Did Lorentz or Einstein theoretically derive special relativity?

[Histspec]

If I may ask you, and even considering Lorentz's modifications, do you assume that the transformations "mean the same thing" in SR and LET? Here's the reason I ask ...

As Samshorn (and Lorentz in the quoted passages) already explained -
Observationally: The same.
Metaphysically: Not the same.
(Of course, this applies to Poincaré's version, not to Lorentz's 1904-theory).

If 2 identical falling weights strike the 2 trays of a balanced scale "simultaneously", with trays-centerline colinear with propagational path, then they should not tilt. However, LET requires that synchronised clocks (per the balance) attached to the each scale pad are not simultaneous per the aether frame. Hence, the scale should tip per LET if the weights strike the pads when they display identical clock readouts.

Simply replace LET with SR, and "aether frame" with "non-co-moving frame". Then you will understand, that if your proposal is correct, not only LET, but also SR would be violated. Since this isn't the case, your thought experiment is wrong.

Regards,

 

[GrayGhost]

As Samshorn (and Lorentz in the quoted passages) already explained -
Observationally: The same.
Metaphysically: Not the same.
(Of course, this applies to Poincaré's version, not to Lorentz's 1904-theory).

Just curious though, was Poincare's re-interpretation published before Einstein's 1905 OEMB?

Simply replace LET with SR, and "aether frame" with "non-co-moving frame". Then you will understand, that if your proposal is correct, not only LET, but also SR would be violated. Since this isn't the case, your thought experiment is wrong.

OK, so per LET, if the clocks attached to the balance-trays are synchronised per the balance POV, then identical weights impacting the trays at identical clock readouts must arrive simultaneously per the balance and the scale does not tip per all ... as in SR.

So a 2-way speed of light of c as measured by contracted moving rulers in LET is not different from a 2-way speed of light of c as measured by uncontracted inertial rulers in SR, yes? You are saying that this is a metaphysical difference alone?

It still seems to me that a test that measures the 1-way speed of light w/o using a 2-way trip should validate which foundation is the correct one, SR vs LET, yes? Or, will you suggest that the choice of clock synchronisation convention dictates the 1-way speed, and so no real 1-way speed of light is determinable in theory?

GrayGhost

 

[PAllen]

It still seems to me that a test that measures the 1-way speed of light w/o using a 2-way trip should validate which foundation is the correct one, SR vs LET, yes? Or, will you suggest that the choice of clock synchronisation convention dictates the 1-way speed, and so no real 1-way speed of light is determinable in theory?

GrayGhost

A worthwhile exercise is to examine the limiting behavior of so called 'slow moving clock synchronization'. To measure one way speed of light you need two clocks synchronized at a distance, in some frame. To synchronize them without light, imagine synchronizing at one location, and moving one away *very* slowly. Then, it seems, you have one way measurement independent of the Lorentz transform. However, this would be wrong. If you examine limiting behavior of Lorentz transform (using the slow velocity), the fact that the slower the speed, the longer it takes to move the clocks, means that moving clocks apart slowly is exactly equivalent to synchronizing them with light. As a result, any version of LET which uses Lorentz transform for all interactions is, in principle, indistinguishable from SR.

 

[GrayGhost]

A worthwhile exercise is to examine the limiting behavior of so called 'slow moving clock synchronization'. To measure one way speed of light you need two clocks synchronized at a distance, in some frame. To synchronize them without light, imagine synchronizing at one location, and moving one away *very* slowly. Then, it seems, you have one way measurement independent of the Lorentz transform. However, this would be wrong. If you examine limiting behavior of Lorentz transform (using the slow velocity), the fact that the slower the speed, the longer it takes to move the clocks, means that moving clocks apart slowly is exactly equivalent to synchronizing them with light. As a result, any version of LET which uses Lorentz transform for all interactions is, in principle, indistinguishable from SR.

Well, let's see ...

t' = gamma(t-vx/c²)​

where gamma = 1/(1-v²/c²)^1/2

Slow clock transport ... Ignoring gravity, with clocks originally in sync, let's say a space shuttle traveled from the ISS at 25,000 mi/hr for 7.44 hr, then decelerates to rest with the ISS. His speed is 3.73357x10^-5 ls/sec. On arrival, the shuttle is ~1 light sec away from the ISS. Gamma = 1.0000000007, so virtually unity. So after 7.44 hr, the shuttle clock is desynchronised from the ISS clock by 0.0000000007 sec ... so virtually in sync. If the 1-way seed of light was in fact not c (as per LET), and the ISS/shuttle velocity wrt the aether frame "somewhat luminal", it seems to make sense that the light speed measured from ISS to shuttle could be notably different from a light speed measured from shuttle to ISS. No?

GrayGhost

 

[PAllen]

Well, let's see ...

t' = gamma(t-vx/c²)​

where gamma = 1/(1-v²/c²)^1/2

Slow clock transport ... Ignoring gravity, with clocks originally in sync, let's say a space shuttle traveled from the ISS at 25,000 mi/hr for 7.44 hr, then decelerates to rest with the ISS. His speed is 3.73357x10^-5 ls/sec. On arrival, the shuttle is ~1 light sec away from the ISS. Gamma = 1.0000000007, so virtually unity. So after 7.44 hr, the shuttle clock is desynchronised from the ISS clock by 0.0000000007 sec ... so virtually in sync. If the 1-way seed of light was in fact not c (as per LET), and the ISS/shuttle velocity wrt the aether frame "somewhat luminal", it seems to make sense that the light speed measured from ISS to shuttle could be notably different from a light speed measured from shuttle to ISS. No?

GrayGhost

I think I wasn't clear enough what I meant. Imagine you believe in a either frame. The problem is to determing the one way spee of light in the aether frame versus the one way sped of light in a fast train, each using slow clock synchronization to try to avoid a circular definition of one way speed of light.

LET posits actual length contractions and time dilation for motion relative to aether. Let's derive the time difference, from the aether frame, for two clocks at the opposite ends of a train, synchronized with slow clock transport.

If the train, in its own frame is L, its length in the aether frame is L/gamma(v). A clock at (say) the back end of the train is going at a rate of t/gamma(v) compared to aether. Suppose slow transport speed is delta, that is, aether frame perceives clock being moved at v+delta. So now transport time is L/(delta*gamma(v)). For this time, the slow clock is moving at t/(gamma(v+delta)) rather than t/gamma(v). So, the accumulated time difference (in the aeither frame) when the slow clock reaches the ed of the train is:

(L/(gamma(v)) * (1/delta) * (1/gamma(v+delta) - 1/gamma(v))

Taking limit as delta->0 is just:

(L/gamma(v)) Dv (1/gamma(v))

where Dv is derivative with respect to v. This is seen to be exactly:

-Lv/c^2

This is time difference in aether frame. Time synch difference in train frame (as seen from aether frame) is -gamma*L*v/c^2.

Note two things. For v=0 (aether frame), difference is zero. That is, you can make slow clock transport have no effect, in the limit of zero transport speed. For any v relative to aether, you get a simultaneity deviation exactly as in the Lorentz transform. Thus slow transport with one way measure of c, produces the same result as Lorentz transform predicts. Thus no way to disinguish moving frame using one way light measurement with slow transport.

 

[PAllen]

-Lv/c^2

This is time difference in aether frame. Time synch difference in train frame (as seen from aether frame) is -gamma*L*v/c^2.

This part of the argument is incorrect in justification (result is right). Carefully reviewing the derivation, I see the de-synchronization of -Lv/c^2 is as perceived in the aether frame, but measured in units of train time. To express in aether time, multiply by gamma.

 

[GrayGhost]

This part of the argument is incorrect in justification (result is right). Carefully reviewing the derivation, I see the de-synchronization of -Lv/c^2 is as perceived in the aether frame, but measured in units of train time. To express in aether time, multiply by gamma.

You lost me at your derivative, however no matter. I will look into that further, afterwards.

Thanx for your response Pallen. I agree that the clocks are observed by the aether to be desynchronised by gamma*(-Lv/c²), and the train records them in sync. One thing though ... I am not quite sure how any of this demands that light's 1-way speed is indeterminable.

GrayGhost

 

[PAllen]

You lost me at your derivative, however no matter. I will look into that further, afterwards.

Thanx for your response Pallen. I agree that the clocks are observed by the aether to be desynchronised by gamma*(-Lv/c²), and the train records them in sync. One thing though ... I am not quite sure how any of this demands that light's 1-way speed is indeterminable.

GrayGhost

The derivative just comes from its definition. We had something of the form:

limit as delta->0 : (f(v+delta)-f(v))/delta

That is the definition of the derivative of f(v) by v.

 

[PAllen]

You lost me at your derivative, however no matter. I will look into that further, afterwards.

Thanx for your response Pallen. I agree that the clocks are observed by the aether to be desynchronised by gamma*(-Lv/c²), and the train records them in sync. One thing though ... I am not quite sure how any of this demands that light's 1-way speed is indeterminable.

GrayGhost

I don't think the one way speed of light is indeterminate. There are different ways of synchronizing clocks and measuring distance without involving light. What *is* true is that these fail to distinguish SR from the final form of LET, even though LET has speed light constant only in the aether frame. In the sense of comparing these two particular models, you fail to establish the one way speed of light. However, you rule out essentially all alternatives to SR except LET.

I will show how LET explain how the moving train measures one way speed of light the same as the aether frame, even though LET says this is really true only in the aether frame.

For train going at +v, rest length L, its measurement of one way speed from - to + end of train is as follows:

[ (L/gamma)/(c-v) - L*v*gamma/c^2)] (1/gamma)

The /(c-v) term is contracted length over slower light speed (giving time pereceived for this measurement in the aether frame). The next term is the clock synchronization difference (as I derived for slow transport) in the aether frame. Finally, we multiply by (1/gamma) to express what is seen on the train clocks. Work this out and you get L/c.

Similarly, for measuring one way speed the other way, you get:

[ (L/gamma)/(c+v) + L*v*gamma/c^2)] (1/gamma)

which again works out to L/c.

It really is thoroughly established the the LET interpretation is indistinguishable by experiment from the standard SR interpretation.

 

[atyy]

http://books.google.com/books?id=4DunN-eD3VIC&vq=one+way&source=gbs_navlinks_s

Ohanian's irritating and fun book discusses how to measure the one way speed of light (p98-100). He does list PAllen's slow clock transport. But I think the funnest one he gives is to send a signal one way, then wait half a day, and send it back. The Earth's rotation means that sending it back is sending it in the same direction. The clocks don't have to be synchronized, they just need to be capable of timing half a day. He then says that GPS has been tested with so many arbitrary delays that the constancy of the one way speed of light is effectively measured.

 

[GrayGhost]

EDIT 1: I just realized your prior response here, after I had already posted this. I'll leave this post up for now, while I go back and anxiously read thru your post there. Thanx.
**********************************

PAllen,

Thanx for the derivative clarification.

SR assumes isotropic light speed in any and all inertial frames, so the 1-way = 2-way = c. The LTs are designed such that space and time possesses a symmetry that allows for this, ie Lorentz symmetry. A spacetime interval is observed by moving others as dilated, by gamma. If in the proper frame light travels 1 ls in 1 sec, in the frame that moves relatively the light travels across 2 ls in 2 sec, so still speed c.

LET assumes isotropic light speed in only the aether frame, so the 1-way = 2-way = c. Per anyone moving thru the aether, the 1-way speed of light is not really c. Yet, the theory determines that the 2-way speed of light must always be measured at c. Moving contracted rulers and slower ticking clocks do not realize they are contracted, and so bodies moving thru the aether never realize they are contracted from their proper values.

What I find interesting though, is this ... SR assumes the 1-way = c, and the LTs are the result of this assumption. LET possesses the very same LTs, and so it seems that its 1-way way light speed should also be assumed at c ... even though it cannot really be as such. This all suggests that measurement errors cause LET to appear as SR ... errors being due to measurements made with contracted rulers and slower ticking clocks (that don't recognize they are as such). Wrt LET upholding the PoR, I can understand why Minkowski called it "a gift from above". However, it seems to me that length contraction and time dilation alone cannot explain how LET allows for a reflection event to bisect the 2-way roundtrip interval ... because this requires the 1-way speed of light be c. Seems to me that something extra is required ... that after a Poincare synchronisation procedure is executed, although train clocks believe themselves to be simultaneous when in sync, that they in fact are not. If this mis-assumption in simultaneity is just right, then light can appear to travel at c out and c back even though it does not, because a misassumption in simultaneity can cause light's 1-way speed to "appear" invariant while it is not in reality. No?

I will have to study Lorentz's 1904 paper, and Poincare's 1905 corrections to get to the bottom of this. IOWs, to see LET as you guys do. I realize it is mathematically equivalent to SR, but I questions whether the meaning is the same. It seems to me they must mean the same for LET to uphold the PoR.

GrayGhost

 

[PAllen]

I will have to study Lorentz's 1904 paper, and Poincare's 1905 corrections to get to the bottom of this. IOWs, to see LET as you guys do. I realize it is mathematically equivalent to SR, but I questions whether the meaning is the same. It seems to me they must mean the same for LET to uphold the PoR.

GrayGhost

I don't think the meaning is the same. Just the predictions are the same. Bohm and many worlds interpretations of QM have radically different meanings, but purport to make identical predictions, in principle. LET and SR are similar - interpretations with very different meanings, but identical predictions.

As harrylin keeps pointing out, there is a simple conceptual proof that the predictions must be the same. SR says any inertial frame is as good as any other. Pick one, call it Bob, and declare Bob's measurements are real, by convention (anyone else transforms to Bob using LTs if they want). Clearly, there cannot be any difference in prediction. Now rename Bob to aether, and call the convention 'reality' and you have LET.

 

[atyy]

I will have to study Lorentz's 1904 paper, and Poincare's 1905 corrections to get to the bottom of this. IOWs, to see LET as you guys do. I realize it is mathematically equivalent to SR, but I questions whether the meaning is the same. It seems to me they must mean the same for LET to uphold the PoR.

As harrylin keeps pointing out, there is a simple conceptual proof that the predictions must be the same. SR says any inertial frame is as good as any other. Pick one, call it Bob, and declare Bob's measurements are real, by convention (anyone else transforms to Bob using LTs if they want). Clearly, there cannot be any difference in prediction. Now rename Bob to aether, and call the convention 'reality' and you have LET.

Is the LET defined by Lorentz's 1904 paper the same as the "modern" LET which is equivalent to SR?

 

[GrayGhost]

Is the LET defined by Lorentz's 1904 paper the same as the "modern" LET which is equivalent to SR?

Atyy,

Depends on who you ask, it seems. Poincare made a small correction and re-interpreted the meaning of "the 1904 paper" in 1905. It is documented that Poincare's 1905 work made LET fully Lorentz covariant, because time dilation was finally given a physical meaning (required to do so) by Poincare. Some contend that Lorentz understood this prior, but various documents suggest Lorentz either did not consider his t' as time dilation (prior to 1906), or that he simply didn't except it ... one or the other. I'm not well versed in LET myself, modern or old, so I'm not sure what changes may have been made to the theory since the 1905 Poincare mods. One of the other fellows here can tell us, I'm sure.

GrayGhost

 

[GrayGhost]

I don't think the meaning is the same. Just the predictions are the same. Bohm and many worlds interpretations of QM have radically different meanings, but purport to make identical predictions, in principle. LET and SR are similar - interpretations with very different meanings, but identical predictions.

Understood. I do understand the foundations differ. It's just that I find it difficult to believe that the solns would be identical and have the same meaning even though the foundations differ. I mean, the LTs transform frame-to-frame, and thus require no knowledge of the master aether frame's whereabouts. I must say, I have to give LET much more respect if that's all true. Need to bone up a bit.

As harrylin keeps pointing out, there is a simple conceptual proof that the predictions must be the same. SR says any inertial frame is as good as any other. Pick one, call it Bob, and declare Bob's measurements are real, by convention (anyone else transforms to Bob using LTs if they want). Clearly, there cannot be any difference in prediction. Now rename Bob to aether, and call the convention 'reality' and you have LET.

Yes, Harrylinn has said such. The problem I have is this ... LET theory assumes apriori that light is isotropic per the aether POV and "per measurement", because it's assumed real, and since the rulers & clock rates used to measure are not contracted. The derivation leads to the LTs, which require that inertial observers moving thru the aether also "measure" light as isotropic (using contracted rulers and contracted clock rate). Is it true that LET assumes isotropy of light within the aether frame "as real", and isotropy of light within moving frames "as measured" but something "less than real"? Or, is that a misconception?

GrayGhost

 

[atyy]

Understood. I do understand the foundations differ. It's just that I find it difficult to believe that the solns would be identical and have the same meaning even though the foundations differ. I mean, the LTs transform frame-to-frame, and thus require no knowledge of the master aether frame's whereabouts. I must say, I have to give LET much more respect if that's all true. Need to bone up a bit.

Let me define modern LET as Maxwell's equations plus the modified Newton's law. While SR is Maxwell's equations plus the principle of relativity.

Thus in modern LET, everything is defined using one canonical frame. However, the form of the equations is covariant under the Lorentz transforms, so modern LET implies SR.

OTOH, SR implies the modified Newton's law, so it implies modern LET.

So in LET, the modified Newton's law must come from a match to an experiment that isn't the Michelson-Morley experiment. I'm not sure how close Lorentz got to the modified Newton's law before Einstein, but John Bell does say that Lorentz did propose a modified Newton's law which looks pretty close. http://books.google.com/books?id=qou0iiLPjyoC&source=gbs_navlinks_s, p64, Eq 5.

 

[PAllen]

Is it true that LET assumes isotropy of light within the aether frame "as real", and isotropy of light within moving frames "as measured" but something "less than real"? Or, is that a misconception?

GrayGhost

Yes, exactly.

 

[GrayGhost]

Yes, exactly.

Well, all very interesting indeed. It becomes rather clear to me now why SR became the accepted theory. There is something that seems very desirable of the notion that nothing contracts in-and-of-itself, and that all measurements are just as real as the next. So it seems that the entire difference between the 2 theories is ...

LET assumes an aether frame exists in which light travels isotropically at c. This leads to the effect that moving bodies length-contract and moving clocks slow down. Contracted rulers and slower clocks cannot know they are as such. Measurements made by moving observers are something less than real, yet assumed correct.

SR is indifferent to whether an aether frame exists, and light is isotropic in all inertial frames. If it does, it is neither preferred or special in any way far as spacetime solns are concerned. Bodies, rulers, and clocks never change in-and-of-themselves, and remain always of their proper configuration. Any measurement is just as real as the next, and assumed correct.​

So where LET observers obtain LT results using unbeknownst contracted rulers and clocks, SR observers obtain the same LT results using uncontracted rulers and clocks ... and if any aether frame really does exist, both theories declare light isotropic in that frame. It makes much sense as to why the community accepted SR over LET, even though they have identical solns. I must say though, it still amazes me that Lorentz could have attained the correct solns, given his starting point. So, I'll need to study the LET to determine how he did so, determine what derivational assumptions allowed it to happen. That's what I'm most interested in at this point.

Thanx for all your inputs. Highly appreciated.

GrayGhost

 

[atyy]

So where LET observers obtain LT results using unbeknownst contracted rulers and clocks, SR observers obtain the same LT results using uncontracted rulers and clocks ... and if any aether frame really does exist, both theories declare light isotropic in that frame. It makes much sense as to why the community accepted SR over LET, even though they have identical solns. I must say though, it still amazes me that Lorentz could have attained the correct solns, given his starting point. So, I'll need to study the LET to determine how he did so, determine what derivational assumptions allowed it to happen. That's what I'm most interested in at this point.

Lorentz did try to derive length contraction from electrodynamics. He needed one assumption which is not true in classical electrodynamics - that the ground state configuration of a system of atoms is unique. Lorentz knew he was making this assumption and stated it clearly in his paper. Some have argued that since this is true in many quantum mechanical systems, this gap in Lorentz's derivation of length contraction has been filled in some cases.

An outline of Lorentz's attempt to derive length contraction is given in Bell's http://books.google.com/books?id=qou0iiLPjyoC&source=gbs_navlinks_s, p63-64.

 

[GrayGhost]

Atyy,

Thanx for the fine reference. I'm looking thru it. BTW, in an attempt to put it in a nutshell:

would you agree that any derivation (no matter what the foundation) that ...

(1) allows for contractions given invariant light in at least 1 frame, and
(2) requires all POVs to agree with the proper frame of the lightclock ...​

must end up Lorentz covariant and uphold the PoR?

GrayGhost

 

[atyy]

Atyy,

Thanx for the fine reference. I'm looking thru it. BTW, in an attempt to put it in a nutshell:

would you agree that any derivation (no matter what the foundation) that ...

(1) allows for contractions given invariant light in at least 1 frame, and
(2) requires all POVs to agree with the proper frame of the lightclock ...​

must end up Lorentz covariant and uphold the PoR?

GrayGhost

I don't understand what invariant light in 1 frame is, nor what a proper frame is (they're both probably right, but I don't know the jargon). But yes, any correct derivation must end up Lorentz covariant and uphold the principle of relativity.

 

[GrayGhost]

I don't understand what invariant light in 1 frame is, nor what a proper frame is (they're both probably right, but I don't know the jargon). But yes, any correct derivation must end up Lorentz covariant and uphold the principle of relativity.

Yes, I do of course recognize that any derivation "that does not result in the LTs" cannot be correct, because it cannot uphold the PoR (nor be Lorentz covariant).

Wrt "invariant light in 1 frame", by 1 frame I mean "the aether frame" per LET, and "any arbitrary frame" per SR. Basically, the starting frame for the LT derivation. By "proper frame of the lightclock", I suppose I could have just left that out and said "the light clock's frame" ... which of course deems itself stationary with the photon bouncing back-and-forth, while it moves thru the starting frame.

Requirement ... the starting frame cannot disagree as to whether (sync'ed) clocks and rulers attached to the reflectors of the lightclock recorded what they did. And said rulers and clocks do their thing no matter if observers of other frames are around to witness it or not, so the ray bounces back and forth per the lightclock POV just as in classical mechanics.

Just for cut-to-the-chase sake ... it seems to me that it's this requirement "in conjunction with the invariant light speed of the starting frame" that forces the LTs to always result as they do ... even though the foundations differ. IOWs, it can end up no other way unless you make a mathematical error in derivarion. no?

GrayGhost

 

[atyy]

Yes, I do of course recognize that any derivation "that does not result in the LTs" cannot be correct, because it cannot uphold the PoR (nor be Lorentz covariant).

Wrt "invariant light in 1 frame", by 1 frame I mean "the aether frame" per LET, and "any arbitrary frame" per SR. Basically, the starting frame for the LT derivation. By "proper frame of the lightclock", I suppose I could have just left that out and said "the light clock's frame" ... which of course deems itself stationary with the photon bouncing back-and-forth, while it moves thru the starting frame.

Requirement ... the starting frame cannot disagree as to whether (sync'ed) clocks and rulers attached to the reflectors of the lightclock recorded what they did. And said rulers and clocks do their thing no matter if observers of other frames are around to witness it or not, so the ray bounces back and forth per the lightclock POV just as in classical mechanics.

Just for cut-to-the-chase sake ... it seems to me that it's this requirement "in conjunction with the invariant light speed of the starting frame" that forces the LTs to always result as they do ... even though the foundations differ. IOWs, it can end up no other way unless you make a mathematical error in derivarion. no?

GrayGhost

The first requirement just seems to mean that we assume classical (not quantum) reality. I don't understand what "invariant light speed in the starting frame" means. (Sorry, you must have discussed this many pages ago while I wasn't paying attention).