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Normandy6644
2004-Jan-31, 04:38 PM
Ok, I'm starting this up because it seems that a lot of people (myself certainly included) want to know more about relativity and understand it better. This thread is absolutely NOT the place to debate relativity, it is only to discuss the theory as it currently stands and to ask questions to clarify any misconceptions or misunderstandings you may have. I think a lot of us learned new things in the "other threads," but we learned them in the wrong way and setting. So from now on anyone who has relativity questions, let's post them here and talk about them in a civilized and intellectual manner. :D

Glom
2004-Jan-31, 05:12 PM
Oh please Thor! Not again!

tuffel999
2004-Jan-31, 05:48 PM
"When you are courting a nice girl an hour seems like a second. When you sit on a red-hot cinder a second seems like an hour. That's relativity."



Ok someone had too.

Eroica
2004-Jan-31, 05:50 PM
I'd be grateful if someone could explain Einstein's mathematics in §3 of his 1905 paper. He's deriving the Lorentz transformation equations, but goes about it in a very obtuse way. Then, in a footnote halfway through his explanation, he writes:

The equations of the Lorentz transformation may be more simply derived directly from the condition that [the speed of light should be the same in all inertial frames]
That, indeed, is how I derived them when I first studied relativity. But, still, I would like to know what Einstein is doing in this section.

On the Electrodynamics of Moving Bodies (http://www.fourmilab.ch/etexts/einstein/specrel/www/)

tuffel999
2004-Jan-31, 05:54 PM
I'd be grateful if someone could explain Einstein's mathematics in §3 of his 1905 paper. He's deriving the Lorentz transformation equations, but goes about it in a very obtuse way. Then, in a footnote halfway through his explanation, he writes:

The equations of the Lorentz transformation may be more simply derived directly from the condition that [the speed of light should be the same in all inertial frames]
That, indeed, is how I derived them when I first studied relativity. But, still, I would like to know what Einstein is doing in this section.

On the Electrodynamics of Moving Bodies (http://www.fourmilab.ch/etexts/einstein/specrel/www/)

"We can't solve problems by using the same kind of thinking we used when we created them."


Sorry again but man did he bank some good quotes for his own work! :lol:

milli360
2004-Jan-31, 07:54 PM
"We can't solve problems by using the same kind of thinking we used when we created them."
Einstein wasn't creating the problem then, though.


Sorry again but man did he bank some good quotes for his own work!
Is he the same guy who said, when all you have is a hammer, all your problems look like nails?

tuffel999
2004-Jan-31, 08:02 PM
"We can't solve problems by using the same kind of thinking we used when we created them."
Einstein wasn't creating the problem then, though.


Sorry again but man did he bank some good quotes for his own work!
Is he the same guy who said, when all you have is a hammer, all your problems look like nails?

I will look that up since I am not sure but I know he said:

"If A is a success in life, then A equals x plus y plus z. Work is x; y is play; and z is keeping your mouth shut."

and

"Two things are infinite: the universe and human stupidity; and I'm not sure about the the universe."

SeanF
2004-Feb-02, 07:33 PM
I'd be grateful if someone could explain Einstein's mathematics in §3 of his 1905 paper. He's deriving the Lorentz transformation equations, but goes about it in a very obtuse way. Then, in a footnote halfway through his explanation, he writes:

The equations of the Lorentz transformation may be more simply derived directly from the condition that [the speed of light should be the same in all inertial frames]
That, indeed, is how I derived them when I first studied relativity. But, still, I would like to know what Einstein is doing in this section.

On the Electrodynamics of Moving Bodies (http://www.fourmilab.ch/etexts/einstein/specrel/www/)

That's kind of an open-ended question. How about this, you start going through §3, and as soon as you get to a step where you're not sure what he's doing (or why he's doing it), ask about it specifically. :)

milli360
2004-Feb-02, 07:59 PM
I'd be grateful if someone could explain Einstein's mathematics in §3 of his 1905 paper. He's deriving the Lorentz transformation equations, but goes about it in a very obtuse way. Then, in a footnote halfway through his explanation, he writes:

The equations of the Lorentz transformation may be more simply derived directly from the condition that [the speed of light should be the same in all inertial frames]
That, indeed, is how I derived them when I first studied relativity. But, still, I would like to know what Einstein is doing in this section.

On the Electrodynamics of Moving Bodies (http://www.fourmilab.ch/etexts/einstein/specrel/www/)

That's kind of an open-ended question. How about this, you start going through §3, and as soon as you get to a step where you're not sure what he's doing (or why he's doing it), ask about it specifically. :)
Eroica left part of the quote out.

Right before the part that Eroica paraphrased as "[the speed of light should be the same in all inertial frames]" should be the phrase " in virtue of those equations". I'll agree the rest of the footnote can be paraphrased that way, but it should be preceded by the "in virtue..." part.

That changes the meaning from what Eroica implied. Instead of proving that the Lorentz equations derive from the constancy of the speed of light, the footnote seems to be talking about assuming the Lorentz equations and deriving that the speed of light is constant.

Eroica
2004-Feb-03, 12:12 PM
you start going through §3, and as soon as you get to a step where you're not sure what he's doing (or why he's doing it), ask about it specifically. :)
OK. I'm referring to the bit of mathematics that follows these words (sorry I can't post the equations themselves):

or, by inserting the arguments of the function T and applying the principle of the constancy of the velocity of light in the stationary system:−
Thanks for the response. 8)

Eroica
2004-Feb-03, 12:27 PM
Right before the part that Eroica paraphrased as "[the speed of light should be the same in all inertial frames]" should be the phrase " in virtue of those equations". I'll agree the rest of the footnote can be paraphrased that way, but it should be preceded by the "in virtue..." part.

That changes the meaning from what Eroica implied. Instead of proving that the Lorentz equations derive from the constancy of the speed of light, the footnote seems to be talking about assuming the Lorentz equations and deriving that the speed of light is constant. [emphasis added]

:-k Hmmm... I'm not so sure.

The equations of the Lorentz transformation may be more simply deduced directly from the condition that in virtue of those equations the relation x²+y²+z²=c²t² shall have as its consequence the second relation ξ²+η²+ζ²=c²t².
deduced, not assumed!

milli360
2004-Feb-03, 03:28 PM
Hmmm... I'm not so sure.
You did leave something out.



The equations of the Lorentz transformation may be more simply deduced directly from the condition that in virtue of those equations the relation x²+y²+z²=c²t² shall have as its consequence the second relation ξ²+η²+ζ²=c²t².
deduced, not assumed!
Right. Let's break it down.

A=The equations of the Lorentz transformation
B=The condition

So, he's saying A may be deduced from B

What is B?

B=that in virtue of those equations the relation x²+y²+z²=c²t² shall have as its consequence the second relation ξ²+η²+ζ²=c²t²

What does that mean? "in wirtue of" means "On the grounds or basis of; by reason of" so if

C=those equations (clearly referring to the Lorentz equations)
D=the relation x²+y²+z²=c²t²
E=the second relation ξ²+η²+ζ²=c²t²

Then
B= C -> (D -> E)

Or since C=A,
(A -> (D -> E)) -> A

Physicists, what do they know about logic? What was meant in the original German, I'm not sure. :)

Eroica
2004-Feb-03, 04:11 PM
What was meant in the original German, I'm not sure. :)
Are you sure the footnote is Einstein's, and not an editorial comment by the translator? It's not in the original German.
Zur Elektrodynamik bewegter Körper (http://www.wiley-vch.de/berlin/journals/adp/historic.html)

Eroica
2004-Feb-03, 04:16 PM
(A -> (D -> E)) -> A
You're not seriously suggesting that the above constitutes a valid deduction of A? :-?

SeanF
2004-Feb-03, 05:12 PM
you start going through §3, and as soon as you get to a step where you're not sure what he's doing (or why he's doing it), ask about it specifically. :)
OK. I'm referring to the bit of mathematics that follows these words (sorry I can't post the equations themselves):

or, by inserting the arguments of the function T and applying the principle of the constancy of the velocity of light in the stationary system:−
Okay, this section is kind of confusing. :) Let's start with this sentence:


If we place x'=x-vt, it is clear that a point at rest in the system k must have a system of values x', y, z, independent of time.

Okay, k is the moving system, with a velocity of v "in the direction of the increasing x of the other" system (K). A point in space that is stationary in k will be moving along the x-axis in K, right? In a duration of time t (as measured in K), that k-stationary point will move a distance of vt along K's x-axis. So, if we set x'=x-vt, then putting in the x and t coordinates of that moving point will give us a constant x'. Boy, I don't know if I'm explaining that very well. :-?

Anyhoo, next we have:


We first define τ as a function of x', y, z, and t. To do this we have to express in equations that τ is nothing else than the summary of the data of clocks at rest in system k, which have been synchronized according to the rule given in § 1.

So, he says that given the coordinates of the event in K (and converting the variable x coordinate to a constant x'), we can calculate the time τ of the event in k. We don't know yet what the actual equation is to calculate τ from those coordinates, but there is one.


From the origin of system k let a ray be emitted at the time τ0 along the X-axis to x', and at the time τ1 be reflected thence to the origin of the co-ordinates, arriving there at the time τ2; we then must have ½(τ0+τ2)=τ1...

This comes from the definition of simultaneity earlier in the paper. Since these times are in the k system, where the emission/reception occurs at a stationary point, then the time out and the time back should be equal. Thus, the reflection time (τ1) should be exactly halfway between the emission time (τ0) and the reception time (τ2).


...or, by inserting the arguments of the function τ and applying the principle of the constancy of the velocity of light in the stationary system:-- ½[τ(0,0,0,t)+τ(0,0,0,t+x'/(c-v)+x'/(c+v))=τ(x',0,0,t+x'/(c-v))

This is just the same previous equation ½(τ0+τ2)=τ1, but with the variables τ0, τ1, and τ2 replaced with the "function(s) of x', y, z, and t" that we decided must exist at the beginning.

The coordinates for τ0 would be (0,0,0,t) {t is the time the signal was emitted as measured in K}
The coordinates for τ1 would be (x',0,0,t+x'/(c-v)) {x' is the converted x coordinate where the reflection occurs. x'/(c-v) is the duration of time the trip would take - adding it to t gives the time of reflection}
The coordinates for τ2 would be (0,0,0,t+x'/(c-v)+x'/(c+v))
{x'/(c-v) is the duration of the outbound trip and x'/(c+v) is the duration of the inbound trip - adding them both to t gives the time of reception}


Thanks for the response. 8)

You're welcome! I hope I'm helping!

milli360
2004-Feb-03, 06:23 PM
What was meant in the original German, I'm not sure. :)
Are you sure the footnote is Einstein's, and not an editorial comment by the translator? It's not in the original German.
Zur Elektrodynamik bewegter Körper (http://www.wiley-vch.de/berlin/journals/adp/historic.html)
That version says, at the bottom "Numbered footnotes are as they appeared in the 1923 edition"

That is, it was taken from the English translation in the volume The Principle of Relativity, which was published in 1923.


(A -> (D -> E)) -> A
You're not seriously suggesting that the above constitutes a valid deduction of A? :-?
Hence the reason I followed it with "Physicists, what do they know about logic? " :)

Deductions don't have to be logical.

Eroica
2004-Feb-03, 08:10 PM
I hope I'm helping!
So far, so good. :D I appreciate the help. (Actually, I already understood this bit. It's the next few steps that have me stumped!)

milli360
2004-Feb-03, 08:43 PM
I hope I'm helping!
So far, so good. :D I appreciate the help. (Actually, I already understood this bit. It's the next few steps that have me stumped!)
I need a little more clarification. What did you mean, "That, indeed, is how I derived them when I first studied relativity. (http://www.badastronomy.com/phpBB/viewtopic.php?p=201302#201302)", now that we've parsed it?

Eroica
2004-Feb-04, 09:14 AM
What did you mean, "That, indeed, is how I derived them when I first studied relativity. (http://www.badastronomy.com/phpBB/viewtopic.php?p=201302#201302)", now that we've parsed it?
Consider a thought experiment identical to the one Einstein describes in §3 of the 1905 paper, but in which the "mirror" which reflects observer k's light signal is at spatial co-ordinates (0,d,0) - that is, it's d units above the moving observer, at right angles to the direction in which he's moving.

From his perspective the light signal moves vertically up to the mirror, is reflected, and moves vertically back down to him - a round trip of 2d units. The time for the round trip by his clock we will call Δť. Since the speed of light is c:

cΔť = 2d ..... Equation 1

Now let's look at the same events from the point of view of the stationary K observer.

During the light signal's round trip, his clock registers a time of Δt. In this interval, the k observer moves a distance of vΔt. This means that the light signal does not move vertically up and down, but diagonally along the arms of a lambda-shape: Λ

By simple geometry, l, the length of one of these arms, is:

l = √[d²+(½uΔt)²]

Since the speed of light is the same for both observers (the condition that footnote is referring to):

cΔt = 2l

=> cΔt = 2√[d²+(½uΔt)²] ..... Equation 2

Solving Equation 1 for d, we get:

d = ½cΔť

Substituting this in Equation 2, we get:

cΔt = 2√[(½cΔť)² +(½uΔt)²]

Solving this for Δt, we get:

Δt = Δť/√[1-(u²/c²)]

This is the time-dilation factor. A similar thought experiment (which I won't rehearse), in which the light pulse is emitted horizontally in the same direction as k's motion, allows us to derive the Fitzgerald-Lorentz-contraction equation:

l = ľ√[1 - (u²/c²)]

It's fairly easy to derive the Lorentz transformation equations once you are equipped with these two relations.

Diamond
2004-Feb-04, 09:21 AM
What did you mean, "That, indeed, is how I derived them when I first studied relativity. (http://www.badastronomy.com/phpBB/viewtopic.php?p=201302#201302)", now that we've parsed it?
Consider a thought experiment identical to the one Einstein describes in §3 of the 1905 paper, but in which the "mirror" which reflects observer k's light signal is at spatial co-ordinates (0,d,0) - that is, it's d units above the moving observer, at right angles to the direction in which he's moving.

From his perspective the light signal moves vertically up to the mirror, is reflected, and moves vertically back down to him - a round trip of 2d units. The time for the round trip by his clock we will call Δť. Since the speed of light is c:

cΔť = 2d ..... Equation 1

Now let's look at the same events from the point of view of the stationary K observer.

During the light signal's round trip, his clock registers a time of Δt. In this interval, the k observer moves a distance of vΔt. This means that the light signal does not move vertically up and down, but diagonally along the arms of a lambda-shape: Λ

By simple geometry, l, the length of one of these arms, is:

l = √[d²+(½uΔt)²]

Since the speed of light is the same for both observers (the condition that footnote is referring to):

cΔt = 2l

=> cΔt = 2√[d²+(½uΔt)²] ..... Equation 2

Solving Equation 1 for d, we get:

d = ½cΔť

Substituting this in Equation 2, we get:

cΔt = 2√[(½cΔť)² +(½uΔt)²]

Solving this for Δt, we get:

Δt = Δť/√[1-(u²/c²)]

This is the time-dilation factor. A similar thought experiment (which I won't rehearse), in which the light pulse is emitted horizontally in the same direction as k's motion, allows us to derive the Fitzgerald-Lorentz-contraction equation:

l = ľ√[1 - (u²/c²)]

It's fairly easy to derive the Lorentz transformation equations once you are equipped with these two relations.

=D>

A simple explanation that everyone can see! *The crowd goes wild*

Normandy6644
2004-Feb-04, 01:31 PM
I always liked that derivation. It's fairly simple and elegant. Well done!!

milli360
2004-Feb-04, 03:21 PM
What did you mean, "That, indeed, is how I derived them when I first studied relativity. (http://www.badastronomy.com/phpBB/viewtopic.php?p=201302#201302)", now that we've parsed it?
I meant, which method are you referring to, the method of Einstein's paper, or the method of the footnote, or the method you thought that the footnote referred to.

]that is, it's d units above the moving observer, at right angles to the direction in which he's moving.
So, d is a measurement in the moving observer's frame.

By simple geometry, l, the length of one of these arms, is:

l = √[d²+(½uΔt)²]

Since the speed of light is the same for both observers (the condition that footnote is referring to):

cΔt = 2l
Did you use d to compute l, a measurement in the non-moving frame?

Eroica
2004-Feb-04, 03:55 PM
I meant, which method are you referring to, the method of Einstein's paper, or the method of the footnote, or the method you thought that the footnote referred to.
Obviously the latter, since I don't understand the method Einstein uses.

Incidentally, you still haven't convinced me that there is any difference between the other two (the method of the footnote and the method I think the footnote is referring to). 8)

Eroica
2004-Feb-04, 03:58 PM
Did you use d to compute l, a measurement in the non-moving frame?
Yes. d is at right angles to the moving observer's motion. Both observer's velocity in that direction is zero, so why should lengths in that direction be different in the two frames?

milli360
2004-Feb-04, 04:30 PM
Incidentally, you still haven't convinced me that there is any difference between the other two (the method of the footnote and the method I think the footnote is referring to).
I'm still not exactly sure which method you think the footnote is referring to. :)

But it appears (to me :) ) to be that one assumes the constancy of the speed of light, and derives the Lorentz equations from that.


Did you use d to compute l, a measurement in the non-moving frame?
Yes. d is at right angles to the moving observer's motion. Both observer's velocity in that direction is zero, so why should lengths in that direction be different in the two frames?
So, you're assuming the contraction is zero?

Eroica
2004-Feb-04, 05:41 PM
So, you're assuming the contraction is zero?
Are you suggesting that the standard physics textbooks are mistaken? The derivation I gave is an accepted one. :-k

Eroica
2004-Feb-04, 05:45 PM
I'm still not exactly sure which method you think the footnote is referring to. :)

But it appears (to me :) ) to be that one assumes the constancy of the speed of light, and derives the Lorentz equations from that.

That's my reading of the footnote, too.

Eroica
2004-Feb-04, 05:49 PM
Einstein has yet another method of deriving the Lorentz Transforms in an appendix to his 1920 Book, Relativity: The Special and General Theory.

Simple Derivation of the Lorentz Transformation (http://www.bartleby.com/173/a1.html)

In this, he considers a light signal which is travelling along the x-axis only, so he avoids the problem you raise.

milli360
2004-Feb-04, 06:13 PM
I'm still not exactly sure which method you think the footnote is referring to. :)

But it appears (to me :) ) to be that one assumes the constancy of the speed of light, and derives the Lorentz equations from that.

That's my reading of the footnote, too.
No, I was asking if that was your reading. I disagree about that, for the reasons given above. It's possible--I'll have to look into it--that Einstein's paper is avoiding the problem that I brought up, and that's what makes it more complicated. He was a very careful guy. :)

PS: I looked at that link Simple Derivation of the Lorentz Transformation (http://www.bartleby.com/173/a1.html), and the first part (most of the page) is concerned with movement along the x-axis, with the light propagating along the x-axis as well. Isn't that different from your method, where the light goes off axis?

Eroica
2004-Feb-04, 09:57 PM
I looked at that link Simple Derivation of the Lorentz Transformation (http://www.bartleby.com/173/a1.html), and the first part (most of the page) is concerned with movement along the x-axis, with the light propagating along the x-axis as well. Isn't that different from your method, where the light goes off axis?
Yes. That was why I brought it up - as an alternative (and still fairly easy) way to derive the transforms that obviates your objection.

milli360
2004-Feb-04, 10:08 PM
Errp. That's what you said. My bad. I'll look into it.

Lorcan Faol
2004-Feb-05, 04:26 AM
I have a question about relativity....
I am relatively new to physics, when compared with most of you. I've been reading about relativity and light lately, and although many questions popped into my head while reading this, one of the more important ones was: HOW do physicists determine the speed of light, and the fact that its relative speed never changes? Since we can't travel at the speed of light, or even remotely close, it confuses me how it is established that no matter how fast you can go, the speed of light still appears to go 670 million mi/h.
Probably a dumb question, especially compared to most of the much more interesting questions I see asked on here, but I just don't understand it - yet.

Sam5
2004-Feb-05, 05:28 AM
I have a question about relativity....
I am relatively new to physics, when compared with most of you. I've been reading about relativity and light lately, and although many questions popped into my head while reading this, one of the more important ones was: HOW do physicists determine the speed of light, and the fact that its relative speed never changes? Since we can't travel at the speed of light, or even remotely close, it confuses me how it is established that no matter how fast you can go, the speed of light still appears to go 670 million mi/h.
Probably a dumb question, especially compared to most of the much more interesting questions I see asked on here, but I just don't understand it - yet.

This is generally based on Einstein’s deduction in 1911 that the “tick rates” of atomic clocks tend to follow the speed rate changes of light. Such as inside a gravity field, the tick rates of atomic clocks slow down as the speed of light slows down in the same gravity field, so atomic clocks in a gravity field will generally measure “c” for the velocity of light at the clock that is used to measure the light speed at that place. An atomic clock slows down and the light slows down and that works out to a “c” measurement for the speed of light at that clock.

Shapiro demonstrated in the early 1960s that light and radio waves sLow down when they pass near the sun and through the sun’s gravitational field, when we use an earth-based clock to measure the time-lag caused by the delay. So the speed of light is not “constant” everywhere in space.

”In 1964, based on Einstein’s theory of general relativity, Shapiro predicted that light rays would be slowed by their passage through the “curved space” around a body such as the sun. Over the next decade, he and his colleagues tested this idea using radar ranging both to planets and spacecraft. And indeed, they found that the sun’s gravity added about 200 microseconds (0.00002 seconds) to the round-trip travel time of a radio signal passing near the edge of the sun.”

www.si.edu/opa/insideresearch/9892/saoside.htm+shapiro+time+delay&hl=en&ie=UTF-8]LIGHT (http://216.239.57.104/search?q=cache:ppbUNAb4k00J:[url) SPEED SLOWS DOWN IN A STRONG GRAVITY FIELD[/url]

Eroica
2004-Feb-05, 08:40 AM
HOW do physicists determine the speed of light, and the fact that its relative speed never changes?
A formula for the speed of light may be deduced from two of Maxwell's Four Laws - Faraday's Law and Ampère's Law, both of which were first arrived at by experimentation.

c = 1/√[εμ]

where ε and μ are universal constants (the permittivity and permeability of free space).

Diamond
2004-Feb-05, 09:06 AM
I have a question about relativity....
I am relatively new to physics, when compared with most of you. I've been reading about relativity and light lately, and although many questions popped into my head while reading this, one of the more important ones was: HOW do physicists determine the speed of light, and the fact that its relative speed never changes? Since we can't travel at the speed of light, or even remotely close, it confuses me how it is established that no matter how fast you can go, the speed of light still appears to go 670 million mi/h.
Probably a dumb question, especially compared to most of the much more interesting questions I see asked on here, but I just don't understand it - yet.

Like Eroica says, the speed of light can be determined experimentally from Maxwell's equation for the speed of electromagnetic waves, which as Einstein pointed out, contains no term for the frame of reference of either source or observer.

There are many ways to measure the speed of light. When I was at college, we measured the speed of light using an 8-sided mirror rotating on what was basically an electric drill.

Recent checks (and this happens all the time, despite what some crackpots may say) show that the speed of light really is constant for all inertial observers regardless of their relative motion to the source. See http://www.space.com/scienceastronomy/lightspeed_031217.html

PS Try to ignore Sam5. He's our resident anti-relativity poster.

Sam5
2004-Feb-05, 02:58 PM
Since we can't travel at the speed of light, or even remotely close, it confuses me how it is established that no matter how fast you can go, the speed of light still appears to go 670 million mi/h.
Probably a dumb question,

That’s a very intelligent question.

The link I gave you is from the Smithsonian Institution website. Here is one from an Australian news service:

“In 1964, Shapiro followed on from Einstein's work, and predicted that strong gravitational fields would cause time itself to slow down in a beam of light, or radio waves. For example, a light or radio wave just kissing the edge of the Sun's disc would have to pass through the Sun's strong gravitational field. Shapiro worked out that the Sun's gravity should slow down a beam of radio waves by about 200 microseconds - and this has been measured, and once again, Einstein's Theory has been proven correct.”

LINK (http://216.239.53.104/search?q=cache:kXEibLgnzZ0J:www.abc.net.au/science/k2/moments/gmis9736.htm+shapiro+light+slows+down&hl=en&ie=UTF-8)

Light speed shows down when it passes through a strong gravity field. Sometimes this is expressed as “time slowing down” in the gravity field. That’s because atomic clocks slow down their tick rates in a strong gravity field.

The Einstein theory this website is talking about is the General Theory. This updated and upgraded the Special Theory.

As Max Abraham said in 1912:

“Already before period of one year A. Einstein, by accepting an influence of the gravitation potential on the speed of light, gave up the postulate of the constant speed of light essential for his earlier theory 1); in a work appeared recently 2)......”

1) A. Einstein, Ann. d. Phys. 35. p 898. 1911.
2) A. Einstein. Ann. d. Phys. 38. p. 355. u. 443. 1912.

So the original “constancy” postulate of the 1905 SR paper no longer applied after 1911. You can find the full Abraham article and the Einstein articles in “The Collected Papers of Albert Einstein”. Be sure to use the paperback version since that contains the English translation. I think these specific articles are in Volume 4 of the paperback version.

What apparently happens in space is that the gravity fields regulate the speed of light here locally to “c” relative to our solar system. We can not change that speed of light through space. However, if we approach a light beam while we are traveling at “v”, then we are approaching that beam at an additive speed of “c + v”. That’s why we would see a blueshift in the light of the beam.

Some people think the original 1905 “constancy” postulate still applies, but it does not. It hasn’t applied since 1911.

As Einstein said in his 1918 paper:

“There [in GR theory], empty space in the previous sense has physical qualities, mathematically characterized by the components of the potential of gravitation that determine the metrical behavior of that portion of space as well as its gravitational field. This situation can very well be interpreted by speaking of an ether whose state varies from point to point.”

This means the gravity fields of our solar system in deep space act as a light-speed regulator and the old SR “constancy” postulate no longer applies, since light-speed slows down when the light passes near to astronomical bodies and its speed slows down in the stronger areas of the gravity fields.

I. I. Shapiro stated in his paper, “Fourth Test of Relativity”, in Physical Review Letters, 13, 26, p. 789-791, 1964:

"According to general relativity, the speed of a light wave depends on the strength of the gravitational potential along its path."

Diamond
2004-Feb-05, 03:29 PM
As I say, we have an anti-relativity poster on the board. :roll:

Normandy6644
2004-Feb-05, 05:06 PM
Sam, do NOT try to hijack this thread. As I said in the original post for this thread, this is for discussing relativity as it stands, not any quibbles with it. If you want to discuss your position, please start a new thread.

Sam5
2004-Feb-05, 05:26 PM
As I said in the original post for this thread, this is for discussing relativity as it stands, not any quibbles with it.

I think you are probably talking about Special Relativity as it stood in 1905. General Relativity superceded that, as Eddington’s 1919 photographs and Shapiro’s experiments proved. This is not “my position”, this is the standard mainstream physics position. Those experiments have been universally accepted as proving the variable light speed as light passes through a gravity field, just as Einstein wrote in his 1916 book, “A curvature of rays of light can only take place when the velocity of propagation of light varies with position.” And he also said in his 1952 Appendix to that book, “The principle of inertia and the principle of the constancy of the velocity of light are valid only with respect to an inertial system.” I suppose the difference between us is that you are a SR relativist while I’m a GR relativist. This is a “Relativity Discussion Thread”, right?

milli360
2004-Feb-05, 06:17 PM
Einstein has yet another method of deriving the Lorentz Transforms in an appendix to his 1920 Book, Relativity: The Special and General Theory.

Simple Derivation of the Lorentz Transformation (http://www.bartleby.com/173/a1.html)
I looked at this a little closer, and it appears to be pretty much what he does in section 3 of his 1905 paper, no? Do you mean, the differential notation?

SeanF
2004-Feb-05, 07:10 PM
I suppose the difference between us is that you are a SR relativist while I’m a GR relativist.

No, actually, you're not. You just think you are, because you don't understand the math of GR either. That's why you've never told us how to calculate the GR effect on an accelerating clock.

Diamond
2004-Feb-05, 07:47 PM
As I said in the original post for this thread, this is for discussing relativity as it stands, not any quibbles with it.

I think you are probably talking about Special Relativity as it stood in 1905.

Nope. We're talking about you hijacking a thread by replying to someone who asked a question about a postulate of SR that all inertial observers measure the same speed of light regardless of their relative motion, and you launch into yet another spiel about how SR is wrong and GR is right.


General Relativity superceded that, as Eddington’s 1919 photographs and Shapiro’s experiments proved. This is not “my position”, this is the standard mainstream physics position.

And irrelevant to you hijacking the thread.


And he [Einstein] also said in his 1952 Appendix to that book, “The principle of inertia and the principle of the constancy of the velocity of light are valid only with respect to an inertial system.

A restatement of the postulate of SR about the constancy of the speed of light to inertial observers. But of course you know better.


I suppose the difference between us is that you are a SR relativist while I’m a GR relativist. This is a “Relativity Discussion Thread”, right?

You're not a GR relativist and I'm not an SR relativist. They are not religious or political persuasions, but you seem to accredit belief systems to people who understand and appreciate the applicabilities of either theory to predict and explain phenomena.

Kaptain K
2004-Feb-05, 08:07 PM
I think you are probably talking about Special Relativity as it stood in 1905. General Relativity superceded that...
Sam5,
You have been told many times, by many people that GR does not "supercede" SR. GR extends SR from special conditions to general conditions. That is why they are known as general relativity and special relativity. GR no more " supercedes" SR than Einstein "supercedes" Newton.

Please quit hijacking threads!!!
:evil: :evil: :evil: :evil:

informant
2004-Feb-05, 08:26 PM
HOW do physicists determine the speed of light, and the fact that its relative speed never changes?

www.si.edu/opa/insideresearch/9892/saoside.htm+shapiro+time+delay&hl=en&ie=UTF-8]LIGHT (http://216.239.57.104/search?q=cache:ppbUNAb4k00J:[url) SPEED SLOWS DOWN IN A STRONG GRAVITY FIELD[/url]
I may be misreading this, I haven't been following this thread very closely, but to me it looks like Sam5 was trying to answer Lorcan's question... with "It actually does vary".

Kaptain K
2004-Feb-05, 08:30 PM
I may be misreading this, I haven't been following this thread very closely, but to me it looks like Sam5 was trying to answer Lorcan's question... with "It actually does vary".
Yep. And has been pointed out to him before, he is still wrong!

informant
2004-Feb-05, 08:56 PM
Lorcan (and Sam5?) may find the following links interesting:

Is the Speed of Light Constant? (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html)
How is the speed of light measured? (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html)

Normandy6644
2004-Feb-06, 01:28 AM
Lorcan (and Sam5?) may find the following links interesting:

Is the Speed of Light Constant? (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html)
How is the speed of light measured? (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html)

Nice links! Thanks! :D

Tensor
2004-Feb-06, 05:53 AM
Since this thread is supposed to be about discussion of current accepted mechanics SR and GR, I've started a new thread here (http://www.badastronomy.com/phpBB/viewtopic.php?t=11020&sid=05bac8d0c03cd565efdc2a25 4fc92e1e) in ATM for those who believe SR or GR are not correct, as currently formulated.

Lorcan Faol, I've answered one of Sam5's posts from this thead in the thread in the link above.

milli360
2004-Feb-06, 12:28 PM
Like Eroica says, the speed of light can be determined experimentally from Maxwell's equation for the speed of electromagnetic waves, which as Einstein pointed out, contains no term for the frame of reference of either source or observer.
In GR, it would.

We're talking about you hijacking a thread by replying to someone who asked a question about a postulate of SR that all inertial observers measure the same speed of light regardless of their relative motion, and you launch into yet another spiel about how SR is wrong and GR is right.
If you are talking about Lorcan Faol's post (http://www.badastronomy.com/phpBB/viewtopic.php?p=202920#202920), I don't see anything in it about SR, or inertial observers.

milli360
2004-Feb-06, 12:31 PM
I may be misreading this, I haven't been following this thread very closely, but to me it looks like Sam5 was trying to answer Lorcan's question... with "It actually does vary".
Yep. And has been pointed out to him before, he is still wrong!
Wrong about what? informant's link to the physics FAQ would indicate that "it actually does vary".

PS: I take that back. The very last line of the FAQ says "Finally we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies."

However, it is clear from the rest of the content that they are only referring to inertial reference frames, or, as they say, in GR, "freely falling reference frame (in a region small enough that tidal effects can be neglected)." OTOH, saying that the speed of light varies in an accelerated reference frame, doesn't seem to contradict that, so I'm not sure why they say "it does not even make any sense."

Eroica
2004-Feb-07, 09:00 AM
Einstein has yet another method of deriving the Lorentz Transforms in an appendix to his 1920 Book, Relativity: The Special and General Theory.

Simple Derivation of the Lorentz Transformation (http://www.bartleby.com/173/a1.html)
I looked at this a little closer, and it appears to be pretty much what he does in section 3 of his 1905 paper, no? Do you mean, the differential notation?
I've just gone through it myself. It's basically the same experiment as the one in the 1905 paper, but I don't see much similarity in the two methods.

Normandy6644
2004-Feb-13, 02:45 PM
Einstein has yet another method of deriving the Lorentz Transforms in an appendix to his 1920 Book, Relativity: The Special and General Theory.

Simple Derivation of the Lorentz Transformation (http://www.bartleby.com/173/a1.html)
I looked at this a little closer, and it appears to be pretty much what he does in section 3 of his 1905 paper, no? Do you mean, the differential notation?
I've just gone through it myself. It's basically the same experiment as the one in the 1905 paper, but I don't see much similarity in the two methods.

I don't remember why he does it both ways, but the easiest method that I've seen is with the train moving with a velocity v and emitting a photon travelling perpendicular the the direction of velocity (i.e., 'up'). Letting the train move from some point A to a point B you eventually get a triangle. Using the pythagorean theorem, we eventually arrive at the time dilation equation. It's quite an elegant derivation actually.

EDIT: This thread was starting to drop, so I'm trying to revive it, because something tells me this stuff is going to come up again. Call it a gut feeling.... :lol:

SeanF
2004-Feb-13, 03:01 PM
Einstein has yet another method of deriving the Lorentz Transforms in an appendix to his 1920 Book, Relativity: The Special and General Theory.

Simple Derivation of the Lorentz Transformation (http://www.bartleby.com/173/a1.html)
I looked at this a little closer, and it appears to be pretty much what he does in section 3 of his 1905 paper, no? Do you mean, the differential notation?
I've just gone through it myself. It's basically the same experiment as the one in the 1905 paper, but I don't see much similarity in the two methods.

I don't remember why he does it both ways, but the easiest method that I've seen is with the train moving with a velocity v and emitting a photon travelling perpendicular the the direction of velocity (i.e., 'up'). Letting the train move from some point A to a point B you eventually get a triangle. Using the pythagorean theorem, we eventually arrive at the time dilation equation. It's quite an elegant derivation actually.

EDIT: This thread was starting to drop, so I'm trying to revive it, because something tells me this stuff is going to come up again. Call it a gut feeling.... :lol:

But as milli360 pointed out (at least, I think this was his point), you have to assume that there's no dilation perpendicular to the direction of travel in order to derive the equations that way, don't you?

The way he does it in the 1905 paper actually leads to the conclusion that there's no perpendicular dilation.

Sam5
2004-Feb-13, 03:23 PM
Using the pythagorean theorem, we eventually arrive at the time dilation equation. It's quite an elegant derivation actually.

The Lorentz Transformation was worked out in Lorentz’s 1895 book, as shown here...

http://im1.shutterfly.com/procserv/47b4dc32b3127cceb821b68ead3f0000001610

milli360
2004-Feb-13, 04:12 PM
But as milli360 pointed out (at least, I think this was his point), you have to assume that there's no dilation perpendicular to the direction of travel in order to derive the equations that way, don't you?
Yep, the method Normandy6644 is talking about, I think, is the same as the one Eroica brought up originally.

SeanF and I do a lot of thinking, because you never know, on the BABB.

Sam5
2004-Feb-13, 04:47 PM
But as milli360 pointed out (at least, I think this was his point), you have to assume that there's no dilation perpendicular to the direction of travel in order to derive the equations that way, don't you?
Yep, the method Normandy6644 is talking about, I think, is the same as the one Eroica brought up originally.

SeanF and I do a lot of thinking, because you never know, on the BABB.

Lorentz said in his 1904 paper:

“Our assumption amounts to saying that in an electrostatic system E, moving with a velocity v, all electrons are flattened ellipsoids with their smaller axes in the direction of motion.”

This comes from his 1895 electrodynamics relativity theory. This contraction is shown in the page I posted above.

But one must remember that in Lorentz theory, the shrinking is the result of a force placed upon the electrons (and atoms) during their motion. The fields they move through put up a resistance to the motion, much like air puts up a resistance to our motion through it.

This was the Lorentz Force felt by the NASA tether as it moved through (not “relative to”) the earth’s magnetic field.

oriel
2004-Feb-13, 05:43 PM
Banned poster content deleted

milli360
2004-Feb-13, 05:57 PM
I have never seen such a bright shining lie as that one by Albert in foisting 'aether' on Newton despite the fact that Newton is explicit on the matter.
Your quotes don't seem to uphold your thesis. Can you be more explicit?

Welcome to the board. Are you related to oriel36 (http://www.badastronomy.com/phpBB/profile.php?mode=viewprofile&u=2474)? :)

Sam5
2004-Feb-13, 06:15 PM
Newton comments on aether


"The fictitious matter which is imagined as filling the whole of space
is of no use for explaining the phenomena of Nature, since the motions
of the planets and comets are better explained without it, by means of
gravity; and it has never yet been explained how this matter accounts
for gravity. The only thing which matter of this sort could do, would
be to interfere with and slow down the motions of those large
celestial bodies, and weaken the order of Nature; and in the
microscopic pores of bodies, it would put a stop to the vibrations of
their parts which their heat and all their active force consists in.
Further, since matter of this sort is not only completely useless, but
would actually interfere with the operations of Nature, and [314]
weaken them, there is no solid reason why we should believe in any
such matter at all. Consequently, it is to be utterly rejected."

Optics 1704


Hmm, that’s odd. I’ve got the 1704 edition of Optics, and in it Newton says,

“Doth not the Aetherial Medium in passing out of Water, Glass, Crystal, and other compact and dense Bodies into empty Spaces, grow denser and denser by degrees, and by that means refract the Rays of Light not in a point, but by bending them gradually in curved lines?”

On the next page he says,

“And though this Increase of density may at great distances be exceeding slow, yet if the elastick force of this Medium be exceeding great, it may suffice to impel Bodies from the denser parts of the Medium towards the rarer, with all that power which we call Gravity.”

Newton, Optics, Book 3, Part 1, 1704

milli360
2004-Feb-13, 06:30 PM
Hmm, that’s odd. I’ve got the 1704 edition of Optics, and in it Newton says
Good one, Sam5. I googled on "fictitious matter which is imagined as filling" and it came up with only one page, this one (http://www.philosophy.leeds.ac.uk/GMR/hmp/texts/modern/newton/optics.html). It appears to be a 1999 translation (by this guy (http://www.philosophy.leeds.ac.uk/GMR/homepage/gmr.html)) of a 1706 Latin version. Anyway, the phrase seems to appear in Book 3, Part 1, Question 20. Whatever that is.

PS: GMR explains it here (http://www.philosophy.leeds.ac.uk/GMR/hmp/texts/modern/newton/optintro.html). He supposes Newton added the questions to the Latin version of the text, I think.

Sam5
2004-Feb-13, 08:27 PM
Good one, Sam5.



Thanks.

Hmm, there were different editions of both Optics and the Principia.

The Question 20 in the 1704 Edition is not the same as what that guys says is in the 1706 Edition.

I think the apparent discrepancy lies in the difference between the terms “medium” and “matter”.

The term “the fictitious matter” in the 1706 Edition suggests a physical substance such as a thin gas or vapour, and this is what Newton was objecting to in that Edition.

However, the term “the Aetherial Medium” referred to in the 1704 Edition is not made up of physical “matter”. This “Aetherial Medium” is generated by the physical matter of the astronomical bodies, and he is saying the “medium” fills the space in-between the bodies. That is, the “medium” is essentially the gravity “fields” of space, but at that time (1704) the term “field” had not yet been invented, so in its place Newton used the term "Atherial Medium”.

These two words, “medium” and “matter”, are very tricky when used in terms of the “ether”, and in some early science publications they seem to be used almost interchangeably, even though they are actually quite different.

daver
2004-Feb-13, 11:37 PM
But as milli360 pointed out (at least, I think this was his point), you have to assume that there's no dilation perpendicular to the direction of travel in order to derive the equations that way, don't you?

The way he does it in the 1905 paper actually leads to the conclusion that there's no perpendicular dilation.

If I understand what you're getting at, you can get consistent equations by assuming either a spatial contraction perpendicular to the velocity vector or a time dilation. A thought experiment should be sufficicient to demonstrate that a space contraction doesn't make sense.

Normandy6644
2004-Feb-14, 06:02 AM
But as milli360 pointed out (at least, I think this was his point), you have to assume that there's no dilation perpendicular to the direction of travel in order to derive the equations that way, don't you?
Yep, the method Normandy6644 is talking about, I think, is the same as the one Eroica brought up originally.

SeanF and I do a lot of thinking, because you never know, on the BABB.

I think it is, and yes you do have to make those assumptions. The reason it's still nice to look it is because you can derive the basic equation in a very simple manner. It won't hold up under intense scrutiny, but if someone ever randomly asks you to prove the time dilation equation on a napkin or something (happens all the time, I know), you can do it without too much trouble.

Also, Lorentz derived the transformations, but as has been said, he didn't know why they worked. Minkowski actually explained them the best, allowing Einstein to use his methods to formulate GR.

Eroica
2004-Feb-14, 08:19 AM
This site has links to PDFs of most editions of Newton's works:

The Online Newton Project (http://dibinst.mit.edu/BURNDY/Collections/Babson/OnlineNewton/OnlineNewton.htm)

Newton's Opticks (http://dibinst.mit.edu/BURNDY/Collections/Babson/OnlineNewton/Opticks.htm)

oriel
2004-Feb-14, 12:27 PM
Banned poster content deleted

Kaptain K
2004-Feb-14, 01:21 PM
... I expect to be banned from the forum...

Why? Is it because you dropped the "36" from your nickname when you rejoined and expect the BA to figure it out soon?

Sam5
2004-Feb-14, 01:49 PM
Mach: on Newton's Absolute Time

"This absolute time can be measured by comparison with no motion; it
has therefore neither a practical nor a scientific value; and no one
is justified in saying that he knows aught about it. It is an idle
metaphysical conception."
Mach, Analyse der Empfindungen, 6th ed.

Why do you suppose that Mach would compare “absolute time” to “no motion”, since no motion means “no time”? Absolute time is merely “steady motion”, where the gaps in between the motion-related events are all of the same duration, whether we measure time by a linear device, counting the increments in inches, or by means of the usual vibratory method, counting the number of vibrations with the duration in between each vibration cycle being exactly the same as the previous one.

There would be such a thing as "absolute time", if we could find something that moved in a straight line at a steady speed or vibrated or rotated steadily, forever, but apparently nothing in the universe does that.

One problem I see with Newton’s short description of “absolute time” is that it tends to suggest time as an independent entity that sort of “permeates” the universe. Whereas I see time is being strictly a local phenomenon, that transpires only where things move and vibrate. Since there are so many things that move and vibrate, all around us, and at fairly steady rates, this tends to give us the impression that “time itself” permeates the universe, but I say it doesn’t. I say it occurs only when and where things are moving. If we could stop things from moving in a small part of space, then all of “time” in that small part of space would stop.

Newton might have known this, but he just didn’t say it in any of his books, and he seemed to think of time as flowing even without motion, especially when he said:

“Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.”

But I disagree. I say motion causes time. Motion generates time. No motion, no time. Steady motion equals steady time. I see time as a product of motion and motion as a product of kinetic energy. Thus, in my view, time starts with energy, energy generates motion, and time is a numerical accumulation of motion-related events, a counting of the events in sequence, and it is localized to the thing that is moving or vibrating. Absolute time would be steady motion or vibration with the same duration in between the events. When motion stops, let’s say within a single mechanical clock, that particular time stops. However, all of time does not stop in the area around the clock, since many other things continue to move and vibrate. In fact, the atoms and molecules inside the clock continue to vibrate and oscillate. Only the time that was being generated by the turning of the hands and the gears stops in the clock. But the rest of time doesn’t stop.

About being banned, just try not to get into any serious personal fights and arguments, and I think everything will be ok.

Uhh, what is your overall point?

oriel
2004-Feb-14, 02:33 PM
Banned poster content deleted

Normandy6644
2004-Feb-14, 04:46 PM
Hey guys, keep in mind this thread is for discussing mainstream relativity as it now stands, not quibbles with the theory. If you want to start debating certain points of it, please go to the Against the Mainstream topic (http://www.badastronomy.com/phpBB/viewtopic.php?t=11020) that Tensor started. Thanks.

oriel
2004-Feb-14, 06:32 PM
Banned poster content deleted

oriel
2004-Feb-14, 06:40 PM
Banned poster content deleted

Kaptain K
2004-Feb-14, 08:06 PM
I apologise Sam5 for making a mess of the posting by putting the thing entirely in 'quote',I am new to that feature and unfortunately when posting I was required to resubmit my password.
There is an "edit" button in the top right corner of your post. Click on it and you can correct your errors.

The Bad Astronomer
2004-Feb-14, 10:10 PM
What is it with some people who cannot stay away from here? Sheesh. I have deleted what he wrote, because it's a very bad idea to come back here after being banned and posting something.

Sam5
2004-Feb-14, 10:15 PM
Newton's Absolute Time

Uhh, nevermind.

Celestial Mechanic
2004-Feb-15, 05:40 AM
Darn! I only saw one of He Who Will Not Name Einstein's posts in his new incarnation before the BA deleted them all! Of course, a leopard does not change his spots, so I imagine it was the same old same old about the Equation of Time, the sidereal rotation being a kludge, cosmic modelling, physics being a total wasteland after 1905, etc., etc.

Kaptain K
2004-Feb-15, 05:51 AM
Nope. Just long rambling disertations about Newton. See some of Sam5's responses to HWSNNE for quotes.

milli360
2004-Feb-23, 09:15 PM
This is generally based on Einstein’s deduction in 1911 that the “tick rates” of atomic clocks tend to follow the speed rate changes of light.
Sam5, I was browsing our high school library, and guess what was on the shelves?

Apparently, Einstein wrote up an article in 1912 On the Special Theory of Relativity, and was set to publish it when the first world war, or something, intervened. When they finally got around to it, he'd published his General Theory, and they decided to not publish the 1912 article. It was published in facsimile in 2000. The great thing about it is that he crossed off whole paragraphs throughout the article--but they are included in the new book. Check it out. There are some interesting comments about the speed of light, crossed out.

Here it is at Amazon.com (http://www.amazon.com/exec/obidos/tg/detail/-/0807614173/qid=1077570611/sr=1-1/ref=sr_1_1/103-6639054-6659014?v=glance&s=books). The editorial review and the customer review seem to assume that it is the original theory article. One of them mentions publication history--I'd have sworn that it said it hadn't been published before this. O well.

Sam5
2004-Feb-24, 01:14 AM
Check it out. There are some interesting comments about the speed of light, crossed out.

Here it is at Amazon.com (http://www.amazon.com/exec/obidos/tg/detail/-/0807614173/qid=1077570611/sr=1-1/ref=sr_1_1/103-6639054-6659014?v=glance&s=books). The editorial review and the customer review seem to assume that it is the original theory article. One of them mentions publication history--I'd have sworn that it said it hadn't been published before this. O well.



Thanks very much for the information. I’ll try to track down a copy of that book. Apparently Einstein did publish an article in the Annalen der Physik in 1912, modifying the original 1905 SR theory. This is what Max Abraham said in a paper of his that was published in 1912:

“Already before period of one year A. Einstein, by accepting an influence of the gravitation potential on the speed of light, gave up the postulate of the constant speed of light essential for his earlier theory 1); in a work appeared recently 2)......

1) A. Einstein, Ann. d. Phys. 35. p 898. 1911.
2) A. Einstein. Ann. d. Phys. 38. p. 355. u. 443. 1912.”

This type of stuff is what I’ve been investigating. Einstein made a major switch-over from the basic “relativity theory” (the 1905 SR theory), to the GR theory of 1916. This switch-over began in 1911 when he realized his 1905 theory contained errors and when he realized that the speed of light is variable and not “constant”. He actually started examining gravitation and accelerative effects as early as 1906-07, but he didn’t make a major breakthrough until his 1911 gravitational redshift theory.

Why don’t you post some quotes from that book?

milli360
2004-Feb-24, 03:49 PM
Apparently Einstein did publish an article in the Annalen der Physik in 1912, modifying the original 1905 SR theory. This is what Max Abraham said in a paper of his that was published in 1912:
Yes, you've posted that before. That's why I thought you'd be interested. Einstein was on a quest almost from day one--he dallied in quantum mechanics, but returned to the general relativity pursuit.

This type of stuff is what I’ve been investigating. Einstein made a major switch-over from the basic “relativity theory” (the 1905 SR theory), to the GR theory of 1916.
Of course. No one denies that.

This switch-over began in 1911 when he realized his 1905 theory contained errors and when he realized that the speed of light is variable and not “constant”.
I disagree. There is a constant trend throughout his works, it appears to me. It's like going from learning to catch fish from the river, to learning to catch different fish from different parts of the river. It's unfair to characterize it as an error, when there is no evidence for that, other than supposition.

He actually started examining gravitation and accelerative effects as early as 1906-07, but he didn’t make a major breakthrough until his 1911 gravitational redshift theory.
I would say he started earlier than that. Too, he was influenced by the philosophy, and physics, of Mach.


Why don’t you post some quotes from that book?
I don't have it. It's a reference book, left in the library.

Sam5
2004-Feb-24, 04:24 PM
I disagree. There is a constant trend throughout his works, it appears to me. It's like going from learning to catch fish from the river, to learning to catch different fish from different parts of the river. It's unfair to characterize it as an error, when there is no evidence for that, other than supposition.



Yes, you are right about the "constant trend". I have Volume 2 of the “Collected Papers”, and I’m surprised by how many “atomic” papers he wrote. He was quite an expert on the inner workings of atoms, and in fact he was fairly well known in theoretical physics before he wrote the first 1905 relativity paper. Volume 2 contains some of his earliest attempts to add “acceleration” to his basic first relativity theory.

I think he did not include acceleration in the first theory because he imagined the “stationary system” to be the surface of the earth, as in the Michelson Morley experiment, and so he wanted to consider a steady relative speed and velocity before he began to inquire about the effects of acceleration. He made several interesting attempts in 1907 and ’09, but he kept getting some of the SR principles mixed up with some of the newly emerging GR principles. The two are not compatible. This is why he said in his 1911 paper:

”To avoid unnecessary complications, let us for the present disregard the theory of relativity, and regard both systems from the customary point of view of kinematics, and the movements occurring in them from that of ordinary mechanics.”

He had to actually start over by leaving out some of the incorrect principles of the 1905 paper. In the 1911 paper, he returned to some of the original relativity ideas that Lorentz had proposed in his 1895 book. By 1911 Einstein realized that “fields” and “acceleration” must be considered in a true relativity theory, and they can not be left out, as they were in his first 1905 relativity paper.

Based on what I’ve read, he actually started his “relativity” thinking as far back as his high school years, and that 1895 Lorentz book influenced him quite a lot. He apparently worked on his first relativity theory for years, long before he first published it in 1905. However, as he began to consider fields and acceleration more an more, he gradually began to realize the 1905 theory contained errors. He finally officially split the theories into two different versions, when, in 1916, he called the first theory, the one without fields and acceleration the “special” theory, and the ones in which he did consider fields and acceleration, he included them in his “general” theory.

So, the 1911 paper fits into the “general” theory, even though he was still calling all his relativity papers “the relativity theory” in 1911. But after 1916, the 1911 paper became classified under the General theory heading. That is why his statement about “the velocity of propagation of light varies with position” is included in the General relativity section of his 1916 book, and not with his earlier Special relativity section. This statement comes right out of his 1911 paper, so the 1911 paper is part of the General theory, not the Special theory.

Regarding whether or not we should call the 1905 mistakes “errors” or not, well I think we should and I’m positive that he realized they were errors. That’s why he had to change and alter the 1905 theory several times between 1907 and 1918. But he never wanted to call them “errors” in any public writings, and I think that’s because he was quite angry at some of the guys who were his most vocal critics. There were political reasons for this, and I’m not sure I blame him for what he did. At the time, I might have done the same thing, considering the hostile climate under which he worked in Europe, around the time of WW I.

Just because there has been a hundred-year tradition of not calling the SR errors “errors”, I don’t see any reason to continue that tradition, since they really were errors and Einstein realized they were errors. What we’ve got now, that most people during the past 100 years did not have, are good English translations of most of his work, so now we can objectively look back and examine this full situation in light of its historical context. And I find it absolutely fascinating. I think it would make a great movie. This involves far more than just physics. It deeply involves the politics of that era too, and those politics continued to intensify right on through the 1920s, the ‘30s, and the 1940s.

Jobe
2004-Feb-24, 04:56 PM
omg he's still going

Normandy6644
2004-Feb-24, 05:42 PM
As I have said numerous times, if you want to debaterelativity, do it here (http://www.badastronomy.com/phpBB/viewtopic.php?t=11020). If you want to discuss relativity, do it here. Note the difference.

Sam5
2004-Feb-24, 05:59 PM
As I have said numerous times, if you want to debaterelativity, do it here (http://www.badastronomy.com/phpBB/viewtopic.php?t=11020). If you want to discuss relativity, do it here. Note the difference.

Milli and I have been discussing relativity, both on the board and in PMs. He posted two messages to me on this thread, and I responded to them. Isn’t that what this thread is for?

There are a lot of old Einstein papers that were never translated into English until just recently. Some of these newly-translated papers contain changes and transitions of his opinions from his original SR attitude to his more advanced and complex GR attitude, and Milli and I have been discussing that. It is a very interesting subject. We generally do our debating in PMs.

milli360
2004-Feb-24, 06:21 PM
Volume 2 contains some of his earliest attempts to add “acceleration” to his basic first relativity theory.
Yes, very early. As I've mentioned before, I consider it to have been done in the original 1905 paper.


I think he did not include acceleration in the first theory because he imagined the “stationary system” to be the surface of the earth, as in the Michelson Morley experiment, and so he wanted to consider a steady relative speed and velocity before he began to inquire about the effects of acceleration.
A more reasonable approach would be to assume that he was just trying to extend Galilean relativity. In retrospect, that would be a good first step, wouldn't it? Plus, that is the reasoning given in the history books.


Based on what I’ve read, he actually started his “relativity” thinking as far back as his high school years, and that 1895 Lorentz book influenced him quite a lot. He apparently worked on his first relativity theory for years, long before he first published it in 1905.
They don't spring instantly from one's mind fully formed, that's for sure.

However, as he began to consider fields and acceleration more an more, he gradually began to realize the 1905 theory contained errors.
You insist on calling them errors, when they don't appear that way, to me.


Regarding whether or not we should call the 1905 mistakes “errors” or not, well I think we should and I’m positive that he realized they were errors. That’s why he had to change and alter the 1905 theory several times between 1907 and 1918. But he never wanted to call them “errors” in any public writings, and I think that’s because he was quite angry at some of the guys who were his most vocal critics. There were political reasons for this, and I’m not sure I blame him for what he did. At the time, I might have done the same thing, considering the hostile climate under which he worked in Europe, around the time of WW I.
Part of the problem with calling them "errors" is that the things which you have called errors, over the last four years, are not errors but only misunderstandings on your part. Clearly, the theory evolved, and things changed as new ideas developed. To call the early things errors is valid--except the that the things that you identify specifically as errors are not errors.


Just because there has been a hundred-year tradition of not calling the SR errors “errors”, I don’t see any reason to continue that tradition, since they really were errors and Einstein realized they were errors.
I fall into many discussions where people disagree with me that Newton has been shown to be wrong. It all boils down to point of view. Is Newton wrong? Yes. Is Newton's theory still useful? Yes--but then how can it be wrong?

But disagreement that I have with you is that you try to say that a specific line of logic is in error, or a particular equation, or a paragraph--and I disagree, when I think that you are wrong.

Of course it would make a great movie, I even enjoyed IQ (http://www.rottentomatoes.com/m/IQ-1058920/about.php).


As I have said numerous times, if you want to debaterelativity, do it here (http://www.badastronomy.com/phpBB/viewtopic.php?t=11020). If you want to discuss relativity, do it here. Note the difference.
That other thread seems to have run out of steam. As near as I can tell, Sam5 was criticized for one of his statements about relativity, but it turned out the statement was compatible with relativity, and not against the mainstream. Sam5 feels that his interpretation is mainstream relativity--if he makes a comment that you feel is outside the mainstream, take it to that thread, and we can discuss it.

Where would be appropriate to dicsuss the hsitory of relativity? Against the Mainstream, or GA? Or BABBling? :)

Sam5
2004-Feb-24, 07:17 PM
That other thread seems to have run out of steam. As near as I can tell, Sam5 was criticized for one of his statements about relativity, but it turned out the statement was compatible with relativity, and not against the mainstream. Sam5 feels that his interpretation is mainstream relativity--if he makes a comment that you feel is outside the mainstream, take it to that thread, and we can discuss it.

Where would be appropriate to dicsuss the hsitory of relativity? Against the Mainstream, or GA? Or BABBling? :)


Yes, that is what we are discussing now, the history. I think you and I have finally gone beyond arguing about SR “time dilation” stuff.

What happened was that he made the errors in 1905 because he was trying to “correct” the 1895 Lorentz book by removing the “ether” from it, but in that process Einstein also left out very important things that Lorentz had included in the original theory, i.e. fields, acceleration, and real physical forces. Leaving out this stuff leads to paradoxes and errors in the 1905 paper.

He began to realize the errors and the reasons for them by 1911. And in 1918 he corrected them by adding fields, acceleration, atomic clocks, and real physical forces to the original 1905 paper. You need to study the original Lorentz theory, and many of Einstein’s papers in which he included gradual changes to the original 1905 paper. The history books usually don’t go into that much detail about the changes and why he made them, and they almost never discuss the original 1895 Lorentz book that started modern “relativity” theory in the first place. Very few people today have read the 1895 Lorentz book or the 1918 Einstein paper. These two works clear up a lot of the mystery.

What tends to “work” in SR, is actually the Lorentz parts of it. That is, if you add back the fields, the acceleration, and the real physical forces, and apply them to specifically atomic clocks (but not to mechanical clocks) then part of the theory works without paradoxes. But the original “relative motion” part does not work, since just “relative motion” doesn’t do anything or place any “forces” on anything. So, add the Lorentz stuff back to the SR theory, and what you have is the Lorentz theory. SR itself disappears when the fields, acceleration, atomic clocks, and real “forces” are added to it.

Kaptain K
2004-Feb-24, 07:31 PM
omg he's still going
What he said! :roll:

Sam5
2004-Feb-24, 07:37 PM
Where would be appropriate to dicsuss the hsitory of relativity? Against the Mainstream, or GA? Or BABBling? :)


Hey, I’ve got an idea. Suppose you do this.... suppose you start a “relativity history” thread in this forum, and we can post on that, while these other guys can talk on this thread about their favorite topics and points of view. Anyone who wants to talk about the history and the gradual changes and the differences between Lorentz theory, SR theory, and GR theory, and what we might think of as the “errors” of the various theories, can do that on the other thread, and these guys can have their thread where they can have their own thread, so we won’t over-lap each other or irritate each other.

milli360
2004-Feb-24, 07:46 PM
Leaving out this stuff leads to paradoxes and errors in the 1905 paper.
Unless you can point to a passage in the literature that says "I made a mistake" or you can point to a math error, then I think you should avoid ascribing motive based upon supposition. You've objected to that before when others have ascribed motive to you, and I don't think it should be done here.

As far as that goes, there is no real paradox, that can be seen in the 1905 paper.


These two works clear up a lot of the mystery.

A calculus book would clear up a lot of the "mystery," too. :)


But the original “relative motion” part does not work, since just “relative motion” doesn’t do anything or place any “forces” on anything.
As we've discussed before (the "potential box"), the force is not necessary, in GR.

Sam5
2004-Feb-24, 08:19 PM
Unless you can point to a passage in the literature that says "I made a mistake"


Sure, I’ve already done that several times.

Here’s what he said in the 1905 paper:

”light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.”

And here is his correction in his 1916 book:

”In the second place our result shows that, according
to the general theory of relativity, the law of the con-
stancy of the velocity of light in vacuo, which consti-
tutes one of the two fundamental assumptions in the
special theory of relativity and to which we have
already frequently referred, cannot claim any unlimited
validity. A curvature of rays of light can only take
place when the velocity of propagation of light varies
with position.”

Here is an additional correction to that original 1905 statement, as published in his 1916 book, in the 1952 Appendix V:

”There is no such thing as an empty space, i.e. a space without field.”

I’ve underlined his original errors, his acknowledgment of the errors, and his corrections.

milli360
2004-Feb-24, 08:26 PM
Sure, I’ve already done that several times.
I've not recognized them. For instance, the one you make below:


And here is his correction in his 1916 book:

”In the second place our result shows that, according
to the general theory of relativity, the law of the con-
stancy of the velocity of light in vacuo, which consti-
tutes one of the two fundamental assumptions in the
special theory of relativity and to which we have
already frequently referred, cannot claim any unlimited
validity.”

With that qualifier, "cannot claim any unlimited validity," it is no longer a correction, since the original 1905 paper did not say that it had unlimited validity, as you know.


I’ve underlined his original errors, his acknowledgment of the errors, and his corrections.
As near as I can tell, it is a misunderstanding.

Not that there might yet be some out there.

Sam5
2004-Feb-24, 08:36 PM
As near as I can tell,

Will respond with a PM.

swansont
2004-Feb-24, 09:03 PM
Here’s what he said in the 1905 paper:

”light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.”

And here is his correction in his 1916 book:

”In the second place our result shows that, according
to the general theory of relativity, the law of the con-
stancy of the velocity of light in vacuo, which consti-
tutes one of the two fundamental assumptions in the
special theory of relativity and to which we have
already frequently referred, cannot claim any unlimited
validity. A curvature of rays of light can only take
place when the velocity of propagation of light varies
with position.”

I’ve underlined his original errors, his acknowledgment of the errors, and his corrections.

This is no different, procedurally, than what is done in many areas of physics. For a simple kinematics example, such as saying that in the absence of a change in height, that work = change in kinetic energy, and then admitting that many problems will involve a change in height, and so adding in potential energy to the equation. The original equation isn't wrong; it just has limits as to when it can be applied.

We physicists do this all the time - define a specific set of conditions so we can study the effects. Then you can add in independent factors, and study their effects. All Einstein was doing was to show that certain effects are present in inertial frames. Other things happen in accelerating frames. They aren't mistakes. They aren't errors.

swansont
2004-Feb-24, 09:05 PM
What tends to “work” in SR, is actually the Lorentz parts of it. That is, if you add back the fields, the acceleration, and the real physical forces, and apply them to specifically atomic clocks (but not to mechanical clocks) then part of the theory works without paradoxes.

Then it should be trivial for you to show exactly how the effects depend on the strength and direction of the fields. Please do so.

Normandy6644
2004-Feb-25, 02:51 AM
Where would be appropriate to dicsuss the hsitory of relativity? Against the Mainstream, or GA? Or BABBling?

I started this thread mainly as a relativity concepts question and answer thread for the people who were just getting into it, but no one seems to be posting really. I don't mind your discussion (actually it's quite fascinating) but this thread wasn't originally intended for it. But now, go for it!!

Jobe
2004-Feb-26, 04:59 AM
Its becoming a trend that certain ppl start posting when the word "Einstein" is mentioned :P

Diamond
2004-Feb-26, 11:53 AM
Anyone noticed that once again, Sam5 hijacks a Relativty thread and posts the same crap over and over again?

How about this Sam5? You bug out of this thread and goto the "Against the Mainstream" thread that Tensor set up, and we won't complain to the BA about your hijacking threads?

Sam5
2004-Feb-26, 04:42 PM
Anyone noticed that once again, Sam5 hijacks a Relativty thread and posts the same crap over and over again?

How about this Sam5? You bug out of this thread and goto the "Against the Mainstream" thread that Tensor set up, and we won't complain to the BA about your hijacking threads?

I had not posted anything on this thread for 10 days. Nobody had posted anything on this thread for 8 days. You have not posted anything on this thread for 21 days.

As far as I was concerned, this thread was dead.

Then Milli posted some messages to me and I responded to them. If you don’t like that, then complain to Milli about it.

Diamond
2004-Feb-26, 05:37 PM
Anyone noticed that once again, Sam5 hijacks a Relativty thread and posts the same crap over and over again?

How about this Sam5? You bug out of this thread and goto the "Against the Mainstream" thread that Tensor set up, and we won't complain to the BA about your hijacking threads?

I had not posted anything on this thread for 10 days. Nobody had posted anything on this thread for 8 days. You have not posted anything on this thread for 21 days.

As far as I was concerned, this thread was dead.

Then Milli posted some messages to me and I responded to them. If you don’t like that, then complain to Milli about it.

The thread was specifically for problems in relativity, and the OP specifically asked that this thread not be hijacked by you in another "einstein was wrong" rant that you like to think impresses anybody.

Sam5
2004-Feb-26, 06:41 PM
Anyone noticed that once again, Sam5 hijacks a Relativty thread and posts the same crap over and over again?

How about this Sam5? You bug out of this thread and goto the "Against the Mainstream" thread that Tensor set up, and we won't complain to the BA about your hijacking threads?

I had not posted anything on this thread for 10 days. Nobody had posted anything on this thread for 8 days. You have not posted anything on this thread for 21 days.

As far as I was concerned, this thread was dead.

Then Milli posted some messages to me and I responded to them. If you don’t like that, then complain to Milli about it.

The thread was specifically for problems in relativity, and the OP specifically asked that this thread not be hijacked by you in another "einstein was wrong" rant that you like to think impresses anybody.

No response.

SeanF
2004-Feb-26, 08:13 PM
No response.

Is this like one of those "This page intentionally left blank" pages I see in instruction manuals occasionally?

(One bad thing about the Internet - you have to tell people when you're ignoring them . . . )

Celestial Mechanic
2004-Feb-29, 04:52 AM
Well, I'd like to bring this thread back to life. In another thread I presented a thought experiment that explained Einstein's "peculiar consequence" and thus, by extension, the "twin paradox" that avoided the usual arguments about accelerations and changes in the local value of c. I've made a few changes since then, so I'm reposting the three parts. Let's disuss!

Celestial Mechanic
2004-Feb-29, 04:53 AM
CM's Angels -- Part One

Well, it's time for another thought experiment fantasy. I call this one "Celestial Mechanic's Angels", or "CM's Angels" for short. My three very lovely (and capable!) assistants are Anne, Barbara, and Charlotte. Each of them has a spaceship with a cesium-133 clock aboard and they have all gone out beyond Pluto. Anne and Charlotte have positioned themselves 3 light-days apart and synchronized their clocks as detailed in Einstein's 1905 paper and as I will repeat shortly. Barbara has gone a much farther distance away, taken careful aim, and accelerated to a cruise velocity of 0.6c. She will first pass Charlotte and then Anne. Anne, Barbara, and Charlotte are in constant communication, exchanging timestamped signals as I will describe below. I communicate with them only via a speakerphone. :)

Anne and Charlotte use the following protocol to determine that their clocks are synchronized. Anne sends out signals at a rate of one per second, each one carrying a timestamp indicating when she sent it. When Charlotte receives this signal, she (well actually her computer!) sends the signal back with her timestamp appended to it. When Anne receives this signal, a timestamp is appended indicating when Anne received it. Charlotte does the same thing, sending out one signal every second that Anne appends her timestamp to and that Charlotte receives and appends a receipt timestamp to.

Their computers analyze each packet examining the quantity t_A - (t_R+t_S)/2, where t_S is the time that the original signal was sent, t_A the time on the other's clock when the signal was received and sent back, and t_R is when the signal completes its round trip. If this quantity is increasing linearly in time the observers are moving towards one another at a constant velocity. If it is decreasing linearly then they are moving away from one another at a constant velocity. If it is constant, then they are at rest with respect to one another, and all one of them has to do is change their clock reading by adding this quantity and then they will be synchronized. Of course it would be a good idea for whoever changes their clock to send a message to that effect to the other!

By the way, I don't know exactly how the clock-setting protocols used by various PC programs handle it, but I suspect it must probably be something like the above. One complication is that the routing of the Internet packets is subject to change, so there is a bit more "jitter" that the program has to analyze before resetting your PC's clock. Of course you don't have to send a signal to the time server that you changed your clock as Anne and Charlotte should!

Back to the experiment. Barbara zooms past Charlotte at a time that we will call zero. Three days later Anne receives a message with Charlotte and Barbara's timestamps. Two days after that Barbara zooms past Anne. When Anne examines the record of Barbara's timestamps, she sees that only four days, not five, have elapsed according to Barbara's clock. What happened? Answer in the next post.

Celestial Mechanic
2004-Feb-29, 04:58 AM
CM's Angels -- Part Two

As Paul Harvey would say, "Page two!"

Anne and Charlotte are in the same inertial frame. They know this because their clocks are synchronous and synchronized, and stay synchronized. Barbara knows that she is in an inertial frame because she turned off her engines and feels no forces. The signals that Anne receives from Barbara are blueshifted and so she receives signals at a greater rate, that is, Barbara's clock seems to run fast. Likewise, all of the signals that Barbara receives from Anne are blueshifted. By the principle of relativity, they see the same amount of blueshifting. Barbara has every right to say that she is at rest and that Anne and Charlotte are moving.

Time to bring in the math. Let us call this factor K. I choose to let it represent the ratio of the wavelengths, so it will be a number less than one for blueshift. Let A be the time from Barbara's passage of Charlotte's position to Barbara's passage of Anne's position as measured by Anne and Charlotte's clocks. A measurement by Charlotte is just as good as a measurement by Anne because their clocks have been synchronized. Let B be the time elapsed according to Barbara's clock between these two events. Finally, let T be the light-travel time between Anne and Charlotte.

When Barbara passes Charlotte at time zero, a signal sent by Anne at time -T reaches Charlotte and Barbara. Barbara receives all of these signals during her time B. She receives 1/K signals each second, so she will receive B/K signals and these will match the number of signals Anne sends, A-(-T) = A+T.

Anne receives the signal from Barbara's flight past Charlotte at time T. During the remaining time from then until time A she receives a total of (A-T)/K signals, and this will equal the number of signals that Barbara emits during that time, B. The equations are:

B / K = A + T, (1)
B = (A - T) / K (2) .

We can rearrange if we like as:

B = (A + T) * K (1')
B = (A - T) / K (2) .

None of these quantities is zero, so we can divide equation (1') by equation (2) in order to eliminate B and solve for K:

K = sqrt( (A - T) / (A + T) ) .

In this thought experiment, A = 5, T = 3, so K = sqrt((5-3)/(5+3)) = sqrt(1/4) = 1/2, thus the wavelengths are half and Anne receives two signals per second from Barbara and vice versa as they approach one another.

If we multiply equation (1') by (2) the K's cancel and we have B*B=(A+T)*(A-T)=(A*A-T*T), therefore B = sqrt(A^2-T^2) = sqrt(5^2-3^2) = sqrt(25-9) = sqrt(16) = 4, as was claimed.

Let's analyze this experiment a bit. First, we are at a reasonable distance from any significant gravity sources. If a gravitational gradient is detectable over three light-days, we could have just as easily made it three light-minutes or even three light-seconds. Also, notice that Anne and Charlotte are able to define a reference frame without reference to the rest of the universe. Nothing material changes velocity during the experiment; only radio signals are exchanged. All accelerations are "off-stage", so to speak, so Barbara's clock has had ample opportunity to "recover" from any jostling it may have experienced during Barbara's acceleration. From analysis of Barbara's clock signals, Anne and Charlotte can tell that Barbara is also in an inertial reference frame. In short, we finally have a statement of the "peculiar consequence" and by extension, of the "twin paradox" that does not involve accelerations and general relativity, thus fulfilling the original topic of this thread.

Now, what about fields? All gravitational fields are negligible, and there are no significant electromagnetic fields other than the signals that they send one another. There are no "Lorentz fields" for CM's Angels to move through. Anne and Charlotte are in the same "c-regulator" and measure the same value of c, and since Barbara moves through this same "c-regulator" she must, by the relativity principle, measure the same value too. The fact that Anne and Charlotte have been able to remain at a constant distance from one another (no accelerations) and have measured constant time for the travel time of their signals indicates that the speed of light has been constant for them and thus for Barbara.

On to part three!

Celestial Mechanic
2004-Feb-29, 05:01 AM
CM's Angels -- Part Three

Anne, Barbara, and Charlotte have returned to the office from their journey to the edge of the Solar System. They listen to the speaker-phone as the Celestial Mechanic speaks:

"As you can see, nothing was wrong with your clocks. Anne and Charlotte's clocks were synchronized and correctly measured the time to be five days in their common reference frame. Barbara's clock correctly measured the time to be four days in her reference frame. Both times are correct, in their respective reference frames.

"Coordinates are not something intrinsic to particles and fields, they are something that scientists and engineers assign in order to analyze the problem. They are not engraved on stone, they have to be measured. A good set of coordinates can make a problem easy to solve, a bad set of coordinates can leave us mired in confusion. More important than the coordinates are the invariants, quantities that are independent of any coordinates used in their calculation. Proper time is such an invariant.

"Time is a coordinate that we have considerable latitude in defining. A clock is a device that measures proper time through the use of repeatable actions of known constant duration. Anne and Charlotte's clocks measured their proper time which also turned out to be their reference frame's time coordinate because they were stationary within their reference frame. Barbara's clock measured her proper time which was not equal to Anne and Charlotte's coordinate time because Barbara was in motion with respect to Anne and Charlotte's frame.

"Let me leave you with the words of Sir Isaac Newton: 'Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration ...'. While he meant this to refer to a 'universal' sort of time coordinate, I think it is actually a good description of the proper time that for each of us 'flows equably without regard to anything external'."

Tensor
2004-Feb-29, 01:02 PM
Well, I'd like to bring this thread back to life. In another thread I presented a thought experiment that explained Einstein's "peculiar consequence" and thus, by extension, the "twin paradox" that avoided the usual arguments about accelerations and changes in the local value of c. I've made a few changes since then, so I'm reposting the three parts. Let's disuss!

CM thanks. The part on how to eliminate the gravitational gradient by choosing a smaller area (days to minutes to seconds) was a very simple, but effective way to show how to get to a frame where SR could be used. Good Job.

milli360
2004-Feb-29, 02:10 PM
In short, we finally have a statement of the "peculiar consequence" and by extension, of the "twin paradox" that does not involve accelerations and general relativity, thus fulfilling the original topic of this thread.
Of course, you mean this thread: Twin Paradox: Definitive Proof That It's SR? (http://www.badastronomy.com/phpBB/viewtopic.php?p=197998&highlight=angels#197998), right?

But we already had a statement of the "peculiar consequence" that does not involve accelerations and general relativity, in the original 1905 paper of Einstein on Special Relativity (http://www.fourmilab.ch/etexts/einstein/specrel/www/#SECTION14). That's where the phrase "peculiar consequence" originates.