Relativity of simultaneity and one-way speed of light

[Andromacus]

 

. Einstein clock synchronization works just fine under Galilean physics, so how can it depend on any postulates of relativity that cause deviations from Galilean physics?

Einstein synch is compatible with galilean relativity because it is also based in the Euclidean homogeneous and isotropic space, but there is a key difference, galilean inertial frames are independent of time, while the Einstein synch is precisely used to construct the relativistic inertial frames that are not time independent, but assign different times to different inertial frames. It is in this sense that the Einstein synch is crutially dependent on the second postulate to avoid contradiction when applying this adjustment because the adjustment hinges on the fact that c is invariant in all inertial frames. At least this is Einstein's view AFAIK.

 

The trick is that in order to do this Einstein needs to define light's null interval in terms of the galilean prerelativistic inertial frame and with this he can adjust clocks with finite speed signals. The galilean and relativistic inertial frames(that are different) are arbitrarily used here as if they were interchangeable for the sake of reconciling the first and second postulate. The relativistic inertial frames are derived from a galilean frame. Mathematical consistency requires a single form of inertial frames IMO.

[Mordred]

Why would mathematical consistency require one inertial frame ? That makes no sense.

 

As long as you have a reference frame you can mathematically show differences from than reference frame and still be consistent and precise.

 

The reference frame doesn't even require the the observer to be at rest. It's certainly easier, however GR can handle it.

David345 posted you the metrics, I also posted a few articles. Did you read them?

 

For example Euclidean geometry is in the form of Cartesian coordinates, however in one of those articles there was a section showing how relativity of simulaneity works in polar coordinates. Which isn't Euclidean.

 

http://arxiv.org/pdf/physics/0511062

One side note the majority of the paradoxes mentioned in that paper, are artifacts of coordinate paradoxes. Even though it doesn't go into detail on which paradoxes its referring to. An excellent article covering numerous "artifact of coordinate paradoxes" and the solutions for them (by selecting a different coordinate system) is the following.

 

http://www.blau.itp.unibe.ch/newlecturesGR.pdf"Lecture Notes on General Relativity" Matthias Blau

 

I think one of the problems you may be having is SR and GR didn't stop with Einstein. Advances in both theories are continuously being developed. This includes different coordinate systems.

For example simultaneity also occurs in Rindler, Born, Fermi coordinates etc. This list includes the FLRW metric, Schwartzchild Metric, Turtle metric and Kruskal Szekures metric

 

https://en.m.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates

 

 

Every coordinate system in relativity follows in one fashion or another relativity of simultaneity

 

In some metrics there are different specialized observers. Commoving, corotating, accelerating etc. not to mentioned different curved spacetimes. Relativity of simultaneity applies in every case.

 

You don't often see it mentioned in the different coordinate systems as its principle is easier to teach in the Minkowskii metric. This doesn't mean it doesn't apply in the more complex GR coordinate systems.

 

They would have to as in every case the speed of light is invariant, and observations by all observer's are equally valid.

I always found this explanation handy, though as I mentioned above its certainly not the only metric.

 

Lorentz transformation.

 

First two postulates.

 

1) the results of movement in different frames must be identical

2) light travels by a constant speed c in a vacuum in all frames.

 

Consider 2 linear axes x (moving with constant velocity and [latex]\acute{x}[/latex] (at rest) with x moving in constant velocity v in the positive [latex]\acute{x}[/latex] direction.

 

Time increments measured as a coordinate as dt and [latex]d\acute{t}[/latex] using two identical clocks. Neither [latex]dt,d\acute{t}[/latex] or [latex]dx,d\acute{x}[/latex] are invariant. They do not obey postulate 1.

A linear transformation between primed and unprimed coordinates above

in space time ds between two events is

[latex]ds^2=c^2t^2=c^2dt-dx^2=c^2\acute{t}^2-d\acute{x}^2[/latex]

 

Invoking speed of light postulate 2.

 

[latex]d\acute{x}=\gamma(dx-vdt), cd\acute{t}=\gamma cdt-\frac{dx}{c}[/latex]

 

Where [latex]\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[/latex]

 

Time dilation

dt=proper time ds=line element

 

since [latex]d\acute{t}^2=dt^2[/latex] is invariant.

 

an observer at rest records consecutive clock ticks seperated by space time interval [latex]dt=d\acute{t}[/latex] she receives clock ticks from the x direction separated by the time interval dt and the space interval dx=vdt.

 

[latex]dt=d\acute{t}^2=\sqrt{dt^2-\frac{dx^2}{c^2}}=\sqrt{1-(\frac{v}{c})^2}dt[/latex]

 

so the two inertial coordinate systems are related by the lorentz transformation

 

[latex]dt=\frac{d\acute{t}}{\sqrt{1-(\frac{v}{c})^2}}=\gamma d\acute{t}[/latex]

 

So the time interval dt is longer than interval [latex]d\acute{t}[/latex]

 

If your not using Lorentz then you need to define the coordinate transformation rules.

Here is relativity of simultaneaty coordinate transformation in Lorentz.

 

[latex]\acute{t}=\frac{t-vx/c^2}{\sqrt{1-v^2/c^2}}[/latex]

 

[latex]\acute{x}=\frac{x-vt}{\sqrt{1-v^2/c^2}}[/latex]

 

[latex]\acute{y}=y[/latex]

[latex]\acute{z}=z[/latex]

 

 

The first article I posted shows the last set of equations in polar coordinates. Once again each type of coordinates will have their own solutions. You can Google the coordinates I posted above to find the different solutions.

 

Another useful item to include is the Levi-Civita connection

 

 

Here is An example on simulaneity in gauge groups of general relativity

 

http://arxiv.org/abs/gr-qc/0204063

PS my earlier post on posting metrics, I was hoping to see you post the metrics to describe what you were getting at. Not pictures and oft confusing verbatim.

Edited September 12, 2015 by Mordred

[studiot]

 

Mordred

A linear transformation

 

To emphasise this, please note this is an unspoken assumption inherent in Einstinian relativity.

[Andromacus]

Why would mathematical consistency require one inertial frame ?

No, you misunderstand. I'm not saying that mathematical consistency requires that no coordinates other than inertial can be used. I'm saying that inertial coordinates are ill defined if they admit two different interpretations within the theory, either as glailean inertial coordinates or as relativistic inertial coordinates. The former are time independent.

Having them(the galilean form) restricted to when we are dealing by stipulation with just one frame doesn't eliminate the problem. It is just a practical safeguard for timelike paths. But the first requirement of a theory like relativiity should be to leave no ambiguity about such a central physical notion within the theory.

PS my earlier post on posting metrics, I was hoping to see you post the metrics to describe what you were getting at.

The only metric needed here is the Minkowski metric. Also it seems to me you might have a confusion between metrics and coordinates. Like when you say "Euclidean geometry is in the form of Cartesian coordinates". Cartesian coordiates are naturally adapted to Euclidean geometry, but the geometry is independent of the local coordinates chosen to describe it.

 

[swansont]

Einstein synch is compatible with galilean relativity because it is also based in the Euclidean homogeneous and isotropic space, but there is a key difference, galilean inertial frames are independent of time, while the Einstein synch is precisely used to construct the relativistic inertial frames that are not time independent, but assign different times to different inertial frames. It is in this sense that the Einstein synch is crutially dependent on the second postulate to avoid contradiction when applying this adjustment because the adjustment hinges on the fact that c is invariant in all inertial frames. At least this is Einstein's view AFAIK.

 

Einstein clock synch occurs only in a single frame, so discussion of multiple frames is moot. Regardless of how relativity is constructed, the synchronization protocol stands on its own. It is independent of relativity. It does not rely AT ALL upon the second postulate.

 

That relativity "depends" on this working is also moot. Relativity only works if nature behaves that way. Einstein clock synchronization works because nature behaves in such a way that it works. They have a commonality there, but the latter does not depend on the former. Synchronization is about how you tell time in one frame, relativity is about how you compare times (and lengths) in two frames.

 

Because nobody seems to have a problem with lengths, Einstein never mentions that you would calibrate two meter sticks by comparing them side-by-side, or you could send parallel light from each end and do this over some distance. Something else that relies in no way on c being invariant. They both rely on space being isotropic, an assumption that is already there and didn't need to be included in the paper. (Also, something he shows isn't the case some years later with GR)

[studiot]

swansont

That relativity "depends" on this working is also moot. Relativity only works if nature behaves that way. Einstein clock synchronization works because nature behaves in such a way that it works. They have a commonality there, but the latter does not depend on the former. Synchronization is about how you tell time in one frame, relativity is about how you compare times (and lengths) in two frames.

 

 

Very succinctly put. I like it and must remember this. +1

 

swansont

Einstein never mentions that you would calibrate two meter sticks by comparing them side-by-side

 

Doesn't he do just that with his train and lightning example?

 

I'm almost sure he notes that you can compare the length of the train and platform (and lightning marks on the train platform) when the train is standing still next to the platform.

Edited September 12, 2015 by studiot

[Andromacus]

 

Einstein clock synch occurs only in a single frame, so discussion of multiple frames is moot. Regardless of how relativity is constructed, the synchronization protocol stands on its own. It is independent of relativity. It does not rely AT ALL upon the second postulate.

Let's see, if I can make it simple enough. Einstein synch uses light signals right? Now to claim that this synch works in arbitrary single inertial frames one must postulate that the speed of these signals is invariant for each single inertial frame, remembert the goal here is being able to transform from a single frame to another single frame, you cannot guarantee this transformation between single frames (within wich the synch must work), unless you have the second postulate without falling into contradiction. So for the synch to work only in a single inertial frame, but obviously an arbitrary single frame, you must ensure that the transformations between such frames is possible, how do you ensure this without the second postulate?

That relativity "depends" on this working is also moot. Relativity only works if nature behaves that way. Einstein clock synchronization works because nature behaves in such a way that it works. They have a commonality there, but the latter does not depend on the former. Synchronization is about how you tell time in one frame, relativity is about how you compare times (and lengths) in two frames.

See above.

 

 

Because nobody seems to have a problem with lengths, Einstein never mentions that you would calibrate two meter sticks by comparing them side-by-side, or you could send parallel light from each end and do this over some distance. Something else that relies in no way on c being invariant. They both rely on space being isotropic, an assumption that is already there and didn't need to be included in the paper. (Also, something he shows isn't the case some years later with GR)

 

You don't see the relation between the isotropicity of light implicit in the second postulate and the isotropy of space?

In the words of Einstein(1912):

" We demand this in order to preserve the homogeneity properties of physical space. If one did not make this assumption, then bodies that are at rest, congruent, and identically located with respect to S' would be differently shaped or located when referred to S; or clocks that are at rest and identically constructed with respect to S' would have different or time-dependent rates when referred to S."

 

But to be honest, I don't know what your point is with this paragraph in reference to what I am saying.

Edited September 12, 2015 by Andromacus

[Mordred]

PS my earlier post on posting metrics, I was hoping to see you post the metrics to describe what you were getting at.

The only metric needed here is the Minkowski metric. Also it seems to me you might have a confusion between metrics and coordinates. Like when you say "Euclidean geometry is in the form of Cartesian coordinates". Cartesian coordiates are naturally adapted to Euclidean geometry, but the geometry is independent of the local coordinates chosen to describe it.

 

I don't see how you can be confused by that. Flat space time is represented by Euclidean geometry. You use Cartesian coordinates in Euclidean geometry. Minkowskii space is a pseudo Euclidean metric.

 

If your basing your assumptions that the only thing you need to define relativity of simultaneity it's no wonder your making the assumptions you have been.

 

I suggest you start looking at Rindler coordinates and relativity of simultaneity.

Start by actually reading the first paper I posted.

Edited September 12, 2015 by Mordred

[Andromacus]

Flat space time is represented by Euclidean geometry.

If you insist on that I would ask you to start a new thread with the claim that flat spacetime is euclidean, but it will probably be sent to speculations as it is well known it is Minkowski space that represents the flat spacetime of special relativity.

[Mordred]

I don't need to, you just need to look at Minkowskii coordinates which is pseudo Euclidean.

 

"The Minkowski metric is sometimes termed a pseudo-

euclidean metric to emphasize that it is euclidean-like ex-

cept for the difference in sign between the time and space

terms in the line element."

 

http://eagle.phys.utk.edu/guidry/astro490/lectures/lecture490_ch4.pdf

 

It is not the only metric where relativity of simultaneity is applied.

Edited September 12, 2015 by Mordred

[swansont]

Let's see, if I can make it simple enough. Einstein synch uses light signals right? Now to claim that this synch works in arbitrary single inertial frames one must postulate that the speed of these signals is invariant for each single inertial frame,

 

No, that's wrong. c does not need to be invariant (which means the same in every frame) it just needs to be constant in any given frame. It need not have the same value, since the value doesn't show up in the synchronization.

 

But since you're convinced it does, come up with an example of the synch not working.

 

remembert the goal here is being able to transform from a single frame to another single frame, you cannot guarantee this transformation between single frames (within wich the synch must work), unless you have the second postulate without falling into contradiction. So for the synch to work only in a single inertial frame, but obviously an arbitrary single frame, you must ensure that the transformations between such frames is possible, how do you ensure this without the second postulate?

 

The goal of clock synchronization is to synchronize the clocks in any given inertial frame. Period. It is a necessary condition for relativity, but the converse doesn't hold. This is a failure of basic logic, "If A then B" B requires A, but B doesn't mandate A. "B, therefore A" is wrong.

 

Your assertion is like saying because we needed Newtonian physics to send a person to the moon, the goal of Newtonian physics was to send a person to the moon. That's hogwash. It is a prerequisite, but that's all.

 

The transformations can't be derived until you have a clock synchronization protocol. The synch is a prerequisite, but it does not depend on the work that came after. It stands on its own. If c was not invariant, the synch would still work. It just requires that c be constant in each frame (i.e. space needs to be isotropic)

 

You don't see the relation between the isotropicity of light implicit in the second postulate and the isotropy of space?

In the words of Einstein(1912):

" We demand this in order to preserve the homogeneity properties of physical space. If one did not make this assumption, then bodies that are at rest, congruent, and identically located with respect to S' would be differently shaped or located when referred to S; or clocks that are at rest and identically constructed with respect to S' would have different or time-dependent rates when referred to S."

 

To be invariant requires space be isotropic, but isotropic does not imply invariance. There are lots of variables that are not invariant.

 

But to be honest, I don't know what your point is with this paragraph in reference to what I am saying.

 

You keep insisting that invariance is a require ment of synchronization, and that's flat-out wrong. The same argument could be made for length as for time, but that doesn't seem to befuddle nearly as many people. Checking that we have consistent lengths in a frame doesn't rely on c being invariant. Since relativity intertwines distance and time, it should depend on it, if you are correct.

[Andromacus]

No, that's wrong. c does not need to be invariant (which means the same in every frame) it just needs to be constant in any given frame. It need not have the same value, since the value doesn't show up in the synchronization.

 

But since you're convinced it does, come up with an example of the synch not working.

 

Aren't you forgetting the first postulate here? C needs to be constant and invariant in any inertial frame. And where did I say that the synch is not working, you are the one claiming that the synch doesn't need to work between frames, but just in one frame. I'm saying that it needs to work in any inertial frame by the postulates and in ordr for the Lorentz transformations to even be possible.

 

 

The goal of clock synchronization is to synchronize the clocks in any given inertial frame. Period. It is a necessary condition for relativity, but the converse doesn't hold. This is a failure of basic logic, "If A then B" B requires A, but B doesn't mandate A. "B, therefore A" is wrong.

You need to be able to transform between any given inertial frame, that is the essence of relativity and the Lorentz transformations, and for that, not for adjusting time in the single frame, you need the postulates of relativity. That's how Einstein derives the transformations, he starts with the postulates and derives the LT.

 

Your assertion is like saying because we needed Newtonian physics to send a person to the moon, the goal of Newtonian physics was to send a person to the moon. That's hogwash. It is a prerequisite, but that's all.

You seem to be misinterpreting and twisting my words beyond recognition.

The transformations can't be derived until you have a clock synchronization protocol. The synch is a prerequisite, but it does not depend on the work that came after. It stands on its own. If c was not invariant, the synch would still work. It just requires that c be constant in each frame (i.e. space needs to be isotropic)

The synch would still work but if c was not invariant how could you derive the lorentz transformations without contradictio, you keep ignoring this point.

 

 

 

 

You keep insisting that invariance is a require ment of synchronization, and that's flat-out wrong.

No, you misunderstood me. Constancy of light is enough for that. What I'm saying is that invariance is required to transform between inertial frames.

The same argument could be made for length as for time, but that doesn't seem to befuddle nearly as many people. Checking that we have consistent lengths in a frame doesn't rely on c being invariant.

It relies in c being constant, it actually is considered the conversion factor between time and length in the time coordinate(ct).

 

 

 

I don't need to, you just need to look at Minkowskii coordinates which is pseudo Euclidean.

 

 

You edited your post to add the bit about pseudo-euclidean" after I replied without making note of it, that doesn't seem to be fair play.

[Mordred]

I think you need to start including some mathematics to go with your statements. It would help avoid numerous confusions.

 

I'm posting from a phone, didn't see your reply when I added the pseudo Euclidean edit. Sometimes happens, for which I apologize

Edited September 12, 2015 by Mordred

[swansont]

Aren't you forgetting the first postulate here? C needs to be constant and invariant in any inertial frame. And where did I say that the synch is not working, you are the one claiming that the synch doesn't need to work between frames, but just in one frame. I'm saying that it needs to work in any inertial frame by the postulates and in ordr for the Lorentz transformations to even be possible.

 

Nope. The first postulate doesn't imply invariance of c. If it did, the second postulate would not be needed.

 

The part I'm objecting to is the "by the postulates" claim. The synchronization works regardless of the validity of SR; the 2nd postulate doesn't enter into it. And you're right, the Lorentz transforms wouldn't work if the synchronization didn't work, but that's not because the synchronization depends on the transforms. They both rely on isotropy. But the transforms also rely on invariance.

 

You need to be able to transform between any given inertial frame, that is the essence of relativity and the Lorentz transformations, and for that, not for adjusting time in the single frame, you need the postulates of relativity. That's how Einstein derives the transformations, he starts with the postulates and derives the LT.

 

You need to transform between frames for SR. Not for synchronization. Part 1 of Einstein's paper is true on its own, regardless of of what he wrote afterwards in the paper. But you can't properly understand what he wrote afterwards without those definitions being in place.

 

You seem to be misinterpreting and twisting my words beyond recognition.

 

The synch would still work but if c was not invariant how could you derive the lorentz transformations without contradictio, you keep ignoring this point.

 

Perhaps you need to be clearer in what your point is. I am objecting to a specific claim, that Einstein synchronization depends on the invariance of c. I'm ignoring the point because it is irrelevant to my objection. You need to have some synchronization protocol in order to do a transform between frames. It is, as I have repeatedly said, a prerequisite. That's why it comes at the beginning of the paper.

 

No, you misunderstood me. Constancy of light is enough for that. What I'm saying is that invariance is required to transform between inertial frames.

 

Then we agree on that. That, of course, is the whole point of the paper. So, then, what's the problem?

[studiot]

Another consequence of measuring in one frame at a time is that you do not need light or time to measure distance.

 

Further you cannot establish primary units of both distance and time with the same light measurement. You can derive one if you have the other and since distance is easier to measure independently it is often preferred to establish a distance standard by other means and use light to measure time.

Edited September 12, 2015 by studiot

[Andromacus]

 

The part I'm objecting to is the "by the postulates" claim. The synchronization works regardless of the validity of SR; the 2nd postulate doesn't enter into it. And you're right, the Lorentz transforms wouldn't work if the synchronization didn't work, but that's not because the synchronization depends on the transforms. They both rely on isotropy. But the transforms also rely on invariance.

I'm not yet sure we agree, yes the synch works regardless of SR as long as you have a fixed value for c. When I say "by the pstulates" I'm not referring to the validity of the synch in one frame, I'm refering to its being valid under an arbitrariy transformation of frame, that is the synch is valid in one frame alright, but without the postulates you don't have the guarantee that the synch works AFTER an arbitrary Lorentz transformation. This is what Einstein writes, and I' sure you must agree with it.

 

 

You need to transform between frames for SR. Not for synchronization. Part 1 of Einstein's paper is true on its own, regardless of of what he wrote afterwards in the paper. But you can't properly understand what he wrote afterwards without those definitions being in place.

Right.

 

Perhaps you need to be clearer in what your point is. I am objecting to a specific claim, that Einstein synchronization depends on the invariance of c. I'm ignoring the point because it is irrelevant to my objection. You need to have some synchronization protocol in order to do a transform between frames. It is, as I have repeatedly said, a prerequisite. That's why it comes at the beginning of the paper.

I hope is clear now what I meant, it only depends on the invariance of c for its validity under transformation not for the synch itself.

 

Then we agree on that. That, of course, is the whole point of the paper. So, then, what's the problem?

 

Well for some reason we got stuck in this point that I thought should have been clear from the beginning. But again communication in a forum is not easy. Glad we reached this point. That means at the very least(unless you come again ) we agree on what the mainstream says about this. Now comes when I deviate from it. It's explained i the several previous posts, but given that you interpreted it as my disagreeing with you in what we actually agreed, I don't know how to start on the problem.

 

Let's see, do you agree there is ambiguity in the definition of inertial frame in SR?:time independent for defining the null interval and its frame transformations versus time dependent on the specific inertial frame for frames transformations involving speeds <c

I think you need to start including some mathematics to go with your statements. It would help avoid numerous confusions.

 

I'm posting from a phone, didn't see your reply when I added the pseudo Euclidean edit. Sometimes happens, for which I apologize

That's ok, no problem.

[swansont]

I'm not yet sure we agree, yes the synch works regardless of SR as long as you have a fixed value for c. When I say "by the pstulates" I'm not referring to the validity of the synch in one frame, I'm refering to its being valid under an arbitrariy transformation of frame, that is the synch is valid in one frame alright, but without the postulates you don't have the guarantee that the synch works AFTER an arbitrary Lorentz transformation. This is what Einstein writes, and I' sure you must agree with it.

 

I don't know what you are trying to say here. A transform puts you into a different frame, and clocks are not synchronized between frames.

[studiot]

swansont

I don't know what you are trying to say here. A transform puts you into a different frame, and clocks are not synchronized between frames.

 

 

Indeed that is the whole point of relativity of simultaneity.

[Andromacus]

A transform puts you into a different frame, and clocks are not synchronized between frames.

Right, it puts you into a different frame, and in that NEW frame what guarantess that Einstein synch is still working IN THAT NEW frame, NOT BETWEEN frames obviously, is the second postulate thru the Lorentz transformation.

Edited September 12, 2015 by Andromacus

[swansont]

Right, it puts you into a different frame, and in that NEW frame what guarantess that Einstein synch is still working IN THAT NEW frame, NOT BETWEEN frames obviously, is the second postulate thru the Lorentz transformation.

 

The synchronization is a prerequisite, and one of the conditions of the derivation of the transform. Of course it's going to work in the other frame. That's how math works.

[Andromacus]

 

The synchronization is a prerequisite, and one of the conditions of the derivation of the transform. Of course it's going to work in the other frame. That's how math works.

Then that would indicate it is not a prerequisite, as you know clocks are not synchronized between the new transformed frame and the old frame, so for one of them it is not a prerequisite. However it can always be re-adjusted to the Einstein synch precisely because the principle of constancy of c in any inertial frame guarantees it.

 

This is an example of the circular reasoning SR allows, as I said you can conclude from the theory that sinchronization is a fixed prerequisite or that is purely conventional. There scholars and relativity specialists holding both views. You hold that it is a prerequisite, that is fine with me, I cannot convince you of the contrary using the theory itself.

 

BTW, could you address the question in my previous post?

Edited September 13, 2015 by Andromacus

[swansont]

Then that would indicate it is not a prerequisite, as you know clocks are not synchronized between the new transformed frame and the old frame, so for one of them it is not a prerequisite. However it can always be re-adjusted to the Einstein synch precisely because the principle of constancy of c in any inertial frame guarantees it.

 

No? Then derive the Lorentz transform without a clock synchronization protocol. How can you transform time from one frame to another if you haven't defined what the time is in the original frame? I don't see how you do that, but if you're going to insist that you can, let's see it. (edit: IOW I expect the Lorentz transform preserves an arbitrary protocol, so I'm not sure what the issue is. The transform preserves the time map you have in a frame, as a transform would be expected to do, and the transform depends on the invariance of c. Nothing controversial in that, IMO. Or circular.)

 

However, once you've defined that it is the same time at all points in a frame, a properly-derived transform is going to have to conform to that prerequisite.

 

This is an example of the circular reasoning SR allows, as I said you can conclude from the theory that sinchronization is a fixed prerequisite or that is purely conventional. There scholars and relativity specialists holding both views. You hold that it is a prerequisite, that is fine with me, I cannot convince you of the contrary using the theory itself.

 

It is a prerequisite, up until you address what I ask above. Whether it's a fixed prerequisite is something I questioned back in post #2. I don't know that it is, or is not. I've not gotten involved in that discussion.

 

BTW, could you address the question in my previous post?

 

AFAIK an inertial frame is defined as one that is not accelerating. I'm not sure what alleged ambiguity you're referring to

[Mordred]

 

AFAIK an inertial frame is defined as one that is not accelerating. I'm not sure what alleged ambiguity you're referring to

Yes that's correct.

"A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame."

 

 

https://en.m.wikipedia.org/wiki/Non-inertial_reference_frame

 

However that being said SR can handle accelerating frames. It's a common misconception that it can't.

 

The article by Beaz has a decent coverage.

http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html

Edited September 13, 2015 by Mordred

[Andromacus]

 

No? Then derive the Lorentz transform without a clock synchronization protocol. How can you transform time from one frame to another if you haven't defined what the time is in the original frame? I don't see how you do that, but if you're going to insist that you can, let's see it.

 

However, once you've defined that it is the same time at all points in a frame, a properly-derived transform is going to have to conform to that prerequisite.

 

 

It is a prerequisite, up until you address what I ask above. Whether it's a fixed prerequisite is something I questioned back in post #2. I don't know that it is, or is not. I've not gotten involved in that discussion.

I was referring to a fixed prerequisite, that is what I understood to be your concern. It is obvious that some synchronization is needed, in this case it is the one that coincides with the isotropy and homogeneity of the inertial time and space coordinates(Einstein's synch). But as you also know this synch derived from the time independent inertial coordinates of Newtonian mechanics is not preserved by the Lorentz transformations:clocks synchronized in the original frame are not in the transformed frame(as studiot remarked earlier that is the essence of the relativity of simultaneity.

 

I find it clarifying to think about this, Einstein intended his synchronization procedure to solve the problem of distant times in a theory with no absolute time, but he assumed first that the distant clock was at rest with respect to the local clock. Assuming a certain state of motion at a distance implies a concept of time, so the synchronization just begs the question.

 

[swansont]

Einstein intended his synchronization procedure to solve the problem of distant times in a theory with no absolute time, but he assumed first that the distant clock was at rest with respect to the local clock. Assuming a certain state of motion at a distance implies a concept of time, so the synchronization just begs the question.

 

Since the distant clock is at rest it means there is no motion, which I guess technically is a state of motion, but one that is time-independent.