 20 years, Peter has aged 3348 years!

But this age difference must be due entirely to the effects of SR, because during the entire experiment Peter and Paul have been subject to exactly the same GR effects. Peter has been on the Earth, whose gravity has been accelerating him at 1g, while Paul has been subject to an identical acceleration of 1g in his ship. By GR’s Principle of Equivalence, these two accelerations are indistinguishable and produce identical effects. Ergo, the age difference at the end of the experiment must be caused entirely by the SR effects of Paul's travelling at high velocities.

QED …? :-k

Diamond
2003-Dec-04, 09:36 AM
Erm. Not quite.

There is the Twin Paradox which is due to SR and involves no acceleration at all see http://www.hawaii.edu/suremath/SRtwinParadox.html

Then there is the issue of acceleration and the equivalence with gravity which is a postulate of GR.

What needs to be remembered in the example above is that each twin travels a different "world-line" through spacetime. The Paul twin undergoes two accelerations and two decelerations. The Peter twin undergoes one acceleration. The two are moving through different world-lines and therefore there will be a time dilation effect due to acceleration as well as motion near light speed relative to the inertial frame.

kilopi
2003-Dec-04, 10:26 AM
"Definitive Proof That It's SR?"

Why do you need to prove it? SR has it's time dilation effects--just read Einstein's original 1905 paper. That's where he calls it a "peculiar consequence," but not a paradox.

http://mentock.home.mindspring.com/twinrdux.htm
http://mentock.home.mindspring.com/twins.htm
http://mentock.home.mindspring.com/twin2.htm

Eroica
2003-Dec-04, 12:18 PM
The Paul twin undergoes two accelerations and two decelerations. The Peter twin undergoes one acceleration.
According to SeanF (http://www.badastronomy.com/phpBB/viewtopic.php?p=170128#170128), that's irrelevant:
That's not right, Eroica - there's no difference between "speeding up" and "slowing down." They're both acceleration, and the GR effects would be the same.

frenat
2003-Dec-04, 12:31 PM
what about Mary? Sorry just had to ask. :D

Eroica
2003-Dec-04, 12:34 PM
Why do you need to prove it?
For the benefit of those people who won't accept that the Twin Paradox is an SR effect.


SR has it's time dilation effects
I know. SR's time dilation effects are what cause the age difference. That's the whole point of my thought-experiment.


just read Einstein's original 1905 paper.
I have, but to properly understand it one must do more than "just read" it.

kilopi
2003-Dec-04, 01:33 PM
Why do you need to prove it?
For the benefit of those people who won't accept that the Twin Paradox is an SR effect.


SR has it's time dilation effects
I know. SR's time dilation effects are what cause the age difference. That's the whole point of my thought-experiment.

Ah. But read my third link above. It shows a time dilation that is not caused by SR effects.



just read Einstein's original 1905 paper.
I have, but to properly understand it one must do more than "just read" it.
Just a casual reader will notice that Einstein establishes the basic facts of the "twin paradox" in that paper.

SeanF
2003-Dec-04, 02:08 PM
Just thought I'd throw my 2¢ in here.

Eroica, I don't think you're example deals with SR at all. Since both twins are constantly experiencing 1g, neither one of them is ever in an inertial frame, are they?

I'm not as up-to-speed (ha!) on GR as I am on SR, but my prediction would be that Peter and Paul would both be the same age at the end of this experiment . . . could be wrong, though.

Now, it'd be different if you have Paul cut his engines at a given velocity and coast for a while before turning around and refiring the engines to slow (doing the same thing on the trip back, of course). Then I think Paul would be younger due to SR on the basis of how much time he spends coasting.

Like I said, though, I'm not clear enough on GR to say whether a 1g gravity well and 1g acceleration would produce equal dilations, but the equivalence principle does seem to suggest it.

Eta C
2003-Dec-04, 02:14 PM
He may undergo the same accelerations, but at a different place in space, and that makes a difference. The space borne twin observes his sibling (nice touch of gender neutrality, don't you think :) ) as being very high up in the gravitational well. This mean he perceives the earth clock as running fast relative to his. This is a GR effect, not SR. To quote Stephen Hawking in "A Brief History of Time" (page 33)


The theory of relativity gets rid of absolute time. Consider a pair of twins. Suppose that one twin goes to live on the top of a mountain while the other stays at sea level. The first twin would age faster than the second. Thus, if they met again, one would be older than the other. In this case the difference in ages would be very small, but it would be much larger if one of the twins went for a long trip in a spaceship at nearly the speed of light. When he returned, he would be much younger than the one who stayed on Earth. This is known as the twins paradox, but it is a paradox only if one has the idea of absolute time at the back of one's mind. In the theory of relativity there is no unique absolute time, but instead each individual has his won personal measure of time that depends on where he is and how he is moving.

Before 1915 (note added: This is not a typo, 1915 is the date of the papers on GR), space and time were thought of as a fixed arena in which events took place, but which was not affected by what happened in it. This was true even of the special theory of relativity... The situation, however, is quite different in the general theory of relativity. Space and time are now dynamic quantities: when a body moves, or a force acts, it affects the curvature of space and time---and in turn the structure of space-time affects the way in which bodies move and forces act.
(emphasis is mine)

Note that Hawking is saying that you get the twin paradox simply by having one twin walk to the top of a mountain. Nothing close to the speed of light or space here. The space and high speed simply make it a larger effect (years instead of nanoseconds). Even these small changes have been observed by taking atomic clocks up in airplanes and observing that the one that flew ran fast compared to the one on the ground.

I will admit that you can compute the outcome of the space thought experiment using only SR, but it requires that you treat the acceleration and the direction change as a sudden shift between two inertial reference frames. That is, you totally ignore what happens during that period. While this use of SR gives you an answer, it does not give you an explanation. That requires general relativity. If you don't believe me, check out the text books. You'll find that they support this position.

SeanF
2003-Dec-04, 02:36 PM
Note that Hawking is saying that you get the twin paradox simply by having one twin walk to the top of a mountain.

He points out that you get a twin paradox here. I'm not sure that it's necessarily the same one.

The SR thought experiment can be set up in intergalactic space, where any gravity well is negligible, and you still end up with one younger twin.

Eta C
2003-Dec-04, 02:41 PM
No, if you read the entire context of the discussion in the book you'll see it's the same one. And you're wrong to say that there is not a gravity well if you do the experiement in deep space. One twin undergoes acceleration to change direction and by the principal of equivalence that is indistinguishable from a gravitational field.

Ryback
2003-Dec-04, 02:53 PM
What are you guys talking about? There is no equivalence here! The twin taking the space flight has to first accelerate to near the speed of light and then change acceleration to head back towards the earth. And then again he changes acceleration to slow down so he doesn't collide with the earth. His acceleration is not constant at all. The twin on the earth, on the other hand, experiences constant acceleration of 1g the entire time. There is no equivalence here and hence no problem.

Eta C
2003-Dec-04, 03:00 PM
The equivalence is between an accelerated reference frame and a gravitational field, not between the two twins. The principle of equivalence is one of the foundations of general relativity. It states that the laws of physics are the same in an accelerated reference frame as they are in a gravitational field. That's why one way of providing "artificial" gravity in a spacecraft is to continuously accelerate.

Ryback
2003-Dec-04, 03:08 PM
The equivalence is between an accelerated reference frame and a gravitational field, not between the two twins. The principle of equivalence is one of the foundations of general relativity. It states that the laws of physics are the same in an accelerated reference frame as they are in a gravitational field. That's why one way of providing "artificial" gravity in a spacecraft is to continuously accelerate.

The original post said "By GR’s Principle of Equivalence, these two accelerations are indistinguishable and produce identical effects. " But the two accelerations are not indistinguishable, are they? Twin 1 is comforable, experiencing the earth's 1G as he sits on the beach sipping Pina Colada. In the meantime, twin 2 is being thrown from one end of his space ship to the other as the outbound rockets extingush and the inbound rockets ignite to change the spacecrafts direction back towards the earth.

Eta C
2003-Dec-04, 03:20 PM
One G in the spacecraft will be indistinguishable from 1 G on Earth. The difference, as I pointed out in my first post is that the space twin experiences this acceleration at a long distance away, and that makes a difference in how the two twins perceive each other's clocks.

In any case, Ryback, we're not really in disagreement here. The accelerations the space twin experiences place him in a very non-inertial frame while the earth twin can be considered to be in an inertial one for the purposes of the experiment. My disagreement with the person who originated the thread is that I (and other physicists) know that SR is not sufficient for a full description of the twin paradox. Because of the accelerations (indistinguishable from gravitational fields) that the space twin experiences a full explanation requires general relativity.

Eroica
2003-Dec-04, 03:39 PM
There is no equivalence here! The twin taking the space flight has to first accelerate to near the speed of light and then change acceleration to head back towards the earth. And then again he changes acceleration to slow down so he doesn't collide with the earth. His acceleration is not constant at all. The twin on the earth, on the other hand, experiences constant acceleration of 1g the entire time. There is no equivalence here and hence no problem.
I say that the acceleration does not change in magnitude, which is the important point. The GR effects of a gravitational field on one's clock are not dependent on the direction of the field, are they? I may be wrong, but I still contend that the GR effects on Peter's clock are identical to the GR effects on Paul's clock.

Eroica
2003-Dec-04, 03:45 PM
Eroica, I don't think you're example deals with SR at all. Since both twins are constantly experiencing 1g, neither one of them is ever in an inertial frame, are they?

I'm not as up-to-speed (ha!) on GR as I am on SR, but my prediction would be that Peter and Paul would both be the same age at the end of this experiment . . . could be wrong, though.
[-X SeanF, SeanF, you surprise me! And to think that I was just waiting for you to leap to my defence :D

You're absolutely wrong here. Of that I'm sure. I stand over my figures. Peter (the traveller) will age just 20 years, while Paul will age 3348 years.

Neither of the twins is in an inertial frame of reference. That's correct. But if the GR effects are the same, then the age difference can only be explained by SR.

SeanF
2003-Dec-04, 04:04 PM
Eroica, I don't think you're example deals with SR at all. Since both twins are constantly experiencing 1g, neither one of them is ever in an inertial frame, are they?

I'm not as up-to-speed (ha!) on GR as I am on SR, but my prediction would be that Peter and Paul would both be the same age at the end of this experiment . . . could be wrong, though.
[-X SeanF, SeanF, you surprise me! And to think that I was just waiting for you to leap to my defence :D

You're absolutely wrong here. Of that I'm sure. I stand over my figures. Peter (the traveller) will age just 20 years, while Paul will age 3348 years.

Neither of the twins is in an inertial frame of reference. That's correct. But if the GR effects are the same, then the age difference can only be explained by SR.

Sorry, Eroica! :( I'm still working this one over in me little ol' mind here.

While Paul is rocketing away, experiencing his own little gravity well, wouldn't he say that since Peter is "below" him and getting farther and farther away, that Peter must be deeper in the gravity well? Now, when he's turned around and decelerating, Peter is "above" him and thus higher in the gravity well - but the difference in their heights (and thus the difference in Paul's opinion of the gravity well depth) is greater, so the GR-Paul-is-aging-faster wouldn't exactly cancel out the GR-Peter-is-aging-faster.

If that's right, wouldn't that mean that GR predicts different ages? Or am I still missing something?

Don't get me wrong, I still think the twin paradox can be dealt with entirely within SR. I'm just still working through this experiment of yours. :)

Ryback
2003-Dec-04, 04:47 PM
Eroica, I don't think you're example deals with SR at all. Since both twins are constantly experiencing 1g, neither one of them is ever in an inertial frame, are they?

I'm not as up-to-speed (ha!) on GR as I am on SR, but my prediction would be that Peter and Paul would both be the same age at the end of this experiment . . . could be wrong, though.
[-X SeanF, SeanF, you surprise me! And to think that I was just waiting for you to leap to my defence :D

You're absolutely wrong here. Of that I'm sure. I stand over my figures. Peter (the traveller) will age just 20 years, while Paul will age 3348 years.

Neither of the twins is in an inertial frame of reference. That's correct. But if the GR effects are the same, then the age difference can only be explained by SR.

I still say that the GR effects are not the same. If you wish to dismiss the obvious issue of acceleration change during the turn around segment of the trip, what about the initial part? As the twin is leaving the earth, he will experience >1g. That is, he will experience the force of the earth's gravity added to the 1G inertial force of the rockets acceleration. A similar argument could be made for the journey back. GR should be able to explain everything here. If I am not mistaken isn't GR a more "general" theory and hence it can explain everything SR can and more?

kilopi
2003-Dec-04, 05:22 PM
But if the GR effects are the same, then the age difference can only be explained by SR.
That is an odd way of expressing the basic idea, since GR subsumes SR. I'm not sure what you are getting at then.

Eroica
2003-Dec-04, 05:26 PM
I still say that the GR effects are not the same.
That's the nub of the problem. I hope someone who knows for sure will post.


If you wish to dismiss the obvious issue of acceleration change during the turn around segment of the trip, what about the initial part? As the twin is leaving the earth, he will experience >1g.
That's why I had him start out in space far from the Earth. Still, if he begins on the Earth, it should be possible to have his rockets give him an initial acceleration that is only a minuscule amount above 1g, gradually increasing as he gets further away from the Earth. It's not going to explain an age difference of 3328 years!


GR should be able to explain everything here. If I am not mistaken isn't GR a more "general" theory and hence it can explain everything SR can and more?
That GR can explain the paradox is not in question. Some people - eg Eta C - insist that the age difference is "caused" by the different GR effects experienced by the twins. I insist that it isn't. This experiment tries to eliminate that possibility by having both twins experience the exact same GR effects.

kilopi
2003-Dec-04, 05:33 PM
That GR can explain the paradox is not in question. Some people - eg Eta C - insist that the age difference is "caused" by the different GR effects experienced by the twins. I insist that it isn't. This experiment tries to eliminate that possibility by having both twins experience the exact same GR effects.
OK, but then you're going to have to calculate the GR effect. I'm looking forward to the results. :)

Eroica
2003-Dec-04, 05:36 PM
OK, but then you're going to have to calculate the GR effect. I'm looking forward to the results. :)
Actually, I was hoping someone else would do that! :D

ExpErdMann
2003-Dec-04, 05:56 PM
Eroica, your post about the constantly accelerating space ship is interesting, but I don't think you're proving that SR is the cause of the time dilation. Critics of SR have oftened used space twins, saying that the aging shouldn't be for one twin only if SR were true. SR proponents then argue (ususally) that the situations arren't the same for the two twins, since one is accelerating on his trip while the stay-at-home isn't. So you're effectively removing that counter argument, and the question then is why should just one twin have aged?

In my view the likley solution is that SR is not the best version of relativity we have. Lorentzian relativity for example uses a preferred reference frame, and time dilation would only be expected in the twin that is moving at a greater speed in that frame.

WorseAstronomer
2003-Dec-04, 05:59 PM
Note that Hawking is saying that you get the twin paradox simply by having one twin walk to the top of a mountain. Nothing close to the speed of light or space here.

Actually, I think Hawking was saying that even with the same relative motion (or non-motion), there are relativistic effects of living on a mountatin top versus living at sea level. True, any motion relative to non-motion, such as walking up a mountain, will have some effect.

But I think Hawking was saying that there is increased gravity at sea level, relative to a mountain top and increased gravity will cause time near it to progress more slowly relative to time with less gravity, in the same manner that increased velocity causes time to progress more slowly for the moving observer than for the motionless one.


As to the rest of this discussion, it's interesting, but I'm sorry it's just a bit too above me.:D

SeanF
2003-Dec-04, 06:03 PM
That GR can explain the paradox is not in question. Some people - eg Eta C - insist that the age difference is "caused" by the different GR effects experienced by the twins. I insist that it isn't. This experiment tries to eliminate that possibility by having both twins experience the exact same GR effects.

I've been trying to do the same thing. I was hoping Eta C would respond to this post (http://www.badastronomy.com/phpBB/viewtopic.php?p=173103&#173103), but nothing yet . . . :(

Eta C
2003-Dec-04, 09:22 PM
Well, sometimes the day job takes over and these little philosophical issues drop to the background. I'll take a look-see and get back to the greater BABB community.

SeanF
2003-Dec-04, 10:01 PM
Well, sometimes the day job takes over and these little philosophical issues drop to the background. I'll take a look-see and get back to the greater BABB community.

What? You've got a real life outside of the BABB? What's up with that? :o

Just kidding, Eta. :)

kilopi
2003-Dec-05, 12:05 AM
I was hoping Eta C would respond to this post (http://www.badastronomy.com/phpBB/viewtopic.php?p=173103&#173103), but nothing yet . . .
I think I answered it. Let me know...

Sam5
2003-Dec-05, 03:23 AM
That GR can explain the paradox is not in question. Some people - eg Eta C - insist that the age difference is "caused" by the different GR effects experienced by the twins. I insist that it isn't. This experiment tries to eliminate that possibility by having both twins experience the exact same GR effects.

I've been trying to do the same thing. I was hoping Eta C would respond to this post (http://www.badastronomy.com/phpBB/viewtopic.php?p=173103&#173103), but nothing yet . . . :(


In the SR theory, the rates of the clocks depend not on what’s going on inside the clocks, but what’s going on outside them. Einstein adjusts the rates of the “moving” clocks by means of an equation derived from his imagining what the “stationary” observer would “see” when looking at the distorted light signals from the frame of the “moving” observer. Once Einstein gets the equation of the distortion of the light signals, the HE, himself, CHANGES THE RATE of the “moving” clock.

He says in the 1905 paper:

”Further, we imagine one of the clocks which are qualified to mark the time t when at rest relatively to the stationary system, and the time t1 when at rest relatively to the moving system, to be located at the origin of the co-ordinates of k, and so adjusted that it marks the time t1. What is the rate of this clock, when viewed from the stationary system?”

He “adjusts” the rate of the clock. HE changes the rate. The “relative motion” has nothing to do with what is going on inside the clock.

Jobe
2003-Dec-05, 03:50 AM
The theory of relativity gets rid of absolute time. Consider a pair of twins.<snip>

Note that Hawking is saying that you get the twin paradox simply by having one twin walk to the top of a mountain. Nothing close to the speed of light or space here.

I don't think Hawking is talking about the 'walking' as being the thing which creates the effect.

I think he's talking about the fact that the person on top of the mountain experiences less gravity from the earth (equivalence)!

Sam5
2003-Dec-05, 04:10 AM
Note that Hawking is saying that you get the twin paradox simply by having one twin walk to the top of a mountain.

Hawking:

”The theory of relativity gets rid of absolute time. Consider a pair of twins. Suppose that one twin goes to live on the top of a mountain while the other stays at sea level. The first twin would age faster than the second.

What Hawking is talking about here is the fact that a manufactured atomic clock will tick out time more rapidly on top of a mountain, because of less gravity at the top. A similar atomic clock will tick out time more slowly at sea level, because the gravitational potential is higher (stronger) at sea level. He suggests that the harmonic oscillation rates of our body’s atoms determine our aging rates. This is pure speculation. It isn’t even “physics” or “biology”. It’s guesswork.

We could just as easily speculate that the twin on top of the mountain will age more slowly if he has an outdoor swing and he swings a lot, since a pendulum clock will tick more slowly on top of a mountain.

You can not believe all these urban legends these guys tell you. Go to any biology book or website and see if any doctor or biologist ever mentions anything about this "mountain top" speculation. They don't do it. Only the physicists do, and Hawking is NOT a biologist

kilopi
2003-Dec-05, 04:37 AM
This is pure speculation. It isn’t even “physics” or “biology”. It’s guesswork.
No it's not. It's physics, an application of relativity theory.

Sam5
2003-Dec-05, 04:52 AM
SeanF,

Here. See just what comes from this urban legend stuff that is taught by some physics teachers today:

“Einstein's Law of Relativity.

We look at the universe, and say, "How old is the universe? Looking back in time, the universe is about 15 billion years old." That's our view of time. But what is the Bible's view of time? How does it see time? Maybe it sees time differently. And that makes a big difference. Albert Einstein taught us that Big Bang cosmology brings not just space and matter into existence, but that time is part of the nitty gritty. Time is a dimension. Time is affected by your view of time. How you see time depends on where you're viewing it. A minute on the moon goes faster than a minute on the Earth. A minute on the sun goes slower. Time on the sun is actually stretched out so that if you could put a clock on the sun, it would tick more slowly. It's a small difference, but it's measurable and measured. If you could ripen oranges on the Sun, they would take longer to ripen. Why? Because time goes more slowly. Would you feel it going more slowly? No, because your biology would be part of the system. If you were living on the Sun, your heart would beat more slowly. Wherever you are, your biology is in synch with the local time.”

SOURCE (http://www.geraldschroeder.com/age.html)

I see this type of stuff all over the internet now. I see it in books and magazine articles. I hear of “Eastern Mystics” talking about it. I see people talking about it on all sorts of internet message boards. These legends have become so much a part of our lives – and most people never remember them correctly – they cause a lot of young people today think we live in a mystical world of magic.

This is a shame.

Eta C
2003-Dec-05, 02:34 PM
That GR can explain the paradox is not in question. Some people - eg Eta C - insist that the age difference is "caused" by the different GR effects experienced by the twins. I insist that it isn't. This experiment tries to eliminate that possibility by having both twins experience the exact same GR effects.

I've been trying to do the same thing. I was hoping Eta C would respond to this post (http://www.badastronomy.com/phpBB/viewtopic.php?p=173103&#173103), but nothing yet . . . :(

OK. Here, at least is my final word on the subject. First, a couple of things I know we all agree on, but I just want to set out.

1) Special and General Relativity are both valid theories. I don't think I've come across as arguing that they aren't, but I just want to make sure.

2) We can consider the Earth as an inertial reference frame for the purposes of the experiment. As Sean pointed out in an earlier post, we can place the experiment in deep space and have the stationary (or inertial) twin sit in a non-moving spacecraft.

So, with that out of the way. I both agree with Sean's post, and to some extent disagree.

Start with the agreement. We have two travelers. One (A) stays in an inertial frame, the other (B) does not. Since A stays in an inertial frame, we can compute all of his observations, as Sean has done many times, using SR. He sees B's clock as running slowly throughout the trip, and is not surprised when his twin returns much younger than he is. Since A's frame remains inertial it is, to some extent, preferred compared to B's. The "paradox" only arises if we do not realize this point. Since we do realize that there is a difference between the two frames, the paradox vanishes. OK, so there's the agreement. We can resolve the twin paradox from A's point of view without reference to GR.

Now the disagreement. How does B describe the situation from his reference frame? We've all agreed that he's in a non-inertial reference frame due to his change in direction. I think we can also agree that we cannot use SR to describe events as observed from a non-inertial reference frame. That requires GR. If you don't believe me, try a textbook. Weidner & Sells' Elementary Modern Physics puts it this way:


Note that the traveler Dick (the space twin whom I've called "B") makes some space and time measurements in one inertial system S2 and some in a second, quite different, inertial system S3. Inasmuch as special relativity is restricted to inertial observers, that is, to observers who always remain in a single inertial system, it is not applicable to Dick's system. Since Dick's system is not a single inertial system throughout but, rather, an accelerating reference frame, one would have to use the theory of general relativity to analyze events in detail as seen from it. A detailed analysis (using general relativity) applied to Dick's system would indeed show that Dick makes exactly the same predictions that Jim (the Earth bound twin) made from the inertial system S1: That Dick, (who did not remain in the same inertial system) would be younger than Jim (who remained in the same inertial system) when they were together again.

Alternate Second Edition, page 63.
Italicized emphasis in the text. My comments in blue

That puts it about as plainly as I think possible. The problem is that from B's point of view there has to be a time where he sees A's clock as running fast compared to his. That can't happen during the coasting periods. We've all agreed that during those periods he sees A's clock as running slow, as predicted by SR. The time when he sees A's clock running fast has to come during the non-inertial accelerations. To determine that, from B's non-inertial reference frame, requires GR.

So, Sean, to summarize, (although I know this won't be the last post anyone makes on this topic). I agree with you that we do not need general relativity to resolve the twin paradox from the point of view of the earth-bound inertial observer A. There is no paradox since we realize that B is in a non-inertial frame and therefore we cannot apply special relativity to his observations. However, to explain the events from the point of view of the traveller B requires general relativity since he is in a non-inertial frame.

Sam5
2003-Dec-05, 03:09 PM
2) We can consider the Earth as an inertial reference frame for the purposes of the experiment. As Sean pointed out in an earlier post, we can place the experiment in deep space and have the stationary (or inertial) twin sit in a non-moving spacecraft.


Non moving relaive to what?

Einstein said in his 1905 paper, “...the view here to be developed will not require an “absolutely stationary space” provided with special properties...”

You can’t have an absolutely "stationary" spacecraft in space.

And both “twins” in his SR theory are “inertial”. Neither feels any acceleration at all.

Sam5
2003-Dec-05, 03:14 PM
Start with the agreement. We have two travelers. One (A) stays in an inertial frame, the other (B) does not.


In the SR theory, both “twins” (both clocks) are “inertial” because neither experiences any acceleration. They are both moving "relatively".

You might as well give up because the paradox of SR can not be resolved.

kilopi
2003-Dec-05, 03:17 PM
And both “twins” in his SR theory are “inertial”. Neither feels any acceleration at all.
Which twins are those, and which theory--I assume you are talking about a specific work?

Sam5
2003-Dec-05, 03:22 PM
We've all agreed that he's in a non-inertial reference frame due to his change in direction.

No we have not "all" agreed to that, and it is not true. In the 1905 theory, there is NO “change in direction”, and both clocks are moving “relatively”.

Einstein specifically said in the theory, “The length of the moving rod measured in the stationary system does not change, therefore, if v and -v are interchanged.”

This means that even if there is a change of direction, the change does not matter and causes no effect on either clock, because, as he said in the paper:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img51.gif

This means that a “change” in direction causes no effect. It is only the “relative motion” that causes an effect.

Ryback
2003-Dec-05, 03:29 PM
Start with the agreement. We have two travelers. One (A) stays in an inertial frame, the other (B) does not.


In the SR theory, both “twins” (both clocks) are “inertial” because neither experiences any acceleration. They are both moving "relatively".

You might as well give up because the paradox of SR can not be resolved.

The reason that this is considered a paradox is that Special Relativity seems to imply that either one can be considered at rest, with the other moving. The confusion arises not because there are two equally valid inertial rest frames, but because there are three. A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, involving GR. Not true.

The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin--they still define different inertial frames.

Hence you have the asymetry, and therefore there is no paradox.

kilopi
2003-Dec-05, 03:31 PM
No we have not "all" agreed to that, and it is not true. In the 1905 theory, there is NO “change in direction”, and both clocks are moving “relatively”.
O yes there is a change of direction in that 1905 paper, concerning the "twin paradox" (it's not called that in the paper, it's mentioned as a "peculiar consequence (http://www.fourmilab.ch/etexts/einstein/specrel/www/#SECTION14)").

The reason that this is considered a paradox is that Special Relativity seems to imply that either one can be considered at rest, with the other moving. The confusion arises not because there are two equally valid inertial rest frames, but because there are three. A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, involving GR. Not true.

The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin--they still define different inertial frames.
Ryback, I'm not sure where you got that, but it is lifted almost directly from this page (http://mentock.home.mindspring.com/twins.htm).

SeanF
2003-Dec-05, 03:44 PM
Eta, thanks for the post. Very informative.

I guess I see it that we can define that the travelling twin instantaneously jumps from one inertial frame to another. Thus, while he does not spend the entire experiment in the same inertial frame, he does not spend any time at all in a non-inertial frame.

I do realize that instantaneous acceleration is not physically possible in reality, but I still think the "twin paradox" can be defined and explained in SR as such.

Basically - we could have two clocks (in different inertial frames) passing each other when they both show the exact same time. This should be indistinguishable from one clock instantaneously switching inertial frames at that point, which should be indistinguishable from one person switching inertial frames at that point.

Oh, well. At least my disagreement (such as it is) with you is a lot easier to deal with than my disagreement with Sam5! :D

Sam5
2003-Dec-05, 03:44 PM
The confusion arises not because there are two equally valid inertial rest frames, but because there are three. A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, involving GR. Not true.

The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin--they still define different inertial frames.

Hence you have the asymetry, and therefore there is no paradox.

See my post above with the equation. In the first place, there is no “turning around” example in the theory itself. In the second place, Einstein said that didn’t matter, since:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img51.gif

So it is not the “turning around” that does it. The “turning around” does nothing. It is the “v” that does it, and it doesn’t matter what direction the clock or twin is moving.

We could have Jack and Jill both go out into space in opposite directions and “turn around”, and SR theory would say that they both see each other’s clocks as ticking slowly. So when they return to earth, they would both disagree as to which clock “lagged behind”.

This paradox has NO resolution, because the theory is incorrect.

SeanF
2003-Dec-05, 03:46 PM
We've all agreed that he's in a non-inertial reference frame due to his change in direction.

No we have not "all" agreed to that, and it is not true. In the 1905 theory, there is NO “change in direction”, and both clocks are moving “relatively”.

Einstein specifically said in the theory, “The length of the moving rod measured in the stationary system does not change, therefore, if v and -v are interchanged.”

This means that even if there is a change of direction, the change does not matter and causes no effect on either clock, because, as he said in the paper:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img51.gif

This means that a “change” in direction causes no effect. It is only the “relative motion” that causes an effect.

That formula refers to the time dilation and length contraction. It does not refer to the simultaneity difference, which is both direction-dependent and distance-dependent.

Sam5
2003-Dec-05, 03:48 PM
Basically - we could have two clocks (in different inertial frames) passing each other when they both show the exact same time.

Right, and the observer with clock A will see the clock B as ticking slow, while the observer with clock B will see the A clock as ticking slow.

Sam5
2003-Dec-05, 03:52 PM
That formula refers to the time dilation and length contraction. It does not refer to the simultaneity difference, which is both direction-dependent and distance-dependent.

Show me where he says the clock rate slowdown is “direction dependent”.

kilopi
2003-Dec-05, 03:53 PM
In the first place, there is no “turning around” example in the theory itself.
Not true. Einstein explicitly described it in his 1905 paper on the subject.

That was the original analysis of the "twin paradox," and the result that Einstein obtained is the same we agree with today--and it wasn't a paradox then, nor now.

SeanF
2003-Dec-05, 03:57 PM
That formula refers to the time dilation and length contraction. It does not refer to the simultaneity difference, which is both direction-dependent and distance-dependent.

Show me where he says the clock rate slowdown is “direction dependent”.

Do you see where I said, "That formula refers to the time dilation . . . "? "Time dilation" and "clock rate slowdown" are the same thing, and it is not direction-dependent.

Simultaneity is a different (though related) issue, and it is direction-dependent.

Diamond
2003-Dec-05, 04:05 PM
This topic has hopelessly confused SR with GR. The Twin Paradox is an issue of GR and the example given at the beginning of the thread involves acceleration and the equivalence with gravity, both GR issues.

Sam5
2003-Dec-05, 04:06 PM
Simultaneity is a different (though related) issue, and it is direction-dependent.


I thought we were talking about “time dilation” here and the “twins paradox”? Time dilation is NOT "direction dependent", so a "turnaround" causes no effect regarding observed time dilation.

If you want to write an essay about “simultaneity”, then go ahead, but tie it into the time dilation issue, and tell us why one “twin” sees something different from the other “twin”, during relative motion only and no “blasting off” of just one twin.

Sam5
2003-Dec-05, 04:12 PM
This topic has hopelessly confused SR with GR. The Twin Paradox is an issue of GR and the example given at the beginning of the thread involves acceleration and the equivalence with gravity, both GR issues.

I say there is no paradox in GR, but there is in SR.

Do you see any way to resolve the “twins paradox” issue in SR, using SR only? I say there is no resolution in SR and that the SR theory is incorrect.

I also say that “relative motion” can not have any possible effect on any kind of clock, since the clock feels no kind of “force” applied to it through “relative motion” alone.

For example, the earth is moving “relative” to billions of other bodies, and we can’t possibly have any kind of real “time dilation” effect caused by our “relative motion” relative to those other bodies.

kilopi
2003-Dec-05, 04:26 PM
Do you see any way to resolve the “twins paradox” issue in SR, using SR only? I say there is no resolution in SR and that the SR theory is incorrect.
I do see a way. You can read it in the very first paper to discuss the issue, Einstein's 1905 paper on special relativity--ten years before his general relativity papers. He discusses the issue, derives the same result that one would derive from general relavity, and does not--even at the time--consider it a paradox. Neither do I.

The SR theory is not incorrect, as far as it goes, but a lot of people misunderstand it.

SeanF
2003-Dec-05, 05:16 PM
Simultaneity is a different (though related) issue, and it is direction-dependent.


I thought we were talking about “time dilation” here and the “twins paradox”? Time dilation is NOT "direction dependent", so a "turnaround" causes no effect regarding observed time dilation.

If you want to write an essay about “simultaneity”, then go ahead, but tie it into the time dilation issue, and tell us why one “twin” sees something different from the other “twin”, during relative motion only and no “blasting off” of just one twin.

For pete's sake, Sam5, you keep quoting from Einstein's book - haven't you read it?

From Part I, Chapter 9, titled The Relativity of Simultaneity:

"We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."

Read the whole chapter, understand why the train observer concludes that lightning flash B took place earlier than lightning flash A. Once you do, it becomes clear that if the train were moving in the opposite direction, the observer would conclude that flash A occurred before flash B.

Ergo, the simultaneity is direction-dependent!

Sam5
2003-Dec-05, 05:29 PM
For pete's sake, Sam5, you keep quoting from Einstein's book - haven't you read it?

From Part I, Chapter 9, titled The Relativity of Simultaneity:

"We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."

Read the whole chapter, understand why the train observer concludes that lightning flash B took place earlier than lightning flash A. Once you do, it becomes clear that if the train were moving in the opposite direction, the observer would conclude that flash A occurred before flash B.

Ergo, the simultaneity is direction-dependent!


We’ve already discussed this many times, and Einstein says in the chapter why the moving train observer sees the B light first:

“Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

That’s because the train observer is traveling toward the source B, and he will receive the beam from B at a velocity of c + v.

If he goes in the opposite direction, the effect would be the same and the numbers and shift would be the same, but the direction reversed, so he would see the A light first. Changing direction in SR does nothing to change the clock rates. The “v” is important but the direction is not.

SeanF
2003-Dec-05, 05:37 PM
For pete's sake, Sam5, you keep quoting from Einstein's book - haven't you read it?

From Part I, Chapter 9, titled The Relativity of Simultaneity:

"We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."

Read the whole chapter, understand why the train observer concludes that lightning flash B took place earlier than lightning flash A. Once you do, it becomes clear that if the train were moving in the opposite direction, the observer would conclude that flash A occurred before flash B.

Ergo, the simultaneity is direction-dependent!


We’ve already discussed this many times, and Einstein says in the chapter why the moving train observer sees the B light first:

“Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

Keep reading:

"Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."



That’s because the train observer is traveling toward the source B, and he will receive the beam from B at a velocity of c + v.

"Considered with reference to the railway embankment," yes. With reference to the railcar, no.


If he goes in the opposite direction, the effect would be the same and the numbers and shift would be the same, but the direction reversed, so he would see the A light first.
Bingo! You've almost got it!

Changing direction in SR does nothing to change the clock rates.

Absolutely true! =D>

The “v” is important but the direction is not.

Oh. :( And you were so close.

Sam5
2003-Dec-05, 06:35 PM
"Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."


What false “conclusion” they might come to on the train, caused by the c + v and c – v phenomena, is not relevant to what actually takes place in both frames at the same time. We could just as easily use an example with two cannon firing at B and A. The train observers might “conclude” that cannon B fired first, but you and I know that it did not, and we will.... no, I will explain the whole situation to the train observers when they stop at the next station. I will explain the phenomena about the light and the sound.

kilopi
2003-Dec-05, 06:41 PM
no, I will explain the whole situation
Either you, or Einstein. Tough choice... :)

Diamond
2003-Dec-06, 10:14 AM
"Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."


What false “conclusion” they might come to on the train, caused by the c + v and c – v phenomena, is not relevant to what actually takes place in both frames at the same time. We could just as easily use an example with two cannon firing at B and A. The train observers might “conclude” that cannon B fired first, but you and I know that it did not, and we will.... no, I will explain the whole situation to the train observers when they stop at the next station. I will explain the phenomena about the light and the sound.

No. No. And No.

There is no such thing as "what happens in both frames at the same time" - that is covered in the chapter about the "relativity of simultaneity". Light waves do not travel as c+v or c-v but at c. There is no preferred frame of reference - each observer correctly describes the phenomena consistently with the same laws of physics.

Eroica
2003-Dec-06, 11:35 AM
The problem is that from B's point of view there has to be a time where he sees A's clock as running fast compared to his. That can't happen during the coasting periods. We've all agreed that during those periods he sees A's clock as running slow, as predicted by SR. The time when he sees A's clock running fast has to come during the non-inertial accelerations. To determine that, from B's non-inertial reference frame, requires GR.
This seems to be the nub of the problem. I for one do not agree that B sees A's clock as running slow during all the coasting periods, and fast during the accelerations. On his way out, B sees A's clock running slow and A sees B's clock running slow. Then B turns for home and immediately B sees A's clock running fast. A's clock continues to run fast from B's perspective all the way home. But A does not see B's clock running fast until some time after B's has turned for home. (Let's say B turns for home when he is 10 uncontracted light-years away: A won't see B's clock running fast until 10 years after B has turned around.)

Eroica
2003-Dec-06, 11:38 AM
This topic has hopelessly confused SR with GR. The Twin Paradox is an issue of GR and the example given at the beginning of the thread involves acceleration and the equivalence with gravity, both GR issues.
You obviously missed the whole point of my OP. Because both twins experience exactly the same accelerations, their age differences at the end of the experiment can have nothing to do with acceleration. They're entirely due to the fact that one twin is travelling at high velocities.

Sam5
2003-Dec-06, 12:52 PM
No. No. And No.

There is no such thing as "what happens in both frames at the same time" - that is covered in the chapter about the "relativity of simultaneity". Light waves do not travel as c+v or c-v but at c. There is no preferred frame of reference - each observer correctly describes the phenomena consistently with the same laws of physics.

I don’t mean they will both “see” the same events “at the same instantaneous moment”. They see the flashes at different moments, but the whole process of the flashes and the movement of the light and the observers’ individual “seeing” of the flashes at different instantaneous moments takes place in both frames “at the same time”, ie during the course of the thought experiment. When one sees a flash, something is going on in both frames at the same time, whether they both “see” the flashes at the same moment or not.

Einstein says in Chapter 9 that the moving train observer encounters the two flashes of light at c + v and c – v. That’s why that observer sees the B flash first. If the moving observer saw both flashes arrive at him at the same time, then he’d be seeing the fronts of both beams travel toward him at c. But if that happened, the embankment observer would see the A flash first at the speed of c + v.

The “relativity of simultaneity” was noticed by way back in history. Soldiers on the battlefield in Newton’s time knew that they heard cannon sound later than the actual firing of the cannon and delayed by more time the further they were away from the cannon. Renaissance scientists knew that simultaneity of “seeing” light and “hearing” sound was just relative and depended on the position and state of motion of the observer. Doppler wrote papers about this in the 1840s. In 1676 Romer knew that when he saw the moons of Jupiter, he was seeing them on a delayed basis.

kilopi
2003-Dec-06, 01:29 PM
Because both twins experience exactly the same accelerations, their age differences at the end of the experiment can have nothing to do with acceleration.
I'm not sure that follows from general relativity though, does it?

Anyone remember Bell's rope (http://www.badastronomy.com/phpBB/viewtopic.php?p=106#106)?

SeanF
2003-Dec-06, 02:02 PM
The problem is that from B's point of view there has to be a time where he sees A's clock as running fast compared to his. That can't happen during the coasting periods. We've all agreed that during those periods he sees A's clock as running slow, as predicted by SR. The time when he sees A's clock running fast has to come during the non-inertial accelerations. To determine that, from B's non-inertial reference frame, requires GR.
This seems to be the nub of the problem. I for one do not agree that B sees A's clock as running slow during all the coasting periods, and fast during the accelerations. On his way out, B sees A's clock running slow and A sees B's clock running slow. Then B turns for home and immediately B sees A's clock running fast. A's clock continues to run fast from B's perspective all the way home. But A does not see B's clock running fast until some time after B's has turned for home. (Let's say B turns for home when he is 10 uncontracted light-years away: A won't see B's clock running fast until 10 years after B has turned around.)

That's not right, Eroica. If we assume normal deceleration and re-acceleration, B will see A's clock running fast during the deceleration and re-acceleration. If we assume "instantaneous" changing of direction without changing speed, B will see A's clock "jump ahead" at the switching point.

At no point, in either case, will A see B's clock running fast.

Note: The word "see" in this post does not refer to the actual detection of light waves by eyes or other detector. It refers to the perception of how and when events occurred.

SeanF
2003-Dec-06, 02:09 PM
No. No. And No.

There is no such thing as "what happens in both frames at the same time" - that is covered in the chapter about the "relativity of simultaneity". Light waves do not travel as c+v or c-v but at c. There is no preferred frame of reference - each observer correctly describes the phenomena consistently with the same laws of physics.

I don’t mean they will both “see” the same events “at the same instantaneous moment”. They see the flashes at different moments, but the whole process of the flashes and the movement of the light and the observers’ individual “seeing” of the flashes at different instantaneous moments takes place in both frames “at the same time”, ie during the course of the thought experiment. When one sees a flash, something is going on in both frames at the same time, whether they both “see” the flashes at the same moment or not.

Einstein says in Chapter 9 that the moving train observer encounters the two flashes of light at c + v and c – v. That’s why that observer sees the B flash first. If the moving observer saw both flashes arrive at him at the same time, then he’d be seeing the fronts of both beams travel toward him at c. But if that happened, the embankment observer would see the A flash first at the speed of c + v.

The “relativity of simultaneity” was noticed by way back in history. Soldiers on the battlefield in Newton’s time knew that they heard cannon sound later than the actual firing of the cannon and delayed by more time the further they were away from the cannon. Renaissance scientists knew that simultaneity of “seeing” light and “hearing” sound was just relative and depended on the position and state of motion of the observer. Doppler wrote papers about this in the 1840s. In 1676 Romer knew that when he saw the moons of Jupiter, he was seeing them on a delayed basis.

But it is accepted that in the atmosphere, the light and sound generated at the same distance simultaneously will not reach the observer at the same time.

However, under SR, it is required that two light beams generated at the same distance simultaneously will reach the observer at the same time.

If they don't, either they weren't at the same distance or they weren't simultaneous.

Sam5
2003-Dec-06, 02:23 PM
But it is accepted that in the atmosphere, the light and sound generated at the same distance simultaneously will not reach the observer at the same time.

Doh.

The Chinese discovered that thousands of years ago, by observing exploding skyrockets and firecrackers at a distance.


However, under SR, it is required that two light beams generated at the same distance simultaneously will reach the observer at the same time.

If they don't, either they weren't at the same distance or they weren't simultaneous.

That is true for observers that are stationary relative to the two emitters. But the moving train observer is not stationary relative to the two emitters. In the Chapter 9 example, the flashes were at the same distance and occurred simultaneously when the train observer was at Point M’ along the track. But since it takes time for light to travel, and since the train observer was moving during that time, he moved closer to the oncoming beam from B, whilst he was “riding on ahead” of the beam coming from A. So he saw flash B first. There is nothing mysterious about this.

SeanF
2003-Dec-06, 04:18 PM
That is true for observers that are stationary relative to the two emitters. But the moving train observer is not stationary relative to the two emitters.

Doesn't matter. The speed of light is a constant regardless of the velocity of the emitters, and in SR the emitters are in motion relative to the stationary train observer.

Speaking of the constancy of c, Einstein mentions de Sitter in Chapter 7, The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity. I'd really like to hear how your "local c-regulator" theory gets around those binary stars.

Eroica
2003-Dec-06, 04:45 PM
If we assume normal deceleration and re-acceleration, B will see A's clock running fast during the deceleration and re-acceleration. If we assume "instantaneous" changing of direction without changing speed, B will see A's clock "jump ahead" at the switching point.

At no point, in either case, will A see B's clock running fast.
I think we're arguing about two completely different meanings of the phrase running fast. I mean that if B looked back at A with his telescope, he would think that A's clock was ticking more slowly than his. But when he turned for home, A's clock would suddenly seem to be ticking faster than his.

Imagine the clocks are transmitting pulses every second. If A's clock is, say, 30 seconds behind B's, how can it jump instantaneously to being 30 seconds ahead? What happened to the 59 other pulses in between?

Eroica
2003-Dec-06, 04:46 PM
I'm not sure that follows from general relativity though, does it?
I'm not sure about anything anymore! ](*,)

SeanF
2003-Dec-06, 05:01 PM
If we assume normal deceleration and re-acceleration, B will see A's clock running fast during the deceleration and re-acceleration. If we assume "instantaneous" changing of direction without changing speed, B will see A's clock "jump ahead" at the switching point.

At no point, in either case, will A see B's clock running fast.
I think we're arguing about two completely different meanings of the phrase running fast. I mean that if B looked back at A with his telescope, he would think that A's clock was ticking more slowly than his. But when he turned for home, A's clock would suddenly seem to be ticking faster than his.

Imagine the clocks are transmitting pulses every second. If A's clock is, say, 30 seconds behind B's, how can it jump instantaneously to being 30 seconds ahead? What happened to the 59 other pulses in between?

In the event of an instantaneous direction change, B would still receive all those pulses, and in the proper order. When B tries to "undo" the Doppler effect, though, figuring out where and when A was when it transmitted those pulses, things would look weird. It would almost seem (I think) kind of like A was in two different places transmitting two different pulses at the same time.

Sam5
2003-Dec-06, 06:10 PM
Doesn't matter. The speed of light is a constant regardless of the velocity of the emitters, and in SR the emitters are in motion relative to the stationary train observer.

The train is not in SR, it’s on the earth. SR is a science fiction story. It should have won the Nobel Prize for Literature.

If the “the emitters are in motion relative to the stationary train observer”, then you’ve got to make a choice. If you want the B flash to travel at c relative to the train, then its speed of light has to slow down relative to the source. In Einstein’s Chapter 9 it’s traveling at c + v relative to the train observer and c relative to the source. So you want to slow it down to c at the train observer? Why would you want to do that? Einstein said, “Now in reality.....” the train observer and the light are moving together at c + v. Why would you want to change that?

Ok, then you’ve got to make it depart the moving source at less than c. It can’t both leave the source at c and encounter the train observer at c while the source is moving. If it leaves the source at c, then you’ve got to add the velocity of the source, v, to c, and that would cause the light to encounter the train observer at c + v. But if you want the light to encounter the train observer at c, then it would have to leave the moving source at c – v, relative to the source, with v being the velocity of the source. And then you would have the velocity of the light at the surface of the earth traveling less than c.

If you want to consider the distance between the two as being great, so that the Vtot light speed transforms between two different comoving spaces, then it could leave the source at c, it could gradually change its Vtot while in route by slowing down relative to the train observer, then it could reach the train observer at c. Much like what we observe in the light from the distant galaxies. But by the time it reaches the train observer, it will be traveling at c – v relative to the source.

Man, this SR stuff has really messed up your way of thinking about how waves, light, and clocks work.


Speaking of the constancy of c, Einstein mentions de Sitter in Chapter 7, The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity. I'd really like to hear how your "local c-regulator" theory gets around those binary stars.


“By means of similar considerations based on observations of double stars, the Dutch astronomer De Sitter was also able to show that the velocity of propagation of light cannot depend on the velocity of motion of the body emitting the light.”

The velocity at the earth, when you view the light, when the photons finally reach us, is c relative to you and the earth. The motion of the “double stars” doesn’t change that. The Vtot change takes place in space, probably closer to the stars than to the earth, so that’s why we see red and blue shifts of revolving binaries, even though we encounter the light at c.

russ_watters
2003-Dec-06, 07:06 PM
I don't understand why you guys keep arguing with Sam5 about the implications of SR. His last post there clearly illustrates that he doesn't understand what SR says, nor does he understand what observations show. Until he understands that, you can't have a conversation about its implications - you can't understand the twins paradox without first understanding SR.

Sam5, I'm trying to decide if I should even attempt to explain it to you. You seem reluctant to learn. But I'll give it one little try: I'll start with the basic error in your post about C and see if we can go from there.

The speed of light is always measured by everyone everywhere - on the train, on earth, on a satellite in space - to be C. Exactly, precisely C.

Yes, that's a postulate of SR, but set relativity aside for now: this is DATA and OBSERVATIONS. It is real and its the way light works and is indisputable even without SR to explain it.

SeanF
2003-Dec-06, 07:36 PM
Einstein said, “Now in reality.....” the train observer and the light are moving together at c + v. Why would you want to change that?
I've explained that "Now in reality" phrase to you twice already. Ignoring explanations and continuing to bring up the same wrong concepts after they've been explained multiple times is the kind of thing that's gotten people banned from this BB before.


Speaking of the constancy of c, Einstein mentions de Sitter in Chapter 7, The Apparent Incompatibility of the Law of Propagation of Light with the Principle of Relativity. I'd really like to hear how your "local c-regulator" theory gets around those binary stars.
“By means of similar considerations based on observations of double stars, the Dutch astronomer De Sitter was also able to show that the velocity of propagation of light cannot depend on the velocity of motion of the body emitting the light.”

The velocity at the earth, when you view the light, when the photons finally reach us, is c relative to you and the earth. The motion of the “double stars” doesn’t change that. The Vtot change takes place in space, probably closer to the stars than to the earth, so that’s why we see red and blue shifts of revolving binaries, even though we encounter the light at c.
Read about de Sitter and the binary stars before you attempt to dismiss it, JW. It's got nothing to do with Doppler, and it's got nothing to do with the speed of the light when it reaches us.

Start with this page (http://www.mathpages.com/home/kmath131.htm) (it is, after all, the first response from Google on a search for "de Sitter" and "binary stars") and get back to me on the de Sitter effect once you understand what it is.

kilopi
2003-Dec-07, 07:33 PM
I don't understand why you guys keep arguing with Sam5 about the implications of SR.
Just making sure that we understand it. Or trying to...

Sam5
2003-Dec-08, 02:04 AM
The speed of light is always measured by everyone everywhere - on the train, on earth, on a satellite in space - to be C. Exactly, precisely C.

So, uhh, this stuff about scientists measuring the speed of light passing the sun as slowing down is wrong? And so light can easily go out of "black holes" at the speed of c? Light is measured to go through glass at c and water at c?

Tensor
2003-Dec-08, 02:43 AM
Just making sure that we understand it. Or trying to...

After going back and reading this thread and the relativity thread, I'm not sure I understand any of it now.... :wink:

Tensor
2003-Dec-08, 03:13 AM
The speed of light is always measured by everyone everywhere - on the train, on earth, on a satellite in space - to be C. Exactly, precisely C.

So, uhh, this stuff about scientists measuring the speed of light passing the sun as slowing down is wrong? And so light can easily go out of "black holes" at the speed of c? Light is measured to go through glass at c and water at c?

Although you would have us believe you have a very good understanding of SR (you must if you claim it's wrong), you have either misunderstood some basic physics and GR analogies or you are being purposely obtuse with these questions. Light doesn't slow down passing the sun, its path is bent by the sun's gravity. Yes, light is moving at c trying to get out of a black hole. Depending on how you want to look at it, light's frequency is infintely redshifted or it's path is curved so much it stays within the horizon. Either way, it's not visible. And it's the time it takes photons to be absorbed and reemitted from the atoms in the water or glass that slows it down, but it's still moving at c between those interactions.

Sam5
2003-Dec-08, 03:19 AM
Yes, light is moving at c trying to get out of a black hole. Depending on how you want to look at it, light's frequency is infintely redshifted or it's path is curved so much it stays within the horizon.

And so, uhh, you believe in the “tired light” theory? The light just gets tired of traveling at “c” but getting no where while trying to get out of the black hole, and it just “gives up”?

Tensor
2003-Dec-08, 03:40 AM
Yes, light is moving at c trying to get out of a black hole. Depending on how you want to look at it, light's frequency is infintely redshifted or it's path is curved so much it stays within the horizon.

And so, uhh, you believe in the “tired light” theory? The light just gets tired of traveling at “c” but getting no where while trying to get out of the black hole, and it just “gives up”?

My, my you are being obtuse. Ok, light's frequency is infintely redshifted by gravity. Now, please explain how a gravitational redshift is the same as tired light, if that's what you believe.

russ_watters
2003-Dec-08, 03:40 AM
I don't understand why you guys keep arguing with Sam5 about the implications of SR.
Just making sure that we understand it. Or trying to...
After going back and reading this thread and the relativity thread, I'm not sure I understand any of it now.. Ever watch a movie and think: 'jeez, I feel dumber for seeing that?' Thats what I think of this thread. I don't think you can increase your own understanding by arguing with him.

Sam5
2003-Dec-08, 04:48 AM
My, my you are being obtuse. Ok, light's frequency is infintely redshifted by gravity. Now, please explain how a gravitational redshift is the same as tired light, if that's what you believe.

The "tired light" theory is silly but it was in a lot of popular physics books in the '80s and early '90s.

I’ve read two different versions of the story about the black hole and gravity. One story says a “gravitational redshift” is actually caused by a slowdown in the internal harmonic oscillation rates of atoms, which causes them to emit a lower frequency of light. So, and “infinite” redshift would seem to be caused by a non-harmonically oscillating atom that does not emit light.

The other version is that I’ve read that a light beam passing near the sun or a black hole “slows down” its speed. Something about the beam acting like a “plane wave” and being “refracted” by the “gravity well”, with the bending being caused by the closest areas of the beam to the sun slowing down the most.

In fact, both of those stories are in "On the Influence of Gravitation on the Propagaton of Light", A. Einstein, 1911, so it was Einstein who first said that light slows down when it passes near the sun. Do you think he might have been wrong about that? I think he was right.

Sam5
2003-Dec-08, 04:55 AM
Ever watch a movie and think: 'jeez, I feel dumber for seeing that?' Thats what I think of this thread. I don't think you can increase your own understanding by arguing with him.

Russ, that is a personal attack, which I think is a poor substitute for your lack of a resolution of the twins paradox.

freddo
2003-Dec-08, 06:03 AM
it was Einstein who first said that light slows down when it passes near the sun.

Not my understanding of it... AFAIK it's not that the light is slowing down, but more that it has further to travel before it is observed? Something moving at a set speed and a set distance - the time it arrives can be calculated. Change the distance, your result will also change.

Sam5
2003-Dec-08, 06:11 AM
Not my understanding of it... AFAIK it's not that the light is slowing down, but more that it has further to travel before it is observed? Something moving at a set speed and a set distance - the time it arrives can be calculated. Change the distance, your result will also change.

I've got his 1911 paper right here. Get out your copy of it and we'll discuss it. He uses c1 and c2 for two different speeds of light.

Diamond
2003-Dec-08, 09:10 AM
Not my understanding of it... AFAIK it's not that the light is slowing down, but more that it has further to travel before it is observed? Something moving at a set speed and a set distance - the time it arrives can be calculated. Change the distance, your result will also change.

I've got his 1911 paper right here. Get out your copy of it and we'll discuss it. He uses c1 and c2 for two different speeds of light.

Personally I think you're just being deliberately obtuse and argumentative for the sake of it. No-one else would spend so much time introducing debunked theories and fallacious arguments into relativity threads.


The “relativity of simultaneity” was noticed by way back in history. Soldiers on the battlefield in Newton’s time knew that they heard cannon sound later than the actual firing of the cannon and delayed by more time the further they were away from the cannon. Renaissance scientists knew that simultaneity of “seeing” light and “hearing” sound was just relative and depended on the position and state of motion of the observer. Doppler wrote papers about this in the 1840s. In 1676 Romer knew that when he saw the moons of Jupiter, he was seeing them on a delayed basis.

...is tremendous nonsense from beginning to end. "Relativity of simultaneity" has nothing to do with two paths of information which travel at different speeds but the consequences of light being measured to be the same regardless of the inertial frame of reference used.

Personally I think you simply lurve the attention. It certainly has nothing to do with wanting to know how or why relativity is such a good scientific theory.

Diamond
2003-Dec-08, 09:26 AM
The Twin Paradox of Einstein is an interesting thought experiment involving two twins (who are nearly exactly the same age), one of whom sets out on a journey into space and back. Because of the time dilation effect of relativity, the twin who left experiences a slowing down of time and will actually be much younger than the twin that stayed behind. The reason that this is considered a paradox is that Special Relativity seems to imply that either one can be considered at rest, with the other moving. It does, and it doesn't.

The confusion arises not because there are two equally valid inertial rest frames, but (here's the tricky part) because there are three. A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, or involve General Relativity. Not so.

The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin--they still define different inertial frames.

OK, let's see: Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger.

Important question: what is the relative speed of the two Bob frames? On first glance, it would appear that one is going 3/5c in one direction and 3/5c in the other direction, so that the difference between the two frames is 6/5c! Faster than light? No, special relativity does not add speeds this way. The actual difference is only 15/17c, fast but not faster than light. Why is this important? We'll see.

Now, since special relativity lets us use either rest frame, we assume Bob is the at-home twin. Ann speeds away at 3/5c. No problem so far. But after 4 years of waiting, Bob must change his inertial frame. If we allow Ann to return, we've only restated the problem with the names switched. In the first version, Ann stayed in an inertial frame, and she must stay in an inertial frame in this version. Bob zooms off after Ann at 15/17 light speed (now we know why it was important), and of course catches up. It takes him 4 years, and he has seen 8 years since Ann left. Ann has aged 10 years. Same result. No paradox.

From: http://mentock.home.mindspring.com/twins.htm

See also the sci.physics.relativity FAQ regarding the Twin paradox:
http://www.weburbia.demon.co.uk/physics/twin_paradox.html



edited to add FAQ reference

kilopi
2003-Dec-08, 04:08 PM
From: http://mentock.home.mindspring.com/twins.htm
Ryback posted some of that earlier in this thread (http://www.badastronomy.com/phpBB/viewtopic.php?p=175379#175379), see my comment right after.

Sam5
2003-Dec-08, 07:01 PM
The Twin Paradox of Einstein is an interesting thought experiment involving two twins (who are nearly exactly the same age),

Actually, in the SR theory, the two clocks are both set to “00” at the start of the experiment before the relative motion begins, and they are both synchronized and synchronous, so they are exactly the "same age".


The reason that this is considered a paradox is that Special Relativity seems to imply that either one can be considered at rest, with the other moving. It does, and it doesn't.

No, it DOES. See these statements from the actual theory:

“For this purpose we introduce a third system of co-ordinates K’, which relatively to the system k is in a state of parallel translatory motion parallel to the axis of X, such that the origin of co-ordinates of system k moves with velocity -v on the axis of X.”

And:

“Since the relations between x', y', z' and x, y, z do not contain the time t, the systems K and K’ are at rest with respect to one another, and it is clear that the transformation from K to K’ must be the identical transformation.”

So, since K’ is the same frame as K, while K sees k as “moving” to the right at +v, k sees K as “moving” to the left at the same relative speed but at -v.

One reason why the “twin paradox” is so confusing, is because most people learn about it from books or websites, but not from Einstein’s original paper. And some of the books and websites change it around, so what you read in them is quite often NOT what Einstein actually said.

I realize it is easier to just read the websites and not the original theory, but the websites can actually confuse readers more by introducing concepts that are not in the original paper.

Sam5
2003-Dec-08, 07:31 PM
OK, let's see: Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger.

Your error here is that Ann sees 5 years pass on her clock, while she sees 4 years pass on Bob’s clock, and then you are turning Bob around when he sees 4 years pass on his clock, as seen by Bob.

But, in the SR theory, Ann sees 5 years pass on her clock, while she sees 4 years pass on Bob’s clock, while Bob sees 5 years pass on his clock while he sees 4 years pass on Ann’s clock.

So you are turning Bob around too soon. You are turning Bob around based on what Ann sees on Bob’s clock, but not based on what Bob should be seeing on his own clock at turn-around time, which should be 5 years on his own clock, not 4 years.

If you turn Bob around when he sees 4 years pass on his clock, then he will have seen only 3.2 years pass on Ann’s clock, so you wind up with the paradox. You wind up with a double Lorentz Transformation, instead of a single one. You have Ann seeing 5 years pass on her clock, but you have Bob seeing only 3.2 years pass on her clock, so you are multiplying the Lorentz Transformation that Bob sees on Ann’s clock by a factor of 2.

5 x .8 = 4, and 4 x .8 = 3.2

So you are having Bob see a double Lorentz Transformation on Ann’s clock, while you are having Ann see only a single Lorentz Transformation on Bob’s clock, and Einstein’s theory never said anything about that.

If you keep on with this, you will have Ann see 10 years on her clock when Bob returns, while she sees 8 years on Bob’s clock, but you will have Bob see only 6.4 years on Ann’s clock, and you will still have a paradox but with different “seen” numbers.

You turned Bob around too soon. He is supposed to turn around when he sees 5 years on his own clock.

If you have Bob turn around at 4 years by his own clock, he will have seen Ann age only 3.2 years, and you will have Ann aged by her clock only 4 years rather than 5.

3.2 / .8 = 4

So you’ve got Ann aging at two different rates. 5 years that she “sees” on her own clock and 3.2 years that Bob sees on her clock when he sees 4 years on his clock. Based on the Lorentz transformation equation, if Bob sees Ann age 3.2 years when he sees his own clock age 4 years, then that means Ann would see her own clock age 4 years.

So this is where your error is. She can’t see both 5 years AND 4 years on her own clock at the same time.

You’ve got Ann aging by her own clock both 5 years and 4 years at the point where Bob turns around.

You can’t use the Lorentz Transformation factor of .8 twice as “seen” by one observer going in one direction.

SeanF
2003-Dec-08, 07:39 PM
Bob sees his own clock tick off 4 years on the way out ( 0 to 4 ) and 4 years on the way back ( 4 to 8 ). Bob sees Ann's clock tick off 3.2 years on the way out ( 0 to 3.2 ) and 3.2 years on the trip back ( 6.8 to 10 ).

No paradox.

Sam5
2003-Dec-08, 08:40 PM
Bob sees his own clock tick off 4 years on the way out ( 0 to 4 ) and 4 years on the way back ( 4 to 8 ). Bob sees Ann's clock tick off 3.2 years on the way out ( 0 to 3.2 ) and 3.2 years on the trip back ( 6.8 to 10 ).

No paradox.


Diamond said:

“Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger.”

And:

“It takes him 4 years, and he has seen 8 years since Ann left. Ann has aged 10 years. Same result. No paradox”

So he says the ratio is 8 to 10, but you say it is 6.8 to 10.

So the paradox not only remains, but you’ve done your math wrong. You got 6.8 when you should have gotten only 6.4.

3.2 + 3.2 = 6.4, not 6.8


I’ve had some difficulty getting this last post to show up on the board, so it might be that I will not be able to respond to any of your posts in the future, so if that turns out to be the case, I would like to say now that I’ve enjoyed our discussion.

SeanF
2003-Dec-08, 08:44 PM
You misunderstand. Bob sees his own clock tick off four years ( from year 0 to year 4 ) on the way out and four years ( from year 4 to year 8 ) on the way back.

Bob sees Ann clock tick off 3.2 years ( from year 0 to year 3.2 ) on the way out and 3.2 years ( from year 6.8 to year 10 ) on the way back.

3.2 - 0 = 3.2
10 - 6.8 = 3.2
3.2 + 3.2 = 6.4

3.2 / 4 = .8
6.4 / 8 = .8

Bob sees his own clock ticking off 8 years on the whole trip, and he sees Ann's clock ticking off 6.4 years on the whole trip, but Ann's clock jumps at turn-around.

kilopi
2003-Dec-08, 11:33 PM
Actually, in the SR theory, the two clocks are both set to “00” at the start of the experiment before the relative motion begins, and they are both synchronized and synchronous, so they are exactly the "same age".
"Actually"? There are more than one instance of the thought experiment, and in some of them, there is no setting to "00", they just have to be synchronous. In the case of the discussion about the twins, very few twins are truly synchronous--but it's close enough for the purpose, when the differences are measured in years.


No, it DOES.
Not necessarily, in SR.


One reason why the “twin paradox” is so confusing, is because most people learn about it from books or websites, but not from Einstein’s original paper. And some of the books and websites change it around, so what you read in them is quite often NOT what Einstein actually said.
In this case, that website is very close to Einstein's original treatment of the "twin paradox" (which he called a "peculiar consequence") in his 1905 paper.


I realize it is easier to just read the websites and not the original theory, but the websites can actually confuse readers more by introducing concepts that are not in the original paper.
But that webpage only introduces the twins. :)

russ_watters
2003-Dec-09, 02:37 AM
Ever watch a movie and think: 'jeez, I feel dumber for seeing that?' Thats what I think of this thread. I don't think you can increase your own understanding by arguing with him.

Russ, that is a personal attack, which I think is a poor substitute for your lack of a resolution of the twins paradox. Negative. I was simply responding to someone's comment that he feels like he understands less than he did before. Whether thats a reflection on you or not I won't say, though I'm sure you know my opinion.

Diamond
2003-Dec-09, 04:14 PM
OK, let's see: Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger.

Your error here is that Ann sees 5 years pass on her clock, while she sees 4 years pass on Bob’s clock, and then you are turning Bob around when he sees 4 years pass on his clock, as seen by Bob.

Your error here is to (intentionally?) misinterpret what was written.


But, in the SR theory, Ann sees 5 years pass on her clock, while she sees 4 years pass on Bob’s clock, while Bob sees 5 years pass on his clock while he sees 4 years pass on Ann’s clock.

Nope.


So you are turning Bob around too soon. You are turning Bob around based on what Ann sees on Bob’s clock, but not based on what Bob should be seeing on his own clock at turn-around time, which should be 5 years on his own clock, not 4 years.

Nope. Not what was written. Is this a test of comprehension?


If you turn Bob around when he sees 4 years pass on his clock, then he will have seen only 3.2 years pass on Ann’s clock, so you wind up with the paradox. You wind up with a double Lorentz Transformation, instead of a single one. You have Ann seeing 5 years pass on her clock, but you have Bob seeing only 3.2 years pass on her clock, so you are multiplying the Lorentz Transformation that Bob sees on Ann’s clock by a factor of 2.

Again, not what was written.


5 x .8 = 4, and 4 x .8 = 3.2

So you are having Bob see a double Lorentz Transformation on Ann’s clock, .................blah blah blah.

All false. Is this "Intentional Misinterpretation Week"?

How does a simple thought experiment generate such nonsense? Have I once said that each can see each other's clocks?

Your error here is that you neither understand special relativity nor general relativity but think you do. All of the statements you produced were fallacious.

Anne does not move. So her spacetime interval (tau) is 10 years because the space interval is zero.

Bob however does move. His total distance moved is s/2 moving out measured by a wristwatch he's carrying onboard the rocket which measures 4 years, then instantaneously gets on another rocket going back at 3/5c for another 4 years. At the end of this time, he flashes by Anne again. She has been waiting for ten years and he for 8 years.

Simple task: Complete the puzzle using the following formula: (tau)^2= t^2 - s^2

From this you can work out how far Bob has travelled (as measured by Anne)

Sam5
2003-Dec-09, 05:50 PM
Bob sees his own clock ticking off 8 years on the whole trip, and he sees Ann's clock ticking off 6.4 years on the whole trip, but Ann's clock jumps at turn-around.



For people who are joining this thread late, let me try to summarize the situation from my point of view.

Special Relativity (1905) “time dilation due to reltive motion” = not correct

Ann and Bob “twins paradox ‘solution’ based on Special Relativity) = not correct

General Relativity (1915) “atomic clock slowdown due to acceleration” = CORRECT

As I understand your thought experiment about Ann and Bob, you are trying to use Special Relativity (the theory with the error) to solve the paradox, and my contention is that you can’t do it because the Special Relativity theory contains an error.

Since there is no “acceleration” in the Special Relativity theory, you can’t use it in the Ann and Bob example, and since there is no “clock jumping” in the Special Relativity theory, you can’t use that in your Ann and Bob example either.

Your own first error is that you have Bob turning around at 4 hours, which is what Ann “sees” on his clock at turn-around time (while she sees 5 on her clock), and you have Bob “seeing” 4 on his clock at turn-around time too. Based on the terms of the original SR theory, that is incorrect. In SR theory, Bob would see 5 on his clock at turn-around time and 4 on Ann’s clock. At the end time, Bob would see 10 on his clock and 8 on Ann’s clock, while Ann would see 10 on her clock and 8 on Bob’s clock. And that reveals the paradox and error of SR theory.

In your attempted “resolution”, when you force Bob to turn around at 4 on his clock, he would see only 3.2 on Ann’s clock, and at end time Bob would see 8 on his clock and 6.4 on Ann’s clock, while you say Ann would see 10 on her clock and 8 on Bob’s clock. So you’ve still got a disagreement between Bob and Ann and a paradox.

You try to “resolve” this paradox by adding an extra 3.6 seconds to what Bob “sees” on Ann’s clock at end time, and you do that by claiming that Ann’s clock somehow “jumps” from 5 to 6.8 when Bob turns around. Then you add Bob’s second “seen” 3.2 to the “jumped” 6.8, and you get “10”, which is what you claim Bob “sees” on Ann’s clock at end time.

But, there are no “jumping clocks” in SR theory (or in GR theory). You’ve just added that “jumping clock” story, even though it is not in the SR theory.

There is no way that either Bob or Ann could see the “jump”, since at turn-around, Ann’s clock is only at 5 and hasn’t yet reached the time of 6.8. Bob can’t “see” the 6.8, since you said all he “sees” is the 3.2 on the way out and the 3.2 on the way back. And of course, in SR theory, none of the observers see a “clock jumping”, either backward or forward. All the observers ever see in SR theory is the the other frame’s clocks “running slow”, but never "jumping" or “running fast”.

Another error you’ve got in this thought experiment is that if Bob turns around at 4 by his clock, and if he “sees” 3.2 on Ann’s clock, then that (based on the Lorentz Transformation equation) means her clock has ticked off only 4 minutes, not 5, since the Lorentz Transformation clock slowdown factor of 3.2 / .8 = 4

So you wind up with a double paradox and too many different numbers “seen” on Ann’s and Bob’s clocks by Ann and Bob at end time. Your “resolution” contains several errors and the paradox still exists.

Glom
2003-Dec-09, 06:01 PM
So the experimental results confirming time dilation due to relative motion mean?

Celestial Mechanic
2003-Dec-09, 06:38 PM
The error that is being made here is that the correct redshift/blueshift formulae are not being used. Read my two posts in the other thread starting with this one: (http://www.badastronomy.com/phpBB/viewtopic.php?p=177048&highlight=harry+sally#17704 8)

The proper redshift during the first phase is sqrt((1-.6)/(1+.6)) = 0.5 and the blueshift during the second phase is 2.0. During the first 4 years Bob sees only 4*0.5 = 2 years of Anne's transmissions, but during the last 4 years he sees the remaining 4*2.0 = 8 years, for a total of 10 years of Anne's transmissions. Anne sees redshifted signals from Bob for (1+.6)/2 = 0.8 of the total time, that is, 8 years. In 8 years she sees 8*0.5 = 4 years of transmissions from Bob, and in the remaining 2 years she sees 2*2.0 = 4 years of transmissions from Bob, for a total of 8 years of Bob's transmissions. Resolved! QED! :D

daver
2003-Dec-09, 06:39 PM
Bob sees his own clock ticking off 8 years on the whole trip, and he sees Ann's clock ticking off 6.4 years on the whole trip, but Ann's clock jumps at turn-around.



For people who are joining this thread late, let me try to summarize the situation from my point of view.

Special Relativity (1905) ?time dilation due to reltive motion? = not correct

You have been provided with popular accounts of experiments that show that time dilation does occur--particles moving close to the speed of light take longer to decay than slower moving particles.


Ann and Bob ?twins paradox ?solution? based on Special Relativity) = not correct

So far you have not convinced many people why this is not correct. SeanF has shown admirable patience in trying to demonstrate to you why there is no fallacy involved. More about this later.


General Relativity (1915) ?atomic clock slowdown due to acceleration? = CORRECT

GR is a superset of SR, since SR can explain the apparent paradox, it's not surprising that GR should manage as well.


As I understand your thought experiment about Ann and Bob, you are trying to use Special Relativity (the theory with the error) to solve the paradox, and my contention is that you can?t do it because the Special Relativity theory contains an error.

Since there is no ?acceleration? in the Special Relativity theory, you can?t use it in the Ann and Bob example, and since there is no ?clock jumping? in the Special Relativity theory, you can?t use that in your Ann and Bob example either.

You can phrase the twin problem in SR such that there is no acceleration--you have the outbound twin tell the inbound twin how much time the outbound twin thinks has elapsed since passing Earth.

SR says that "simultaneity" is not well defined--after four hours travelling away from earth, the outbound twin might think that only 3.2 hours had passed on Earth, whereas the inbound twin would think that 6.8 hours Earth time had elapsed. Switching from the outbound reference frame to the inbound reference frame involves a change in the interpretation of "Now".


Your own first error is that you have Bob turning around at 4 hours...

Not an error


But, there are no ?jumping clocks? in SR theory (or in GR theory). You?ve just added that ?jumping clock? story, even though it is not in the SR theory.

Again, "simultaneous" is not well defined--how much time the outbound twin thinks has elasped on earth is not the same as how much time the inbound twin thinks has elasped.


And of course, in SR theory, none of the observers see a ?clock jumping?, either backward or forward. All the observers ever see in SR theory is the the other frame?s clocks ?running slow?, but never "jumping" or ?running fast?.

Right. However, when you switch reference frames you may see a jump. Of course, if you're watching the earth clock via telescope you don't see the jump even when switching reference frames, you only get the jump when you try to compensate for distance (when you try to figure out "What time is it NOW on Earth").

Sam5
2003-Dec-09, 07:29 PM
So the experimental results confirming time dilation due to relative motion mean?


First, just consider, for a moment, that there are no “time dilations” due only to “relative motion”, since both of two relatively moving clocks don’t know the other clock exists or is moving.

However, there can be clock slowdowns due to the motion of clocks through electric, magnetic, and gravitational fields at the surface of the earth (or anywhere else), even if the clocks never experience “acceleration”.

Earlier I gave an example of a small electric-motor clock either slowing down or speeding up, when a large industrial magnet is moved near it. This clock rate change is NOT due to “relative motion”, it is due to the coil of wire in the armature of the clock experiencing a strong changing magnetic field, a changing “flux” or changing magnetic field “potential” at the clock’s coil.

Sure, the magnet has to “move” near the clock for the magnetic field potential to change at the coil, but the clock rate change is NOT due to the “relative motion”. If it was due only to “relative motion”, then the clock rate would change if the clock were in New York while the magnet moved in Los Angeles. But of course this does not happen, since the clock in New York can’t feel the magnetic field potential change of the moving industrial magnet while the magnet moves in Los Angeles, since the distance between the clock and the magnet is so great. So, the “relative motion” does not cause the speed up or slowdown effect, since at large distances the clock coil doesn’t “know” that the magnet is moving and at large distances it doesn’t “feel” any change in the local magnetic field potential at the coil inside the clock.

So, the “motion” of the magnet near the clock causes the magnetic field potential to change at the coil of wire inside the motor, and this causes the clock to either speed up or slow down.

I’ve seen “relativity” websites that claim the clock rate change IS due to “relative motion”, but they don’t provide any examples of the magnet and the coil being separated by great distances.

Eroica
2003-Dec-09, 07:56 PM
Of course, if you're watching the earth clock via telescope you don't see the jump even when switching reference frames, you only get the jump when you try to compensate for distance (when you try to figure out "What time is it NOW on Earth").
The truth comes out at last! So I was right all along. Bob "sees" no jump in Ann's clock. Nor does he "infer" a jump when he tries to figure out what time it is NOW on Earth. Why? Because Bob is not an idiot. He understands relativity and is familiar with thing like time dilation, Fitzgerald-Lorentz contraction and the relative nature of simultaneity. He does the math and is not surprised to discover that 5 years have passed on Ann's clock when he turns around, even though only four have passed on his clock.

Sam5
2003-Dec-09, 08:05 PM
You have been provided with popular accounts of experiments that show that time dilation does occur--particles moving close to the speed of light take longer to decay than slower moving particles.

Well, I’ve pointed out several times that particles moving inside particle accelerators are accelerated, and I’ve also pointed out that acceleration causes slowdowns in atomic clocks. In fact, muons are accelerated as they move rapidly toward the earth’s surface. Anything falling from great heights toward the surface of the earth is accelerated.

You have probably heard that atomic clocks located inside an accelerator lab but outside the actual accelerator, do not tick more slowly as the result of the “relative motion” of the particle inside the accelerator. And the “relative motion” of the lab, relative to the so-called “stationary particle” moving inside the accelerator is NOT what causes the “time dilation" in the accelerating particle.

Sam5
2003-Dec-09, 09:06 PM
Although you would have us believe you have a very good understanding of SR (you must if you claim it's wrong), you have either misunderstood some basic physics and GR analogies or you are being purposely obtuse with these questions.

No, not exactly. There is still a mystery going on in the SR theory that I’m trying to work out right now. Based on many of the responses I’ve read here, I think we’ve both been “missing” something. You and I understand some of the phenomena of the SR theory differently, and I think I’ve recently begun to understand the reason why. I have been figuring out what I’ve been missing, and what you’ve been missing, and I think I’m just about ready to lock in on it. It is absolutely fascinating.

It has to do with a fundamental difference between plain ordinary “relative motion” at a distance, and the “relative motion” of atoms and electrons through fields at close range to where the two objects are “relativity moving”.

If the two objects are at a great distance from one another, such as our galaxy and a very distant galaxy, the “c” limit does not apply, since neither of the objects is moving through the fields of the other object. But if the objects are moving at close range to one another, such as a particle being accelerated here on the surface of the earth, then the “c” limit does apply, since their fields put up a “resistance” to the motion. At great universal distances, our local fields can’t put up any “resistance” to the motion of the most distance galaxies.

This is something like the Lorentz Force, that allowed NASA to generate electricity through a long tether wire that was pulled along behind the space shuttle. I’ve read several reports that say the motion of the metal tether through the magnetic field of the earth not only generates an electron flow in the wire, but it causes a slight slowdown in the space shuttle, because the earth’s magnetic field is putting up a resistance to the motion of the long tether through it. This resistance apparently isn’t noticed with short wires or vehicles moving fast relative to the earth’s magnetic field, or when short wires and vehicles move at slow speeds relative to the earth’s magnetic field, but it is noticed when the tether is several miles long and its speed is fast relative to the earth’s magnetic field.

So, apparently, the tether experiment would not work in deep space, since the wire would not be moving directly through any astronomical body’s local magnetic field.

And so, in the electrodynamical part of the SR theory, (the second half of the theory), Einstein might have correctly calculated a true speed limit of “c” for masses moving through strong fields, such as the fields that are located here at the surface of the earth and that travel through space with the earth. If I am correct about this, then that means the “speed limit” would apply here on earth (and near other astronomical bodies), but it would not apply to distant galaxies relative to our galaxy, since they aren’t moving through our own local fields or any other fields.

So, while the local “speed limit” and some kinds of “clock rate changes” are often thought of as “an SR effect” due to “relative motion” and the “relative motion speed limit”, they might actually be “an SR effect” due to the motion of masses through the strong local fields of other masses.

So my disagreement with Sean about what I call the fundamental “difference” between the small masses in the SR theory thought experiments moving relative to one another at great distances from one another, and the separate train example where a fairly small mass moves across the surface of a great mass, the earth, does represent a fundamental difference in the types of and the causes of the “observed” effects due to the “relative motions” in both cases. Meaning, the relative motion of the small masses at great distances in the SR theory’s first half, can NOT have any influence on either mass, while the motion of the train across the surface of the massive earth CAN cause an effect at the train. Sean and I disagree as to what that “effect” is, but we both agree that there IS an effect.

Celestial Mechanic
2003-Dec-09, 09:07 PM
I was a bit careless in my earlier post in my haste to gallop off to the conclusion. I should have said that the redshift during the first phase is sqrt((1+.6)/(1-.6)) = 2.0 (consistent with my terminology in my "When Harry Meets Sally" posts) which results in a frequency shift of 0.5. Likewise, the blueshift is 0.5 which results in a frequency shift of 2.0. I still stand by my earlier calculations, all clock pulses are accounted for!

daver
2003-Dec-09, 10:00 PM
Of course, if you're watching the earth clock via telescope you don't see the jump even when switching reference frames, you only get the jump when you try to compensate for distance (when you try to figure out "What time is it NOW on Earth").
The truth comes out at last! So I was right all along. Bob "sees" no jump in Ann's clock. Nor does he "infer" a jump when he tries to figure out what time it is NOW on Earth. Why? Because Bob is not an idiot. He understands relativity and is familiar with thing like time dilation, Fitzgerald-Lorentz contraction and the relative nature of simultaneity. He does the math and is not surprised to discover that 5 years have passed on Ann's clock when he turns around, even though only four have passed on his clock.
If Bob were watching the earth through a telescope, he would see no jump in Ann's clock when he made the turnaround. His calculation of what time it is "Now" on earth changes when his reference frame changes. Outgoing Bob thinks that ingoing Bob was travelling very fast and his clock was running very slow, ingoing Bob thinks the same about outgoing Bob.

Sam5
2003-Dec-09, 10:00 PM
Glom,


Just so I can make this clear again about my point of view, when I say that a “relative motion” all by itself can not possibly slow down any clock: When the moving magnet is in Los Angeles and the electric clock is in New York, we’ve still got the original “relative motion” between the two, but the New York clock doesn’t “feel” it this time, since the magnet is so far away.

The magnet has to be right up close to the clock, so the electrons inside the wire coil of the motor of the clock can “feel” something, which is the changing magnetic field at those electrons.

So it isn’t the basic “relative motion” that slows down the electric clock, it is motion of the coil through the magnetic flux lines of the magnet, and this can be accomplished by either moving the magnet close to the coil or by moving the coil close to the magnet, but the magnet and the coil must be at close range to one another, or else the coil won’t “feel” the changing flux lines.

So, this is what I’ve been ranting about when I’ve said, “relative motion alone can’t possibly cause any clock to change its rate”, and I’ve said “something physical has to happen to the clock, and the clock has to “feel” some kind of ‘force’ upon it, or a changing force, before it can change its rate.”

I think maybe some of you thought I meant that unaccelerated motion can’t cause any kind of clock to slow down, but that’s not what I meant. I meant that the clock has to “feel” something as a result of the relative motion before it can change rates.

daver
2003-Dec-09, 10:17 PM
Well, I?ve pointed out several times that particles moving inside particle accelerators are accelerated, and I?ve also pointed out that acceleration causes slowdowns in atomic clocks. In fact, muons are accelerated as they move rapidly toward the earth?s surface. Anything falling from great heights toward the surface of the earth is accelerated.

And I pointed out that the decay particles I'm talking about are generated outside of the accelerator--after the accelerated particle has rammed into the target. Was I unclear?

It sounds as if you're blaming the extended lifetime of muons produced by cosmic ray interactions with the atmosphere on GR. Does it bother you that the data fit SR, and that nobody seems to be invoking GR to explain it? Do you have equations that would predict the expected time dilation imposed by your version of GR? Is the time dilation dependent on the velocity of the particle, the distance it falls, or the time it takes it to fall?


You have probably heard that atomic clocks located inside an accelerator lab but outside the actual accelerator, do not tick more slowly as the result of the ?relative motion? of the particle inside the accelerator. And the ?relative motion? of the lab, relative to the so-called ?stationary particle? moving inside the accelerator is NOT what causes the ?time dilation" in the accelerating particle.
Do you think that SR implies that a clock C1 near the high-speed particle runs at a different rate than a clock C2 away from the high-speed particle but in the same reference frame as C1?

Sam5
2003-Dec-09, 11:43 PM
And I pointed out that the decay particles I'm talking about are generated outside of the accelerator--after the accelerated particle has rammed into the target.

Yes, and I've asked you for a scientific paper source of that information but you never provided one. We might be talking about two different things here.


Do you think that SR implies that a clock C1 near the high-speed particle runs at a different rate than a clock C2 away from the high-speed particle but in the same reference frame as C1?

No.

In SR theory, the “rate of clock slowdown” is determined by the relative “v” only.

And by this equation

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img51.gif

the direction of the relative motion doesn’t matter, so a so-called “frame change” does not affect the rate of a clock, and it doesn’t cause any clock in the SR theory to “jump”. There are no “jumping clocks” in SR theory.

Here is the rate of the change of the relatively moving clock in SR theory:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img62.gif

You will notice that it doesn’t include any “jumps”. Since the motion is “inertial” with no acceleration, even a direction change has no affect on any of the clocks. Only the relative “v” determines the rate of the change, and of course the “v” doesn’t “jump” since there are no accelerations. Any real life “turn-around” acceleration affects are simply ignored in SR theory, because:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img51.gif

SeanF
2003-Dec-10, 12:20 AM
You will notice that it doesn’t include any “jumps”. Since the motion is “inertial” with no acceleration, even a direction change has no affect on any of the clocks. Only the relative “v” determines the rate of the change, and of course the “v” doesn’t “jump” since there are no accelerations. Any real life “turn-around” acceleration affects are simply ignored in SR theory, because:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img51.gif

Don't stop there, Sam5. Read the very end of Section 3, right after that equality:


It follows from this relation and the one previously found that http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img52.gif, so that the transformation equations which have been found become
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img53.gif
where
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img54.gif


That first transformation equation, which converts time in one frame to time in a relatively moving frame, is clearly dependent on the sign of v (as well as x, the distance). In fact, I think you'll find that if you enter in 4 years for t (the time Bob travelled), 0.6c for v (Bob's velocity), and 2.4 light years for x (the distance Bob would be from Ann after 4 years at 0.6c), you'll get http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img17.gif=3.2 years.

If you put in those same numbers for t and x but put in negative 0.6c for v, you'll get http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img17.gif=6.8 years.

And just in case you forgot:


Bob sees Ann clock tick off 3.2 years ( from year 0 to year 3.2 ) on the way out and 3.2 years ( from year 6.8 to year 10 ) on the way back.

See? No paradox.

Sam5
2003-Dec-10, 12:43 AM
See?

There is no year 6.8 until Bob is most of the way back to the earth. The year 6.8 certainly doesn’t turn up at the end of 50% of the travel time or 50% of the waiting time.

8 – 6.8 = 1.2 years, when Bob is almost home, not when he’s just halfway home.

10 – 6.8 = 3.2 years when Ann’s clock is just 3.2 years away from 10, 32% away from 10, but NOT when her clock is 50% away from 10.

You are now trying to claim that Bob turns around when about 2/3 of the time has elapsed on Ann’s clock but you said earlier he turns around when 1/2 of the time had elapsed on her clock. [-X

When Bob is 50% away from 8, his clock is at 4, not 6.8, and when Ann is 50% away from 10, her clock is at 5, not 6.8.

You are trying to claim that the distance and time on the way out is longer than on the way back, and that’s not in SR theory.

So you've still got a paradox.

daver
2003-Dec-10, 12:55 AM
Yes, and I've asked you for a scientific paper source of that information but you never provided one. We might be talking about two different things here.

I pointed you to the Stanford page, which alludes to the tau particle decay times. I haven't tried too hard to check for other references.


the direction of the relative motion doesn?t matter, so a so-called ?frame change? does not affect the rate of a clock, and it doesn?t cause any clock in the SR theory to ?jump?. There are no ?jumping clocks? in SR theory.

There are no jumping clocks in SR theory until you start changing reference frames.



Here is the rate of the change of the relatively moving clock in SR theory:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img62.gif

You will notice that it doesn?t include any ?jumps?.

This equation is describing the relative rates of the clocks, it doesn't say anything about the actual values on the clocks. SeanF's previous post discusses this.


Since the motion is ?inertial? with no acceleration, even a direction change has no affect on any of the clocks. Only the relative ?v? determines the rate of the change, and of course the ?v? doesn?t ?jump? since there are no accelerations. Any real life ?turn-around? acceleration affects are simply ignored in SR theory, because:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img51.gif
SeanF's post discusses this. Again, the formula concerns the rate at which the clocks are ticking, not the time the clock shows. Observers in different reference frames have different concepts of "Now". Two observers at the same point in space but in different reference frames would see the same time on a distant clock if peering at it through their telescopes, but would have different opinions about what time it showed if they compensated for the distance to the clock.

Sam5
2003-Dec-10, 01:24 AM
Don't stop there, Sam5.

You’ve got things all mixed up.

You have Ann “seeing” Bob travel an un-contracted distance of 3 light years, 558000 miles for 5 years on her clock, while she “sees” 4 years transpire on Bob’s clock.

You have Bob “seeing” himself travel a contracted distance of 2.4 light years, 446400 miles while he “sees” 4 years on his clock and 3.2 years on Ann’s clock.

So you’ve got two different distances and three different times for just two clocks.

So you are having Bob travel one distance for Ann and a different distance for Bob.

Paradox.

If you had Bob travel 558000 miles at .6 c it would take him 5 years.

And remember:

“The shape of a body in the sense indicated we will call its ‘geometrical shape.’ The latter obviously does not depend on the state of motion of a reference body.” A. Einstein, 1907

So there is no real “length contraction”.

Anyway, if this is all “relative motion”, then Bob would “see” himself as stationary and Ann as “moving”. He would see himself “stationary” for 5 years until Ann “turns around”, and he would “see” 4 years transpire on her clock.

Paradox.

Remember, this is SR, not GR, so the motion is “relative” not “absolute”. Remember what you were saying about the train being “stationary” while the “earth moved”? Why don’t you apply that here? Bob is “stationary” while Ann “moves”.

Sam5
2003-Dec-10, 01:26 AM
There are no jumping clocks in SR theory until you start changing reference frames. :^o

SeanF
2003-Dec-10, 02:01 AM
Don't stop there, Sam5.

You’ve got things all mixed up.

You have Ann “seeing” Bob travel an un-contracted distance of 3 light years, 558000 miles for 5 years on her clock, while she “sees” 4 years transpire on Bob’s clock.

You have Bob “seeing” himself travel a contracted distance of 2.4 light years, 446400 miles while he “sees” 4 years on his clock and 3.2 years on Ann’s clock.

So you’ve got two different distances and three different times for just two clocks.

So you are having Bob travel one distance for Ann and a different distance for Bob.

Paradox.

Why is that a paradox? They're trillions of miles apart (by the way, you better check your conversion factor on light-years to miles). How can it possibly matter if they disagree on the time on Ann's clock?


If you had Bob travel 558000 miles at .6 c it would take him 5 years.

And remember:

“The shape of a body in the sense indicated we will call its ‘geometrical shape.’ The latter obviously does not depend on the state of motion of a reference body.” A. Einstein, 1907

So there is no real “length contraction”.

Anyway, if this is all “relative motion”, then Bob would “see” himself as stationary and Ann as “moving”. He would see himself “stationary” for 5 years until Ann “turns around”, and he would “see” 4 years transpire on her clock.

Paradox.

Bob turns around after only 4 years of travel by his time, not 5. That's why he says Ann's clock has only ticked 3.2 years.


Remember, this is SR, not GR, so the motion is “relative” not “absolute”. Remember what you were saying about the train being “stationary” while the “earth moved”? Why don’t you apply that here? Bob is “stationary” while Ann “moves”.
You really don't understand SR, do you? t and x are the measurements in the "stationary" reference frame in that equation, and I put Bob's numbers in there. That was with Bob being "stationary"!

daver
2003-Dec-10, 02:06 AM
See?

There is no year 6.8 until Bob is most of the way back to the earth. The year 6.8 certainly doesn?t turn up at the end of 50% of the travel time or 50% of the waiting time.

Is there any point in working through the math?

Call outgong Bob BobO, incoming Bob BobI. BobO thinks that when he passes BobI that 3.2 years have elapsed for Alice since BobO left. BobI thinks that when he passes BobO that 6.8 years have passed for Alice since BobO left. When BobO switches reference frames to become BobI, his concept of what time it is "Now" for Alice has to change. However, if BobO was keeping an eye on Alice through a telescope, he wouldn't see any sudden jump in her wristwatch.

The math isn't too complicated if you want to go through it--it doesn't involve anything worse than a square root (and these square roots are all rational). Take it from the viewpoint of both Bobs--start BobI 6 ly out (from Alice's point of view), BobO at earth, run through for each of them what time they SEE (1) BobO leave earth, (2) BobO pass BobI, and (3) BobI pass earth. Figure from there what time they THINK the various events occurred for the other people, compensating for distance. You'll find that (1) everyone agrees how much time has elapsed for each observer between the light from one event arriving and the light for another event arriving, and (2) they disagree about when the non-local events occur (BobI and BobO disagree about what time it is for Alice when BobI passes BobO, BobI and Alice disagree about what time it is for BobO when BobI passes Alice, BobO and Alice disagree about what time it is for BobI when BobO passes Alice).

I think the confusion between what time BobI and BobO think it is for Alice when BobI passes BobO is causing you problems.

daver
2003-Dec-10, 02:12 AM
There are no jumping clocks in SR theory until you start changing reference frames. :^o
Not quite sure what you mean by the Pinocchio nose Sam5. Could you be a bit more explicit?

Sam5
2003-Dec-10, 02:32 AM
They're trillions of miles apart (by the way, you better check your conversion factor on light-years to miles).

Yes, thanks, you are right. I was discussing this subject on another board with a guy who was talking about light “seconds” rather than light years. Just multiply all my miles by 31557600 seconds in a year.



How can it possibly matter if they disagree on the time on Ann's clock?

According to SR they are supposed to "agree" at the end. That's why you have to add the 3.6 seconds to what Bob "sees" on Ann's clock at the end. So you add the 3.6 to the first 3.2 to get the 6.8 at turn-around, and then you add the second 3.2 to that and you wind up with Bob "seeing" 10 on Ann's clock.

3.2 + 3.6 = 6.8

6.8 + 3.2 = 10

That's why you have to have Bob "see" Ann's clock "jump from 3.2 years to 6.8 years at turn-around, even though it's still only 5 years on her own clock and only 4 years on Bob's clock.

And you've still got them traveling different distances.

Paradox.

Sam5
2003-Dec-10, 02:44 AM
Is there any point in working through the math?

Well yes, because Sean is applying a double Lorentz Transformation to Ann’s clock as “seen” by Bob, while he’s applying only a single one to Bob’s clock as “seen” by Ann.

You can’t do that in SR theory.

I know the theory and I know what he is doing. I’m not a kid just reading the twins paradox thought experiment on the internet and just accepting his numbers on blind faith. I don't accept things I read on the internet on blind faith.

5 x .8 = 4

4 x .8 = 3.2

That’s a double application of the Lorentz Transformation, whereas Einstein in his actual theory says we are to apply it only once.

And also, Sean has Bob and Ann traveling different distances, which is not correct according to the SR theory.

Sam5
2003-Dec-10, 02:58 AM
I think the confusion...


When young kids go on a “twins paradox resolution” page on the internet, and if the page is done by an adult, the kids tend to believe the numbers without question. And then if they don’t understand what’s going on, then they feel bad about themselves and think they are “stupid”, when in reality the adult who put the “resolution” page on the internet is either mistaken or is just not telling the truth or is not telling the whole story about the SR theory, and the whole story is very complex. You can’t “solve it” all and “explain” the theory on just one computer-screen page.

Someone needs to tell the public that these guys who make up the internet pages are making mistakes themselves. This is not Einstein’s fault, it’s the fault of the guys who make up the internet pages, and a lot of people need to tell the kids what’s going on and how these adults are making their mistakes, and they need to assure the kids who don’t understand it that they (the kids) are NOT stupid.

It’s not the kids’ fault that they don’t understand this. It’s the fault of the guys who put the wrong “resolutions” on the internet.

Celestial Mechanic
2003-Dec-10, 05:37 AM
Please look at my earlier posting in this thread for the resolution of the twin "paradox". The proper formulae for the redshift and blueshift are still not being used which is why you are arguing about a non-existent "jump". Please read my two "When Harry Meets Sally" posts in the "Einstein's Theories ..." thread where the K-calculus is used to derive the proper formulae.

daver
2003-Dec-10, 06:45 AM
Is there any point in working through the math?

Well yes

OK. Back to two Bob's. BobI is the inbound Bob, BobO the outbound Bob.

From Alice's point of view, the experiment starts at time 0 with BobI six light years out, coming towards her at .6 c. BobO leaves, heading towards BobI, also at .6 c. Alice flashes BobI a message at this time.

Alice thinks BobI receives the message 3.75 light years out. BobI thinks it is 3 light years to Alice when he receives the message, he thinks Alice must have sent it 7.5 years ago, although to Alice it would seem only 6.

Perhaps I should do the math. 6 l.y / (1 + .6) = 3.75 years for the signal to meet BobI. 3.75 * gamma = 3 light years for the distance from BobI to Alice. 3 ligiht years / (1 - .6) = 7.5 years BobI thinks the message was in transit. 7.5 * gamma = 6 years elapsed for Alice.

OK. Alice thinks BobI and BobO cross 3 light years out. BobI and BobO think they cross 2.4 light years out. BobI thinks that an additional year has passed since he received the message from Alice, although he thinks Alice would think only 0.8 years have passed, so BobI thinks 6.8 years have passed for Alice when he and BobO cross paths. BobO has been journeying for 4 years when he and BobI cross paths, and think only 3.2 years have passed for Alice.

BobI thinks that 10 years will have passed for Alice since BobO passed her. BobI thinks that four years will have passed for BobO since BobO passed Alice, and four years will have passed for him since he passed BobO. If BobO had passed BobI a stopwatch (probably a Timex), the watch will read eight years since BobO started.

Nobody is surprised. Everybody, at every well defined moment in the example agrees about how much time has elapsed for the participants. I haven't worked through all the numbers, but feel free. Alice, BobI, and BobO agree how much time has passed for BobO from when he passed Alice to when he passed BobI. Alice, BobI, and BobO agree how much time has passed from BobI from when he received Alice's signal to when he passed BobO. Alice, BobI, and BobO agree how much time passed for BobI from when he passed BobO to when he passed Alice. Alice, BobI, and BobO agree on how much time passed for Alice from when she was passed by BobO to when she was passed by BobI.

What they don't agree on are the non-local events--they will get different numbers for how much time had passed for BobO or Alice when BobI received the message from Alice, how much time passed for Alice when BobO passed BobI, and how much time passed for BobO when BobI passed Alice.

daver
2003-Dec-10, 06:52 AM
Please look at my earlier posting in this thread for the resolution of the twin "paradox". The proper formulae for the redshift and blueshift are still not being used which is why you are arguing about a non-existent "jump". Please read my two "When Harry Meets Sally" posts in the "Einstein's Theories ..." thread where the K-calculus is used to derive the proper formulae.

The "jump" exists when trying to define "Now" for distant events in different reference frames. Certainly if you look at things from a redshift/blueshift perspective, and just keep track of what time you see when looking through a telescope you don't have any of these problems. Maybe your approach is the better one--it leaves off a lot of the fiddly bits.

freddo
2003-Dec-10, 07:41 AM
I'm inclined to agree. I think whatever Sam5 is misunderstanding is pretty fundamental, so a simple solution to this non-paradox has got to be a help.

Jobe
2003-Dec-10, 07:49 AM
I'm inclined to agree. I think whatever Sam5 is misunderstanding is pretty fundamental, so a simple solution to this non-paradox has got to be a help.

I don't think Sam5 is ever going to agree with any of you, no matter how patiently you explain it to him.

Diamond
2003-Dec-10, 09:17 AM
Here's the answer using simple equations:

(tau)^2 = (time)^2 - (distance)^2

Bob travels at 3/5c. Therefore in 10 years (as measured by Anne's clock) he moves a total distance of 6 light years (as measured by Anne). But Bob does not move at all in his own frame of reference!

So Bob's wristwatch time is tau.

(tau)^2 = (10)^2 - 6^2 = 100-36 = 64 (years)^2

Therefore Bob's time elapsed is 8 years but Anne measures 10 years. QED.

I'm also of the opinion that Sam5 will take no notice of clear explanations.

kilopi
2003-Dec-10, 09:36 AM
Why don’t you apply that here? Bob is “stationary” while Ann “moves”.
That is done on this page (http://mentock.home.mindspring.com/twin2.htm).

It’s not the kids’ fault that they don’t understand this.

It's not an adult's fault either, this is not an easy subject.

It's not their fault, unless they just don't want to understand it.

SeanF
2003-Dec-10, 03:38 PM
Okay, Sam, I've realized that your misunderstanding of SR is much more basic than I previously thought. So, let's start at the very beginning. Much of the next couple of paragraphs is real basic stuff, and I am not implying that you don't understand it. I just want to plainly set out what we're talking about.

First of all, take a plain piece of paper (not graph paper this time) and mark a point on it. Now, how can we define that point? We can use cartesian coordinates, and say it is (x,y). No two points on the paper will have the same x,y values, so those values uniquely identify that particular point . . . except: those numbers, by definition, only define that point relative to another point, (0,0). On a sheet of paper, we can easily identify a corner as (0,0), with the edges as the axes. However, if the paper were infinite in size, we would have to simply arbitrarily define an origin point (0,0) and arbitrarily define our x- and y-axes, and then we can define all other points relative to that point.

Now, to move into three-dimensional space, we need to add a third coordinate, z, with its own arbitrary axis. To locate an event, in space-time, we add a fourth coordinate, t, with its own axis. So, once we define our arbitrary origin point at (0,0,0,0), any other point can be defined relative to that origin by it's own coordinates (x,y,z,t).

Let's say you've got a light bulb sitting next to you. You turn the light bulb on. That's our first event, so we'll designate that as the origin and call it (0,0,0,0). Five minutes later, you turn off the light. That event occurs at (0,0,0,5) - our spatial coordinates stay the same. Five minutes after that, you smash the bulb. That event, then, is at (0,0,0,10).

Now, here's where SR gets a little complicated. Consider that under SR there is no absolute motion, only relative motion. That means that from a reference frame that is in relative motion to that light bulb, the spatial events would change for those events. For this discussion, we'll limit the movement to being along the x-axis. So, if our reference frame says the light bulb is moving to the left at 0.6c, then the light-bulb can't even be at (0,0,0,5) for that second event. At best, it would have to be at (-3,0,0,5). Now, keep in mind that we are not physically changing anything. All we are doing is changing the designation of that point in space-time. With me so far?

Now, here's where SR get's really complicated. The speed of light, c, must remain a constant. If we consider two events - a pulse of light being emitted at an emitter, and that light being received at a receiver - then, we can conclude that the values of x (in light-minutes) and t (in minutes) must be the same. So, if relative motion causes us to conclude that the value of x changes, then so too must the value of t change.

Now, again, we are not physically changing anything. All we're doing is saying that a point in space-time corresponding to (0,0,0,5) relative to the origin in one reference frame would correspond to (-3.75,0,0,6.25) relative to the same origin point but in the other reference frame. [NOTE: I had the numbers wrong in this last sentence and have corrected them]

Now, I think I'm just going to leave it at that for now and we'll make sure this is clear before we move on any further.

Sam5
2003-Dec-10, 05:29 PM
Bob travels at 3/5c. Therefore in 10 years (as measured by Anne's clock) he moves a total distance of 6 light years (as measured by Anne). But Bob does not move at all in his own frame of reference!

You can’t mix distances like that. You have Ann seeing Bob move 6 light years in distance at the velocity of .6 c, while you have Bob seeing Ann move only 4.8 light years distance at the velocity of .6 c, so you’ve got two different experiments, two different “trips” mixed into one.

In one trip, you’ve got Ann seeing Bob moving 6 light years, and in the next trip you’ve got Bob seeing Ann moving 4.8 light years. Then you are comparing Ann’s clock time at the end of the first thought experiment to Bob’s time at the end of the second thought experiment.

Of course if Ann sees Bob move 6 light years at .6 c that will take 10 years by her clock. And if Bob sees Ann move 4.8 light years at .6 c, that will take 8 years by his clock.

Your thought experiment has Bob turning around too soon, at 4 years on his clock, which is the same dilated 4 years that Ann sees on his clock while she sees 5 years on her clock. But Bob doesn’t “see” that same dilation on his own clock because he is in his own inertial frame and he sees Ann, not himself, as moving and time dilating.

By having Bob turn around based on what Ann “sees” on his clock, the guy who invented this thought experiment is not following SR theory and he is purposely making the distances and times traveled asymmetrical.

Einstein didn’t do this, the guy who wrote the thought experiment did this.

Einstein created the clock paradox by reporting only what one observer saw on all the clocks, and he left out any mention of what the other observer saw. That was a small error on his part.

In the Ann and Bob thought experiment, the inventor of it has Ann and Bob moving different distances just so they can both “see” different times for the other to travel those distances. That is not an “error”, it is something else.

Sam5
2003-Dec-10, 05:40 PM
You are playing with early 20th Century mathematical diagrams and you aren’t even paying attention to what happens in reality. This kid has a good grasp of what happens in reality:

“The light from a distant star passing right near the surface of the Sun on the way to the observer takes the form of a plane wave. The rays of the plane wave of light traveling closer to the Sun (source of gravitation) are in essence slowed due to the effect of time dilation only. If the light of the rays closer to the Sun travel slower over a reference time increment than the rays farther away, then using Huyghens’ principle, the plane wave is deflected toward the source of gravity (see figure 25)........ The light pulse moves with a velocity less than "c" along the curve relative to reference observers far away......”

SOURCE (http://216.239.57.104/search?q=cache:Z48FPjGkBWoJ:www.physicspost.com/articles.php%3FarticleId%3D101%26page%3D12+sun+lig ht+plane+wave+%22slows+down%22&hl=en&ie=UTF-8)

If in reality, your reference frame is a galaxy moving at .6 c relative to the earth, which is just about the only thing that actually does move at .6 c relative to the earth, then the speed of light inside that galaxy is “c” relative to the stars in the galaxy, but photons of light inside that galaxy that are aimed in the direction of the earth and that will eventually reach the earth are moving at less than c relative to the earth, while they are inside that galaxy.


Now, I think I'm just going to leave it at that for now and we'll make sure this is clear before we move on any further.


Before we move on any further, you need to understand what is happening in physics and cosmology today.

On the large astronomical scale, “c” is no longer a “limiting speed”, and “c” is no longer the only speed of light relative to all observers.

Things have changes during just the past 10 years.

“in these cosmological variables the speed of light is c with respect to local comoving observers.

The time and distance used in the Hubble law are not the same as the x and t used in special relativity, and this often leads to confusion. In particular, galaxies that are far enough away from us necessarily have velocities greater than the speed of light:

(diagram)

The light cones for distant galaxies in the diagram above are tipped over past the vertical, indicating v > c. ”

SOURCE (http://216.239.57.104/search?q=cache:2VLA-v5k9zUJ:www.astro.ucla.edu/~wright/cosmo_02.htm+wright+comoving+&hl=en&ie=UTF-8)

I’ve mentioned to you before that modern cosmology theory is no longer bogged down in the old transitory Edwardian era of electrodynamics and kinematics theoretics, and it has now entered the 21st Century.

SeanF
2003-Dec-10, 06:02 PM
Now, I think I'm just going to leave it at that for now and we'll make sure this is clear before we move on any further.

Before we move on any further, you need to understand what is happening in physics and cosmology today.

On the large astronomical scale, “c” is no longer a “limiting speed”, and “c” is no longer the only speed of light relative to all observers.

Things have changes during just the past 10 years.

“in these cosmological variables the speed of light is c with respect to local comoving observers.

The time and distance used in the Hubble law are not the same as the x and t used in special relativity, and this often leads to confusion. In particular, galaxies that are far enough away from us necessarily have velocities greater than the speed of light:

(diagram)

The light cones for distant galaxies in the diagram above are tipped over past the vertical, indicating v > c. ”

SOURCE (http://216.239.57.104/search?q=cache:2VLA-v5k9zUJ:www.astro.ucla.edu/~wright/cosmo_02.htm+wright+comoving+&hl=en&ie=UTF-8)

I’ve mentioned to you before that modern cosmology theory is no longer bogged down in the old transitory Edwardian era of electrodynamics and kinematics theoretics, and it has now entered the 21st Century.

You still don't understand what you're talking about. "[L]ocal comoving observers" in your quote above refers to observers close enough to the emitter that the expansion of space has no effect, whether those observers are at rest relative to the emitter or not. They're saying exactly what I said, that the expansion of space contributes to the recession values of distant galaxies (and the light coming from them), but it does not invalidate Special Relativity.

However, I am now forced to conclude that you no longer insist that SR is flawed in and of itself, but only consider it flawed in that it doesn't deal with the expansion of space. If you did consider SR to be internally inconsistent, then you would be willing to discuss it under those terms.

SeanF
2003-Dec-10, 06:08 PM
Hey, Sam5, did you read that whole page (http://www.astro.ucla.edu/~wright/cosmo_02.htm) before you posted it?

"But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get: (diagram)"

How about them apples?

russ_watters
2003-Dec-10, 07:01 PM
I'm inclined to agree. I think whatever Sam5 is misunderstanding is pretty fundamental, so a simple solution to this non-paradox has got to be a help.

I don't think Sam5 is ever going to agree with any of you, no matter how patiently you explain it to him. Agreed. His misunderstandings are SO fundamental that he simply won't even acknowledge them when pointed out. He won't discuss the basics, only the more complicated impications. Until he's willing to step back and start from the beginning and ACCEPT the facts (there are many factual errors in his posts, not just errors in the application of the theory), he won't be able to learn why he is wrong.

All of the math you guys are doing is pointless until he learns what the theory SAYS. Then he can learn how to calculate what it says.

crazy4space
2003-Dec-10, 07:27 PM
Eroica, I just read this entire thread and wow did you open up a can of worms however, I am learning more every day. I love this board. 8)

daver
2003-Dec-10, 07:52 PM
Eroica, I just read this entire thread and wow did you open up a can of worms however, I am learning more every day. I love this board. 8)

Well, it's not so much that Eroica opened up a can of worms as the can of worms leaped from another thread to this one (leaping worms. I assume they manage that something like a pogo stick).

I think the worms first started in the Einstein's Theory of Relativity thread before hopping here. If I may, I'd like to suggest that we make some attempt to isolate the worms to this thread--if they show signs of spreading to yet another thread, just refuse to reply. Even better, perhaps they can be shovelled into the Against the Mainstream section.

Cougar
2003-Dec-10, 07:56 PM
....This kid has a good grasp of what happens in reality: ...The rays of the plane wave of light traveling closer to the Sun (source of gravitation) are in essence slowed due to the effect of time dilation only.... The light pulse moves with a velocity less than "c" along the curve relative to reference observers far away......” SOURCE (http://216.239.57.104/search?q=cache:Z48FPjGkBWoJ:www.physicspost.com/articles.php%3FarticleId%3D101%26page%3D12+sun+lig ht+plane+wave+%22slows+down%22&hl=en&ie=UTF-8)
Though some of the contributing authors to the "Physics Post" website you linked to are respected and quite well known (Paul Davies, Michio Kaku), there are other contributors who are students and amateurs. Now, certainly students and amateurs have the potential to be correct, but I don't think it is at all effective or compelling to cite such Physics Post contributors as authorities on topics as well investigated as general relativity. Erich Schoedl, the author of the post you cited, includes nothing in his biographical thumbnail about who he is, what his background or qualifications are, and he appears nowhere else on the internet.... For me, this does not instill much confidence in his particular interpretation of the reality behind geodesics.

Wally
2003-Dec-10, 08:43 PM
I also say that “relative motion” can not have any possible effect on any kind of clock, since the clock feels no kind of “force” applied to it through “relative motion” alone.



Sam, you've said this over an over. What you need to understand is that it's not the clock that's affected by time dialation, it TIME that's affected by time dialation. The clock is merely part of that reference frame, and is used to represent this difference in the passage of time. There doesn't need to be any kind of "force" involved

Wally
2003-Dec-10, 08:48 PM
For example, the earth is moving “relative” to billions of other bodies, and we can’t possibly have any kind of real “time dilation” effect caused by our “relative motion” relative to those other bodies.

Sure we can experience time dilation! We ARE experiencing time dilation, when observed from a another reference frame moving at relativistic speeds compared to our frame. We, just as they, say "all is normal here, while time is slow over there". This is what makes SR such an interesting topic!

Jim
2003-Dec-10, 08:56 PM
... (leaping worms. I assume they manage that something like a pogo stick.)

Worms? Probably some form of quantum tunneling.

SeanF
2003-Dec-10, 08:58 PM
... (leaping worms. I assume they manage that something like a pogo stick.)

Worms? Probably some form of quantum tunneling.

Wow! Is the BABB the location of the first stable wormhole in the Internet Quadrant? Should we start calling this place BAjor? :D

Wally
2003-Dec-10, 08:59 PM
The problem is that from B's point of view there has to be a time where he sees A's clock as running fast compared to his. That can't happen during the coasting periods. We've all agreed that during those periods he sees A's clock as running slow, as predicted by SR. The time when he sees A's clock running fast has to come during the non-inertial accelerations. To determine that, from B's non-inertial reference frame, requires GR.
This seems to be the nub of the problem. I for one do not agree that B sees A's clock as running slow during all the coasting periods, and fast during the accelerations. On his way out, B sees A's clock running slow and A sees B's clock running slow. Then B turns for home and immediately B sees A's clock running fast. A's clock continues to run fast from B's perspective all the way home. But A does not see B's clock running fast until some time after B's has turned for home. (Let's say B turns for home when he is 10 uncontracted light-years away: A won't see B's clock running fast until 10 years after B has turned around.)

Sorry yet again for lagging a couple day's behind. . .

Eroica, as stated in the other thread, the above is not correct. SR time dilation has nothing to do with direction. A's clock appears to run slow to B both going away and heading back home.

daver
2003-Dec-10, 09:07 PM
Eroica, as stated in the other thread, the above is not correct. SR time dilation has nothing to do with direction. A's clock appears to run slow to B both going away and heading back home.

I don't remember the post of Eroica's that you're quoting, but if B is observing A's clock through a telescope, B will see A's clock as running slow on the way out and fast on the way back (Doppler effect). If B is trying to compensate for Doppler by using the classical equation, or looks at A's clock while passing, then Yes, A's clock will appear to be running slowly.

SeanF
2003-Dec-10, 09:10 PM
The problem is that from B's point of view there has to be a time where he sees A's clock as running fast compared to his. That can't happen during the coasting periods. We've all agreed that during those periods he sees A's clock as running slow, as predicted by SR. The time when he sees A's clock running fast has to come during the non-inertial accelerations. To determine that, from B's non-inertial reference frame, requires GR.
This seems to be the nub of the problem. I for one do not agree that B sees A's clock as running slow during all the coasting periods, and fast during the accelerations. On his way out, B sees A's clock running slow and A sees B's clock running slow. Then B turns for home and immediately B sees A's clock running fast. A's clock continues to run fast from B's perspective all the way home. But A does not see B's clock running fast until some time after B's has turned for home. (Let's say B turns for home when he is 10 uncontracted light-years away: A won't see B's clock running fast until 10 years after B has turned around.)

Sorry yet again for lagging a couple day's behind. . .

Eroica, as stated in the other thread, the above is not correct. SR time dilation has nothing to do with direction. A's clock appears to run slow to B both going away and heading back home.

The time dilation (if a clock is running fast or slow) is direction independent. However the simultaneity difference (if a clock is ahead or behind) is direction-dependent.

Sam5
2003-Dec-10, 09:14 PM
Hi Cougar,

I never said that the kid was an “authority”. In fact, I started to post his comments a few days ago, but I decided not to because he is not an authority.

What I said was, “This kid has a good grasp of what happens in reality:”

But this does not make him any kind of “cosmology authority”.

There is another kid on that board that has one of the worst “twins paradox” stories I’ve ever seen, and last night I started typing up a response to him to let him know what all he is doing wrong. But my response got up to be several paragraphs in length, and it pointed out so many things he said that are incorrect, I decided that I didn’t want to hurt the kids feelings by criticizing his paper so much, so I just didn’t say anything to him.



Erich Schoedl, the author of the post you cited, includes nothing in his biographical thumbnail about who he is, what his background or qualifications are, and he appears nowhere else on the internet....

I could tell by what he wrote that this particular kid is very smart. He has the light beam slowing down at the sun, as "seen" from the earth, but not slowing down at the sun, as "seen" from the sun, and that is correct. However, he didn't mention that at the sun, the beam in deep space will be "seen" as moving faster than c. It slows down to "c" at the sun only in reference to local sun atomic clocks. That is because the beam at the sun is in the same local "comoving space" as the sun and its local atomic clocks.

Celestial Mechanic
2003-Dec-10, 09:19 PM
[Snip!]... but if B is observing A's clock through a telescope, B will see A's clock as running slow on the way out and fast on the way back (Doppler effect). If B is trying to compensate for Doppler by using the classical equation, or looks at A's clock while passing, then Yes, A's clock will appear to be running slowly.
Someone else here gets it. You cannot use the dilation factor gamma all by itself, nor the classical Doppler formula (1+beta for redshift of wavelength, 1-beta for blueshift of wavelength), but both together. In the example of Anne and Bob cited earlier, with the velocity of 0.6c, this means that both see the other's clock run half as fast during the redshift phase, and twice as fast during the blueshift phase.

Bob sees redshift for 4 years and blueshift for 4 years. During the redshift phase he receives 4*0.5 = 2 years of Anne's signals, and during the blueshift phase he receives 4*2.0 = 8 years more of Anne's signals, for a total of 10 years of Anne's signals received in 8 years.

Anne sees redshift for 8 years and blueshift for 2 years. During the redshift phase she receives 8*0.5 = 4 years of Bob's signals, and during the blueshift phase she receives 2*2.0 = 4 years more of Bob's signals for a total of 8 years of Bob's signals received in 10 years.

daver
2003-Dec-10, 09:21 PM
The time dilation (if a clock is running fast or slow) is direction independent. However the simultaneity difference (if a clock is ahead or behind) is direction-dependent.

Yes, what he said. I had interpreted "running slow" as time dilated.

Wally
2003-Dec-10, 09:24 PM
Of course, if you're watching the earth clock via telescope you don't see the jump even when switching reference frames, you only get the jump when you try to compensate for distance (when you try to figure out "What time is it NOW on Earth").
The truth comes out at last! So I was right all along. Bob "sees" no jump in Ann's clock. Nor does he "infer" a jump when he tries to figure out what time it is NOW on Earth. Why? Because Bob is not an idiot. He understands relativity and is familiar with thing like time dilation, Fitzgerald-Lorentz contraction and the relative nature of simultaneity. He does the math and is not surprised to discover that 5 years have passed on Ann's clock when he turns around, even though only four have passed on his clock.

But, the point remains, Bob does NOT "see" ann's clock running faster than his on the return trip. It continues to run slower, just like it did during his outbound trip.

SeanF
2003-Dec-10, 09:25 PM
I could tell by what he wrote that this particular kid is very smart. He has the light beam slowing down at the sun, as "seen" from the earth, but not slowing down at the sun, as "seen" from the sun, and that is correct. However, he didn't mention that at the sun, the beam in deep space will be "seen" as moving faster than c. It slows down to "c" at the sun only in reference to local sun atomic clocks. That is because the beam at the sun is in the same local "comoving space" as the sun and its local atomic clocks.

Are you using "comoving" in the same context that Wright does on the pages (http://www.astro.ucla.edu/~wright/cosmo_01.htm) you linked to? He uses it to mean "motionless relative to the Hubble flow":



The Hubble law defines a special frame of reference at any point in the Universe. An observer with a large motion with respect to the Hubble flow would measure blueshifts in front and large redshifts behind, instead of the same redshifts proportional to distance in all directions. Thus we can measure our motion relative to the Hubble flow, which is also our motion relative to the observable Universe. A comoving observer is at rest in this special frame of reference. Our Solar System is not quite comoving: we have a velocity of 370 km/sec relative to the observable Universe. The Local Group of galaxies, which includes the Milky Way, appears to be moving at 600 km/sec relative to the observable Universe.
(Bolding in the above is mine, italics are in the original)

That's not what you mean, though, is it?

Wally
2003-Dec-10, 09:46 PM
Eroica, as stated in the other thread, the above is not correct. SR time dilation has nothing to do with direction. A's clock appears to run slow to B both going away and heading back home.

I don't remember the post of Eroica's that you're quoting, but if B is observing A's clock through a telescope, B will see A's clock as running slow on the way out and fast on the way back (Doppler effect). If B is trying to compensate for Doppler by using the classical equation, or looks at A's clock while passing, then Yes, A's clock will appear to be running slowly.

This thought experiment doesn't take actual doppler effects into account. The "seeing" bob does of Ann's clock is merely an illustration that Bob still perceives time going slower for Ann than he does for himself at relativistic speeds, regardless of direction. I think Eroica wanted (wants???) to have Bob perceive time as going faster for Ann on the trip home, in order to account for her being older when he gets back. This is what I'm trying to clarify.

Eroica
2003-Dec-10, 09:59 PM
A's clock appears to run slow to B [when B is] both going away and heading back home.
I still disagree. If Bob keeps his telescope trained on Ann during the whole of his trip, he will see events on Earth taking place at slower than the normal rate during the outgoing phase of his trip. It would be like watching a movie in slow motion.

Once he turns around, events on Earth will appear to pass at an accelerated rate. Now it's as though Bob is watching one of those old Charlie Chaplin movies.

If this is not what Bob perceives, then how can he possibly observe all 10 years of Ann's life in just 8 years of his life? Perhaps we're still confusing two different meanings of the expression running slow?

SeanF
2003-Dec-10, 10:05 PM
A's clock appears to run slow to B [when B is] both going away and heading back home.
I still disagree. If Bob keeps his telescope trained on Ann during the whole of his trip, he will see events on Earth taking place at slower than the normal rate during the outgoing phase of his trip. It would be like watching a movie in slow motion.

Once he turns around, events on Earth will appear to pass at an accelerated rate. Now it's as though Bob is watching one of those old Charlie Chaplin movies.

If this is not what Bob perceives, then how can he possibly observe all 10 years of Ann's life in just 8 years of his life? Perhaps we're still confusing two different meanings of the expression running slow?

I think we may be. If Ann is sending out "pulses" every second, Bob will receive all 10 years worth of pulses. Some of them he will receive faster than one per second, some slower. It is only when he tries to reconcile the observed Doppler effect with the predicted Lorentz contraction that he will notice something wrong.

As I said before (maybe in the other thread), I think it will appear to Bob as if there were two Anns for a period of time sending overlapping signals - they just don't arrive overlapping because some of them are coming from "farther away."

daver
2003-Dec-10, 10:24 PM
As I said before (maybe in the other thread), I think it will appear to Bob as if there were two Anns for a period of time sending overlapping signals - they just don't arrive overlapping because some of them are coming from "farther away."

No, Bob should only see one Ann. She will be red-shifted when he's moving away, and blue shifted when he returns. If we're doing the 4 years out, 4 years back at .6 c (from Bob's point of view), he
sees (through his telescope) that two years for Ann will have passed during his outbound trip, and 8 years during his return trip (he sees her clock run at half speed on the way out and double time on the way back).

SeanF
2003-Dec-10, 11:03 PM
{EDIT} This post of mine is complete and utter cr*p. I'm not going to delete or edit it, because it will serve to remind me of the dangers of doing math in my head and posting too quickly. However, please ignore this post and just read my next one. :-?



As I said before (maybe in the other thread), I think it will appear to Bob as if there were two Anns for a period of time sending overlapping signals - they just don't arrive overlapping because some of them are coming from "farther away."

No, Bob should only see one Ann. She will be red-shifted when he's moving away, and blue shifted when he returns. If we're doing the 4 years out, 4 years back at .6 c (from Bob's point of view), he
sees (through his telescope) that two years for Ann will have passed during his outbound trip, and 8 years during his return trip (he sees her clock run at half speed on the way out and double time on the way back).

Let me ask you this. I'm Bob. Four years after Ann leaves me, I receive a light-signal from her that has a Doppler red-shift indicating she was moving away from me at 0.6c when she sent it. Assuming her velocity is constant, how far away was she when she sent that signal, and how long ago was that? My math says she would have been 2.5 light years away and it was 2.5 years ago.

Now let me ask you this. I'm Bob. Four years before Ann reaches me, I receive a light-signal from her that has a Doppler blue-shift indicating she was moving towards me at 0.6c when she sent it. Assuming her velocity is constant, how far away was she when she sent that signal, and how long ago was that? My math says she would have been 6 light years away and it was 6 years ago.

So the light I received during the first four years tells me she was moving away from me for 2.5 years at 0.6c, but the light I receive during the second four years tells me she was moving towards me for 6 years at 0.6c, even though she was only gone for a total of 8 years, and if she was moving the same velocity out as back it had to be the same time and distance.

From Bob's "I'm not moving" point of view, it's not as simple as "her clock was running slow on the way out and fast on the way back."

SeanF
2003-Dec-10, 11:47 PM
As I said before (maybe in the other thread), I think it will appear to Bob as if there were two Anns for a period of time sending overlapping signals - they just don't arrive overlapping because some of them are coming from "farther away."

No, Bob should only see one Ann. She will be red-shifted when he's moving away, and blue shifted when he returns. If we're doing the 4 years out, 4 years back at .6 c (from Bob's point of view), he
sees (through his telescope) that two years for Ann will have passed during his outbound trip, and 8 years during his return trip (he sees her clock run at half speed on the way out and double time on the way back).

I'm Bob. Ann is right next to me and starts moving away. For four years, I receive light from her that has a Doppler red-shift indicating she was moving away from me at 0.6c. This tells me that she spent 2.5 years moving away from me and got 1.5 light-years away. The signal I receive from her right at the four-year mark says her clock says "2 years" (remember, this signal was sent 2.5 years after she left me, when both our clocks read 0).

Now, for the next four years, I receive light from her that has a Doppler blue-shift indicating she was moving towards me at 0.6c, right up until the point where she reaches me again. This tells me that she spent 10 years moving towards me and started 6 light-years away. The signal I received from her right at the four-year mark says her clock said "2 years" (remember, this signal was sent 10 years before she reaches me, when my clock will read 8 and hers will read 10).

So, I can now conclude that Ann spent only 2.5 years moving away from me (and only got 1.5 light years away), but somehow managed to spend 10 years moving back towards me, from a distance of 6 light-years, even though only 8 years passed between her departure and her return. Not only is the 4.5 light-year distance jump unexplained, but so is the 4.5 year jump into the "past."

On a side note, this would mean that Ann spent a total of 12.5 years moving at 0.6c relative to Bob, and her clock ticked off a total of 10 years, which is exactly what SR predicts. \:D/

So, from Bob's "I'm not moving" point-of-view, it's not as simple as "Ann's clock runs slow on the way out and fast on the way back."

Sam5
2003-Dec-11, 12:06 AM
Are you using "comoving" in the same context that Wright does on the pages (http://www.astro.ucla.edu/~wright/cosmo_01.htm) you linked to? He uses it to mean "motionless relative to the Hubble flow":

I’m working on a response to your question, but I have to keep changing and rewriting it so it will make some sense. I hope we all don’t go bonkers over this stuff. I’m beginning to babble to myself when I’m out in public. I think we should be a little forgiving of each other if we start making simple mistakes, so we won’t get upset or go bonkers. I’ll get back to you later.

daver
2003-Dec-11, 02:01 AM
So, from Bob's "I'm not moving" point-of-view, it's not as simple as "Ann's clock runs slow on the way out and fast on the way back."
Bob, watching Ann through the telescope, sees 10 years go by for Ann, in a not particularly steady progression.

Bob, desparately trying to pretend that he doesn't shift reference frames, sees that his interpolated position for Ann takes a huge jump just at the moment he is denying his reference frame changed.

I don't really see a conflict here.

Sam5
2003-Dec-11, 02:51 AM
On a side note, this would mean that Ann spent a total of 12.5 years moving at 0.6c relative to Bob, and her clock ticked off a total of 10 years, which is exactly what SR predicts. \:D/

By who's clock do you measure the 12.5 years?

Surely you're not saying that inside her own inertial frame, Ann saw her own clock slow down? By which reference clock did she measure this slowdown?

For the past several days you've been saying that Ann in this experiment spent a total of 10 years moving relative to Bob.

So far, we've seen these statements from you about Ann's trip:

Somebody’s clock measures Ann's trip taking 12.5 years, proclaimed by Sean
Ann’s clock runs 10 years, proclaimed by Sean and seen by Ann
Ann’s clock runs 6.4 years, seen by Bob
Ann’s clock jumps once, suddenly, from 3.2 years to 6.8 years, as observed by Sean

SeanF
2003-Dec-11, 03:07 AM
[Bob] sees (through his telescope) that two years for Ann will have passed during his outbound trip, and 8 years during his return trip (he sees her clock run at half speed on the way out and double time on the way back).

Bob does not see that those 8 years on Ann's clock as having happened "during his return trip." Those 8 years on Ann's clock (apparently) started ten years before Ann and Bob met up again, by Bob's clock. Bob simply didn't receive the light from her until four years before they met. He does not, can not, conclude that Ann's clock ticked off 8 years during the same time that his own clock ticked off 4 years.

SeanF
2003-Dec-11, 03:09 AM
Sam5, I need your comments on this post (http://www.badastronomy.com/phpBB/viewtopic.php?t=9731&postdays=0&postorder=asc&star t=125). I'm not going to even try to reach a consensus with you on the results of SR until we reach one on the mechanics of it.

Please read that post, and give me your comments on it in and of itself.

Celestial Mechanic
2003-Dec-11, 05:08 AM
[Bob] sees (through his telescope) that two years for Ann will have passed during his outbound trip, and 8 years during his return trip (he sees her clock run at half speed on the way out and double time on the way back).

Bob does not see that those 8 years on Ann's clock as having happened "during his return trip." Those 8 years on Ann's clock (apparently) started ten years before Ann and Bob met up again, by Bob's clock. Bob simply didn't receive the light from her until four years before they met. He does not, can not, conclude that Ann's clock ticked off 8 years during the same time that his own clock ticked off 4 years.
I'm sorry, but this is wrong. daver agrees with my accounting of the clock signals. Draw a Minkowski diagram of this for yourself. Every light signal that Anne sends out is received by Bob. There are no gaps. Every light signal that Bob sends out is received by Anne. There are no gaps. The redshift factor is (1+0.6)/0.8 = 2.0, equal to the classical value times the dilation factor of 1/0.8. The blueshift factor is (1-0.6)/0.8 = 0.5, again equal to the classical value times the dilation factor of 1/0.8.

SeanF
2003-Dec-11, 01:08 PM
[Bob] sees (through his telescope) that two years for Ann will have passed during his outbound trip, and 8 years during his return trip (he sees her clock run at half speed on the way out and double time on the way back).

Bob does not see that those 8 years on Ann's clock as having happened "during his return trip." Those 8 years on Ann's clock (apparently) started ten years before Ann and Bob met up again, by Bob's clock. Bob simply didn't receive the light from her until four years before they met. He does not, can not, conclude that Ann's clock ticked off 8 years during the same time that his own clock ticked off 4 years.
I'm sorry, but this is wrong. daver agrees with my accounting of the clock signals. Draw a Minkowski diagram of this for yourself. Every light signal that Anne sends out is received by Bob. There are no gaps. Every light signal that Bob sends out is received by Anne. There are no gaps. The redshift factor is (1+0.6)/0.8 = 2.0, equal to the classical value times the dilation factor of 1/0.8. The blueshift factor is (1-0.6)/0.8 = 0.5, again equal to the classical value times the dilation factor of 1/0.8.
What exactly is wrong? I can draw the Minkowski diagram. If I do, I'll see that Bob received eight years of Ann's signals in four years of his time, yes. However, I will not see that Ann broadcast eight years of signals in four years of Bob's time. Are you claiming that I will? If not, then I don't understand what you're saying was wrong about what I said. If you do see Ann broadcasting eight years of signals in four years of Bob's time, then I'd sure like to see that Minkowski diagram.

Sam5
2003-Dec-11, 02:49 PM
Sam5, I need your comments on this post (http://www.badastronomy.com/phpBB/viewtopic.php?t=9731&postdays=0&postorder=asc&star t=125).


I’ve already given you my comments about that post. My response is just two posts down from your post.

In your post you said, “The speed of light, c, must remain a constant.”

But it doesn’t remain constant. I’ve already given you links to mainstream websites that say that, including Ned Wright’s website, but you just won’t accept the observational truth of even the most respected of mainstream scientists.

The speed of light, c, remains a “constant” inside local “comoving spaces” at the surfaces of astronomical bodies that are at the centers of those “comoving spaces”, and a local “comoving space” contains a local gravitational field, that is centered on the center of the body the "comoving space" contains. And that field impresses a certain accelerative “force” upon local atoms at the surface of that body. This specific amount of “force”, which is different at the surface of each different body, depending on their mass, causes the atoms at that body’s surface to vibrate at certain rates and emit light of certain frequencies. This action causes the body’s local atomic clocks to “tick” at a certain local rate, and that local “tick rate” is what determines the velocity of light at that body. And that velocity at the surface of that body is “c”, since the velocity of the light is being measured by the local atomic clocks that are located at the surface of that body.

That’s why the kid on that physics website said the light photons passing near the sun are traveling at “c” as measured by the sun’s local atomic clock tick rate, but they are measured at the earth (while they are traveling near the sun) as being less than “c” when compared to the faster tick rates of the earth’s atomic clocks.

This effect and dual speed for light in this real observed phenomenon was brilliantly predicted by Einstein in his 1911 gravitational redshift theory, and this is where GR began to take over from SR.

So, what Ned Wright calls a local “comoving space”, I would call a “local gravitational field”. The local field controls the local speed of the light and it controls the local rates of the local atomic clocks that measure the local speed of the light within the local gravitational field, while the photons are inside that field where their local speed (and the local vibration rates of atoms inside atomic clocks) aren’t influenced by any other gravitational field of any other astronomical body. This happens right at the surfaces of bodies, because a little distance away from the surfaces, light begins to speed up a little and atomic clocks begin to tick faster.

The tick rates of local atomic clocks parallel the speed of the local light photons, and that’s why the photons are measured locally as traveling at “c” when their speed is measured by means of local atomic clocks. When the atomic clock tick rate goes up locally, the speed of the photons go up locally, so every atomic clock will measure the local speed of local photons at “c”, but the local atomic clocks might measure distant photons traveling at more or less than “c”. This is what Einstein basically predicted in his 1911 paper.

It might have made everything more understandable if in 1911 Einstein had said, “The speed of light is measured to be ‘c’ by atomic clocks located at the place where the local photon speed is to be measured.”

That way, if local atomic clocks at the sun measure the speed of light at the surface of the sun, they measure “c”. If local atomic clocks at the earth measure the speed of light at the earth, they measure “c”. But if local earth-based atomic clocks measure the speed of light as the light photons pass near the sun, the earth clocks will measure the speed of the photons, as they pass near the sun, to be less than “c”.

So you can no longer say, “The speed of light, c, must remain a constant.” First, you must tell where the photons are located at the time you measure their speed, and you must tell where the atomic clock (by which you measure their speed) is located. If the clock is in the same gravitational field as the photons, then the clock will measure the local speed of the photons as “c”, but if the clock is someplace else, in a different gravitational field than the photons, or is moving relative to the body that emitted the photons as they are being emitted, then that clock will measure the photon speed as being different from “c”.

So, in your thought experiment, you are proclaiming the speed of light to be whatever you want it to be, which you call “constant”, but you can’t do that. Based on observational evidence, Einstein’s 1911 theory is correct, and, thus, the speed of light is variable as it moves from place to place and body to body in space, and as its speed is measured by different atomic clocks that are located in different gravitational fields and different places.

You see? The speed of light depends on where the photons are located at the moment you measure their speed and where the atomic clock, which you use to measure the speed of the photons, is located.

SeanF
2003-Dec-11, 03:51 PM
Sam5, I need your comments on this post (http://www.badastronomy.com/phpBB/viewtopic.php?t=9731&postdays=0&postorder=asc&star t=125).

I’ve already given you my comments about that post. My response is just two posts down from your post.

In your post you said, “The speed of light, c, must remain a constant.”

But it doesn’t remain constant. I’ve already given you links to mainstream websites that say that, including Ned Wright’s website, but you just won’t accept the observational truth of even the most respected of mainstream scientists.

No, you haven't. Even Ned Wright's website (http://www.astro.ucla.edu/~wright/relatvty.htm) says it:


Thus the fundamentals of relativity that are important for cosmology are:

The speed of light is a constant independent of the velocity of the source or the observer.
...

And on this page (http://www.astro.ucla.edu/~wright/cosmo_02.htm), Wright says:


But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get: (diagram)

Ned Wright quite clearly accepts the validity of Special Relativity.


The speed of light, c, remains a “constant” inside local “comoving spaces” at the surfaces of astronomical bodies that are at the centers of those “comoving spaces”, and a local “comoving space” contains a local gravitational field, that is centered on the center of the body the "comoving space" contains. And that field impresses a certain accelerative “force” upon local atoms at the surface of that body. This specific amount of “force”, which is different at the surface of each different body, depending on their mass, causes the atoms at that body’s surface to vibrate at certain rates and emit light of certain frequencies. This action causes the body’s local atomic clocks to “tick” at a certain local rate, and that local “tick rate” is what determines the velocity of light at that body. And that velocity at the surface of that body is “c”, since the velocity of the light is being measured by the local atomic clocks that are located at the surface of that body.

That’s why the kid on that physics website said the light photons passing near the sun are traveling at “c” as measured by the sun’s local atomic clock tick rate, but they are measured at the earth (while they are traveling near the sun) as being less than “c” when compared to the faster tick rates of the earth’s atomic clocks.

This effect and dual speed for light in this real observed phenomenon was brilliantly predicted by Einstein in his 1911 gravitational redshift theory, and this is where GR began to take over from SR.

So, what Ned Wright calls a local “comoving space”, I would call a “local gravitational field”. The local field controls the local speed of the light and it controls the local rates of the local atomic clocks that measure the local speed of the light within the local gravitational field, while the photons are inside that field where their local speed (and the local vibration rates of atoms inside atomic clocks) aren’t influenced by any other gravitational field of any other astronomical body. This happens right at the surfaces of bodies, because a little distance away from the surfaces, light begins to speed up a little and atomic clocks begin to tick faster.

Again, from Ned Wright's website (http://www.astro.ucla.edu/~wright/cosmo_01.htm):


The Hubble law defines a special frame of reference at any point in the Universe. An observer with a large motion with respect to the Hubble flow would measure blueshifts in front and large redshifts behind, instead of the same redshifts proportional to distance in all directions. Thus we can measure our motion relative to the Hubble flow, which is also our motion relative to the observable Universe. A comoving observer is at rest in this special frame of reference. Our Solar System is not quite comoving: we have a velocity of 370 km/sec relative to the observable Universe. The Local Group of galaxies, which includes the Milky Way, appears to be moving at 600 km/sec relative to the observable Universe.

Wright uses "comoving" to mean "motionless relative to the Hubble Flow," not "motionless relative to some nearby massive body." You and he are not talking about the same thing.

Sam5, you do not understand what you read. You read Wright's website and you see the word "comoving," but it doesn't mean what you think it means. You read Einstein's book and you see the words "Now in reality," but they don't mean what you think they mean.

At any rate, what you are claiming now is that SR's postulate that c is a constant is false. You had previously given indications that you believed SR to be internally inconsistent. While those two beliefs are certainly reconcilable, they are not the same thing. So I need to know from you:

Do you believe that the conclusions of SR flow logically from its postulates, and the wrong conclusions are reached solely because the postulates are wrong?

Do you believe that the conclusions of SR do not flow logically from its postulates, and thus the wrong conclusions will be reached even if the postulates are correct?

Sam5
2003-Dec-11, 04:42 PM
No, you haven't. Even Ned Wright's website (http://www.astro.ucla.edu/~wright/relatvty.htm) says it:


Thus the fundamentals of relativity that are important for cosmology are:

The speed of light is a constant independent of the velocity of the source or the observer.
...

I think that statement needs to be qualified the way I qualified it in my post above. The speed of light photons at an atomic clock is “constant” at the atomic clock that is measuring the local speed of the photons at the clock. And he qualified that statement you quoted on his other webpage (http://www.astro.ucla.edu/~wright/cosmo_02.htm) by saying, “Note how the lightcones must tip over along with the worldlines of the galaxies, showing that in these cosmological variables the speed of light is c with respect to local comoving observers.”

And that is what I said.

And I think his statement, “Each observer can define his own proper time -- the time measured by a good clock moving along his worldline,” would be better expressed by saying, “each observer can define his own local time by means of a local atomic clock that is sitting on the desk in front of him.”



And on this page (http://www.astro.ucla.edu/~wright/cosmo_02.htm), Wright says:


But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get: (diagram)


His full statement is: “In these variables, velocities greater than c are certainly possible, and since the open Universes are spatially infinite, they are actually required. But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get:”

I’ve already explained this. Objects do not travel faster than light within their own “comoving space”, but “comoving spaces” can travel relative to each other at speeds faster than light. This essentially means that the speed of light is a “limiting speed” for masses moving within a gravitational field, but it is not a “limiting speed” for a mass in one field that is moving relative to another mass that is located in a different and distant relatively moving field.

In other words, “c” is a limiting speed for a mass moving inside its own local gravitational field, but two different fields can move relative to one another at speeds greater than “c” if the fields are separated by large distances. I think the large distances are required so the masses that generate the two separate relatively moving fields can not impede the motion through space of each other or each other’s fields. If you put the masses close together, such as the earth and the sun, their two gravitational fields will interact, since their field strengths will be strongest when they are closest together. But if we have our galaxy here, with all its own local fields being nearly “comoving” together in this area of local space, and we have a very distant galaxy in space with all its own local fields being nearly “comoving” where it is, the two galaxies are so far apart that our galaxy doesn’t influence or restrict the motion of the distant galaxy.

If the two galaxies were close together their gravitational fields would interact, and they could actually revolve around one another, but if the two galaxies are very far apart, the local gravitational field of one galaxy doesn’t influence or restrict the motion of the distant galaxy in the part of space where that distant galaxy is located. Since the distant galaxies are not moving through other gravitational fields, they can exceed the radial velocity of “c” relative to our own galaxy.

Sam5
2003-Dec-11, 05:04 PM
The Hubble law defines a special frame of reference at any point in the Universe. An observer with a large motion with respect to the Hubble flow would measure blueshifts in front and large redshifts behind, instead of the same redshifts proportional to distance in all directions. Thus we can measure our motion relative to the Hubble flow, which is also our motion relative to the observable Universe. A comoving observer is at rest in this special frame of reference. Our Solar System is not quite comoving: we have a velocity of 370 km/sec relative to the observable Universe. The Local Group of galaxies, which includes the Milky Way, appears to be moving at 600 km/sec relative to the observable Universe.


Well, what I actually think he means is that our solar system is revolving around the center of our galaxy at about 370 km/sec, while our local group is moving in the direction toward the constellation Centaurus at 600 km/sec. A few years ago this area toward which our local group is apparently moving was called “The Great Attractor”.

Look, Ned Wright doesn’t ask me to proofread his text before he posts it on his website, so we might wind up with two different ways of expressing the same concepts.

And also, concepts are changing. I’ve got a top university astronomy textbook published in 1993 that says no distant galaxy can ever exceed the relative speed of “c”, relative to our own galaxy, but now that concept is obsolete just 10 years later.

SeanF
2003-Dec-11, 05:12 PM
No, you haven't. Even Ned Wright's website (http://www.astro.ucla.edu/~wright/relatvty.htm) says it:


Thus the fundamentals of relativity that are important for cosmology are:

The speed of light is a constant independent of the velocity of the source or the observer.
...

I think that statement needs to be qualified the way I qualified it in my post above.

I'm not going to just pretend that Ned Wright meant to agree with you, Sam5. You can if you want to, but I won't.



And on this page (http://www.astro.ucla.edu/~wright/cosmo_02.htm), Wright says:


But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get: (diagram)

His full statement is: “In these variables, velocities greater than c are certainly possible, and since the open Universes are spatially infinite, they are actually required. But there is no contradiction with the special relativistic principle that objects do not travel faster than the speed of light, because if we plot exactly the same space-time in the special relativistic x and t coordinates we get:”

Look at the diagram he shows. Not one of those distant galaxies is moving away from the central galaxy at a velocity greater than c - not a single one. It's not about objects within some galaxy moving relative to other objects in the same galaxy, it's about those galaxies moving relative to our galaxy - and they don't violate SR.


I’ve already explained this. Objects do not travel faster than light within their own “comoving space”, but “comoving spaces” can travel relative to each other at speeds faster than light. This essentially means that the speed of light is a “limiting speed” for masses moving within a gravitational field, but it is not a “limiting speed” for a mass in one field that is moving relative to another mass that is located in a different and distant relatively moving field.

But Ned Wright does not agree with you on this, either. His "comoving space" is space motionless relative to the Hubble flow. He explicitly says, "The Hubble law defines a special frame of reference at any point in the Universe . . . A comoving observer is at rest in this special frame of reference. Our Solar System is not quite comoving: we have a velocity of 370 km/sec relative to the observable Universe." See? That's what comoving means.

SeanF
2003-Dec-11, 05:20 PM
Well, what I actually think he means is that our solar system is revolving around the center of our galaxy at about 370 km/sec, while our local group is moving in the direction toward the constellation Centaurus at 600 km/sec. A few years ago this area toward which our local group is apparently moving was called “The Great Attractor”.

Yeah, what you "actually think he means" is in complete agreement with you (which is unsurprising), but what he "actually says" isn't.


Look, Ned Wright doesn’t ask me to proofread his text before he posts it on his website, so we might wind up with two different ways of expressing the same concepts.

It's not the same concept, Sam5. Ned Wright would not agree with any of your interpretations of his website. He's got a page for sending him e-mail (http://www.astro.ucla.edu/~wright/b4u-write.html). Why don't you ask him? Maybe invite him to come over and take a gander at your posts and give you a response to them?

{Edited to add}" Or, you could just read his FAQ (http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL):


This is not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and the age of the Universe is not the same as the time used in SR.


And also, concepts are changing. I’ve got a top university astronomy textbook published in 1993 that says no distant galaxy can ever exceed the relative speed of “c”, relative to our own galaxy, but now that concept is obsolete just 10 years later.

Ned Wright doesn't seem to think so . . .

SeanF
2003-Dec-11, 05:21 PM
Oh, by the way, Sam5:


I need to know from you:

Do you believe that the conclusions of SR flow logically from its postulates, and the wrong conclusions are reached solely because the postulates are wrong?

Do you believe that the conclusions of SR do not flow logically from its postulates, and thus the wrong conclusions will be reached even if the postulates are correct?

Sam5
2003-Dec-11, 05:36 PM
Look at the diagram he shows. Not one of those distant galaxies is moving away from the central galaxy at a velocity greater than c - not a single one.


He says on that page:

“In these variables, velocities greater than c are certainly possible, and since the open Universes are spatially infinite, they are actually required.”

Nothing can be clearer than that.

Say, how are you progressing on figuring out the reason for the paradox in the Ann and Bob example?

SeanF
2003-Dec-11, 06:20 PM
Say, how are you progressing on figuring out the reason for the paradox in the Ann and Bob example?

::Sigh:: There is no paradox.

Ann and Bob are in the same place and they begin moving apart. We'll call the point in space-time where they begin moving apart A. At another point in space-time, Bob changes direction. We'll call this point B. At a third point in space-time, Bob and Ann meet up again. We'll call this point in space-time C.

In the reference frame in which the line A-C is considered "at rest," C-A=10 years, C-B=5 years, and B-A=5 years. We'll call this reference frame K1.

In the reference frame in which the line A-B is considered "at rest," C-A=12.5 years, C-B=8.5 years, and B-A=4 years. We'll call this reference frame K2.

In the reference frame in which the line B-C is considered "at rest," C-A=12.5 years, C-B=4 years, and B-A=8.5 years. We'll call this reference frame K3.

Ann stays in K1, going right from A to C, and so ages 10 years.

Bob starts out in K2, going from A to B, and so ages 4 years. He then switches to frame K3, going from B to C, and so ages another 4 years.

At C, Ann has aged 10 years since A and Bob has aged 8.

Now:


I need to know from you:

Do you believe that the conclusions of SR flow logically from its postulates, and the wrong conclusions are reached solely because the postulates are wrong?

Do you believe that the conclusions of SR do not flow logically from its postulates, and thus the wrong conclusions will be reached even if the postulates are correct?

daver
2003-Dec-11, 08:35 PM
[Bob] sees (through his telescope) that two years for Ann will have passed during his outbound trip, and 8 years during his return trip (he sees her clock run at half speed on the way out and double time on the way back).

Bob does not see that those 8 years on Ann's clock as having happened "during his return trip." Those 8 years on Ann's clock (apparently) started ten years before Ann and Bob met up again, by Bob's clock. Bob simply didn't receive the light from her until four years before they met. He does not, can not, conclude that Ann's clock ticked off 8 years during the same time that his own clock ticked off 4 years.

Is there still an issue with this? I've only skimmed the replies.

During his return trip he SEES eight years tick by on Ann's clock. Let's split Bob down the middle again; BobI when he passes BobO thinks that Ann is currently 2.4 l.y. out, that he is seeing her clock as it was six years ago when she was .6*6+2.4 = six l.y. away, which was 2.5 years after BobO passed her.. BobO thinks that Ann is also 2.4 ly away, and that he is seeing her clock as it was when she was 1.5 ly out, again when she was 2.5 years into her journey.

BobI and BobO agree as to how much time had passed for Ann from when BobO passed her to when the light left Ann that they see as they pass each other. They agree as to where Ann is now. They disagree about how far away Ann was when the light left Ann, which can hardly be a surprise, since that signal must have been sent earlier, when BobI was farther from Ann and BobO closer.

OK, let's put the Bobs back together again. Bob after turnaround knows that the simple algebra problem that he used to figure out how far away Ann was when the signal he's seeing is invalid--he knows that an hour ago she was red-shifted and moving away from him, whereas now she's blue shifted and moving towards him.

Oh--kind of an interesting observation. Bob notices that Alice spent an equal amount of time being red-shifted and then blue-shifted. Alice notices that Bob spends more time being red-shifted.

SeanF
2003-Dec-11, 09:22 PM
I think we're talking past each other here.

I'm sitting right next to a clock. There's another clock sitting motionless relative to me, one light minute away.

I "see" my clock say "12:00:00" at the same time I "see" the other clock say "11:59:00".

I "see" my clock say "12:01:00" at the same time I "see" the other clock say "12:00:00".

Now, I could truthfully say "I see my clock as being a minute ahead of the other clock."

I could also truthfully say "I see my clock as being synchronized with the other clock."

Those two sentences use two different meanings of the word "see." In the first, it refers to the actual impacting of light on retinas. In the second, it refers to the understanding of what's really going on at the other clock.

In our "Twin Paradox": During the return trip, Bob "sees" Ann's clock as running fast in the first sense of "see," but he "sees" Ann's clock as running slow in the second sense.

Agreed?

daver
2003-Dec-11, 10:00 PM
I think we're talking past each other here.

I expect so.


Now, I could truthfully say "I see my clock as being a minute ahead of the other clock."

I could also truthfully say "I see my clock as being synchronized with the other clock."

Yep, "see" is ambiguous. For discussions like this, involving speed-of-light lags and interpolated positions and ages, it would help to be as specific as possible--in this case, i'd suggest using "SEE" as denoting what he actually sees (through his super-duper telescope).


In our "Twin Paradox": During the return trip, Bob "sees" Ann's clock as running fast in the first sense of "see," but he "sees" Ann's clock as running slow in the second sense.

Agreed?
Agreed. When Bob passes Ann, he sees that her clock actually is running slowly (adverb), even though it shows more time has elapsed than his clock.

You had a problem towards the top of the page where Bob thought that Ann had jumped several light years when Bob changed direction. Is that still an issue?

SeanF
2003-Dec-11, 10:11 PM
Yep, "see" is ambiguous. For discussions like this, involving speed-of-light lags and interpolated positions and ages, it would help to be as specific as possible--in this case, i'd suggest using "SEE" as denoting what he actually sees (through his super-duper telescope).

See, I'd disagree with that (Get it? I said, "see!"). Actually, when discussing time dilation and simultaneity under SR, it's a lot easier (at least at the start) to just ignore the signal delay altogether. If two clocks are synchronized in a particular observer's reference frame, it's a lot easier to just say "He sees the clocks as synchronized," then to try to explain why he's getting signals at different times but still concluding the clocks are synchronized.

Plus I think it then tends to confuse people who start to believe that those light delays are part of Einstein's SR equations, that somehow the fact that light takes longer to get from one clock to another is part of the reason why one clock is running slower than the other.


You had a problem towards the top of the page where Bob thought that Ann had jumped several light years when Bob changed direction. Is that still an issue?

I didn't have a problem. If we allow for Bob to not be aware that he changed reference frames, so that the signals he receives from Ann are the only information he has, then that's what it would look like to him.

D**n it, there's "look," the same as "see" . . . That's the way it would seem to him. :D

Sam5
2003-Dec-11, 10:18 PM
SeanF,

We all need to know from you why your Ann and Bob clock times aren’t working out the way you want them to. You started out with just two different end-times, 10 and 8, but now you are up to at least 4 different end-times for just two different clocks: 12.5, 10, 8, and 6.4

So far I’ve counted these turn-around times: 6.8, 5, 4, 3.2

And just recently these new clock times have turned up in your calculations: 8.5 and 2.5

Regarding your questions, I think the first postulate: That the laws of physics are the same everywhere, is just common sense. Why would the laws of physics be different in different places, and where in the history of the world has there ever been any evidence of such a thing?

Regarding the second postulate, I’ve explained my opinion about that several times: When an atomic clock is resting on the surface of an astronomical body, that clock will measure “c” for the local speed of the light photons when the photons are passing close by the atomic clock that is measuring their local speed. When the place of the clock and the photons are separated by some distance, and are within gravitational fields of different potential, the clock will measure the speed of light to be more or less than “c”. You can find this information in Einstein’s papers and on different mainstream physics websites.

SeanF
2003-Dec-11, 10:49 PM
SeanF,

We all need to know from you why your Ann and Bob clock times aren’t working out the way you want them to. You started out with just two different end-times, 10 and 8, but now you are up to at least 4 different end-times for just two different clocks: 12.5, 10, 8, and 6.4

So far I’ve counted these turn-around times: 6.8, 5, 4, 3.2

And just recently these new clock times have turned up in your calculations: 8.5 and 2.5

That's relativity, son, that's Relativity.

As I said in that previous post, we've got three reference frames (K1, K2, and K3) and we've got three Events (A, B, and C).

12.5 is the duration from A to C in either K2 or K3.
10 is the duration from A to C in K1
8.5 is the duration from A to B in K3 and the duration from B to C in K2.
8 is the duration from A to B in K2 added to the duration from B to C in K3.
5 is the duration from A to B in K1 and the duration from B to C in K1.
4 is the duration from A to B in K2 and the duration from B to C in K3.

3.2 and 6.8 come into it when we start asking what time on Ann's clock is simultaneous with certain times on Bob's clock. Specifically, Ann's clock=3.2 is simultaneous with event B in K2. Ann's clock=6.8 is simultaneous with event B in K3.

3.2 is also, therefore, the duration between A and B as ticked off by Ann's clock as viewed from K2 (3.2-0=3.2). It is also the duration between B and C as ticked off by Ann's clock as viewed from K3 (10-6.8=3.2).

6.4 is the sum of those two durations (3.2+3.2=6.4).

Whoops, I almost missed 2.5. That's just the the duration between A and {when Ann transmits the light signal that Bob receives at B} as viewed from K2. That only came up because of mine, daver's, and Celestial Mechanics discussions about Doppler within this experiment.

All of that comes from the first of those four "transformation equations" at the end of Section 3 of Einstein's 1905 paper.

But, of course, if you don't understand Special Relativity . . .


Regarding your questions, I think the first postulate: That the laws of physics are the same everywhere, is just common sense. Why would the laws of physics be different in different places, and where in the history of the world has there ever been any evidence of such a thing?

Regarding the second postulate, I’ve explained my opinion about that several times: When an atomic clock is resting on the surface of an astronomical body, that clock will measure “c” for the local speed of the light photons when the photons are passing close by the atomic clock that is measuring their local speed. When the place of the clock and the photons are separated by some distance, and are within gravitational fields of different potential, the clock will measure the speed of light to be more or less than “c”. You can find this information in Einstein’s papers and on different mainstream physics websites.

So, given that you think the second postulate of SR is wrong, will you still concede that the conclusions of SR do flow logically from that postulate? Those conclusions would still be wrong, but I'm just wondering if you'll acknowledge that the logic flow from the postulates to the conclusions is sound.

{This post was edited for clarity. In certain places the word "time" was changed to "duration" - then edited again for the same reason}

Sam5
2003-Dec-11, 11:22 PM
That's relativity, son, that's Relativity. :^o


A = Ann
B = Bob
C = Charlie

You never mentioned Charlie before. Where did he come from?

daver
2003-Dec-12, 01:36 AM
That's relativity, son, that's Relativity. :^o


A = Ann
B = Bob
C = Charlie

You never mentioned Charlie before. Where did he come from?
No, A, B, and C are the points in space time the various measurable events occurred--A is when Bob left Ann, B is where Bob turned around, C is where Bob met Ann again. Look up the page a bit where he starts with ::Sigh:: There is no paradox.

freddo
2003-Dec-12, 02:11 AM
SeanF, you deserve all the credit in the world for you efforts in explaining the concepts to Sam5, you've shown a level of patience which puts even persistent me to shame. =D>

But I think it's for naught. Sam5 is either unable or unwilling to grasp what you're trying to explain. It's getting to the stage where you're having to repeat yourself, which I'm sure is no fun at all.

Sam5
2003-Dec-12, 02:30 AM
freddo,

Ok, freddo, what is your solution to the twins paradox, in your own words?

Can you explain why Sean has wound up with so many different end-times and turn-around times on just two clocks? What am I missing here? Explain it to me. What function does the K’ frame serve in “On the Electrodynamics of Moving Bodies”?

Tensor
2003-Dec-12, 02:51 AM
SeanF, you deserve all the credit in the world for you efforts in explaining the concepts to Sam5, you've shown a level of patience which puts even persistent me to shame. =D>

Yeah, he does. I gave up 10 pages and another thread ago.


edited for a stray quote

SeanF
2003-Dec-12, 02:52 AM
That's relativity, son, that's Relativity. :^o


A = Ann
B = Bob
C = Charlie

You never mentioned Charlie before. Where did he come from?

Wow! I'm so stunned, I honestly can't figure out what to say here.

Sam5, do you even read what I write?!

freddo
2003-Dec-12, 02:57 AM
freddo,

Ok, freddo, what is your solution to the twins paradox, in your own words?


It has been pointed out to you that there is no paradox. This has been explained several different ways. Nothing I can add will be anything more than a regurgitation of previous explanations.

Sam5
2003-Dec-12, 03:08 AM
Sam5, do you even read what I write?!


I paid a lot of detailed attention when you first started out your thought experiments with just two turn-around times and two end-times. Then I pointed out how you were wrong.

So you started making up more complex thought experiments with additional turn-around times, “clock jumps”, and extra end-times. I paid a little attention to some of those and I refuted some of them.

So you started making up even more elaborate thought experiments and you began accumulating four or more turn-around times and end-times for just two clocks.

So when that happened, I decided it would just take too much of my time to try to wade through each of them and refute them, so I stopped paying attention to your thought experiments. I enjoyed seeing some of your friends point out some of your errors. And I really enjoyed it when you had to change some of your posts to correct numerous errors. =D>

Jobe
2003-Dec-12, 03:11 AM
So when that happened, I decided it would just take too much of my time to try to wade through each of them and refute them, so I stopped paying attention to your thought experiments. I enjoyed seeing some of your friends point out some of your errors. And I really enjoyed it when you had to change some of your posts to correct numerous errors. =D>

At least SeanF is open and accountable for his errors. It's completely apparent to everyone apart from yourself that your entire argument is one big error.

Sam5
2003-Dec-12, 03:16 AM
Nothing I can add will be anything more than a regurgitation of previous explanations.

There have been no “previous explanations”. No one here has been able to explain how two relatively moving observers can “see” each other’s clock “slow down”, at exactly the same rate, yet with only one clock being “really” lagged behind at the end.

And you really don’t know what I mean when I say Sean used a “double Lorentz Transformation for fame K, up against a single Lorentz Transformation for K1”, do you?

Sam5
2003-Dec-12, 03:20 AM
It's completely apparent to everyone apart from yourself that your entire argument is one big error.

Then you think it is ok for Sean to use a double Lorentz Transformation factor to calculate the rate of one clock while he uses a single Lorentz Transformation factor to calculate the rate for the other clock? Does “On the Electrodynamics of Moving Bodies” allow this? If so, in what section of the paper can I find that information?

freddo
2003-Dec-12, 03:29 AM
That's beside the point. Additionally, you've just claimed to be ignoring SeanF's examples.

daver, Celestial Mechanic, Kilopi, Diamond, Eroica, russ_watters, Tensor, & Wally have all given you their own reasons why there is no paradox. Their source material is the same as yours - the math they use is the math you should have used. Yet you are the only one claiming paradox. Are you ignoring everyone in this thread?

Sam5
2003-Dec-12, 03:42 AM
freddo,

Maybe you can answer my question: Do you think it is ok for Sean to use a double Lorentz Transformation factor to calculate the rate of one clock while he uses a single Lorentz Transformation factor to calculate the rate for the other clock?

Can you tell me how two relatively moving observers can “see” each other’s clock “slow down”, at exactly the same rate, yet with only one clock being “really” lagged behind at the end. Nobody has answered that question yet.

Sean started out with a fallacy in his own thought experiment. He started out by turning around Bob by the dilated time that Ann saw on Bob’s clock, and Sean claimed that that was also the undilated time that Bob saw on his own clock. Do you undertand how that is an error?

Do you understand why he can not use a double Lorentz Transformation dilation factor in one calculation?

Diamond
2003-Dec-12, 10:11 AM
freddo,

Maybe you can answer my question: Do you think it is ok for Sean to use a double Lorentz Transformation factor to calculate the rate of one clock while he uses a single Lorentz Transformation factor to calculate the rate for the other clock?

Can you tell me how two relatively moving observers can “see” each other’s clock “slow down”, at exactly the same rate, yet with only one clock being “really” lagged behind at the end. Nobody has answered that question yet.

Sean started out with a fallacy in his own thought experiment. He started out by turning around Bob by the dilated time that Ann saw on Bob’s clock, and Sean claimed that that was also the undilated time that Bob saw on his own clock. Do you undertand how that is an error?

Do you understand why he can not use a double Lorentz Transformation dilation factor in one calculation?

No you don't understand time dilation and especially the Relativity of Simultaneity, that much is certain. This is where most anti-relativity cranks fall down, and you're not the first.

You've also taken over another relativity thread, and posted fallacy after fallacy. Well done. =D>

kilopi
2003-Dec-12, 12:29 PM
Can you tell me how two relatively moving observers can “see” each other’s clock “slow down”, at exactly the same rate, yet with only one clock being “really” lagged behind at the end. Nobody has answered that question yet.
Einstein did, in his original 1905 paper. Check out section 1.4 (http://mentock.home.mindspring.com/twinrdux.htm).

SeanF
2003-Dec-12, 03:09 PM
Sean started out with a fallacy in his own thought experiment. He started out by turning around Bob by the dilated time that Ann saw on Bob’s clock, and Sean claimed that that was also the undilated time that Bob saw on his own clock. Do you undertand how that is an error?

A-ha! You need to go back and read Einstein's 1905 paper again. Pay special attention to the math in Section 3. You don't fully understand how coordinates transform from one reference frame to another.

Look closely at those four transformation equations at the end. Do you see that the variable x is included in the first equation? That's because the distance between two events is directly related to the time between two events.

In Ann's reference frame, the turn-around occurred five years later and 3 light-years distant. So, if you put the appropriate variables in for x (3 light-years), t (5 years), and v (0.6c - velocity of Bob's reference frame relative to Ann's reference frame), you'll get x'=0 light-years and t'=4 years (I'm going to use x' and t' instead of the Greek characters Einstein used). That's exactly what we'd expect in Bob's reference frame. Specifically, note that we got x'=0. In Bob's reference frame, the "turn-around" point is the same point in space as the original passing, so we would expect the the location value to remain at zero.

Now, should we verify by going back the other way? In this case, we're going from Bob's reference frame to Ann's, so the appropriate variables would be x=0 light-years, t=4 years, and v=-0.6c (velocity of Ann's reference frame relative to Bob's reference frame - see the negative sign?). When we do this, we get x'=3 light-years and t'=5 years. Exactly what we started with.

What this all means is that 4 is not "the amount of ticks of Bob's clock during the trip when viewed from Ann's reference frame," but rather it is "the amount of time the trip actually takes when viewed from Bob's reference frame."

Sam5
2003-Dec-12, 03:15 PM
This is where most anti-relativity cranks fall down, and you're not the first.

You've also taken over another relativity thread, and posted fallacy after fallacy. Well done. =D>

You need to keep this personal stuff out of this science debate. I haven’t taken over anything. I'm responding to posts from you guys. I’m expressing my informed science opinion about an important topic that a lot of people are interested in while most of you have attacked me personally and tried to get rid of me because you prefer the urban legend to the real science facts. All I am doing is proving that the urban legend is wrong, which I believe is the right thing to do in science.

Now, please tell me, according to Einstein’s 1907 update of the Special Relativity paper, how cold will Ann get during the relative motion? Since when her “time slows down”, as seen by Bob, her molecular vibration rate will be "seen" to slow down, so, according to Einstein, how cold will Ann get while traveling at .6c?

kilopi
2003-Dec-12, 03:21 PM
Now, please tell me, according to Einstein’s 1907 update of the Special Relativity paper
Do you have a URL to an online version of that paper handy?

SeanF
2003-Dec-12, 03:24 PM
You need to keep this personal stuff out of this science debate.

I enjoyed seeing some of your friends point out some of your errors. And I really enjoyed it when you had to change some of your posts to correct numerous errors. =D>

:o


Now, please tell me, according to Einstein’s 1907 update of the Special Relativity paper, how cold will Ann get during the relative motion? Since when her “time slows down”, as seen by Bob, her molecular vibration rate will be "seen" to slow down, so, according to Einstein, how cold will Ann get while traveling at .6c?

Wow! Don't the Laws of Physics prohibit changing directions that fast?

BTW, what difference does it make? In her own reference frame, her molecular vibration rate is still the same, so she's not going to freeze to death or anything.

Sam5
2003-Dec-12, 03:32 PM
What this all means is that 4 is not "the amount of ticks of Bob's clock during the trip when viewed from Ann's reference frame," but rather it is "the amount of time the trip actually takes when viewed from Bob's reference frame."

Sean, in real life, the number of “ticks” is the “time” on Bobs clock. If his clock hasn’t been tampered with, then he will see 5 years of ticks on his clock while he is watching Ann travel travel 3 light years at .6c.

.6 = 3/5 the speed of light

3/5 = 6/10

3ly / .6c = 5 years for Ann's trip, as seen by Bob

Bob sees 5 years on his own clock at turn-around time, and there is nothing in “relative motion” that will cause his clock to slow down, especially since from his point of view, he is not moving, it is Ann who is moving.

Sam5
2003-Dec-12, 03:42 PM
Wow! Don't the Laws of Physics prohibit changing directions that fast?

BTW, what difference does it make?


In SR theory, this thermodynamic dilation doesn’t happen at turn-around, it happens all during the trip, which you should already know if you are an “expert” on the theory.

The “difference” it makes is that this thermodynamic thing in the 1907 paper contains its own paradox, and I’m trying to show that the concept of “time” and “temperature” dilation due only to “relative motion” is an urban legend, not a “true fact” of science.

I’m also trying to show that most people who believe in the urban legend have NEVER read Einstein’s own words and own theories that set up the paradox. Most people just read crackpot urban-legend websites that tell untrue stories about the SR theory. I’m not the “crackpot” here, the guys who write the incorrect websites that defend the urban legend are the crackpots.

SeanF
2003-Dec-12, 03:43 PM
What this all means is that 4 is not "the amount of ticks of Bob's clock during the trip when viewed from Ann's reference frame," but rather it is "the amount of time the trip actually takes when viewed from Bob's reference frame."

Sean, in real life, the number of “ticks” is the “time” on Bobs clock. If his clock hasn’t been tampered with, then he will see 5 years of ticks on his clock while he is watching Ann travel travel 3 light years at .6c.

Bob and Ann first turned up in this thread in this post (http://www.badastronomy.com/phpBB/viewtopic.php?t=9731&postdays=0&postorder=asc&star t=84) of Diamond's.


Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger.

See that? "Bob lets 4 years pass." Where do you get that he's turning around when his clock says 5?

SeanF
2003-Dec-12, 03:45 PM
Wow! Don't the Laws of Physics prohibit changing directions that fast?

BTW, what difference does it make?


In SR theory, this thermodynamic dilation doesn’t happen at turn-around, it happens all during the trip, which you should already know if you are an “expert” on the theory.
That was a joke in reference to your changing of directions - you all of a sudden want to talk about temperature instead of time.


The “difference” it makes is that this thermodynamic thing in the 1907 paper contains its own paradox, and I’m trying to show that the concept of “time” and “temperature” dilation due only to “relative motion” is an urban legend, not a “true fact” of science.

Why don't we stick with dealing with the time dilation for now and save the temperature for later?

Sam5
2003-Dec-12, 03:49 PM
In her own reference frame, her molecular vibration rate is still the same, so she's not going to freeze to death or anything.

That reveals the paradox even better than the clock thing. Because in Bob’s frame, Ann freezes to death, while in Ann’s frame, she does not. But this greater evidence of the error in SR theory is never mentioned on the crackpot SR websites, because the thermodynamic paradox that Einstein added to the theory in 1907 is NEVER posted on crackpot internet websites about the twins paradox. That paradox makes it too obvious that the "seen" things in SR are merely illusions and not real.

kilopi
2003-Dec-12, 03:53 PM
Bob and Ann first turned up in this thread in this post (http://www.badastronomy.com/phpBB/viewtopic.php?t=9731&postdays=0&postorder=asc&star t=84) of Diamond's.
Diamond's post was lifted in total from the webpage he references--it's a page I wrote seven years ago and posted on the web. J* has read it before, as have you I'm sure (you both were thanked at the bottom of a follow up (http://mentock.home.mindspring.com/twinrdux.htm), but J* asked that his nick be removed).

SeanF
2003-Dec-12, 03:58 PM
...in Bob’s frame, Ann freezes to death...

What makes you think . . . no, never mind.


Why don't we stick with dealing with the time dilation for now and save the temperature for later?

Sam5
2003-Dec-12, 04:03 PM
Why don't we stick with dealing with the time dilation for now and save the temperature for later?

The title of this thread is “Twins Paradox: Definitive Proof That its SR?” The “freezing” of Ann is the most effective way to teach the error of the “dilation” mistake in SR theory, and the best way to show that the guys who make up the “twins paradox resolution” pages are the “crackpots” who are promoting an urban legend about science. And you are one of the victims of their hoax.

I’ve already pointed out your most fundamental mistake. At turn-around time, Bob has “seen” 5 years pass, not 4, because he has “seen” Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock. That’s where you error is.

The “freezing” of Ann is part of SR theory. It is a consequence of all of “time slowing down” in her “frame” as “seen” by Bob. According to SR theory, when she “moves” and her “time” slows down, then her molecular vibration rates slow down too, and at .6c, she freezes to death. So Bob can’t see her “alive” at the end of the trip. But she also “sees” Bob freeze to death, so she can’t “see” him alive at the end of the trip. In fact neither one can “see” anything, since they are dead. But, also, they are “alive”, since they didn’t see themselves “freeze” to death.

I suppose that if one of them took Schrodinger’s cat along, they'd “see” him both “dead” and “alive” at the same time.

kilopi
2003-Dec-12, 04:07 PM
According to SR theory, when she “moves” and her “time” slows down, then her molecular vibration rates slow down too, and at .6c, she freezes to death. So Bob can’t see her “alive” at the end of the trip. But she also “sees” Bob freeze to death, so she can’t “see” him alive at the end of the trip. In fact neither one can “see” anything, since they are dead. But, also, they are “alive”, since they didn’t see themselves “freeze” to death.
"According to SR theory"? Do you have a reference for that, which mentions freezing to death?

According to relativity, she would not see her temperature drop, right? So, from her point of view, she does not get cold, and does not freeze to death. So, he cannot see her freeze to death.

SeanF
2003-Dec-12, 04:19 PM
I’ve already pointed out your most fundamental mistake. At turn-around time, Bob has “seen” 5 years pass, not 4, because he has “seen” Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock. That’s where you error is.

You're back to not reading what I write again, aren't you? The thought experiment we've been discussing comes from this webpage (http://mentock.home.mindspring.com/twins.htm), where it explicitly states:


Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years.

4, not 5. 4. FOUR. Thou shalt count to four, and the number of thy counting shall be four. Thou shalt not count to five, neither shalt thou count to three, excepting that thou then proceedest to four. six is right out.

(With apologies to Monty Python)

SeanF
2003-Dec-12, 04:38 PM
"According to SR theory"? Do you have a reference for that, which mentions freezing to death?

Of course he doesn't. Don't you realize that when Sam5 says something about SR that Einstein never said, he's simply pointing out the things that Einstein missed (or intentionally left out), but when we say something about SR that Einstein never said, we're just making s**t up, and that's not allowed?

Sam5
2003-Dec-12, 04:51 PM
"According to SR theory"? Do you have a reference for that, which mentions freezing to death?

Of course he doesn't. Don't you realize that when Sam5 says something about SR that Einstein never said, he's simply pointing out the things that Einstein missed (or intentionally left out), but when we say something about SR that Einstein never said, we're just making s**t up, and that's not allowed?

Why would you tell a lie about me?

If you order the book: “The Collected Papers of Albert Einstein, Volume 2, The Swiss Years: Writings, 1900-1909”, English translation by Anna Beck, and look on page 300, you’ll see what I’m talking about.

I went to the trouble of ordering the book and studying it, and you can do the same. But don’t say the book and the paper don’t exist, because I can photocopy the page and post the photo on this board.

kilopi
2003-Dec-12, 04:55 PM
"According to SR theory"? Do you have a reference for that, which mentions freezing to death?

Of course he doesn't. Don't you realize that when Sam5 says something about SR that Einstein never said, he's simply pointing out the things that Einstein missed (or intentionally left out), but when we say something about SR that Einstein never said, we're just making s**t up, and that's not allowed?

Why would you tell a lie about me?

If you order the book: “The Collected Papers of Albert Einstein, Volume 2, The Swiss Years: Writings, 1900-1909”, English translation by Anna Beck, and look on page 300, you’ll see what I’m talking about.
That has a paper by Einstein that mentions freezing to death? Which paper?

Sam5
2003-Dec-12, 05:02 PM
I’ve already pointed out your most fundamental mistake. At turn-around time, Bob has “seen” 5 years pass, not 4, because he has “seen” Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock. That’s where you error is.

You're back to not reading what I write again, aren't you? The thought experiment we've been discussing comes from this webpage (http://mentock.home.mindspring.com/twins.htm), where it explicitly states:


Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years.

4, not 5. 4. FOUR.

Sean, this is where the mistake is. Einstein did NOT say this. Some non-physicist amateur guy said this. Somebody told me this guy has a geology degree, not a physics degree. You won’t find this in Einstein’s paper. You can not trust these amateur “reconciliations” that are posted on the internet because they contain mistakes. They are no more “valid” than all the cemtrail and UFO stories.

kilopi
2003-Dec-12, 05:08 PM
Some non-physicist amateur guy said this. Somebody told me this guy has a geology degree, not a physics degree. You won’t find this in Einstein’s paper. You can not trust these amateur “reconciliations” that are posted on the internet because they contain mistakes.
Shows what happens when you trust the internet. "This guy" has a masters degree in math.

SeanF
2003-Dec-12, 05:09 PM
I’ve already pointed out your most fundamental mistake. At turn-around time, Bob has “seen” 5 years pass, not 4, because he has “seen” Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock. That’s where you error is.

You're back to not reading what I write again, aren't you? The thought experiment we've been discussing comes from this webpage (http://mentock.home.mindspring.com/twins.htm), where it explicitly states:


Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years.

4, not 5. 4. FOUR.

Sean, this is where the mistake is. Einstein did NOT say this. Some non-physicist amateur guy said this. Somebody told me this guy has a geology degree, not a physics degree. You won’t find this in Einstein’s paper. You can not trust these amateur “reconciliations” that are posted on the internet because they contain mistakes. They are no more “valid” than all the cemtrail and UFO stories.

Ah, but you said "At turn-around time, Bob has 'seen' 5 years pass, not 4, because he has 'seen' Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock." I've got a copy of Einstein's 1905 paper, and the words "Ann" and "Bob" don't occur anywhere in it. (Notice what I said a couple posts up about how it seems you're allowed to say things Einstein didn't but nobody else is?)

(While you're scanning in that "freezing to death" quote from Einstein, why don't you scan in and post your Physics degree as well. After all, if you're just a "non-physicist amateur guy," there's no point in listening to anything you say, either)

Sam5
2003-Dec-12, 05:15 PM
Of course


The 1907 paper doesn’t mention “freezing to death”, just as his 1905 paper didn't mention "Bob and Ann". The 1907 paper gives a formula that shows how the temperature of the “seen” “moving frame” drops based on relative “v”. You can calculate the temperature inside the “frame” with the formula. If a spaceship’s ambient temperature is consistently very low inside the cabin, then the humans inside the cabin “freeze to death”. If you will study Einstein’s work, you will see that he did not specifically mention any “Bob and Ann” in his SR theory. He mentioned only “clocks” in 1905, and then in 1907 he mentioned clock time and thermometer temperature.

So, what we should really talk about are clocks and thermometers. But since we are talking about an amateur’s thought experiment with “Bob and Ann”, the consequence of their thermometer drop, based on Einstein’s 1907 formula, would be that they would “freeze to death”.

kilopi
2003-Dec-12, 05:26 PM
The 1907 paper doesn’t mention “freezing to death”, just as his 1905 paper didn't mention "Bob and Ann".
Figured

The 1907 paper gives a formula that shows how the temperature of the “seen” “moving frame” drops based on relative “v”. You can calculate the temperature inside the “frame” with the formula.
That would be from the point of view of the non-moving frame though. Inside the moving frame, the temperature does not drop. You have it backwards. Just as time appears to slow down, from the point of view of the non-moving frame, it doesn't from the point of view of the moving frame--they don't see their actions taking inordinately longer to perform.


If a spaceship’s ambient temperature is consistently very low inside the cabin, then the humans inside the cabin “freeze to death”.

Just another misapplication of the theory. You can't hold that against Einstein. This is difficult stuff.


But since we are talking about an amateur’s thought experiment with “Bob and Ann”, the consequence of their thermometer drop, based on Einstein’s 1907 formula, would be that they would “freeze to death”.
Not true.

Sam5
2003-Dec-12, 05:28 PM
Shows what happens when you trust the internet. "This guy" has a masters degree in math.


As far as I can tell, the math in the theory is ok, but the basic concept in the theory of clock slow-downs due only to “relative motion” is not ok. The math on the internet website is not ok, since according to SR theory, Bob would not see Ann turn around for 5 years, since Ann is traveling 3 light years at .6c.

Can you tell me how Ann can travel 3 light years at .6c in only 4 years?

The double use of the Lorentz Transformation to calculate what Bob sees of Ann’s clock during the 5 years, is not correct. This is not allowed in the SR theory. So if anyone says that Ann travels 3 light years at .6c in 5 years, but Bob “sees” Ann’s clock tick only 3.2 years, it doesn’t matter how many “math degrees” he has, because he is not using the Lorentz Transformation properly, since it should be used only one time (resulting in 4, not 3.2 years), and he shouldn’t use it twice, based on what Einstein says in his paper. So, if someone uses it twice, that guy is disagreeing with Einstein on that particular math issue, while I'm agreeing with Einstein on that partcular math issue.

kilopi
2003-Dec-12, 05:35 PM
Can you tell me how Ann can travel 3 light years at .6c in only 4 years?
Are you talking about this page (http://mentock.home.mindspring.com/twins.htm)?

Sam5
2003-Dec-12, 05:44 PM
Ah, but you said "At turn-around time, Bob has 'seen' 5 years pass, not 4, because he has 'seen' Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock." I've got a copy of Einstein's 1905 paper, and the words "Ann" and "Bob" don't occur anywhere in it.

Doesn't everyone here know that??

Yes, “Bob and Ann” are in the internet website, but NOT in the 1905 SR theory. I thought everyone knew that.

So, if you have Bob see Ann move 3 light years at .6c, then according to the 1905 theory, 5 years, not 4, will lapse on Bob’s clock. But the website that we are discussing has only 4 years lapse on Bob’s clock at turn-around time, so the website does not conform to the 1905 theory. That's what I've been trying to explain to you.

I’ve also warned you not to trust any of the popular websites about this subject. That’s why I started off discussing the actual clock thought experiment in the SR theory, the A B and K K1 experiment. It was you who brought up the incorrect numbers that are contained in the amateur website. I think you and I should stick strictly to the numbers in the 1905 theory, but you keep insisting on bringing up the incorrect numbers in the amateur website which contains additional mistakes that aren’t even in the original Einstein theory.

Sam5
2003-Dec-12, 05:53 PM
Sean,

It is your reliance on the incorrect numbers contained in the amateur website that causes you to use the double Lorentz Transformation factor to get 3.2 for what Bob “sees” on Ann’s clock. I keep asking you why you use the double Transformaton factor instead of just the single factor, but you never answer my question. Einstein says we are to use a single Transformtion factor only, but you use a double Transformation factor. That’s why you get 3.2 for what Bob “sees” on Ann’s clock while Ann “sees” 5 on her clock.

One use of the Lorentz Transformation factor of .8, based on a velocity of .6c:

5 x .8 = 4

The second use of the Lorentz Transformation factor in the same Bob/Ann frames:

4 x .8 = 3.2

This double use of the LT factor is incorrect, and Einstein never used it twice in one calculation to calculate the amount of “time dilation” on the other frame’s clock. But you incorrectly use it twice, so that’s why you get 3.2 rather than 4 for what Bob “sees” on Ann’s clock during Ann’s 5 (Bob-time) years of Ann’s travel.

SeanF
2003-Dec-12, 05:55 PM
Ah, but you said "At turn-around time, Bob has 'seen' 5 years pass, not 4, because he has 'seen' Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock." I've got a copy of Einstein's 1905 paper, and the words "Ann" and "Bob" don't occur anywhere in it.

Doesn't everyone here know that??

Yes, “Bob and Ann” are in the internet website, but NOT in the 1905 SR theory. I thought everyone knew that.

So, if you have Bob see Ann move 3 light years at .6c, then according to the 1905 theory, 5 years, not 4, will lapse on Bob’s clock. But the website that we are discussing has only 4 years lapse on Bob’s clock at turn-around time, so the website does not conform to the 1905 theory. That's what I've been trying to explain to you.(emphasis mine)

Where does that website (http://mentock.home.mindspring.com/twins.htm) say that Bob sees Ann move 3 light-years at 0.6c?


I’ve also warned you not to trust any of the popular websites about this subject. That’s why I started off discussing the actual clock thought experiment in the SR theory, the A B and K K1 experiment. It was you who brought up the incorrect numbers that are contained in the amateur website. I think you and I should stick strictly to the numbers in the 1905 theory, but you keep insisting on bringing up the incorrect numbers in the amateur website which contains additional mistakes that aren’t even in the original Einstein theory.

All right, I'll make you a deal. I'll be willing to stick strictly to Einstein's 1905 paper for this discussion if you will. So, what exactly is your problem with Einstein's 1905 paper?

kilopi
2003-Dec-12, 06:11 PM
So, if you have Bob see Ann move 3 light years at .6c, then according to the 1905 theory, 5 years, not 4, will lapse on Bob’s clock. But the website that we are discussing has only 4 years lapse on Bob’s clock at turn-around time, so the website does not conform to the 1905 theory. That's what I've been trying to explain to you.

Where does that website (http://mentock.home.mindspring.com/twins.htm) say that Bob sees Ann move 3 light-years at 0.6c?
That's apparently derived from your post (http://www.badastronomy.com/phpBB/viewtopic.php?p=178902#178902), where you have Ann perceiving five years have passed. But that's in Ann's reference frame. Sam5 (http://www.badastronomy.com/phpBB/viewtopic.php?p=178917#178917) responded a couple of posts later with a calculation that converted the three lightyears into five years as seen by Bob.

Tensor
2003-Dec-12, 06:17 PM
As far as I can tell, the math in the theory is ok, but the basic concept in the theory of clock slow-downs due only to “relative motion” is not ok.

The slow down of time is not a concept of SR. There are two postulates of SR(which has been mentioned to you before):

1) The laws of physics are the same in all inertial frames.
2) The speed of light is the same as observed in all inertial frames

Which of the above don't you agree with and why? The slowing of time follows in the math from the second postulate. If you agree with the postulates, and you say the math in the theory is good, then you have to concluded (using the math) that there is no paradox. Celestial Mechanic's post (in the previous thread) using the math demonstrates this. You have never commented on those posts. If you believe there is a paradox, could you show us exactly where Celestial Mechanic is wrong?

daver
2003-Dec-12, 06:27 PM
The slow down of time is not a concept of SR. There are two postulates of SR(which has been mentioned to you before):

1) The laws of physics are the same in all inertial frames.
2) The speed of light is the same as observed in all inertial frames

Which of the above don't you agree with and why?

Sam5 before has posted about c-regulators--he seems to think that large bodies regulate the speed of light around them--that they drag the ether somehow. So it would appear that he doesn't believe 2.

Sam5 has also posted about cooler temperatures slowing down biological functions, as if that had something to do with time dilation. I haven't seen this lately, so maybe he's changed his mind about that.

Celestial Mechanic
2003-Dec-12, 07:04 PM
I am going to try to dispel a few more misconceptions by giving coordinates for 6 events that are relevant to our thought experiment involving Anne and Bob. These events are:

A: Anne and Bob are together. Bob sets off at 0.6c in the x-direction.
B: Two years have elapsed for Anne. All signals that she sends to Bob before this time reach him before his turn-around and are redshifted, all signals she sends after this time are blueshifted.
C: Five years have elapsed for Anne.
D: Eight years have elapsed for Anne. All signals that she received from Bob before this time were redshifted. All signals she receives after this time are blueshifted.
E: Ten years have elapsed for Anne. Bob returns from his journey. Eight years have elapsed for Bob.
F: The turnaround point for Bob. Four years have elapsed for him.

In Anne's rest frame, the coordinates of these points are ( (t, x) where time is in years and distance in light-years) :

A: (0, 0)
B: (2, 0)
C: (5, 0)
D: (8, 0)
E: (10, 0)
F: (5, 3)

Notice that C and F are simultaneous in this frame. Notice that the lines BF and FD are null geodesics.

Now we perform a Lorentz transformation to Bob's frame on the outward bound leg of the journey. The transformation is t' = (5/4)*t-(3/4)*x, x' = (-3/4)*t+(5/4)*x .

A: (0, 0)
B: (2.5, -1.5)
C: (6.25, -3.75)
D: (10, -6)
E: (12.5, -7.5)
F: (4, 0)

Notice that F is earlier than C in this frame. Even though a "coordinate time" of 12.5 years separates A and E, the proper time interval between the two events is still 12.5^2 - 7.5^2 = 156.25 - 56.25 = 100 = 10^2, so the proper time is still 10 years.

Finally, we consider Bob's frame on the inward bound leg, using his clock time as the time coordinate.

A: (-4.5, -7.5)
B: (-2, -6)
C: (+1.75, -3.75)
D: (5.5, -1.5)
E: (8, 0)
F: (4, 0)

Notice that here C is earlier than F in this frame.

Some exercises for the student:

1) Show that the proper time from F to E is four years in Bob's outbound frame.
2) Verify that BF and FD are null geodesics in both of Bob's frames.
3) Even though C and F are simultaneous for Anne, C is later than F for outbound Bob and earlier than F for inbound Bob, show that the separation between them is timelike and equal to 3 light-years in all three frames.
Extra Credit) Find the transformation to go from Anne's frame to Bob's inbound frame. Hint: Translate the origin to E, perform the inverse of the transform that got us to Bob's outbound frame, then translate E to (8, 0).

BTW, thank you for reading my posts, Tensor. It's good to know that someone is paying attention.

kilopi
2003-Dec-12, 07:08 PM
So, CM, in your opinion, does my Ann/Bob page describe anything wrongly?

Sam5
2003-Dec-12, 07:22 PM
All right, I'll make you a deal. I'll be willing to stick strictly to Einstein's 1905 paper for this discussion if you will. So, what exactly is your problem with Einstein's 1905 paper?


Ok, let me see if I can explain my point of view about his 1905 paper, without bringing in any amateur websites.

I think the Electrodynamical part of the 1905 paper is mostly ok, because of the way he used the two “frames” in that part. With is moving atoms and electrons, he actually has them “moving through” a medium, which I believe is the earth’s local fields. The “medium” is the “c-regulator” of the other “relatively moving” frame, just as Lorentz had used a “medium” in his 1895 and 1904 electrodynamics papers. This “motion of atoms through the fields” later allowed Einstein to deduce parts of his GR theory and be correct about what he decuced.

Parts of the Kinematical part of the 1905 theory are ok, since he has two relatively moving frames with two relaively moving sets of fields or “c-regulators”.

But, the part of the Kinematical part of the 1905 paper that has “time dilation” due ONLY to “relative motion”, is NOT correct.

Why do some “experiments” tend to seem to “support” all of the Kinematical part of the 1905 theory? These experiments tend to support the whole Kinematical part ONLY when the “relative motion” of the experiments have objects MOVING THROUGH LOCAL FIELDS.

That is why “c” is a “limiting speed” here at the earth (and inside fields), but not when we consider the most distant galaxies. Because objects here at the earth are moving through local fields, but the distant galaxies are apparently not moving through any fields at all.

For example, what I said earlier about the moving magnet and the coil. If you move the magnet AT THE COIL, then the coil FEELS the changing magnetic flux. But, if you move the magnet in Los Angeles, while the coil is in New York, the coil DOES NOT FEEL the changing flux.

This is the crux of the situation. If the two relatively moving frames are CLOSE ENOUGH TO EACH OTHER for their FIELDS TO INTERACT, then there can be a real effect that occurs because of the motion, such as the example I gave about the large magnet being moved NEAR an electric clock. That will cause the coil inside the little electric motor inside the clock to FEEL the changing flux of the large magnet’s magnetic field, and that will alter the motor rpm rate of the electric clock.

BUT if we move the large magnet in Los Angeles while the electric clock is in New York, then the electric clock WILL NOT FEEL the changing flux.

This is a direct analogy to the local “speed limit of c”, as compared to the distant-galaxy non-limit. The distant galaxies are a long way away from our local fields.

Eintein’s slight mistake in the Kinematical part of the 1905 theory was in not recognizing, in 1905, that the thing that caused a real “effect” was the motion of a mass or a clock THROUGH the fields, rather than just the “relative” motion of the two frames, no matter how far apart they were.

This is a fairly minor mistake. It’s no big deal, because later in GR theory he added the FIELDS to the considerataion and he cleared up some of his 1905 errors.

This change in attitude of his is why he said there was “no ether” in 1905, but later in 1920 he said there “was an ether”, and in 1920 he recognized that “ether” to be the “fields”. He actually said so here:

”Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only wonld be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.”

Read his whole 1920 paper at this link to see what he said about the fields (http://www.mountainman.com.au/aether_0.html)

I realize this might at first be difficult to understand. It took me about 8 years of studying a lot of his papers to figure this out. And after a couple of years I stayed completely away from the error-filled amateur explainaitons of this stuff. He figured some of this out by 1907, more by 1915, and even more by 1920.

What he actually discovered was a “limiting speed of c” for masses moving INSIDE strong fields. But this rule does not apply to the distant galaxies, since they apparently are NOT moving THORUGH strong fields. But he died before he ever learned of galaxy redshift examples that suggest higher than “c” speeds for the distant galaxies.

If he were here today, he would certainly understand all of this and he would probably be the leading cosmologist of our era, and we wouldn’t even need to be arguing about this stuff. One reason I understand some of this stuff is because I have had the advantage of being able to study the past 48 years of experimental and observational data gathered by physicists and cosmologists. He did not have that advantage. If he had known about the high-z galaxies in 1930, 1940, or 1950, he would have worked all this stuff out within a couple of years, and I think he COULD have eventually said something like this: “The Special Relativity principle of relatively-moving frame transformation effects applies on a local level where fields interact between relatively moving frames, but if the frames are so far apart that their fields do not directly interact, then the principle has no actual practical application at such great distances,” just as he DID say in the 1905 paper: “For velocities greater than that of light our deliberations become meaningless;”

By the year 2,000, he could have merely added a couple of extra phrases to that sentence that could have said, “ "superluminal velocities of masses through powerful local fields, on a local level, are apparently impossible, but superluminal relative velocities of masses that are separated by great distances and that are not traveling through any fields, apparently are possible.”

And he could have further said: “The apparent ‘clock paradox’ of Special Relativity only arises if two clocks that are each resting within their own powerful and separate local fields pass each other, relatively, close by one another, and in that case, if the two field strengths are of the same magnitude, then BOTH clocks will exhibit exactly the same clock-rate change, depending on the types of clocks used in the experiment. But if only one of the clocks, which possesses no strong local fields of its own, moves through the other clock’s strong fields, such as the moving clock moving near the surface of the earth, then only the moving clock will experience a rate change.”

Of course he can’t say that now, since he died in 1955, and I think it is incorrect to assume that he never would have amended his 1905 theory to take into account the new physics knowledge that has been gained since his death. And I think it is unfair to try to claim that he would have continued to insist that his 1905 theory should not be amended in any way. Certainly he would have amended it by now, had he survived till now. And it is unfair for anyone to call me a “crackpot” simply because I insist on amending his 1905 paper to include modern physics and astronomical observational data. The crackpots are the ones who won’t allow any amendments to the 1905 papers that are based on modern observational data.

SeanF
2003-Dec-12, 07:24 PM
So, CM, in your opinion, does my Ann/Bob page describe anything wrongly?

I don't know about CM, but I still think your Twin Paradox Redux (http://mentock.home.mindspring.com/twinrdux.htm) page explains clock synchronicity wrongly . . . :)

SeanF
2003-Dec-12, 07:30 PM
Well, Sam5, first of all, you sure made reference to an awful lot of papers other than the 1905 paper. I thought we were just going to talk about that one? At any rate, I realize that my question was too generalized. Let me be more specific.


And he could have further said: “The apparent ‘clock paradox’ of Special Relativity only arises if two clocks . . . "

What "apparent 'clock paradox'"? I do not see any clock paradox in Einstein's 1905 paper. Where do you?

Sam5
2003-Dec-12, 07:35 PM
Sean,

I wish I had explained it this way when I first started out arguing about this topic, but frankly, I didn’t think of explaining it this way at that time.

What the amateurs are doing on their “Ann and Bob” websites, is just the same as if some crank read in an old book that said some old Pope, 450 years ago, said, “The sun revolves around the earth”, and then the internet guys would post webpages trying to “prove” the sun revolves around the earth. Whereas in reality, a modern Pope has had the advantage of the past 450 years of scientific observation, and so he wouldn’t say such a thing.

So what these internet guys are doing is taking something Einstein said in 1905, which contained some minor flaws ONLY because he did not have access to the past 98 years of modern observation data. He was basing his 1905 paper on what he had read about the 1886 Michelson-Moreley experiment and some of the attempts to explain the “null” result.

Einstein did NOT base his 1905 theory on year-2003 observational data. He based it on year-1886 observational data.

Had Einstein lived until now, he would have AMENDED his 1905 theory to take into account all the modern observational data, and we wouldn’t be here arguing about this.

kilopi
2003-Dec-12, 07:38 PM
Of course he can’t say that now, since he died in 1955, and I think it is incorrect to assume that he never would have amended his 1905 theory to take into account the new physics knowledge that has been gained since his death. And I think it is unfair to try to claim that he would have continued to insist that his 1905 theory should not be amended in any way. Certainly he would have amended it by now, had he survived till now.
He did amend his theory, before he died. It's called general relativity. He made many (self-admitted) false starts.


And it is unfair for anyone to call me a “crackpot” simply because I insist on amending his 1905 paper to include modern physics and astronomical observational data. The crackpots are the ones who won’t allow any amendments to the 1905 papers that are based on modern observational data.
It would be unfair to label me as a crackpot just because I am trying to explain the mathematics and theory behind the 1905 papers. You have asserted that he didn't treat the details of the twin paradox properly in his 1905 paper, that he somehow misapplied his own theory. He did not, you are wrong.

Sam5
2003-Dec-12, 07:55 PM
What "apparent 'clock paradox'"? I do not see any clock paradox in Einstein's 1905 paper. Where do you?


The “apparent” clock paradox occurs when we consider the results from the K1 frame-observer’s point of view that the K frame is the one that is “moving” and “time dilating”, while we also consider the K frame-observer’s point of view that the K1 frame is the one that is “moving” and “time dilating”.

But, if we consider that the K clock is moving “through” the K1 frame’s “fields”, or that the K1 clock is moving “through” the K frame’s “fields”, then there would be no paradox; however, we must also accept the real-life observational data that “c” is NOT “always” the speed of light everywhere and relative to every “frame”. We must accept the modern observational data that explains how a light beam passing near the sun “slows down” relative to the earth’s frame and the earth’s atomic clocks, while the photons are at the sun, while the photons are judged to be traveling faster than “c” by sun clocks and observers, when the photons are traveling a long way from the sun. While they are at the sun, they would be seen as traveling at “c” by the sun observers and clocks, but they would be seen as traveling faster than c by those observers and clocks when they are not near the sun.

Einstein includes this basic information in his 1911 theory, and I’ve pointed that out to you many times.

What you want to do is not allow him to ever “update” his theories so they can conform to modern observational data. And I don’t understand why you would not allow Einstein to take modern observational data into consideration. I don’t understand why you insist on keeping his old theories “as is” with “no updates” based on new scientific information learned during the past 98 or 48 years.

Had he lived longer, he would have made more “updates” than he actually did make. If he were alive today, his 1916 book would probably contain 7 or 8 Appendices, or maybe 9 or 10, rather than just 5. You are the guys who are harming his reputation by not allowing him to “update” his theories past the year 1955.

Sooner or later, some of these new physics whiz kids coming along are going to realize that the Kinematical part of the 1905 paper needs to be amended to take into account modern observational data. That kid whose link I posted here already knows it. That’s why he said that the light photons actually DO slow down at the sun, as measured from the earth.

SeanF
2003-Dec-12, 07:59 PM
What "apparent 'clock paradox'"? I do not see any clock paradox in Einstein's 1905 paper. Where do you?


The “apparent” clock paradox occurs when we consider the results from the K1 frame-observer’s point of view that the K frame is the one that is “moving” and “time dilating”, while we also consider the K frame-observer’s point of view that the K1 frame is the one that is “moving” and “time dilating”.

More specific, please? Einstein doesn't use K1. You're paraphrasing, and that's okay, but I don't know what part of the paper you're referring to.

Sam5
2003-Dec-12, 08:24 PM
More specific, please? Einstein doesn't use K1. You're paraphrasing, and that's okay, but I don't know what part of the paper you're referring to.

I’m talking about his original clock paradox thought experiment, the “peculiar consequence” one. The peculiar consequence results when he examines his own theory from the point of view of ONLY the K observer, and he doesn’t report what the K1 observer “sees”. When we realize that the K1 observer would “see” the K frame “moving” and “time dilating”, that results in the paradox. In other words, if we examined what BOTH observers would “see”, then we’ve got TWO conflicting “peculiar consequences”, and that causes the paradox, but just a few years later he began to remove that paradox from his overall relativity theories and various NEW relativity papers.

Since we live in a unified world, and since “the laws of physics are the same everywhere”, then we CAN’T just look at the phenomena from the K “point of view”. We also must look at it from the K1 “point of view”.

He did actually amend part of the 1905 theory with the 1911 theory, and he pointed that out when he said in 1911, (my emphasis in bold):

“The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity.”

That’s because in THIS theory he has only ONE of two clocks actually “slowing down”, so there is no paradox. You can read about it in his dialogue about the two “U” clocks in the 1911 theory. In this theory, the speed of light DOES slow down relative to a DISTANT observer, but NOT relative to a LOCAL observer. This is why the light bends when it passes near the sun, because the gravitational field at the sun, which is strongest nearest the sun, causes the beam of light to act like a plane wave encountering a glass interface. That’s what causes the light to bend at the sun.

So you can’t say his 1905 theory is all “absolutely correct and true and never doesn’t apply to nature under any circumstances”, because he said so himself in 1911 that this new 1911 theory adds some new material to the 1905 theory and so the “ordinary theory of relativity” doesn’t apply here, or it applies “in a different form”, meaning that the sun observer with his local atomic clocks “sees” the light traveling at “c” only when the photons are nearest the sun, while the earth observe “sees” the photons pass near the sun at “less than c” as their speed is measured by the earth clocks.

But you are disagreeing with Einstein’s 1911 statement and you are saying, in effect, that he was wrong in 1911, while I’m saying he was right in 1911. I think you are mad at me because you think that I’m the one who is trying to amend the 1905 paper, but it was actually Einstein himself who did it in 1911.

Flaney
2003-Dec-12, 08:30 PM
Tensor wrote:
The slow down of time is not a concept of SR. There are two postulates of SR(which has been mentioned to you before):

1) The laws of physics are the same in all inertial frames.
2) The speed of light is the same as observed in all inertial frames

Which of the above don't you agree with and why?

2)

How does the reciept of a photon translate into speed? It is an event with no other information (except energy). Subsequent photon receptions build an event history where derived speed can be calculated (based on local clocks). Any event chain variations can be attributed to relative velocity differences.

Photons I emit are not detectble by me any more. As I travel along, I release an additional photon, which I have carried away some distance; it will be farther from the previous photon I emitted by vt. These photons get detected at some point as events that occur in a dilated history: the transmit events no longer coincide with detection events.

Should the reciever think the emitters clock is running slow because the events come less frequently?

To measure a photon's speed, I need to measure it's position at two places and the times it reaches each position. But once I have detected it, it is gone. I have to detect some other photon that was moving near it at the second location, where it subsequenly vanishes. Only if we assume all photons are equal can a specific speed be determined.

When I test a photon's speed in my reference frame, I use a local source and detector. If my reference frame velocity has been added to photon speed, the excess is canceled between the source and detector. That which I added at the emitter gets subtracted at the detector.

This does not need to mean photons are racing around with different speeds. How quickly does the photon speed drop when traversing a non-vacua medium? Space itself might 'force' photons to a local C in a similar manner. Fast photons would not pass up its slower brothers if some depth or maximum transmission transition is exceeded. Beyond such a point, the events would be compressed, but all would be finally zipping along at C.

SR is time series information propagation.

Sam5
2003-Dec-12, 08:36 PM
Sean,

If you let your focus drift away from Einstein’s actual papers, and if you let it drift toward the internet’s self-appointed amateur self-proclaimed “experts”, then you will get completely confused.

The reason I was able to figure some of this stuff out was because I stopped reading the amateur stuff early on, and I persisted in studying the real original Einstein stuff, and I’m sure you know, that’s not “easy” stuff to study.

That stuff about the “U” clocks in the 1911 paper is mind-bending, but I finally worked through it and came out on the other side with a better understanding of the 1911 theory, and THEN I knew EXACTLY what he meant when he said in 1911:

“The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity.”

OF COURSE it applies “in a different form”, because the sun observers will measure the photons to travel at “c” ONLY while they are passing through the sun’s gravitational field, while the earth observers will see them “slow down”, at the sun, when observed FROM the earth!

The guy was a GENIUS!

But I think he could have used a good manuscript editor, because the way he worded things is really confusing to the rest of us.

SeanF
2003-Dec-12, 08:58 PM
More specific, please? Einstein doesn't use K1. You're paraphrasing, and that's okay, but I don't know what part of the paper you're referring to.

I’m talking about his original clock paradox thought experiment, the “peculiar consequence” one. The peculiar consequence results when he examines his own theory from the point of view of ONLY the K observer, and he doesn’t report what the K1 observer “sees”. When we realize that the K1 observer would “see” the K frame “moving” and “time dilating”, that results in the paradox. In other words, if we examined what BOTH observers would “see”, then we’ve got TWO conflicting “peculiar consequences”, and that causes the paradox, but just a few years later he began to remove that paradox from his overall relativity theories and various NEW relativity papers.


From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2(tv^2/c^2) (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

That the one? Okay let's see. Einstein gives the equations for converting coordinates from one reference frame to another at the end of Section 3. These are, as he points out, simplified in that they assume that the origins of both reference frames are at the same point and that motion is restricted to the x-axis. This "peculiar consequence" can be dealt with under those restrictions, though, so we can use the equations as-is.

So. We'll start out with the A clock having (x,t) coordinates of (0,0) in the initial reference frame. The B clock is located 3 light-years away at coordinates (3,0) in the initial reference frame. He says "the clock at A is moved with the velocity v along the line AB to B." We'll use our standard velocity of 0.6c. So, B's going to stay where its at (spatially speaking) and end up at (3,5) [t=d/v=3/.6=5]. A's going to end up in the same place - (3,5)

So, let's use his equations and transform those coordinates into the other reference frame. The two equations are:

t' = (t - vx/c^2)/(1-v^2/c^2)^0.5
x' = (x - vt)/(1-v^2/c^2)^0.5

so the three coordinate points become:

A's starting point = (0,0) = (0,0)
B's starting point = (3,0) = (3.75,-2.25)
A&B's ending point = (3,5) = (0,4)

The first reference frame has B remaining stationary at x=3 and A moving from x=0 to x=3. In that reference frame, B's time coordinates go from 0 to 5, a total of 5. A's time coordinates also go from 0 to 5, but since we expect A's clock to be dilated to 80%, we expect to see A only show a duration of 4 (5*.80).

The second reference frame has A remaining stationary at x=0 and B moving from x=3.75 to x=0. In that reference frame, A's time coordinates go from 0 to 4, a total of 4. B's time coordinates go from -2.25 to 4, a total of 6.25, but since we expect B's clock to be dilated to 80%, we expect to see B only show a duration of 5 (6.25*.80).

So, regardless of whether A or B is considered to be stationary, they both expect to see A show a duration of 4 and B show a duration of 5.

Where's the paradox?

SeanF
2003-Dec-12, 10:56 PM
Uh, Sam5? You still there?

Starbuck
2003-Dec-12, 11:43 PM
Everybody's gotta eat dinner sometime...

kilopi
2003-Dec-13, 12:30 AM
But you are disagreeing with Einstein’s 1911 statement and you are saying, in effect, that he was wrong in 1911, while I’m saying he was right in 1911. I think you are mad at me because you think that I’m the one who is trying to amend the 1905 paper, but it was actually Einstein himself who did it in 1911.
In effect, I am saying that certain parts of the 1905 paper, that you say are wrong, are not wrong. And we're just trying to explain the math.

Sam5
2003-Dec-13, 01:08 AM
Uh, Sam5? You still there?



Yeah, yeah, I’m back. Look, I’ve been sitting in this chair so much during the past couple of weeks, bent over my keyboard so much, my feet have been swelling up. I think the circulation has been cut off to them. So, to keep me from having to have my feet amputated, I’ve had to get out some and walk around. I’ll study your last stuff a little later.

In the meantime, while I was out, I thought of this. We are not that far apart, if we totally leave out the amateur internet Bob and Ann type stuff.

And think of this, the speed of light is apparently fixed at “c”, relative to an observer who has an atomic clock sitting on his desk, if he and the clock are resting somewhere on the surface of an astronomical body, and if they are measuring the speed of the local photons that are passing by them at the moment they measure the local speed of light. So, the local speed of light is apparently tied directly to the tick rates of local atomic clocks, if those clocks are resting inside a gravitational field when the local photons pass close by the clocks.

But, if the observer and the clocks measure the speed of photons that are traveling somewhere else, such as they are just passing by the sun, close to the sun, while the observer and the clocks are on the earth, then that speed they would measure would be more or less than “c”. In the case of the sun photons and the earth observer, the sun photons would be measured by the earth observer as traveling less than c, while they are passing near the sun.

But, a sun observer, using a sun-based atomic clock, would measure “c” for the speed of the photons as they pass near to the sun, while he would measure the photons moving faster than c when they are well away from the sun, such as when they are passing by the earth when the sun observer measures their speed.

So, it depends on where the observer is and where his atomic clock is, and whether or not he’s resting inside a gravitational field, and where the photons are that he is measuring. I think Einstein did not know that in 1905, since he didn’t mention the role the gravitational field plays in all of this, but I think he figured it out by 1911.

I’ll get back to you later.

kilopi
2003-Dec-13, 01:24 AM
In the meantime, while I was out, I thought of this. We are not that far apart, if we totally leave out the amateur internet Bob and Ann type stuff.
If you left off the amateur internet stuff, you'd be out of business yesterday. :)


I think Einstein did not know that in 1905, since he didn’t mention the role the gravitational field plays in all of this, but I think he figured it out by 1911.
By his own admission, not until 1915 and after. It doesn't excuse your errors in math in trying to discredit his early work, and, having admitted that Einstein was a genius, and that he eventually got his complete theory in order, I'm not sure what your purpose is.

Tensor
2003-Dec-13, 02:16 AM
BTW, thank you for reading my posts, Tensor. It's good to know that someone is paying attention.

To your posts, always. You belong to a group, (the BA, Kilopi, Tim, Eta, JSPrinceton before his banning, and a few others) that I learn something from almost all the time.

Sam5
2003-Dec-13, 02:35 AM
Sean,

You:
”The first reference frame has B remaining stationary at x=3 and A moving from x=0 to x=3

The second reference frame has A remaining stationary at x=0 and B moving from x=3.75 to x=0.’

Me:
This is incorrect.

A the beginning of the thought experiment, points A and B are stationary in K and K1. Since no one is moving, K and K1 overlap along their x axes.

Distance AB = BA

So, you can’t change the distance from B=x3 to B=x3.75 in the middle of the thought experiment.

That’s like saying the distance from Los Angeles to New York is 3,000 miles, but the distance from New York to Los Angeles is 3,750 miles. You can’t do that because you’ve already set the distance at B=x3.

You’ve got to tell what B “sees” when A moves from x=0 to x=3, and then you have to tell what A “sees” when B moves from x=3 to x=0.

You’ve got to tell what a Los Angeles resident “sees” when a New Yorker flies to Los Angeles and you’ve got to tell what a New Yorker “sees” when a Los Angeles resident flies to New York.

You can’t have the New Yorker leaving from Nova Scotia on the way to Los Angeles, while the Los Angeles resident leaves from Los Angeles on the way to New York.

Einstein said in the paper: “It is clear that the same results hold good of bodies at rest in the “stationary'' system, viewed from a system in uniform motion.”

He also said:

“whence it follows that the time marked by the clock (viewed in the stationary system) is slow by http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img62.gif seconds per second”

From B’s point of view, B is in “the stationary system”. From A’s point of view, A is in “the stationary system”.

You:
”So, regardless of whether A or B is considered to be stationary, they both expect to see A show a duration of 4 and B show a duration of 5.”

Me:
No. You’ve been misled by the Ann and Bob example. You’ve got to put it completely out of your mind.

Sam5
2003-Dec-13, 02:53 AM
SeanF,


One of Einstein’s errors in the paper is that he says this:

“If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img64.gif
(up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.”

And then he stopped that particular thought experiment.

Had he gone on to say what the A observer “saw”, it would be like this:

“If at the points A and B of K1 there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at B is moved with the velocity v along the line AB to A, then on its arrival at A the two clocks no longer synchronize, but the clock moved from B to A lags behind the other which has remained at A by
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img64.gif

(up to magnitudes of fourth and higher order), t being the time occupied in the journey from B to A.”

When people, including legitimate physics professors who I’ve discussed this with, follow Einstein’s symmetry rule that says: “It is clear that the same results hold good of bodies at rest in the “stationary” system, viewed from a system in uniform motion,” then that’s when they see the paradox, since the A system is “stationary” to the A observer, and the A observer “sees” the B clock as the one that “moves”.

This is one of the hazards of purely “theoretical” physics, ie leaving something out or forgetting something or not following one of your own rules, and this often comes from working on a theory and a thought experiment completely by yourself without much feedback from other physicists. This is why he had to backtrack in 1907 and admit that none of the frames actually “shrivel up”, since “relative motion” alone can’t cause any frame to really shrink. Lorentz’s frames could “shrunk” in his theory because they were moving through an “ether”, and he thought that one arm of the Michelson Morley apparatus might have really shrunk because of its motion through the ether as the earth moved around the sun at 18.6 mps.

Tensor
2003-Dec-13, 02:57 AM
Tensor wrote:
The slow down of time is not a concept of SR. There are two postulates of SR(which has been mentioned to you before):

1) The laws of physics are the same in all inertial frames.
2) The speed of light is the same as observed in all inertial frames

Which of the above don't you agree with and why?



2)
How does the reciept of a photon translate into speed? It is an event with no other information (except energy). Subsequent photon receptions build an event history where derived speed can be calculated (based on local clocks). Any event chain variations can be attributed to relative velocity differences.

What about single photon emission and detection? If we know the emitted time, detection time, and the distance we can get the velocity of a single photon.


Photons I emit are not detectble by me any more. As I travel along, I release an additional photon, which I have carried away some distance; it will be farther from the previous photon I emitted by vt. These photons get detected at some point as events that occur in a dilated history: the transmit events no longer coincide with detection events.

Sure they do. All it requires is a frame transformation.


Should the reciever think the emitters clock is running slow because the events come less frequently?

Nope. Because if doesn't matter if the emitter is moving away or approaching, the clock of the emitter is running slow either way. By your logic, the clock should appear to be running faster, if approaching, because events come more frequently when approaching.


To measure a photon's speed, I need to measure it's position at two places and the times it reaches each position. But once I have detected it, it is gone. I have to detect some other photon that was moving near it at the second location, where it subsequenly vanishes. Only if we assume all photons are equal can a specific speed be determined.

Do you have a reference showing all photons are not the same (except for energy)? How are photons of monochromatic light different?


This does not need to mean photons are racing around with different speeds. How quickly does the photon speed drop when traversing a non-vacua medium?

That would depend on the index of refraction for that medium, wouldn't it?


Space itself might 'force' photons to a local C in a similar manner.

Might? You have a reference for this happening?

Tensor
2003-Dec-13, 03:00 AM
So, CM, in your opinion, does my Ann/Bob page describe anything wrongly?

I know you didn't ask me Kilopi, but your page described it very well, IMHO.

Tensor
2003-Dec-13, 03:02 AM
Just in case you forgot Sam:


Celestial Mechanic's post (in the previous thread) using the math demonstrates this. You have never commented on those posts. If you believe there is a paradox, could you show us exactly where Celestial Mechanic is wrong?

Sam5
2003-Dec-13, 03:11 AM
To measure a photon's speed, I need to measure it's position at two places and the times it reaches each position.

Right, exactly.

To actually measure the speed of starlight at the earth, I think we would have to find a star that blinks, such as a pulsar. Then we would have to set up two telescopes with light receptors, one on a mountain top, and another in-line with that one, down in a valley. Then we would have to measure the time it takes between when the first receptor sees the blink and when the second one sees it, and we need to know the exact distance between the first and second receptor. And we would have to calculate the different rates of the two atomic clocks due to altitude differences.

But I suspect it would be measured at “c” here on earth, because I think our gravitational field regulates light speed here and it also regulates the rates of the atomic clocks, different rates at different altitudes.

Sam5
2003-Dec-13, 03:28 AM
Just in case you forgot Sam:


Celestial Mechanic's post (in the previous thread) using the math demonstrates this. You have never commented on those posts. If you believe there is a paradox, could you show us exactly where Celestial Mechanic is wrong?

Tensor,

Thanks. I haven’t had time to get to those posts yet. It takes me a lot of time to figure out the exact errors in some of the other paradox resolution thought experiments. Plus, I’ve got to get out a lot so my feet won’t go dead on me.

I think it would almost be easier if everyone just forgot about the 1905 paradox, that can not be resolved, and they should go on to study the 1911 paper. That paper adds a gravitational field and that takes away the paradox, since in the 1911 paper, only one clock actually slows down, it really slows down, and both observers agree. The slow observer “sees” the fast one running fast, and the fast one “sees” the slow one running slow. In this, there is no paradox.

He left out “fields” and “acceleration” in the 1905 theory, and this is one reason he got the paradox.

The little error in the 1905 theory wasn’t bad in and of itself. What makes it seem bad are all the guys who claim it is not an error. They are, in effect, trying to “prove” Einstein’s 1905 error to be correct and not an error. And that drives some of us up the wall, those of us who have studied many of his other time-related papers. He actually corrects the error in the 1911 paper, but his wording is not very easy to understand.

He was a theoretical physicist, so he couldn’t come right out and say in his 1911 paper, “Opps, I made a blooper back in my 1905 paper, and I’d like to correct it now.” If he had said that, no publisher would have trusted his 1911 paper. That’s why he had to be careful how he worded the 1911 paper, so it wouldn’t strongly admit the blooper in the 1905 paper. That’s why he said in 1911:

“The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity.”

See? He couldn’t say outright, “I was wrong in part of my 1905 paper, and this paper includes my correction.” No theoretical physicist can say that in a subsequent paper and still expect his latest papers to be taken seriously and be published.

Sam5
2003-Dec-13, 03:36 AM
Space itself might 'force' photons to a local C in a similar manner. Fast photons would not pass up its slower brothers if some depth or maximum transmission transition is exceeded. Beyond such a point, the events would be compressed, but all would be finally zipping along at C.


Hey! That’s something like what I said earlier! I think it is “the fields” of space, not just “empty space”, that control the speed of light through different areas of space. Sort of like an airplane flying in air. Some air is turbulent. Some air is moving one way. Some air is moving the other way. So, the GROUND SPEED changes, but the AIR SPEED does not. In the case of light I think the “space speed” changes in different places in space, but the “ground speed” is determined by the gravitational potential at the surface of the astronomical body where the local light photon speed is measured by means of an atomic clock that is also “geared” to the local gravitational potential.

SeanF
2003-Dec-13, 03:39 AM
Sean,

You:
”The first reference frame has B remaining stationary at x=3 and A moving from x=0 to x=3

The second reference frame has A remaining stationary at x=0 and B moving from x=3.75 to x=0.’

Me:
This is incorrect.

A the beginning of the thought experiment, points A and B are stationary in K and K1. Since no one is moving, K and K1 overlap along their x axes.

Distance AB = BA

So, you can’t change the distance from B=x3 to B=x3.75 in the middle of the thought experiment.


I'm going to bed now, and I will probably sleep in (I think I might be coming down with the flu). Before I do, I'm going to say this:

Some time ago in this thread, I offered you the opportunity to simply say, "I believe that SR's constant-speed-of-light postulate is flawed, and thus the theory will necessarily reach the wrong conclusions, but the logic from the postulate to the conclusions is sound." You refused to accept it, because you believe that SR is internally flawed.

Now, you originally stated that this flaw was apparent in the clock paradox, because it predicts different times for the two clocks from the two observers. I just showed you how the math in SR (Einstein's own equations!) show that there is no paradox.

So now you say "But you can't change distances." I'm sorry, but the non-absoluteness of time and space is another part of SR. I will show you exactly how SR says the distance does change. Then you'll go back another step up the logic chain and say, "But you can't do this." and then I'll show you how SR leads to that.

Eventually, we'll get all the way back up to the beginning, and you'll say "But the speed of light is not a constant for all observers, even though everything after that works!"

Why don't you just say it now?

Flaney
2003-Dec-13, 04:06 AM
Photons I emit are not detectble by me any more. As I travel along, I release an additional photon, which I have carried away some distance; it will be farther from the previous photon I emitted by vt. These photons get detected at some point as events that occur in a dilated history: the transmit events no longer coincide with detection events.

Sure they do. All it requires is a frame transformation.

How would the photon know (or the receiver) what the state of the source is in order to establish a frame transformation?



Should the reciever think the emitters clock is running slow because the events come less frequently?

Nope. Because if doesn't matter if the emitter is moving away or approaching, the clock of the emitter is running slow either way. By your logic, the clock should appear to be running faster, if approaching, because events come more frequently when approaching.

So, the event chain of photon detections won't be compressed when the source is approaching?



To measure a photon's speed, I need to measure it's position at two places and the times it reaches each position. But once I have detected it, it is gone. I have to detect some other photon that was moving near it at the second location, where it subsequenly vanishes. Only if we assume all photons are equal can a specific speed be determined.

What about single photon emission and detection? If we know the emitted time, detection time, and the distance we can get the velocity of a single photon.

Doesn't this assume information transfer between reference frames beyond photon communication?




This does not need to mean photons are racing around with different speeds. How quickly does the photon speed drop when traversing a non-vacua medium?

That would depend on the index of refraction for that medium, wouldn't it?


Space itself might 'force' photons to a local C in a similar manner.

Might? You have a reference for this happening?

No reference. But it seems to follow from refraction indexes. What might the refraction index of the vacua between various locales?

Sam5
2003-Dec-13, 04:27 AM
Sean,

The kinematical part of the paper has several flaws in it. First, he claims “no ether”, but he uses two of them in the theory. The c-regulator for K and the separate c-regulator for K1. These c-regulators serve as light-propagating “ethers” or “media”, and they are both moving relatively when the frames move relatively. It is with this media that he sets his light-clocks, by sending a beam between A and B and reflecting it back to A.

When each medium is “stationary” with an observer, either B or A, then the times for the light to travel from A to B and back from B to A are the same. But if the observers attempt to measure the travel times for the beams in a moving medium, then the times are not the same. The different path times in moving and non-moving media are reflected in these equations of his:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img11.gif

This is where the relative c – v and c + v photon speeds turn up, as they must turn up with observers and emitters moving within a stationary medium.

Next, the kinematical part doesn’t consider acceleration or gravitational fields. That was a mistake. It’s my understanding that there is no place in observable space where there are “no fields”. In 1911 he switched over to "atomic clocks" rather than light clocks, and atomic clock rates are also affected by acceleration and fields, which reveals his more realistic approach to this subject in 1911.

Third, he is the one who published the symmetry principle that says both observers will see the same thing, but in reverse, when they look at each other.

Four, he is the one who left out the opinion of the A observer in the “peculiar consequence” thought experiment.

You are the one who has his mind fixed on the Bob and Ann example. That’s why you wind up with these four conflicting end times: 12.5, 10, 8, 6.4, whereas Einstein only wound up with two conflicting end times.

You change B from x=3 to x=3.75 before any motion begins.

Tell me, when A and B are stationary, what is the distance from A to B and from B to A? When A moves, why does B’s position remain at x=3, but when B moves, you have him suddenly start from x=3.75? Start him from x=3 and see what happens. Remember, before the motion, AB = BA.

No motion:

A----------B

Ok, now, move B to A and tell me what A sees, and move A to B and tell me what B sees.

Einstein corrected his errors in 1911. He knew more in 1911 than he knew in 1905. You need to study the 1911 paper and forget about Bob and Ann.

Celestial Mechanic
2003-Dec-13, 05:04 AM
Kilopi:

I sat down and carefully read your explanations of the Twin Paradox, both the original and the "Redux". They are correct and not "amateurish". If I had done more than skim them initially, I might not have wound up spelling "Ann" as "Anne" in my examples! :)