# Relativity vs competing theories

by mangaroosh
Tags: competing, relativity, theories
P: 3,188
 Quote by DaleSpam I agree. This is why my understanding is that LET regards the PoR as being something that is violated in nature but cannot be detected.
I'm fed up with the strawman called "LET"; I now conclude that it is less than useless - thus I will from now on ban it completely.
P: 359
 Quote by ghwellsjr Exactly the same way as under SR. Yes, but nobody knows by what amount.
Apologies, I was probably a bit vague in the question. I thought I had read on here (may have been elsewhere) that LET would treat the slowing of the ticking clock as being a result of the mechanics of the clock being affected by the motion i.e. that the moving clock ticks slower because the photon has a longer distance to travel.

 Quote by ghwellsjr The difference is that LET would never consider the ground frame because it represents the stationary ether and we don't know where that is. We're all doomed to ride around on the train having our clocks running slow (by an unknown amount) and having our lengths contracted along the direction of the train (again, by an unknown amount). Einstein said, "You don't need the ground--just assume that you are stopped and anyone moving with respect to you is on a different train. All you care about is the relative difference in your respective trains. And everybody agreed.
Could LET be formulated without the superfluous rest frame? For example, if we were to say that if an absolute rest frame were to exist, then the earth would be moving relative to it with a velocity v and if an absolute rest frame were to exist, a train moving relative to the earth would be moving with a velocity u relative to that absolute rest frame.

Instead of assuming that we are stopped in the absolute rest frame, and considering everything else in motion with respect to us, could we assume that if an absolute rest frame were to exist, then we would be in motion with respect to it, as would everything else?

Again, we don't need the rest frame, we can just hypothesise that if one were to exist, that we would be in motion relative to it.
PF Gold
P: 4,779
 Quote by mangaroosh Apologies, I was probably a bit vague in the question. I thought I had read on here (may have been elsewhere) that LET would treat the slowing of the ticking clock as being a result of the mechanics of the clock being affected by the motion i.e. that the moving clock ticks slower because the photon has a longer distance to travel.
Prior to Einstein, Lorentz and others spent a lot of time trying to figure out the mechanics of length contraction and time dilation but nowadays, when we speak of LET, we have striped it of everything except the idea of a preferred rest frame.
 Quote by mangaroosh Could LET be formulated without the superfluous rest frame?
Well the idea of LET is that nature needs it in some unknown way to make things happen so there wouldn't be much point in formulating LET without that rest frame. It's not superfluous to LET.
 Quote by mangaroosh For example, if we were to say that if an absolute rest frame were to exist, then the earth would be moving relative to it with a velocity v and if an absolute rest frame were to exist, a train moving relative to the earth would be moving with a velocity u relative to that absolute rest frame. Instead of assuming that we are stopped in the absolute rest frame, and considering everything else in motion with respect to us, could we assume that if an absolute rest frame were to exist, then we would be in motion with respect to it, as would everything else? Again, we don't need the rest frame, we can just hypothesise that if one were to exist, that we would be in motion relative to it.
Sure, even in SR you don't have to pick a Frame of Reference in which you are at rest or the earth is at rest or the solar system is at rest or the galaxy is at rest. You can pick one in which you are traveling at any speed in any direction (as long as it is less than the speed of light).
P: 359
 Quote by ghwellsjr Prior to Einstein, Lorentz and others spent a lot of time trying to figure out the mechanics of length contraction and time dilation but nowadays, when we speak of LET, we have striped it of everything except the idea of a preferred rest frame.
Sorry, I'm not sure I get what you mean by "stripped it of everything".

 Quote by ghwellsjr Well the idea of LET is that nature needs it in some unknown way to make things happen so there wouldn't be much point in formulating LET without that rest frame. It's not superfluous to LET.
I'm just wondering, does it actually require an absolute rest frame? Again, we could hypothesise that if one were to exist, then we would be moving relative to it, but we don't really need to assert that it actually exists, simply that we [the earth] are in motion and not at absolute rest.

 Quote by ghwellsjr Sure, even in SR you don't have to pick a Frame of Reference in which you are at rest or the earth is at rest or the solar system is at rest or the galaxy is at rest. You can pick one in which you are traveling at any speed in any direction (as long as it is less than the speed of light).
Does that carry with it an implicit assumption that some reference frame is at rest?
PF Gold
P: 4,779
 Quote by mangaroosh Sorry, I'm not sure I get what you mean by "stripped it of everything".
Stripped of any characteristics of an ether to explain why lengths contract and clocks run slower. I thought I explained that. And I didn't say "everything", I said "everything except the idea of a preferred rest frame." Think of it exactly like any rest frame in Special Relativity except that there is only one in which the speed of light is actually c.
 Quote by mangaroosh I'm just wondering, does it actually require an absolute rest frame? Again, we could hypothesise that if one were to exist, then we would be moving relative to it, but we don't really need to assert that it actually exists, simply that we [the earth] are in motion and not at absolute rest.
LET postulates that there exists a single rest frame in which light travels at c. There is no proof or evidence for this but neither is there any proof or evidence that denies that it can't happen.
 Quote by mangaroosh Does that carry with it an implicit assumption that some reference frame is at rest?
Yes.

It's no different than Einstein's second postulate that light travels at c in any reference frame. That also has no proof or evidence but neither is there any proof or evidence that denies that it can't happen.

It sure seems to me like you're understanding this. I don't see why you keep asking the same questions and getting the same answers. Maybe you could explain why you're struggling with this.
P: 3,188
 Quote by mangaroosh [..] Could [..] be formulated without the superfluous rest frame?
That is just what Einstein did in 1905, and the result was SR. For that purpose he rephrased Maxwell's assumption about light propagation in vacuum by the same assumption relative to an unidentified but presumably arbitrary Newtonian system of reference (which he identified with "empty space") and made it a postulate. I find that physically a bit messy (discarding a physical model while keeping the phenomenon that is based on it), but it did the trick.
- http://www.fourmilab.ch/etexts/einstein/specrel/www/
- http://www.bartleby.com/173/7.html
 For example, if we were to say that if an absolute rest frame were to exist, then the earth would be moving relative to it with a velocity v and if an absolute rest frame were to exist, a train moving relative to the earth would be moving with a velocity u relative to that absolute rest frame.
That is correct of course. See also the discussion here which highlights the philosophical differences between interpretations:
- http://www.bartleby.com/173/7.html
 Instead of assuming that we are stopped in the absolute rest frame, and considering everything else in motion with respect to us, could we assume that if an absolute rest frame were to exist, then we would be in motion with respect to it, as would everything else? [..]
Obviously.
P: 3,188
 Quote by harrylin [..] in an earlier discussion I did refer to a better English translation which however is not online; and I also gave a link to the German original. And once more: if you like to discuss that paper in detail, I propose to start it as a topic, so that we not further hijack this thread and avoid diluting the same information in different threads. [..]
As a correct understanding of that paper may be of general interest, I now started a discussion of it as a new topic.

Harald
P: 359
 Quote by ghwellsjr The first rule of PF is that "All posts must be in English".
I thought the first rule of PF was "don't talk about fight club"
P: 359
 Quote by ghwellsjr It sure seems to me like you're understanding this. I don't see why you keep asking the same questions and getting the same answers. Maybe you could explain why you're struggling with this.
I think I am getting an understanding of it, but I'm not yet certain I understand the nuances of both; so my apologies if the questions are repetitive, but I'm not sure I that I have fully understood the implications; also, the statement that LET and SR would treat the light clock [on the train] thought experiment exactly the same, kind of threw me; because I thought both offered different explanations for what happens.

 Quote by ghwellsjr Stripped of any characteristics of an ether to explain why lengths contract and clocks run slower. I thought I explained that. And I didn't say "everything", I said "everything except the idea of a preferred rest frame." Think of it exactly like any rest frame in Special Relativity except that there is only one in which the speed of light is actually c.
I'm not sure if you expressed it exactly so, but the understanding I've garnered, from discussing it with you, would definitely be in accord with that; as mentioned though, the statement above kind of threw me. With regard to the "stripping of everything"; I probably should have been more explicit in my reference, because it was the "everything [else]" that I wasn't 100% on.

Please forgive my continual recourse to the light clock thought experiment, if it seems either naiive or monotonous; it's just that I [personally] find it quite helpful as a visual aid to addressing my understanding, or lack thereof. Essentially, the differences [as I understood them] are:

• the reciprocity of the contractions i.e. there is reciprocity under SR but not LET
Essentially, under SR each observers clock ticks normally, from their perspective, and it's the moving clock that ticks slower; but under LET, both clocks tick slower than the rest frame clock, but the trains clock ticks slowest (assuming a higher velocity relative to the rest frame)

• -the attributed cause of the contractions i.e. under SR time slows down, under LET it's the mechanics of the clock.
My understanding is that, under SR, the relative motion of the reference frame causes spacetime to be affected, such that lengths contract and time slows down; but under LET a slower ticking clock is ascribed to the mechanics of the clock arising from the motion relative to the rest frame - i.e. the photon has a longer distance to travel between mirrors in a moving clock.

My understanding of LET is that, if the observer on the train were in a windowless carriage - like Galileo's observer on the ship - they would not be able to determine if they were at absolute rest, so they could not tell if their clock was ticking at the "normal" rate, or if it was actually ticking slower, because they would have nothing to compare it to. If, however, they were able to see the earthbound clock, they would presumably be able to calculate that it was ticking faster (assuming the earth is traveling with a lower velocity relative to the rest frame)

I had a more detailed explanation of what I mean typed out, but I wanted to try and make it more concise. I can post that if the above isn't very clear.

 Quote by ghwellsjr LET postulates that there exists a single rest frame in which light travels at c. There is no proof or evidence for this but neither is there any proof or evidence that denies that it can't happen. Yes. It's no different than Einstein's second postulate that light travels at c in any reference frame. That also has no proof or evidence but neither is there any proof or evidence that denies that it can't happen.
I'm still a bit unclear as to the status of the second postulate; initially I thought it was absolutely set in stone, but I'm a lot less certain of that now. I fully trust what you say about it, but when others reference experiments which purportedly verify the second postulate, I wonder if there is some nuance that I haven't picked up on. To me it seems as though there is [at least limited] scope in the formulation of this postulate.

Again, just to return to the light clock thought experiment, to try and clarify my [lack of] understanding: the tick-tock of a light clock is determined by the distance the photon has to travel in the light clock; under SR this is represented by a line perpendicular to the midpoint of both mirrors. This would be the same as if the clock were at absolute rest.

I've been told that this representation of the path of the photon is not based on an assumption, but is something that is borne out by experiment; or from the verification of the second postulate; that it is because the speed of light is constant, regardless of motion relative to the source, that it has to be so, otherwise the observer on the train would measure a slower speed of light.

To me it appears as though this is not the case under LET, where, as you mention, we can just consider the train's clock from the absolute rest frame - which would be the same as the observer on the platform's view, in the Einsteinian version. In this case the tick-tock of the trains clock is not simply the perpendicular line between the midpoints of the two mirrors, rather the line as represented by the hypotenuse of a right angled triangle; and this would be as true for the observer on the train as for the observer in the absolute rest frame - even if the observer on the train could not determine that it was so.

Hopefully the above makes sense, and if I haven't entirely exhausted your patience, if you could point out anywhere I might be going wrong, I would be very greatful.
P: 3,188
 Quote by mangaroosh [..] I thought both offered different explanations for what happens. [..]
Well yes, but the explanations are at different levels, just as Newton's explanations differ from what nowadays is called classical mechanics. As Lorentz later put it: “Einstein simply postulates what we have deduced [...] from the fundamental equations of the electromagnetic field”. Note that that remark refers to the second postulate: the PoR was not deduced from the field equations but appeared to be at odds with it.

 [..] if the observer on the train were in a windowless carriage - like Galileo's observer on the ship - they would not be able to determine if they were at absolute rest, so they could not tell if their clock was ticking at the "normal" rate, or if it was actually ticking slower, because they would have nothing to compare it to. If, however, they were able to see the earthbound clock, they would presumably be able to calculate that it was ticking faster (assuming the earth is traveling with a lower velocity relative to the rest frame)
I can see no reason for such an assumption in any interpretation of SR.

 I'm still a bit unclear as to the status of the second postulate; initially I thought it was absolutely set in stone, but I'm a lot less certain of that now. [..]
There are several formulations of it; its purpose was to provide a necessary condition based on Maxwell's electrodynamics for the derivation of the new transformation equations. A postulate based on an alternative electrodynamics theory such as by Stokes or Ritz leads to other transformations.
 Again, just to return to the light clock thought experiment, to try and clarify my [lack of] understanding: the tick-tock of a light clock is determined by the distance the photon has to travel in the light clock; under SR this is represented by a line perpendicular to the midpoint of both mirrors. This would be the same as if the clock were at absolute rest. I've been told that this representation of the path of the photon is not based on an assumption, but is something that is borne out by experiment; or from the verification of the second postulate; that it is because the speed of light is constant, regardless of motion relative to the source, that it has to be so, otherwise the observer on the train would measure a slower speed of light.
That is slightly inaccurate; as I think was highlighted in this thread or in another recent thread, experimental results of that time discarded all light models except that of Maxwell-Lorentz. However, in view of several other experiments such as MMX also that one was in problems, and a fix was needed to make it PoR-compatible.
 [..] we can just consider the train's clock from the absolute rest frame - which would be the same as the observer on the platform's view, in the Einsteinian version. In this case the tick-tock of the trains clock is not simply the perpendicular line between the midpoints of the two mirrors, rather the line as represented by the hypotenuse of a right angled triangle; and this would be as true for the observer on the train as for the observer in the absolute rest frame - even if the observer on the train could not determine that it was so. [..]
Your line of thinking seems to be a preparation for MMX, as well as, potentially the later KTX:
http://en.wikipedia.org/wiki/Kennedy...ike_experiment

With such known and future experimental results was dealt with here:
http://en.wikisource.org/wiki/Electromagnetic_phenomena

Harald
P: 359
Hey Harry, thanks for replying. Firstly, can I assume, from the lack of comment, that what I wrote about the reciprocity of contractions and the attributed cause of contractions is accurate?
 Quote by harrylin Well yes, but the explanations are at different levels, just as Newton's explanations differ from what nowadays is called classical mechanics. As Lorentz later put it: “Einstein simply postulates what we have deduced [...] from the fundamental equations of the electromagnetic field”. Note that that remark refers to the second postulate: the PoR was not deduced from the field equations but appeared to be at odds with it.
I would potentially question what is deduced from the fundamental equations, particularly because Lorentz's ether theory appears to be based on a slightly different deduction; am I right in that?

 Quote by harrylin I can see no reason for such an assumption in any interpretation of SR.
It wasn't an assumption for SR, it was the application of the principle of relativity to LET; at least that was the intention.

 Quote by harrylin There are several formulations of it; its purpose was to provide a necessary condition based on Maxwell's electrodynamics for the derivation of the new transformation equations. A postulate based on an alternative electrodynamics theory such as by Stokes or Ritz leads to other transformations.
Would it be equally possible to formulate it as, the speed of light is constant with respect to the point of emission, but independent of the motion of the source? Would that conflict with any experimental evidence?

 Quote by harrylin That is slightly inaccurate; as I think was highlighted in this thread or in another recent thread, experimental results of that time discarded all light models except that of Maxwell-Lorentz. However, in view of several other experiments such as MMX also that one was in problems, and a fix was needed to make it PoR-compatible.
Apologies, I keep having to refer back to the light clock on the train thought experiment; does that mean that both the treatment of the path of the photon in SR and LET are possible?

When I say the treatment of the photon under LET, I mean my understanding as I've outlined above i.e. that the path of the photon is not necessarily the perpendicular line between the midpoints of the two mirrors, but rather the path represented by the hypotenuse of a right angled triangle.

 Quote by harrylin Your line of thinking seems to be a preparation for MMX, as well as, potentially the later KTX: http://en.wikipedia.org/wiki/Kennedy...ike_experiment With such known and future experimental results was dealt with here: http://en.wikisource.org/wiki/Electromagnetic_phenomena Harald
To a certain extent it is a prep. for MMX; again, I'm wondering if the representation of the path of a photon [in a light clock] under LET were a representation of a photon in the MMX, would the null result still arise; I presume it would, but I'm not sure.
PF Gold
P: 4,779
 Quote by mangaroosh the reciprocity of the contractions i.e. there is reciprocity under SR but not LET Essentially, under SR each observers clock ticks normally, from their perspective, and it's the moving clock that ticks slower; but under LET, both clocks tick slower than the rest frame clock, but the trains clock ticks slowest (assuming a higher velocity relative to the rest frame)
There is no difference in what we know is actually happening under SR or under LET. It is only a difference in what you are assigning to things that you can't know are happening. In SR once you assign a Frame of Reference, which defines times and distances, then the reciprocity disappears. If you select a FoR in which you are not at rest, or if you start moving after you select a FoR in which you started out at rest, then time for you is dilated and your lengths are contracted, although you can't tell that. It's only when you then transform all the distances and times (events) into a new definition (a different FoR) that what was assigned a shorter distance or a longer time in one FoR takes on a longer distance or a shorter time in the other FoR.

The easiest way I know to communicate this idea is to think just about relative motion. If A and B are in relative motion, in one FoR, A is assigned a speed of zero and B is assigned a non-zero speed. In another FoR, B is assigned a speed of zero and A is assigned non-zero speed. Do you think that using a different FoR caused A to suddenly start moving? I don't think so, I think with regard to motion, different frames make perfect sense. The same thing applies to length contraction and time dilation. The ones that have motion according to the FoR that you are using are the ones for which lengths and times take on a different meaning.

 Quote by mangaroosh -the attributed cause of the contractions i.e. under SR time slows down, under LET it's the mechanics of the clock. My understanding is that, under SR, the relative motion of the reference frame causes spacetime to be affected, such that lengths contract and time slows down; but under LET a slower ticking clock is ascribed to the mechanics of the clock arising from the motion relative to the rest frame - i.e. the photon has a longer distance to travel between mirrors in a moving clock.
Do you think that just because in one FoR B is stationary and in another one B is moving that spacetime is affected? Nothing is happening in space or time or spacetime just because you choose to use a different FoR to assign distances and times differently such that A is stationary under one of those definitions and moving under a different definition.

In the early days, Lorentz and others were trying to determine how the mechanics of a clock would cause it to slow down as it traveled through the ether but now we don't worry about that. What we do instead is verify that the laws of physics transform intact under the Lorentz transformation. If they don't, we know they are not valid and we change them until they do. If they do, then we don't have to be concerned about the specific mechanics, it will happen automatically.
P: 3,188
 Quote by mangaroosh Hey Harry, thanks for replying. Firstly, can I assume, from the lack of comment, that what I wrote about the reciprocity of contractions and the attributed cause of contractions is accurate?
Not really, it only means that when skimming over that part I didn't see anything shocking.
I wasn't sure about what you meant and decided to leave it. [Addendum: I agree with George's clarifications.]
However, with my remark in post #38 I meant that I decided from now on to abstain from discussions about a hypothetical competing theory to "relativity theory" as I find it too artificial - surely you notice that "ban" in my latest posts.
Historically there are different interpretations of what started out as the "Lorentz-Einstein theory of relativity" and the idea that Lorentz and Einstein proposed competing theories emerged later. In the early years they promoted the new theory together and their interpretations were not distinguished in presentations and papers. That should hardly be surprising, as physicists tend to focus on the predictions of a theory and not on "metaphysics".
 I would potentially question what is deduced from the fundamental equations [..]
Lorentz already answered that: deduced was what Einstein made a postulate. The fundamental equations suggested to Maxwell and followers that light is a wave with propagation constant c in vacuum.
 Would it be equally possible to formulate it as, the speed of light is constant with respect to the point of emission, but independent of the motion of the source? Would that conflict with any experimental evidence?
Not clear what distinction you make: the speed with respect to one point is equal to the speed with respect to all points - that makes no difference.
 [..] I mean my understanding as I've outlined above i.e. that the path of the photon is not necessarily the perpendicular line between the midpoints of the two mirrors, but rather the path represented by the hypotenuse of a right angled triangle. [..]
I'm not sure that I understood your set-up, if it wasn't a bit like MMX; and as I already indicated, basic (x,t) problems like MMX and the later KTX were perfectly dealt with in Lorentz's 1904 paper.
P: 359
 Quote by ghwellsjr There is no difference in what we know is actually happening under SR or under LET. It is only a difference in what you are assigning to things that you can't know are happening. In SR once you assign a Frame of Reference, which defines times and distances, then the reciprocity disappears. If you select a FoR in which you are not at rest, or if you start moving after you select a FoR in which you started out at rest, then time for you is dilated and your lengths are contracted, although you can't tell that. It's only when you then transform all the distances and times (events) into a new definition (a different FoR) that what was assigned a shorter distance or a longer time in one FoR takes on a longer distance or a shorter time in the other FoR. The easiest way I know to communicate this idea is to think just about relative motion. If A and B are in relative motion, in one FoR, A is assigned a speed of zero and B is assigned a non-zero speed. In another FoR, B is assigned a speed of zero and A is assigned non-zero speed. Do you think that using a different FoR caused A to suddenly start moving? I don't think so, I think with regard to motion, different frames make perfect sense. The same thing applies to length contraction and time dilation. The ones that have motion according to the FoR that you are using are the ones for which lengths and times take on a different meaning.
Thanks gh; I think I understand the scenario above.

If we consider both A and B as "objective" observers, which I think we can do because it is a thought "experiment". From A's perspective, he can consider himself at rest and so the instruments in B's reference frame undergo contraction; while B can also consider himself at rest and it is A's instruments that contract, form B's perspective. The instruments will contract by the same amount.That is what I meant by reciprocity.

As I understand it, under LET the contractions aren't reciprocal, in this way. If for example we were to have 3 observers: A is in the absolute rest frame; B is at rest on earth; C is on the train; where the train is moving with a higher relative velocity to the rest frame, than the earth. Then A will see the instruments in the other reference frames contract; B will see C's instruments contract but A's will "expand" [just to contrast with "contract"]; while C will see the other instruments [in both reference frames] expand.

 Quote by ghwellsjr Do you think that just because in one FoR B is stationary and in another one B is moving that spacetime is affected? Nothing is happening in space or time or spacetime just because you choose to use a different FoR to assign distances and times differently such that A is stationary under one of those definitions and moving under a different definition. In the early days, Lorentz and others were trying to determine how the mechanics of a clock would cause it to slow down as it traveled through the ether but now we don't worry about that. What we do instead is verify that the laws of physics transform intact under the Lorentz transformation. If they don't, we know they are not valid and we change them until they do. If they do, then we don't have to be concerned about the specific mechanics, it will happen automatically.
I suppose I'm just trying to see what the logical conclusion is. If there is absolute simultaneity under LET, but there are clocks which tick at different times, then it seems like it has to be the mechanics which causes the clocks to slow down and not "time" slowing down. Under SR, it appears as though the slowing of the clocks is attributed to the slowing of time.

Does that make sense, or is it way off?
P: 359
 Quote by harrylin Not really, it only means that when skimming over that part I didn't see anything shocking. I wasn't sure about what you meant and decided to leave it. [Addendum: I agree with George's clarifications.] However, with my remark in post #38 I meant that I decided from now on to abstain from discussions about a hypothetical competing theory to "relativity theory" as I find it too artificial - surely you notice that "ban" in my latest posts. Historically there are different interpretations of what started out as the "Lorentz-Einstein theory of relativity" and the idea that Lorentz and Einstein proposed competing theories emerged later. In the early years they promoted the new theory together and their interpretations were not distinguished in presentations and papers. That should hardly be surprising, as physicists tend to focus on the predictions of a theory and not on "metaphysics".
It wasn't immediately clear, probably because I was reading them through the lens of "relativity vs competing theories"; though, I was wondering how you managed to quote a part of my post and leave out the important qualifier referencing LET I presumed it was intentional but I wasn't clear as to what the intention was.

I know physicists tend not to focus on the "metaphysics" but scientific theories have "metaphysical" implications, and insofar as physicists are concerned with accurately describing reality they are concerned with metaphysics; of course, where they are not concerned with accurately describing reality, they are not concerned with metaphysics. Given that the differences between [what has been described in this thread as] LET and Einsteinian relativity are effectively metaphysical, it is probably unavoidable to discuss them without discussing the metaphysics. Who knows a certain level of metaphysical consideration could actually facilitate the unification of QM and SR.

[QUOTE=harrylin;3754767]Lorentz already answered that: deduced was what Einstein made a postulate. The fundamental equations suggested to Maxwell and followers that light is a wave with propagation constant c in vacuum.[/quote
The speed of light being a constant (c) in vacuum, and the speed of light being c regardless of the motion relative to the source, appear to be somewhat different.

 Quote by harrylin Not clear what distinction you make: the speed with respect to one point is equal to the speed with respect to all points - that makes no difference.
This is an area where I am not clear. The speed of light being constant with respect to one point, doesn't necessarily mean that it is constant with respect to all points - which I know is not what you were suggesting.

Has the latter been borne out by experimental evidence, or has it just not been contradicted by experimental evidence?

Part of my confusion arises because it seems as though LET has a different "second postulate" than Einsteinian relativity, which also fits the evidence. This leads me to believe there is limited scope for deducing a postulate with respect to the speed of light - would that be correct?

 Quote by harrylin I'm not sure that I understood your set-up, if it wasn't a bit like MMX; and as I already indicated, basic (x,t) problems like MMX and the later KTX were perfectly dealt with in Lorentz's 1904 paper.
If we consider the two light clock examples, form SR and LET (as I understand it).

Under SR the path of the photon traces a line perpendicular to the two mirrors; while under LET [as I understand it] the photon traces a line as represented by the hypotenuse of a right angled triangle.

Under SR, the photon has a strictly vertical velocity component of c, and so the observer would measure the speed of light to be c, relative to the carriage.

Under LET, the photon has a velocity of c in the horizontal (or diagonal) direction - due to the motion of the train and the clock - but not a velocity of c in the vertical direction. If the observer can only measure the speed relative to his reference frame he would not measure the speed of light to be c, but some lower value.

If both theories equally explain the evidence, then it suggests that the speed of light is not necessarily constant in all directions, regardless of the motion relative to the source.

It has been suggested [by others, elsewhere] that the MMX demonstrates that the speed of light is constant in all directions, regardless of the motion relative to the source; however, if the null result of the MMX is equally explained under LET, then this seems to suggest that this isn't the case.

Again, hopefully the above makes sense.
PF Gold
P: 4,779
 Quote by mangaroosh Thanks gh; I think I understand the scenario above. If we consider both A and B as "objective" observers, which I think we can do because it is a thought "experiment". From A's perspective, he can consider himself at rest and so the instruments in B's reference frame undergo contraction; while B can also consider himself at rest and it is A's instruments that contract, form B's perspective. The instruments will contract by the same amount.That is what I meant by reciprocity. As I understand it, under LET the contractions aren't reciprocal, in this way. If for example we were to have 3 observers: A is in the absolute rest frame; B is at rest on earth; C is on the train; where the train is moving with a higher relative velocity to the rest frame, than the earth. Then A will see the instruments in the other reference frames contract; B will see C's instruments contract but A's will "expand" [just to contrast with "contract"]; while C will see the other instruments [in both reference frames] expand. I suppose I'm just trying to see what the logical conclusion is. If there is absolute simultaneity under LET, but there are clocks which tick at different times, then it seems like it has to be the mechanics which causes the clocks to slow down and not "time" slowing down. Under SR, it appears as though the slowing of the clocks is attributed to the slowing of time. Does that make sense, or is it way off?
You have to make a distinction between what an observer actually sees or perceives or measures and what is defined by a Frame of Reference which includes things that observers cannot see or perceive or measure. A theory such as SR or LET cannot have any bearing on what an observer sees or measures or perceives, can it? If a theory said that an observer sees or measures or perceives something different than what the observer is experiencing, then that theory does not comport with reality.

No observer will ever see, perceive or measure another object to be expanded (or time to be contracted), they always see things moving with respect to themselves as contracted and clocks running slower.

A Frame of Reference is a scheme to allow us to assign dimensions of space and time. When we say that an object is contracted in a given FoR and other objects are normal, we don't mean that the contracted object (or observer) will see the normal one as expanded, they are still going to see it as contracted.

Under the idea of LET, there is only one Frame of Reference that was considered to be real. All objects moving in that frame will be contracted and time will be running slower depending on their speeds. These were considered to be real contractions and clocks slowing down but the observer cannot be aware of this. When they view other objects and clocks, even ones that are at rest in the ether, they still see them as contracted and time dilated, but it is not considered reality, it is considered in LET to be an artifact.

So under LET, the contractions are perceived to be reciprocal but they are not believed to be actually reciprocal. Under SR, under any particular FoR, the contractions are also not reciprocal although they will be perceived to be reciprocal. It's just that under SR, we don't regard any one FoR to be preferred so we don't claim that one FoR is the only one for which the contractions are actual and other contractions are artifacts.

When we are talking about reference frames, we don't say that A sees B to be contracted, everybody that is using the assigned dimensions for the frame of reference says that B is contracted while A is not if B is the one that is moving and A is stationary.
P: 359
 Quote by ghwellsjr You have to make a distinction between what an observer actually sees or perceives or measures and what is defined by a Frame of Reference which includes things that observers cannot see or perceive or measure. A theory such as SR or LET cannot have any bearing on what an observer sees or measures or perceives, can it? If a theory said that an observer sees or measures or perceives something different than what the observer is experiencing, then that theory does not comport with reality.
Apologies, this is somewhat like learning a new language for me; as with learning a new language it is usually easier to understand what is being said, than it is to express oneself. Similarly, I think my understanding is somewhat betrayed by my inability to express that understanding clearly and using the correct terminology. Hopefully it isn't as frustrating for you [and others] as it is for me.

I understand that theories, such as SR and LET, cannot affect what an observer measures or perceives; am I right in saying that a theory is an explanation of what an observer sees and/or perceives, which also makes predictions about what an observer should see under certain conditions; the veracity of these predictions makes or breaks the theory. In the case of both LET and SR, both have stood up to the test - LET indirectly at least.

 Quote by ghwellsjr No observer will ever see, perceive or measure another object to be expanded (or time to be contracted), they always see things moving with respect to themselves as contracted and clocks running slower. A Frame of Reference is a scheme to allow us to assign dimensions of space and time. When we say that an object is contracted in a given FoR and other objects are normal, we don't mean that the contracted object (or observer) will see the normal one as expanded, they are still going to see it as contracted. Under the idea of LET, there is only one Frame of Reference that was considered to be real. All objects moving in that frame will be contracted and time will be running slower depending on their speeds. These were considered to be real contractions and clocks slowing down but the observer cannot be aware of this. When they view other objects and clocks, even ones that are at rest in the ether, they still see them as contracted and time dilated, but it is not considered reality, it is considered in LET to be an artifact. So under LET, the contractions are perceived to be reciprocal but they are not believed to be actually reciprocal. Under SR, under any particular FoR, the contractions are also not reciprocal although they will be perceived to be reciprocal. It's just that under SR, we don't regard any one FoR to be preferred so we don't claim that one FoR is the only one for which the contractions are actual and other contractions are artifacts. When we are talking about reference frames, we don't say that A sees B to be contracted, everybody that is using the assigned dimensions for the frame of reference says that B is contracted while A is not if B is the one that is moving and A is stationary.
I'm not sure I fully understand, so forgive me if I return to the comfort blanket of the light clock thought experiment.

Reciprocity in SR
According to SR, the observer on the platform will see the clock on the train ticking slower, because, from their perspective, the photon travels a longer distance between the mirrors. Simultaneously [in the relative sense], the observer on the train will see the exact same for the clock on the platform. In this sense the observed contraction (or time dilation) is reciprocal. Why does the perception differ from the actual; does time dilation actually occur in any of the reference frames?

I know that A will perceive it to happen in B's reference frame; while simultaneously [again, in the relative sense] B will perceive it to happen in A's reference frame; but both are free to label themselves as being at rest, so it should be reciprocal. But if it is not actually reciprocal in which reference frame does it occur, if at all?

Reciprocity in LET
I also have trouble seeing why, according to LET, an observer will perceive reciprocal contractions, just the same as in the SR interpretation.

As I understand it, there is a key difference between SR and LET [in terms of the light clock thought experiment]; according to SR both observers clocks will tick at the "normal" rate in their own reference frames, and this is partly what leads to them observing the other clock running slow; because it is by comparison. If their clock were running just as slow, then they would presumably see both clocks ticking equally.

This is slightly different under LET, as I understand it; if we, again, just stick with the observer on the platform as being in the absolute rest frame, and the train moving relative to it, then, according to LET, the trains clock will actually be running slower in the observer on the train's reference frame as well. They, however , will not be able to tell by how much it is running slower because they cannot detect the absolute rest frame - in this case, they are in a windowless carriage and can't see the clock on the platform.

However, if they could see the clock on the platform, they would presumably be able to calculate that it is ticking faster; if they knew the distance from themselves to the platform clock at any given moment. In terms of what they would perceive, I find it difficult to imagine, perhaps the further away they are the slower the clock would appear to tick, but it would probably appear to speed up as they approach it, peaking as they are in line with it and then slowing down again because the light from the clock has further to travel to meet their retina. Again, though, I presume they would be able to calculate that it was ticking faster.

Remove absolute rest
Of course, they cannot detect the absolute rest frame, they can only observe other objects that are moving relative to this fantasy FoR. If we imagine that the train is traveling relative to the earth, such that the train has the higher velocity relative to the rest frame, then the earth's clock would be ticking faster than the trains clock, and just as they would do with the absolute rest frame clock [if they could detect it], they could presumably calculate that the earth's clock was ticking faster - by a smaller amount than the rest frame clock (if they were able to detect it).

That would be my understanding of it, but I'm not sure if there is something I've overlooked, or that I'm not aware of.
P: 3,188
 Quote by mangaroosh [..] The speed of light being a constant (c) in vacuum, and the speed of light being c regardless of the motion relative to the source, appear to be somewhat different.
Not if you understand the physical concept behind it: it was (and still is) taken for granted that the speed of a wave is completely independent of that of the source. In the introduction of his 1905 paper Einstein simply phrased it as follows:

"light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body"
 This is an area where I am not clear. The speed of light being constant with respect to one point, doesn't necessarily mean that it is constant with respect to all points - which I know is not what you were suggesting.
According to SR (but not GR) it is everywhere the same constant relative to all points in space as defined with a Newtonian reference system ("inertial frame"). Thus, probably I did not understand what you meant (and I still don't!).
 Has the latter been borne out by experimental evidence, or has it just not been contradicted by experimental evidence?
That is the same thing: the best that can be borne out by experimental evidence is a persistent lack of contradiction. In practice that ideal can't even be reached as no experiment is perfect.
 Part of my confusion arises because it seems as though [Lorentz] has a different "second postulate" than Einstein[..], which also fits the evidence. This leads me to believe there is limited scope for deducing a postulate with respect to the speed of light - would that be correct? [..]
I don't know what you mean with that; Lorentz did not really work with "postulates" but developed theories based on physical models and the results of experiments.

However, as Lorentz came to prefer Einstein's derivation over his own (which indeed was much more complicated), perhaps it's useful to highlight how they they fit together, although Lorentz might phrase a few sentences a little different from Einstein. For the subtlety of the difference is, if I see it correctly, what you are missing.

So, please take Einstein's 1905 derivation and I'll show you how easy it is to switch between Lorentz and Einstein. The following translation is quite OK:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

To make his derivation perfectly "Lorentz compatible", only a few sentences need slight modification (in italics) as follows:

Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties that permit the detection of absolute velocity. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies. The concept of a “luminiferous ether” will be helpful to explain the second postulate; however the theory will not provide a “preferred stationary space” with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.

That's about it; if I see it correctly, there isn't much else that really needs to be modified although Lorentz would add here and there some more qualifiers as "true", "apparent", "local" etc.

However, Einstein makes a subtle switch from "empty space" to "reference system" without a clear motivation. To make the logic as well as the derivation easier to follow for the readers, Lorentz could instead stick with the original, physical meaning of the second postulate as formulated in the introduction - let's call it Maxwell's light postulate.

Next, Lorentz could explain that if we combine Maxwell's light postulate with the PoR, it follows that this postulate should also appear to hold in an inertial reference system that is in motion with respect to the ether, so that it could appear to be a "stationary" system just as in Newton's mechanics. He could refer to his 1895 and 1899 papers that explain how this works.

If we next operationally define all terms such as "speed", "time" etc. as described in section 1 (free from metaphysical meaning), then we obtain the following result:

Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.

I hope that this sufficiently clarifies the perceptual differences as well as the complete lack of difference in practice.

Harald

ADDENDUM: I forgot to point out that from Lorentz perspective one may proceed the derivation directly based on Maxwell's version of the light postulate, it is not necessary to make the intermediate step from "empty space" to an arbitrary Newtonian reference system.
Einstein wouldn't like that but it's much more straightforward (and of course, Newton would like that).

The Lorentz transformations that then result describe primarily a transformation between a system that is at rest in the ether and one in inertial motion. Thanks to the form of those transformation equations (they form a group), the same transformation equations are valid between inertial reference systems - just as is the case with the Galilean transformations.

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