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Silmatan
2001-Nov-09, 07:10 AM
Ok, according to relativity, if one twin stays on earth while the other one goes on a trip really fast, the one who went on the trip will not have aged as much as the one who stayed home. But, relative to the person taking the trip, isn't that one standing still while the one at home is moving? Why is it that time "slows down" for the one on the trip when spacetime isn't supposed to make the distinction between a fast rocket and stationary planet and a stationary rocket and fast planet?

Wally
2001-Nov-09, 12:13 PM
the one that ends up younger is the one that "changes direction" to catch back up with the original. i.e. if the "stationary" twin stays where he is, and the "moving" twin turns around and races back, then it's the second one that'll be younger. If, on the other hand, the "stationary" twin decides to take off and catch up with the "moving" twin, then he'll be the younger one once they meet. It all has to do with the 3rd inertial time frame that's introduced once the action is made to get back together with each other.

SeanF
2001-Nov-09, 12:35 PM
Wally's got it exactly right. There are three inertial frames in the experiment as it is normally given, and it is the fact that the "rocket" twin is the one who switches inertial frames that causes the time dilation to be one-sided like it is.

BTW, it'd be possible for one twin to rocket off and then stop, and then the other twin rockets off in the same direction (and velocity) and catches up to the first. In this case, both twins would still be the same age at the end, because in this case, there are only two inertial frames.

/phpBB/images/smiles/icon_smile.gif

[Editing for spelling]
_________________
SeanF

<font size=-1>[ This Message was edited by: SeanF on 2001-11-09 07:37 ]</font>

Mr. X
2001-Nov-09, 01:38 PM
Okay, twins.

It's been explained before, but the idea of twins seems to be confusing people.

Why should two twins always be the same age?
Here's some stupid analogy:
Find two twins. Kill one. You'll probably be amazed to see that the one you didn't kill is still alive! Now you have something to think about in prison. /phpBB/images/smiles/icon_smile.gif

Twins are two separated individuals, like you and me. Aside from have identical DNA (my biology is very very bad!) they are not linked.

Please don't use twins, they're just used to introduce an unecessary parameter to confuse. Call them "two individuals of same age" or something similar, it doesn't change anything at all. Or correct me if I'm wrong. /phpBB/images/smiles/icon_biggrin.gif

SeanF
2001-Nov-09, 01:58 PM
On 2001-11-09 08:38, Mr. X wrote:
Okay, twins.

It's been explained before, but the idea of twins seems to be confusing people.

Why should two twins always be the same age?
Here's some stupid analogy:
Find two twins. Kill one. You'll probably be amazed to see that the one you didn't kill is still alive! Now you have something to think about in prison. /phpBB/images/smiles/icon_smile.gif

Biologically speaking, twins are almost necessarily the same age within a couple of days. I'm not sure how far apart two twins have ever been born, but I'm sure it's not too far. And we're not talking about killing anybody! /phpBB/images/smiles/icon_smile.gif

Twins are two separated individuals, like you and me. Aside from have identical DNA (my biology is very very bad!) they are not linked.

Please don't use twins, they're just used to introduce an unecessary parameter to confuse. Call them "two individuals of same age" or something similar, it doesn't change anything at all. Or correct me if I'm wrong. /phpBB/images/smiles/icon_biggrin.gif

Well, if it doesn't change anything, then why change it? /phpBB/images/smiles/icon_smile.gif

Twins are used in the paradox because it drives home the point more. The basic idea that two people born on the same day end up years apart in age is just, well, cool!

Besides, any time you're doing an experiment with a subject and a control, it's necessary that the two be as much alike as possible to prevent any biological (or other) differences from causing differences in the outcome . . .

2001-Nov-09, 02:23 PM
My thoughts in this thread? no that it matters
"WAS" how many Frames?
I use this string (1{2[3:4|5|:]}) Five frames?
or from from a real life event
(Earth{ocean[typhoon:ship|Gravity Wave pod
NOT THAT THIS MATTERS, probably not
but while i was in the "POD"
time did seam to slow : noticably :
and when I "LEFT" the pod
returned to the "SHIP"'s frame
the Time accumulated in the POD
was decompress "RAPPIDLY"
what can i say ? getting back was not much fun?
anyway? My other example a TV picture
of a TV picture |...| called a picture in
a picture maybe |.[]| where the time in the
small picture delayed some amount from the
primary time. the step rates the same one
second = one second but its not the same
second. to get the second second to be a
different second than the first second
I `poise that a negative Zoom maight work?
although i've not tried this yet myself
there probably is a manipulation that
would cause the small seconds to actually
be longer than the large seconds. Like I say
even I have not tried to do this "YET"
now going out five frames ({[:|what
well its to small to see ? maybe but i try it today

Wally
2001-Nov-09, 03:31 PM
Don't do it HUb'!!! You'll end up seeing the back of your own head as you regress back thru time to a point where you're nothing but a fetus floating quietly thru space.

I'd hate to see that happen. . . /phpBB/images/smiles/icon_biggrin.gif /phpBB/images/smiles/icon_wink.gif

DStahl
2001-Nov-10, 06:23 AM
Warning! Material that is not mathematically rigorous follows!

Why does the twin moving at .7 c (209,854,720 km/sec) experience 'slow time' relative to the homebody twin? Let's imagine the traveller turning on her ship's headlights. Now the photons from the lights must travel at the same rate as viewed by both the homebody and the traveller. During one second of the homebody's time, photons from the headlight travel 299,792,458 km, and the ship travels 209,854,720 km. So from the perspective of the homebody, only 89,937,738 km seperates the photon emitted from the headlight and the ship.

So, if both twins measured time the same, the the traveller would see light moving at only 89,937,738 km/sec, or a bit less than a third of the speed of light! This will not do, cries the Universe. In order to balance the books, the Universe slows the traveller's time so that it takes a bit more than three times as long for the traveller's clock to tick as for the homebody's clock. Voila! Now, during the 'long second' of the traveller, a photon from her headlights has the time to travel a proper 299,792,458 km.

The Universe rejoices. The homebody applies wrinkle-creme and worries about grey hairs, whilst the traveller wishes she were old enough to get a driver's license.

If that is not clear as mud, then my name is not DStahl.

BIG FAT CAVEAT, added later: The above is not the way velocities are actually figured in relativistic situations. I just used simple arithmetic to make the point that the traveller's time must dilate with respect to the homebody's in order to preserve the speed of light in her reference frame. Do not use this math on your final exam. The professor will not be amused.

<font size=-1>[ This Message was edited by: DStahl on 2001-11-11 11:21 ]</font>

2001-Nov-10, 10:29 AM
On 2001-11-09 10:31, Wally wrote:
Don't do it HUb'!!! You'll end up seeing the back of your own head as you regress back thru time to a point where you're nothing but a fetus floating quietly thru space.

I'd hate to see that happen. . . /phpBB/images/smiles/icon_biggrin.gif /phpBB/images/smiles/icon_wink.gif
4:03 A.M. TO Late: I already tried it
I get two versions on my pic.pic
1. {I call the Time Tunnel} ({[]}) smaller & smaller
with a time delay at each increment
2: {I call it the Space Pace} [.].].] wher its Blue shifted ?

Garrette
2001-Nov-10, 11:18 AM
I must admit, DStahl, that you have the most consistently accessible and informative explanations. I can't comment on the technical accuracy of your stuff, but if I was taking astronomy at school, I feel I could learn from you. G'job.

David Hall
2001-Nov-10, 12:27 PM
On 2001-11-09 08:38, Mr. X wrote:
Okay, twins.

It's been explained before, but the idea of twins seems to be confusing people.

Ok, if twins aren't good enough, then let's use clones instead. You can have as many of them as you like, as long as they were all produced at the same time. /phpBB/images/smiles/icon_biggrin.gif /phpBB/images/smiles/icon_biggrin.gif /phpBB/images/smiles/icon_biggrin.gif

Hat Monster
2001-Nov-10, 09:20 PM
Yep, light in a vacuum has got to travel at exactly c. The Universe will bend and break laws as it sees fit, as long as that prime directive is upheld.
So if my rocket is travelling at c/2 and i measure the speed of photons coming to me from my destination I will not measure 3c/2 like Newtonian dynamics says I would. The Universe holds it's arms up in disgust and sayeth "Thou shalt see'th slower time!" and so since my seconds become longer, then I measure the photons coming towards me at exactly c.
So if I travelled at light speed, then time for me would have to stop so that I could measure photons hitting me at light speed. Interesting.

Mr. Wree
2001-Nov-11, 12:18 AM
<<...The Universe will bend and break laws as it sees fit, as long as that prime directive is upheld...>>

And that characterization, advocating any other dissimilar (even a personally prefered) point of view on how the Universe operates, itself isn't an attempted prime directive? And one with considerably less empirical evidence to support it.

It's not to say you're certainly wrong, just certainly lacking in proffered supporting evidence for your particular hypothesis.

GrapesOfWrath
2001-Nov-11, 06:36 PM

Mr. X
2001-Nov-11, 07:48 PM
If that is not clear as mud, then my name is not DStahl.

I hate nitpicking! /phpBB/images/smiles/icon_biggrin.gif

<font size=-1>[ This Message was edited by: Mr. X on 2001-11-11 14:48 ]</font>

DStahl
2001-Nov-12, 06:37 PM
Mr. X:

Oh do not misrepresent us any more misrepresentations! You do so like nitpicking. And...maybe my name is really DStahl D. DStahl, though my parents call me DeeDee. Well, it's not, but maybe in some parallel universe? *grin*

Garrette:

Thanks for the kind words. If the stuff I spout is too inaccurate or just plain wrong I hope fergawdsake that someone will speak up! There are several places on the Internet where one can find the proper formulae for adding velocities and figuring time dilation in relativistic situations. It's not obscenely difficult to do, either.

<font size=-1>[ This Message was edited by: DStahl on 2001-11-12 13:44 ]</font>

SeanF
2001-Nov-12, 07:07 PM
DStahl (if that is your real name),

You're description is slightly misleading . . .

What about when the traveller turns on her taillights? All observers need to see that light moving at the same velocity as well, no?

A stationary observer says that after one second, the headlight light has moved 299,792,458 km; the taillight light has moved 299,792,458 km; and the ship has moved 209,854,720 km. Therefore the headlight light is only 89,937,738 km away from the ship, as you stated, but the taillight light is 509,647,178 km away!

So, how does the traveller explain the fact that one photon has traveled more than five times as far in the same amount of time?

(BTW, I do know the answer to this, but it's something for you and others to think about . . .) /phpBB/images/smiles/icon_wink.gif

Mr. X
2001-Nov-13, 12:04 AM
On 2001-11-12 13:37, DStahl wrote:
Mr. X:
Oh do not misrepresent us any more misrepresentations! You do so like nitpicking. And...maybe my name is really DStahl D. DStahl, though my parents call me DeeDee. Well, it's not, but maybe in some parallel universe? *grin*

I objectionationate...nation...ate...
I objectionationatenationate!
I demand you provide proof to dismiss my wild suppositionitions and accusationations! /phpBB/images/smiles/icon_biggrin.gif
At which point I will proceed and do some more!

DStahl
2001-Nov-13, 09:24 PM
SeanF: //So, how does the traveller explain the fact that one photon has traveled more than five times as far in the same amount of time?//

Tail lights! Why did I never bother to think of that? Well, you're simple question forces me to think hard--which reveals my fundamental understanding of relativity to be shallow to begin with, my thinking to be sloppy and weak...or both!

Thanks for pointing out that my explanation was incomplete. I, er, really appreciate it. *sighs, scratches head*

Mr. X
2001-Nov-13, 11:08 PM
On 2001-11-13 16:24, DStahl wrote:
Tail lights! Why did I never bother to think of that? Well, you're simple question forces me to think hard--which reveals my fundamental understanding of relativity to be shallow to begin with, my thinking to be sloppy and weak...or both!

Thanks for pointing out that my explanation was incomplete. I, er, really appreciate it. *sighs, scratches head*

Geez, DStahl! You have lots of problems! I'm just glad I am not you right now! /phpBB/images/smiles/icon_biggrin.gif

2001-Nov-16, 09:05 PM
:-| In a 1922 book, Einstein defined
a stationary frame as one where the laws of physics are simplest. An inertial frame is one where all the observers are moving at a constant velocity (speed and direction) in the stationary frame. Not every frame is an inertial frame. An accelerating frame is one where the laws of physics are more complicated than in an inertial frame.
The law of reciprocity states that the physical laws are the same in all inertial frames. The law of reciprocity is the most important postulate of special relativity. However, it does not apply to accelerated frames.

On 2001-11-09 02:10, Silmatan wrote:
Ok, according to relativity, if one twin stays on earth while the other one goes on a trip really fast, the one who went on the trip will not have aged as much as the one who stayed home. But, relative to the person taking the trip, isn't that one standing still while the one at home is moving?
No! Einstein did not say that "the one taking the trip is moving." He said that an observer in one inertial frame sees the system in another inertial frame slow down. This applies as long as the "one taking the trip" is in an inertial frame. For example, Newton's third law applies to everything on the ship, and that is as simple as one could get. For every reaction force on one body, there is a reaction force on another body.
Pretend that the one taking the trip thinks that he isn't moving. The one taking the trip has to turn around. During the interval when he turns around, the laws of physics grow more complicated. For example, the observer feels an action force ((weight pushing him down) but no reaction force (a large mass exerting gravitational pull). Of course, someone actually standing still would see the third law still applied, that the "reaction force" is the thrust of the rockets. The rule that an observer in one inertial frame sees the system in another inertial frame "slow down time" does not apply. In fact, he would see his earth bound twin speed up in time.

Why is it that time "slows down" for the one on the trip when spacetime isn't supposed to make the distinction between a fast rocket and stationary planet and a stationary rocket and fast planet?
Space time does have a distinction between an a rocket under thrust and a stationary planet. The thrust is a force. The law of reciprocity, and all derived from it, only applies to observers on whom no force is applied.

Although there are variations where forces are not involved (e.g., the ships passing problem), all of them can be resolved using the definition of inertial frame.

The law of reciprocity states that all inertial frames have the same physical laws, which are simpler than frames where the observer accelerates. The time dilation formula was derived using the law of reciprocity. Therefore, the time dilation formula does not apply to observers that are accelerating, where accelerating here means being under the influence of a force.

<font size=-1>[ This Message was edited by: Rosen1 on 2001-11-16 16:10 ]</font>

<font size=-1>[ This Message was edited by: Rosen1 on 2001-11-16 16:12 ]</font>

Hat Monster
2001-Nov-17, 08:45 PM
What about when the traveller turns on her taillights? All observers need to see that light moving at the same velocity as well, no?

Tell me, how can one deduce a velocity as you are assuming?
It cannot be done. Redshift.
Galaxies (pick one) are receding at very high speeds, but they're not superluminal.

SeanF
2001-Nov-18, 01:52 AM
On 2001-11-17 15:45, Hat Monster wrote:

What about when the traveller turns on her taillights? All observers need to see that light moving at the same velocity as well, no?

Tell me, how can one deduce a velocity as you are assuming?
It cannot be done. Redshift.
Galaxies (pick one) are receding at very high speeds, but they're not superluminal.

Um, you lost me . . . how can one deduce what velocity?

(BTW, apparently there are very distant galaxies which are receding superluminally -- we've been discussing that in another thread (http://www.badastronomy.com/phpBB/viewtopic.php?topic=153&forum=2&14))

2001-Nov-19, 12:56 PM
All observers need to see that light moving at the same velocity as well, no?
No. An accelerating observer does not have to see light travel at the same speed all over the universe. The constant speed of light applies only to an inertial frame. However, that only applies when the travelor changes direction.

A stationary observer says that after one second, the headlight light has moved 299,792,458 km; the taillight light has moved 299,792,458 km; and the ship has moved 209,854,720 km. Therefore the headlight light is only 89,937,738 km away from the ship, as you stated, but the taillight light is 509,647,178 km away!
Only if the stationary observer observes both headlight and taillight go on at the same time. If they go on at different times, your numbers are wrong.
Of course, the stationary observer did not turn on either headlight or taillight. He can only deduce the simultaneity of the lights turning on by indirect measurements, using instruments calibrated for inertial frames.

So, how does the traveller explain the fact that one photon has traveled more than five times as far in the same amount of time?
The traveler believes that he turned on the tail lights before he turned on the headlights. The taillight light had a longer period to travel than the headlight light. This assumes that the travelor is not changing his velocity. He is not at turn around. The situation at turn around is more complicated.
The situation without acceleration is easy. The stationary observer saw the two lights go on at the same time, although the travelor thought that he had turned on the lights at different times.
Since the travelor turned the lights on, one can say that his observation is more direct than the stationary observer. Or as we physicists say, his time measurements are proper. Hey, maybe that is why they call it proper time|:-o

(BTW, I do know the answer to this, but it's something for you and others to think about . . .) /phpBB/images/smiles/icon_wink.gif

Did I get it right? |:-)

<font size=-1>[ This Message was edited by: Rosen1 on 2001-11-19 08:08 ]</font>

SeanF
2001-Nov-19, 01:34 PM
On 2001-11-19 07:56, Rosen1 wrote:

All observers need to see that light moving at the same velocity as well, no?
No. An accelerating observer does not have to see light travel at the same speed all over the universe. The constant speed of light applies only to an inertial frame. However, that only applies when the travelor changes direction.

Quite right. I really should have said "both observers," since I was just thinking of the two in this particular experiment, neither of whom is accelerating.

A stationary observer says that after one second, the headlight light has moved 299,792,458 km; the taillight light has moved 299,792,458 km; and the ship has moved 209,854,720 km. Therefore the headlight light is only 89,937,738 km away from the ship, as you stated, but the taillight light is 509,647,178 km away!
Only if the stationary observer observes both headlight and taillight go on at the same time. If they go on at different times, your numbers are wrong.
Of course, the stationary observer did not turn on either headlight or taillight. He can only deduce the simultaneity of the lights turning on by indirect measurements, using instruments calibrated for inertial frames.

This, of course, is true, and having separate headlights and taillights does complicate the issue.

Of course, if there were a single open light bulb located on top of the ship, both observers would agree that the light from that bulb began moving forward and backward at the same time, but the question of how far the light travels in how much time still remains.

So, how does the traveller explain the fact that one photon has traveled more than five times as far in the same amount of time?
The traveler believes that he turned on the tail lights before he turned on the headlights. The taillight light had a longer period to travel than the headlight light. This assumes that the travelor is not changing his velocity. He is not at turn around. The situation at turn around is more complicated.
The situation without acceleration is easy. The stationary observer saw the two lights go on at the same time, although the travelor thought that he had turned on the lights at different times.
Since the travelor turned the lights on, one can say that his observation is more direct than the stationary observer. Or as we physicists say, his time measurements are proper. Hey, maybe that is why they call it proper time|:-o

(BTW, I do know the answer to this, but it's something for you and others to think about . . .) /phpBB/images/smiles/icon_wink.gif

Did I get it right? |:-)

Yep, for the most part, but there would still be a problem with a single bulb, in which case there would be no disagreement about the simultaneity of the light(s) coming on.

Think about two stationary light sensors located 599,584,916 km apart along the travellers flight path. The traveller turns on that single bulb at the moment the ship is located exactly half-way between the two sensors (299,792,458 km from each sensor). Consider when each observer would see (or should see) the two sensors get hit by the light -- would it be one second later?

BTW, when I say "see the two sensors get hit," I'm not worried about the time it would take for the light of that event to get from the sensors back to the observer. Just figure how long until the light hits the sensors . . .

/phpBB/images/smiles/icon_smile.gif

2001-Nov-19, 02:01 PM
Of course, if there were a single open light bulb located on top of the ship, both observers would agree that the light from that bulb began moving forward and backward at the same time, but the question of how far the light travels in how much time still remains.

OOOPPPPSSSS!!!! Well, I still think that this is a an explanation for the situation where there is only one sensor and two bulbs far apart. However, this is a approximation. Let me try for the other approximation: only one light source and two sensors far apart.

Yep, for the most part, but there would still be a problem with a single bulb, in which case there would be no disagreement about the simultaneity of the light(s) coming on.

Alas, yes /phpBB/images/smiles/icon_frown.gif

Think about two stationary light sensors located 599,584,916 km apart along the travellers flight path. The traveller turns on that single bulb at the moment the ship is located exactly half-way between the two sensors (299,792,458 km from each sensor). Consider when each observer would see (or should see) the two sensors get hit by the light -- would it be one second later?

However, the stationary observer has to use a different pair of sensors than the traveler. That is why each inertial frame is called a "frame." The sensors are not moving relative to the observer.
The pair of sensors used by the traveler are moving at a nonzero velocity relative to the pair of sensors used by the stationary observer.
The clocks on the travelers pair were offset in time relative to the stationary observers pair by an amount equivalent to the "vx/c^2" term. Instead of "x" being the distance between bulbs, now x is the distance between sensors.

BTW, when I say "see the two sensors get hit," I'm not worried about the time it would take for the light of that event to get from the sensors back to the observer. Just figure how long until the light hits the sensors . . .
In both extreme cases (bulbs a long distance away and one bulb), the paradox is resolved by the difficulty in establishing that simultaneity between events occurring at distant points.
I think that some explanation is needed as to why the one bulb, one sensor experiment is not an option. It is not an option because such an experiment can not establish the simultaneity of any events at different points due to the existence of a minumum propagation speed in forces.

Do I get my NO PRIZE now?

Russ
2001-Nov-20, 04:14 PM
Just to muddy up the waters a little /phpBB/images/smiles/icon_lol.gif I will throw in the fact that tail lights are red and if they are on a vehicle that is traveling away from the inertial frame at a large fraction of the speed of light, the observer in said frame will not be able to see them. This is because the light from them will be red shifted and the frequency of said light will be too low for the observer to see without IR sensitive equipment.

I suggest for this discussion that the red tail lights be replaced with blue or UV lights so that the observer can see the red shifted light without expensive IR equipment.
/phpBB/images/smiles/icon_smile.gif /phpBB/images/smiles/icon_lol.gif

_________________
"She made the Kessel run in less than three parsecs." Han Solo

<font size=-1>[ This Message was edited by: Russ on 2001-11-20 11:20 ]</font>