Relativity of simultaneity and one-way speed of light

[Andromacus]

In Special relativity, the relativity of simultaneity and absence of an absolute time makes synchronization of clocks a conventional procedure, and therefore prevents from having a measurable one-way speed of light independent of the convention of simultaneity chosen.

By choosing Einstein's standard synchronization we get the one-way speed of light equal to the measurable round-trip speed.

 

The issue I have with this is that it would seem like the second postulate of invariance of the speed of light seems to impose(by the postulated isotropy of space) that the only valid synchronization is Einstein's, wich would be incompatible with the conventionality of synchronization. In fact they need to use this convention(and an absolute time t) to define the null interval ds^2=0 using the equation "distance travelled by a ray of light=ct, since only Eistein's synchronization is compatible with this equation that implies that the speed of the light from point one to point 2 equals that from point 2 to point one. Besides, as mentioned above, isotropy and homogeneity of the space where this distance is computed should assure this result.

 

But then how do we reconcie this with the conventionality of synchronicity?(i.e. we should be able to choose any convention, not just one), imposed by the first postulate of relativity, the usual answer is that special relativity don't have an absolute time, but at least when dealing with light and null intervals it is obvious that only one absolute time is allowed by the second postulate.

 

Any way out of this conundrum, or is this just a known inconsistency of the theory that we must live with?

 

 

[swansont]

(i.e. we should be able to choose any convention, not just one)

 

On the one hand, do you have evidence that this is true?

 

On the other, no, we are not always free to choose conventions, since science must reflect how nature behaves. IOW it's entirely possible that you could come up with a synchronization procedure that is different and self-consistent, but if nature doesn't behave that way, you are compelled to discard it. e.g. Galilean physics is self-consistent, but we can't use it for high speeds, because it gives errors. You could adopt absolute time, but again, nature doesn't behave that way.

[Andromacus]

 

On the one hand, do you have evidence that this is true?

 

On the other, no, we are not always free to choose conventions, since science must reflect how nature behaves. IOW it's entirely possible that you could come up with a synchronization procedure that is different and self-consistent, but if nature doesn't behave that way, you are compelled to discard it. e.g. Galilean physics is self-consistent, but we can't use it for high speeds, because it gives errors. You could adopt absolute time, but again, nature doesn't behave that way.

The evidence is the theory of special relativity, where it is assumed by definition if one is to have relativity of simultaneity, because in special relativity this(the relativity of simultaneity, i.e. arbitrary choice of clock synchronization to determine which events are simultaneous) is a feature that ought to reflect how nature behaves(the fact that there is no absolute time/space and therefore we can talk about stuff like time dilation and length contraction).

The thing is that if one commits oneself to just one synchronization procedure, like the second postulate demands(at least for lightlike paths) in inertial frames(essentially one must use the galilean concept of time and synchronization of clocks to describe the velocity of light,except of course in galilean physics this speed was not a limit) then it is hard to see how one must at the same time demand arbitrariness in the choice of clock synchronization wich is consubstantial to the relativity of simultaneity.

In other words we have to reconcile absolute (global) time for null intervals that relies in the particular Einstein's synchronization(used to derive the Lorentz transformations in most SR textbooks and the foundational 1905 paper by Einstein) with relative (local) time, subject to conventional synchronization of clocks.

Edited August 31, 2015 by Andromacus

[studiot]

SR deals with one section, called mechanics, of the stuff of our universe.

 

More disciplines such as thermodynamics and electrodynamics deal with other sections.

 

All employ certain properties that we plot on orthogonal axes, yet there is interaction between the properties plotted along these axes, despite the orthogonality.

 

This is another way of saying you cannot affect one property with affecting at least some of the others.

 

In the case of relativity one of these relationships is described by simultaneity, and, as swansont says, of the many and various conceivable relationships we must go with the one that we observe to fit.

[Andromacus]

In the case of relativity one of these relationships is described by simultaneity, and, as swansont says, of the many and various conceivable relationships we must go with the one that we observe to fit.

The fact is that the one-way speed of light is not observable by definition, it is subject to the synchronization procedure chosen, in the case we choose Einstein's synchronization we have that by definition it must be equal to the round-trip speed that is observable.

The conundrum arises because on the one hand we must use Einstein's synchronization to respect the light postulate and on the other hand the relativity of simultaneity forces us to consider arbitrary different synchronizations as possible, not only Einstein's. I guess it is subtle to see this, but it is simple enough if one looks at it carefully. I'm not sure if this deserves to be called a contradiction if it doesn't lead to serious consequences, but it sure looks like sort of an inconsistency of the theory.

[swansont]

The evidence is the theory of special relativity, where it is assumed by definition if one is to have relativity of simultaneity, because in special relativity this(the relativity of simultaneity, i.e. arbitrary choice of clock synchronization to determine which events are simultaneous) is a feature that ought to reflect how nature behaves(the fact that there is no absolute time/space and therefore we can talk about stuff like time dilation and length contraction).

The thing is that if one commits oneself to just one synchronization procedure, like the second postulate demands(at least for lightlike paths) in inertial frames(essentially one must use the galilean concept of time and synchronization of clocks to describe the velocity of light,except of course in galilean physics this speed was not a limit) then it is hard to see how one must at the same time demand arbitrariness in the choice of clock synchronization wich is consubstantial to the relativity of simultaneity.

In other words we have to reconcile absolute (global) time for null intervals that relies in the particular Einstein's synchronization(used to derive the Lorentz transformations in most SR textbooks and the foundational 1905 paper by Einstein) with relative (local) time, subject to conventional synchronization of clocks.

 

SR works, but is that evidence that an alternative system would not? I don't see how the second postulate "demands" a particular synchronization protocol. If one chose a protocol where the time was not corrected by t = L/c, it would have no effect on time intervals, just on what time it is. And the latter, I think, is only a matter of convenience. Every point having its own time and requiring a correction for location within a frame would be a horrible mess to keep track of, but that's not the same as being wrong.

[Andromacus]

 

SR works, but is that evidence that an alternative system would not? I don't see how the second postulate "demands" a particular synchronization protocol. If one chose a protocol where the time was not corrected by t = L/c, it would have no effect on time intervals, just on what time it is. And the latter, I think, is only a matter of convenience. Every point having its own time and requiring a correction for location within a frame would be a horrible mess to keep track of, but that's not the same as being wrong.

Yes, I see your point, that system would not be wrong, that's what I'm saying too, and that's what SR says. But only t=L/c(with this particular global t) allows us to put forward the second postulate, any other doesn't give us a c invariant in any inertial frame.

But as I said, I guess by defining an unobservable one-way speed that loophole is maintained without much harm to the theory,

For instance the timelike paths are not affected by this problem but then again the Lorentz transformations for massive particles can be derived independently of the second postulate like they were by Lorentz, Poincare or Voigt before Einstein's paper.

It is the null paths that according to Einstein can only be derived by using the equation of the quotient between an absolute distance and an absolute time to give an invariant c in every inertial frame. It is paradoxical that from this one can obtain the Lorentz transformations that exemplify the relativity of simultaneity and therefore the end of absolutes.

[swansont]

Now that I think about this more, the system I described won't work. If you send a signal out at noon and I get it, I can't set my clock to noon, since if I sent a signal out at noon, your clock would say it's 2L/c after noon. But that points to symmetry being the requirement here, not the invariant speed of light.

[Andromacus]

Now that I think about this more, the system I described won't work. If you send a signal out at noon and I get it, I can't set my clock to noon, since if I sent a signal out at noon, your clock would say it's 2L/c after noon. But that points to symmetry being the requirement here, not the invariant speed of light.

Actually the symmetry argument is defended by Malament(see:Malament, 1977. "Causal Theories of Time and the Conventionality of Simultaniety,") but he is the only author that argues against the conventionality of synchronization.

 

In any case regardless of whether one considers conventionality a requirement of the theory or not the contradiction comes from the fact that only with Einstein's standard synchronization(with equal times for a ray going from A to B and from B to A) can one obtain a speed c invariant for all inertial frames and define a null interval as an invariant, but at the same time the Lorentz transformations require arbitrary (conventional) synchronizations that allow for one-way light speed being different from A to B than from B to A.

 

Take for example the famous train thought experiment where different one-way speeds are needed for the passenger in the train frame and the embarkment person. This relativity of simultaneity is represented in Minkowski diagrams by using non-orthogonal coordinates for the frame arbitrarily not considered at rest(either the passenger's or the embankment's, i.e. causal symmetry).

[md65536]

Take for example the famous train thought experiment where different one-way speeds are needed for the passenger in the train frame and the embarkment person. This relativity of simultaneity is represented in Minkowski diagrams by using non-orthogonal coordinates for the frame arbitrarily not considered at rest(either the passenger's or the embankment's, i.e. causal symmetry).

This sounds like a misunderstanding of some basics that makes it difficult to make sense of the rest of what you're saying.

In the famous experiment, all of the individual observers are inertial, and they all measure a one-way speed (using Einstein synchronization or Einstein's definition of simultaneity) of light that is equal to c. No different one way speeds of light are needed. The different observers measure time differently, but they also measure distance differently.

 

 

 

There is no inconsistency in SR that you're speaking of. SR does not state whether or not Einstein's definition of simultaneity, and the resulting means of synchronizing clocks and measuring one-way speeds with a single observer, are conventional. SR is simply presented in a way that makes use of Einstein's definitions, so I think the second postulate must be read within the context of those definitions. If simultaneity is not conventional, and if Einstein's definitions are the only ones that truly "work" (eg. if we found evidence that ruled out other conventions), SR remains consistent because there is nothing in it that requires conventionality (I believe you're mistaken about that). If simultaneity truly is conventional, a formulation of SR that makes use of only one convention (as Einstein's) remains consistent.

 

You have some definitions (eg. simultaneity).

You have some quantities and measurements (eg. v) that use those definitions.

You have some statements based on those measurements (eg. second postulate).

I don't think it makes sense to look at it in way where you change the definitions, but expect that the statements making use of them must still hold or else it's "inconsistent".

[swansont]

In any case regardless of whether one considers conventionality a requirement of the theory or not the contradiction comes from the fact that only with Einstein's standard synchronization(with equal times for a ray going from A to B and from B to A) can one obtain a speed c invariant for all inertial frames and define a null interval as an invariant, but at the same time the Lorentz transformations require arbitrary (conventional) synchronizations that allow for one-way light speed being different from A to B than from B to A.

 

What would be an example of an arbitrary synchronization?

 

And I now think your argument is backwards. Einstein clock synchronization is a result of an invariant (and finite) c, not the other way around.

[md65536]

And I now think your argument is backwards. Einstein clock synchronization is a result of an invariant (and finite) c, not the other way around.

I don't think that's true. I think you could make the case, but that might involve circular reasoning. I think at best you could start at either point and get to the other.

 

In Einstein's 1905 paper, he doesn't use the speed of light in his definition of synchronization. http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.

It is only time, and not speed of light that is used here. Next, the travel times of light signals are used to define synchronization. THEN the quantity equal to the speed of light is assumed to be a universal constant.

 

 

You can do it the other way around, but not without making some similar assumptions.

 

A one-way speed between two points but measured by a single observer needs some way to relate the time at the different locations. If you define speed first such that the speed of light is invariant, and use that to synchronize clocks, I think that you have already implicitly defined simultaneity in your definition of speed.

[swansont]

I don't think that's true. I think you could make the case, but that might involve circular reasoning. I think at best you could start at either point and get to the other.

 

In Einstein's 1905 paper, he doesn't use the speed of light in his definition of synchronization. http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

Not the value, no, since that's irrelevant, and not what I claimed. He uses the propagation of light and the delay it engenders in the definition, as you show.

 

It is only time, and not speed of light that is used here. Next, the travel times of light signals are used to define synchronization. THEN the quantity equal to the speed of light is assumed to be a universal constant.

 

But does it follow from that protocol? Synchronizing clocks within a frame only assumes that the speed of light in any direction is the same within that frame. How do you extrapolate from that to an invariant c?

[md65536]

 

Not the value, no, since that's irrelevant, and not what I claimed. He uses the propagation of light and the delay it engenders in the definition, as you show.

 

But does it follow from that protocol? Synchronizing clocks within a frame only assumes that the speed of light in any direction is the same within that frame. How do you extrapolate from that to an invariant c?

I mean he makes no mention at all of any concept of speed in his definition of a common time at the two locations. Propagation time of light isn't the same as speed.

 

No it doesn't follow from that protocol. Simultaneity is by definition, and invariance of speed of light by assumption. Indeed, after defining synchronization, Einstein specifically states (at least according to this translation),

 

In agreement with experience we further assume the quantity

[math]\frac{2{\rm AB}}{t'_A-t_A}=c, [/math]

to be a universal constant—the velocity of light in empty space.

(emphasis mine)

 

 

So I may be nitpicking, but when I went from my initial misunderstanding that Einstein assumes his definition of simultaneity describes reality (he doesn't, he simply makes use of it as a tool without commenting on its reality, which is what allows SR to be compatible with conventionality of simultaneity in the first place), to realizing what he has actually done, and how the way he did it is "bulletproof" (you can't prove a definition is "wrong", even if you could find it somehow doesn't conform to reality)... it gave me a sense that Einstein knew exactly what he was doing and was extremely careful, while so many others since have been too sloppy with their assumptions.

 

 

Say on the other hand that Einstein didn't do it this way, but instead just assumed that the speed of light is equal to c, and from that concluded that events are simultaneous in accordance with Einstein-simultaneity. Then the definition of simultaneity is assumed to be true, and essentially that simultaneity is not conventional. This would be a mistake, I believe. Einstein truly seemed to grasp that we had not (still haven't) been able to measure whether two distant events are truly simultaneous or not, and it is only within the context of some assumptions that we can say they are.

 

Equating equal timing and equal speed requires another assumption, that too many people make. Einstein's definition is free from problems or ambiguities in all of these intricate details that people could argue over.

Edited September 1, 2015 by md65536

[Andromacus]

 

What would be an example of an arbitrary synchronization?

 

 

 

I just gave an example of an arbitrary sync needed to make the Einstein's train and lightnings thought experiment work. In the frame of the train (and we only need this frame so no length contraction or time dilation need to be invoke), we have the passenger in the middle that observes the front lightning(emitted at A) flash before the rear one(emitted at B). Since she is exactly in the middle of A and B it follows that since lightning hit the points A and B light must have travelled at different speeds in the segments A to passenger and passenger to B. That is irrespective of the frame's constant velocity(since it is equivalent to rest) and the frame transformation between the embarkment and the passenger. So here a synchronization different to the standard one is needed, agree?

 

But does it follow from that protocol? Synchronizing clocks within a frame only assumes that the speed of light in any direction is the same within that frame. How do you extrapolate from that to an invariant c?

 

Invariant c is a postulate, it doesn't have to be extrapolated from anything.

 

 

Equating equal timing and equal speed requires another assumption, that too many people make. Einstein's definition is free from problems or ambiguities in all of these intricate details that people could argue over.

I agree with most of the rest of this post but this last sentence is a non-sequitur, you are just making a judgement call.

The issue I'm raising is indeed an ambiguity at the least, even if I agree Einstein probably realized it but he was sly enough to write it in a way very difficult to attack, and also realizing his assumptions and definitions or stipulations made impossible to measure the one-way speed directly and you haven't made a single argument to counter it. From what you write in a previous post it seems to me you are missing my point or maybe didn't completely understood it.

This sounds like a misunderstanding of some basics that makes it difficult to make sense of the rest of what you're saying.

In the famous experiment, all of the individual observers are inertial, and they all measure a one-way speed (using Einstein synchronization or Einstein's definition of simultaneity) of light that is equal to c. No different one way speeds of light are needed. The different observers measure time differently, but they also measure distance differently.

Observers in different frames measure time dilation and length contraction between frames, but as explained in a previous post, I'm only analyzing the train's frame to conclude that measuring equal distances(the 2 halves of the train) in different times(as required by the simultaneity of relativity) within one frame implies choosing a sync convention different to the standard, and in wich the one-way speed is different to the 2-way speed. While by the postulate of c invariance (and in order to define null intervals) the standard sync is necessary. I'd say this implies certain contradiction.

 

 

There is no inconsistency in SR that you're speaking of. SR does not state whether or not Einstein's definition of simultaneity, and the resulting means of synchronizing clocks and measuring one-way speeds with a single observer, are conventional. SR is simply presented in a way that makes use of Einstein's definitions, so I think the second postulate must be read within the context of those definitions. If simultaneity is not conventional, and if Einstein's definitions are the only ones that truly "work" (eg. if we found evidence that ruled out other conventions), SR remains consistent because there is nothing in it that requires conventionality (I believe you're mistaken about that). If simultaneity truly is conventional, a formulation of SR that makes use of only one convention (as Einstein's) remains consistent.

Right but what I'm doing is giving you an example where two conventions(a standard and a non-standard sync) are used at the same time. How do you call that?

 

You have some definitions (eg. simultaneity).

You have some quantities and measurements (eg. v) that use those definitions.

You have some statements based on those measurements (eg. second postulate).

I don't think it makes sense to look at it in way where you change the definitions, but expect that the statements making use of them must still hold or else it's "inconsistent".

Name one definition that I changed.

Edited September 1, 2015 by Andromacus

[swansont]

I mean he makes no mention at all of any concept of speed in his definition of a common time at the two locations. Propagation time of light isn't the same as speed.

 

 

No, there's no mention, because he's not teaching physics 101. Anyone reading the paper knows d = vt. It's a given.

Invariant c is a postulate, it doesn't have to be extrapolated from anything.

 

You seemed to be asserting that you needed the clock synchronization protocol to be able to postulate it. But, as you say, it doesn't have to be extrapolated from anything.

I just gave an example of an arbitrary sync needed to make the Einstein's train and lightnings thought experiment work. In the frame of the train (and we only need this frame so no length contraction or time dilation need to be invoke), we have the passenger in the middle that observes the front lightning(emitted at A) flash before the rear one(emitted at B). Since she is exactly in the middle of A and B it follows that since lightning hit the points A and B light must have travelled at different speeds in the segments A to passenger and passenger to B. That is irrespective of the frame's constant velocity(since it is equivalent to rest) and the frame transformation between the embarkment and the passenger. So here a synchronization different to the standard one is needed, agree?

 

Can you do an arbitrary synchronization that way?

 

The thing about the invariance of c is that it comes from electrodynamics. So E&M stops working in your example. Einstein "postulated" it, but really, it was a postulate that it works for kinematics (because it didn't already show up in the equations) as well as electrodynamics, because why wouldn't it?

[Andromacus]

No, there's no mention, because he's not teaching physics 101. Anyone reading the paper knows d = vt. It's a given.

 

But note that the physics 101 newtonian equation d=vt uses euclidean d and absolute t, it is ironic to say the least that Einstein is forced to use this formula with absolute t and euclidean geometry to define the null interval c2t2-r(x,y,z)2=0 in a minkowski geometry with local time.

 

 

You seemed to be asserting that you needed the clock synchronization protocol to be able to postulate it. But, as you say, it doesn't have to be extrapolated from anything.

I was just asserting that the postulate and the synchronization must be consistent with each other.

 

Can you do an arbitrary synchronization that way?

You must whenever yo are to explain simultaneous events involving light signals in one frame that are not simultaneous in another frame.

 

The thing about the invariance of c is that it comes from electrodynamics. So E&M stops working in your example. Einstein "postulated" it, but really, it was a postulate that it works for kinematics (because it didn't already show up in the equations) as well as electrodynamics, because why wouldn't it?

I'm just expressing what seems to me like an inconsistency of SR, I don't think that EM stops working because if there really is a contradiction one cannot derive any physical consequence from it .

 

I find strange that there are no more people spotting this, I guess most people gets lost in the analysis of the transformation between frames with all the unintuitive time dilations and length contractions and don't spend much time to analyse what relativity of simultaneity implies for measurements in just one frame.

[md65536]

In the frame of the train (and we only need this frame so no length contraction or time dilation need to be invoke), we have the passenger in the middle that observes the front lightning(emitted at A) flash before the rear one(emitted at B). Since she is exactly in the middle of A and B it follows that since lightning hit the points A and B light must have travelled at different speeds in the segments A to passenger and passenger to B.

No, that doesn't follow. In SR the respective signals from A and B travelled at the same speed, but were not emitted simultaneously in the train's frame (this is relativity of simultaneity, eg. the signals may have been emitted simultaneously in the track's frame).

 

measuring equal distances(the 2 halves of the train) in different times(as required by the simultaneity of relativity) within one frame implies choosing a sync convention different to the standard, and in wich the one-way speed is different to the 2-way speed. While by the postulate of c invariance (and in order to define null intervals) the standard sync is necessary. I'd say this implies certain contradiction.

No, that's not right. You have the clocks synchronized in one frame. They're not synchronized in the other frame. Where they're not synchronized, they're simply not synchronized. That's not "synchronized using a different convention."

 

Right but what I'm doing is giving you an example where two conventions(a standard and a non-standard sync) are used at the same time. How do you call that?

I don't see an alternative convention that fits the definition of "synchronization", but if it's there I'd call that "different synchronization conventions that are consistent with the predictions of SR" or something like that.

 

Name one definition that I changed.

I should have said "I don't think it makes sense to look at it in way where one changes the definitions, but expects that the statements making use of them must still hold or else it's 'inconsistent'."

But in Einstein's paper, he defines simultaneity and synchronization. If you provide alternative conventions, they don't use those definitions, and some statements that *do* use those definitions (such as the second postulate, I argue) do not apply to the alternative definitions, and that doesn't make them inconsistent. The statements are made with respect to the given definitions.

 

No, there's no mention, because he's not teaching physics 101. Anyone reading the paper knows d = vt. It's a given.

But what is the meaning of t? Have you read the section "Definition of Simultaneity", in the 1905 paper? http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by time.

Einstein does NOT just assume d=vt has meaning independent of time (including simultaneity), instead he says that "speed" only makes sense with respect to the meaning of "time". That's surely why he avoids using speed in defining simultaneity (otherwise why mention it at all?).

 

Paraphrasing, I think Einstein says, "Given this definition of simultaneity, we can define a one-way measure of the speed of light, which in agreement with experience we accept is always equal to c."

 

How would you go about it the other way, given Einstein's quote above? Is this fair:

"Without a definition of simultaneity, there is no means of measuring the one-way speed of light, but let us assume that it is equal to c, which then gives us a definition of simultaneity, which gives meaning to the one-way measure of speed that we've used." How do you avoid problems if you define time according to an assumption about speed, if the meaning of "speed of light" depends on how you define time?

From what you write in a previous post it seems to me you are missing my point or maybe didn't completely understood it.

By the way, I'm sure this is true. You seem to have a better understanding of simultaneity and conventionality arguments than anyone I remember posting here, definitely better than mine and I've focussed on simultaneity more than anything else in science. But I haven't bothered with Malament etc much, because when I look into stuff like that I find too many people go off track, focussing on things like "symmetries" which add additional assumptions, and too often they lose sight of the core theory, so I've focussed on Einstein's stuff. Where I think you've made statements that contradict SR, I can't get past that to try to understand what you're saying. Edited September 2, 2015 by md65536

[swansont]

But note that the physics 101 newtonian equation d=vt uses euclidean d and absolute t, it is ironic to say the least that Einstein is forced to use this formula with absolute t and euclidean geometry to define the null interval c2t2-r(x,y,z)2=0 in a minkowski geometry with local time.

 

The notion of a Minkowski geometry didn't exist then, and you don't need absolute d and t for the formula to work. t is a time interval (starting from zero) and d is a space interval. Both are relative, and neither is affected by relativity.

I was just asserting that the postulate and the synchronization must be consistent with each other.

 

I think it's obvious that they have to be for this to work.

You must whenever yo are to explain simultaneous events involving light signals in one frame that are not simultaneous in another frame.

 

But does that synchronization work in general, rather than in this ad-hoc manner? Because if it doesn't, the explanation fails.

 

I'm just expressing what seems to me like an inconsistency of SR, I don't think that EM stops working because if there really is a contradiction one cannot derive any physical consequence from it .

 

I find strange that there are no more people spotting this, I guess most people gets lost in the analysis of the transformation between frames with all the unintuitive time dilations and length contractions and don't spend much time to analyse what relativity of simultaneity implies for measurements in just one frame.

 

Maybe nobody is spotting it because it's not really a problem.

But what is the meaning of t? Have you read the section "Definition of Simultaneity", in the 1905 paper? http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

Yes, he defines simultaneity, and what it means to mean "at the same time". d=vt does not use the concept of simultaneity.

 

Einstein does NOT just assume d=vt has meaning independent of time (including simultaneity), instead he says that "speed" only makes sense with respect to the meaning of "time". That's surely why he avoids using speed in defining simultaneity (otherwise why mention it at all?).

 

Einstein never mentions speed. He says that it's necessary to understand the values of its co-ordinates as functions of the time. But d = vt doesn't rely on that, since it's a relative equation.

 

Further, if d = vt isn't assumed, you must be scratching your head at the equation at the end of the section, that c = 2AB/t'_A-t_A

 

_{Where did he magically get THAT equation?}

[md65536]

Further, if d = vt isn't assumed, you must be scratching your head at the equation at the end of the section, that c = 2AB/t'_A-t_A

 

_{Where did he magically get THAT equation?}

It's not magical. Einstein explains what is needed for measuring time in different places, provides it, and then can use it.

 

That equation is beside the point anyway. It uses two times measured at A, and represents a two-way speed of light. It alone cannot be used to define simultaneity, or to measure the one-way speed of light. Simultaneity is defined just before that, without making reference to the speed of light.

 

I incorrectly paraphrased Einstein as saying that given his definition of simultaneity, the one-way speed of light is measured as c. This is true, but it seems he didn't make that claim and didn't have to.

 

Do you understand that Einstein defined simultaneity on its own, he did not derive it from an invariant speed of light? Do you accept that SR still maintains that definition of simultaneity, ie. that it is not certainly superfluous? This is important because a conversation about conventionality of simultaneity will not go very far if you refute that SR does make use of a convention.

[swansont]

It's not magical.

 

Right. It's d = vt (and it was sarcasm)

[Andromacus]

No, that doesn't follow. In SR the respective signals from A and B travelled at the same speed, but were not emitted simultaneously in the train's frame (this is relativity of simultaneity, eg. the signals may have been emitted simultaneously in the track's frame).

This is a common misconception about the train thought experiment, even for people supposedly not new to relativity. The train observer could infer that at that moment based on her detecting the front flash before the rear flash, but we should know better that both the observer in the train and the observer at the embankment must agree about the events we are analysing from two different frames, if the events are not the same there is not much to discuss is there?. There is evidence we are talking about the same events(lightnings) because it can be ascertained afterwards the damages caused to the front and rear of the train and the corresponding points in the railway. So the events "lightnings hitting the train and railway" i.e. the emission of the flashes must coincide for both observers if we are to analyze the same events(lightnings) from two different frames. (note that we could just the same agree that in the thought experiment one levent ocurred before the other and analyze the frames fron that premise, but the original thought experiment as written bu Einstein in his popularization book:"Relativity, the special and the general" clearly stipulated that each lightning strikes the train and embankment such that only a simultaneous strike is compatible with the description)

 

No, that's not right. You have the clocks synchronized in one frame. They're not synchronized in the other frame. Where they're not synchronized, they're simply not synchronized. That's not "synchronized using a different convention."

 

This doesn't make much sense, whenever you have clock at distant points, you must have some synchronization procedure, unless you are using absolute(global time) and that is the case of the frame in the train, the only one I'm refering to in the paragraph you quote. I haven't the slightest what is this other frame "simply not synchronized" you are talking about.

 

The next part of your post is too confused for me to comment on it

 

 

 

By the way, I'm sure this is true. You seem to have a better understanding of simultaneity and conventionality arguments than anyone I remember posting here, definitely better than mine and I've focussed on simultaneity more than anything else in science. But I haven't bothered with Malament etc much, because when I look into stuff like that I find too many people go off track, focussing on things like "symmetries" which add additional assumptions, and too often they lose sight of the core theory, so I've focussed on Einstein's stuff. Where I think you've made statements that contradict SR, I can't get past that to try to understand what you're saying.

 

The very existence of an unsolved debate about the conventionality of simultaneity for so many decadesis logical if there is contradiction because it is well known contradiction lead to unsolvable debates.

 

 

[pzkpfw]

This is a common misconception about the train thought experiment, even for people supposedly not new to relativity. The train observer could infer that at that moment based on her detecting the front flash before the rear flash, but we should know better that both the observer in the train and the observer at the embankment must agree about the events we are analysing from two different frames, if the events are not the same there is not much to discuss is there?. There is evidence we are talking about the same events(lightnings) because it can be ascertained afterwards the damages caused to the front and rear of the train and the corresponding points in the railway. So the events "lightnings hitting the train and railway" i.e. the emission of the flashes must coincide for both observers if we are to analyze the same events(lightnings) from two different frames. (note that we could just the same agree that in the thought experiment one levent ocurred before the other and analyze the frames fron that premise, but the original thought experiment as written bu Einstein in his popularization book:"Relativity, the special and the general" clearly stipulated that each lightning strikes the train and embankment such that only a simultaneous strike is compatible with the description)

No, you're way off. The events are the events, and all observers will agree that the events occurred, but the whole point of "relativity of simultaneity" is that observers in relative motion can't agree whether the events were simultaneous.

 

The thought experiment happens to have the events simultaneous in the embankment frame, and shows why they can't be in the train frame. It is clear that two other strikes might be simultaneous in the train frame - and they won't be simultaneous in the embankment frame.

[Andromacus]

 

The notion of a Minkowski geometry didn't exist then, and you don't need absolute d and t for the formula to work. t is a time interval (starting from zero) and d is a space interval. Both are relative, and neither is affected by relativity.

It certainly wasn't formalised by Minkowski yet but it was implicit in the math by Einstein.

In d=vt you are assuming the galilean notion of simultaneity and galilean relativity, the Einstein's synchronization is equivalent except that there is a finite limit speed, but both Einstein's sync are isotropic, meaning a notion of simultaneity in wich the speed in one direction equals the speed in the opposite direction. The isotropy is an additional assumption Einstein made when requiring coordinates in wich the laws of Newton hold good.

 

I think it's obvious that they have to be for this to work.

It should be, but I'm showing hot it isn't. The reasons "for this to work" despite the contradiction are again first that the Lorentz transformations can be derived independently of this contradictory way used by Einstein, and second that the one-speed of light is declared unmeasurable by definition.

 

But does that synchronization work in general, rather than in this ad-hoc manner? Because if it doesn't, the explanation fails.

In SR the relativity of simultaneity(equivalent to demanding synchronization to be convntional) is used in every transformation of frames, I wouldn't call that ad hoc.

 

Maybe nobody is spotting it because it's not really a problem.

It's not a practical problem for the reasons I gave above, but I guess it could hamper progress to a better theory. Of course for many people SR cannot be improved so this kind of contradiction is of no concern to them.

I'm speaking from personal experience here, I've taught relativity to mathematicians at the university in an Applied math program, and when commenting this issue with coleagues the usual reaction is something along the lines of "That's fine but SR is still the best thing we have", or "if it ain't broke don't fix it".

 

No, you're way off. The events are the events, and all observers will agree that the events occurred, but the whole point of "relativity of simultaneity" is that observers in relative motion can't agree whether the events were simultaneous.

 

You are confusing the events "observing flash of light" with the obvious fact that they must agree the lightnings struck and about where they struck.

 

The thought experiment happens to have the events simultaneous in the embankment frame, and shows why they can't be in the train frame. It is clear that two other strikes might be simultaneous in the train frame - and they won't be simultaneous in the embankment frame.

 

Again by events everybody should obviously understand the event of observing something. What they observe is the light flashed by lightning. Light speed should be infinite for them to observe them instantaneously. The "point" of relativity is that unlike what is assumed in newtonian mechanics propagation of signals is NOT instantaneous.

[pzkpfw]

You are confusing the events "observing flash of light" with the obvious fact that they must agree the lightnings struck and about where they struck.

No. In fact you're confused about what observing the flashes means.

 

However, you are more or less correct that they must agree that the strikes struck, and where. (It's the when that's in question).

 

Again by events everybody should obviously understand the event of observing something. What they observe is the light flashed by lightning. Light speed should be infinite for them to observe them instantaneously. The "point" of relativity is that unlike what is assumed in newtonian mechanics propagation of signals is NOT instantaneous.

Again, way off. Events are events. Observing those events is something different.

 

For example, someone who isn't exactly between two lightening strikes could still determine if they were simultaneous - in their frame - by using the non-infinite speed of light and the distances from the strikes; it doesn't matter that they observed those strikes at different times. The events of the strikes and the observing of those strikes are different things.

 

 

In the train-embankment-lightening thought experiment, the setup is that both the embankment observer and train observer are exactly between the two strikes. Since both observers may consider themselves as at rest *, they are both entitled to know the strikes were simultaneous - in their frame - if they observe the strikes simultaneously. Since they can't both observe the strikes at the same time, they can't both consider the same two strikes to have been simultaneous.

 

 

(* there's no absolute to motion. The train observer can consider themselves as at rest, and the embankment (and its observer) are moving. Relativity tells us the rules of physics are the same for both observers.)