Clock synchronization and relativity of simultaneity

[Ibix]

If I'm understanding right, fantasist, you're defining two clocks to be synchronised if identically time-stamped pulses arrive simultaneously at the point half-way between the clocks.

Where relativity of simultaneity comes from is the realisation that "half-way between" means different things in different frames. This is the point of Einstein's train struck by lightning at both ends. According to an observer on the platform, "half-way between" the strikes is the middle of the platform; to an observer on the train it is the middle of the train. These are not the same place. And since you cannot have the light from the strikes arriving simultaneously at the center of the train and also simultaneously at the center of the platform, one or other must say that the strikes were not simultaneous.

Everyone agrees that the light from the strikes arrives simultaneously at the center of the platform. But since they don't agree that the center of the platform is half-way between the strikes, they don't think that is relevant to their definition of simultaneity.

The same is true of your clocks. Everyone agrees that the pulses arrive simultaneously at your detector. But since they don't agree that the detector is at the point half-way between the emission points, this is not relevant to them.

 

[DrGreg]

Edit: why are my LaTex at the centre?

Use "itex" instead of "tex" if you want inline LaTeX.

 

[Dale]

shouldn't the clock synchronization be carried in their own rest frame? i mean observers who are there in that frame itself.

They do this to understand the timings of the different events in their own frame... the clock nearer to the event measures this and then it becomes the time at which that event occurred in that frame..

Yes, this is how it is done in Einsteins paper.

He then shows how doing so leads to something that does not meet the definition of synchronization in the moving frame.

 

[Fantasist]

If I'm understanding right, fantasist, you're defining two clocks to be synchronised if identically time-stamped pulses arrive simultaneously at the point half-way between the clocks.
Where relativity of simultaneity comes from is the realiation that "half-way between" means different things in different frames. .

If the detector half-way between the clocks is co-moving with latter, then it is half-way between them in any reference frame.

Anyway, to avoid confusion, note that we have been switching here back and forth between Einstein's original version of the synchronization procedure (which doesn't involve a separate detector but instead a signal round-trip) and my own version. The last few posts have actually been dealing more with the former rather than the latter.

 

[Fantasist]

If the clocks which are separated by a certain distance are synchronized in their rest frame,then they are not synchronized in a frame where they are seen to be moving... In fact the clock at the rear is ahead of the clock at the front by the amount { \frac{L_0v}{c^2}} where L_0 is the rest separation between the clocks and v the velocity of the clocks.

Note that we should not have to resort to the Lorentz transformation formula to prove the frame dependence of the clock synchronization. Einstein claims it already when he defines his clock synchronization formula in paragraphs 2&3 in his paper, before he even starts to derive the Lorentz transformation. It is something that should follow from his definitions alone.

 

[Fantasist]

This is incorrect. Since the moving clocks are (by design) synchronized in the stationary system they cannot be synchronized in the moving frame, regardless of what you might want.

The times in Einstein's synchronization equation for the stationary frame (assuming synchronized clocks in that frame)

t_B' - t_A1' = r_AB/(c-v)
t_A2' - t_B' = r_AB/(c+v)

are solely determined by the positions of the moving clocks and the light signal in that frame. How should the display of the moving clocks come into it? The latter might even stand still i.e. always display the same time, still the same equation would apply in the stationary frame, simply because a) only the positions of the moving clocks are timed, and b) these timings are obtained by a completely unrelated set of clocks.

 

[Ibix]

If the detector half-way between the clocks is co-moving with latter, then it is half-way between them in any reference frame.

Half-way between the clocks, yes. Half-way between the emission events at the reception time, no.

 

[Dale]

The times in Einstein's synchronization equation for the stationary frame (assuming synchronized clocks in that frame)

t_B' - t_A1' = r_AB/(c-v)
t_A2' - t_B' = r_AB/(c+v)

are solely determined by the positions of the moving clocks and the light signal in that frame. How should the display of the moving clocks come into it?

Because the display of the moving "clocks" are forced, by design (not by nature), to display the same number as that of a co-located synchronized stationary clock. This is given in the setup as described by Einstein. The moving clocks are not normal clocks that measure proper time along their worldline, they are forced to keep coordinate time in the stationary frame.

The latter might even stand still i.e. always display the same time

Then it wouldn't be the setup that Einstein is describing. Nothing inherently wrong with that, but I am not sure what your point is.

I still cannot tell if you are just complaining about Einstein's presentation or if you have a substantive problem with the relativity of simultaneity. Can you clarify that? Do you understand the Lorentz transform itself and how the relativity of simultaneity follows? Is it just Einstein's derivation that you object to or do you object to the Lorentz transform itself?

 

[Dale]

Note that we should not have to resort to the Lorentz transformation formula to prove the frame dependence of the clock synchronization. Einstein claims it already when he defines his clock synchronization formula in paragraphs 2&3 in his paper, before he even starts to derive the Lorentz transformation. It is something that should follow from his definitions alone.

Here it sounds like you do not have substantive concern about the relativity of simultaneity, but just an objection to Einstein's presentation.

 

[John F. Gogo]

Here it sounds like you do not have substantive concern about the relativity of simultaneity, but just an objection to Einstein's presentation.

Einstein's ideas are 100 plus years old. It is no wonder that scientists tend to look for the future of science if one assumes that science is a progression.

 

[John F. Gogo]

Einstein's ideas are 100 plus years old. It is no wonder that scientists tend to look for the future of science if one assumes that science is a progression.

Ultimately, I always give weight to the idea. For instance, how is knowing that the speed of light is c helping man leverage nature?

 

[ash64449]

Note that we should not have to resort to the Lorentz transformation formula to prove the frame dependence of the clock synchronization. Einstein claims it already when he defines his clock synchronization formula in paragraphs 2&3 in his paper, before he even starts to derive the Lorentz transformation. It is something that should follow from his definitions alone.

Actually i got this formula from a different book which used different definition to synchronize the clocks in their rest frame. Even then after using a different definition,formula is one and the same.

Yes. i do notice formula i quoted is present in Lorentz Transformation.

EDIT: reference: H C Verma Concepts of Physics 2

 

[Fantasist]

Because the display of the moving "clocks" are forced, by design (not by nature), to display the same number as that of a co-located synchronized stationary clock. This is given in the setup as described by Einstein.

The usual convention is that clocks are synchronized in their own frame, not the other frame. Einstein has it actually the wrong way around in § 2 where he makes the case for the frame dependence of the clock synchronization. In § 3 he changes it around again and requires that the clocks are synchronized in their own frame when he goes about to derive the Lorentz transformation.

I still cannot tell if you are just complaining about Einstein's presentation or if you have a substantive problem with the relativity of simultaneity. Can you clarify that? Do you understand the Lorentz transform itself and how the relativity of simultaneity follows? Is it just Einstein's derivation that you object to or do you object to the Lorentz transform itself?

Maybe I did not express myself clearly enough, so let me expand on what I said before: the issue I am having is with the fact that the events in question (the light signals being registered by the moving clocks) is physically not the same events that are associated with it in the stationary frame. In the latter the timings are obtained by associating with the events the times of the corresponding stationary clocks that happen to be at the location where the paths of the moving clocks and the light signal as defined by clocks/detectors in the stationary frame intersect. If you do this however, you should also associate the velocities c-v and c+v in the timing equations of the stationary frame with the speed of light in the moving frame, which obviously would contradict the postulate of the invariance of c.

 

[Dale]

The usual convention is that clocks are synchronized in their own frame, not the other frame.

At the time that Einstein wrote it there was no established convention. Nobody else had recognized that clock synchronization required a convention. That is one reason that it is generally better to learn scientific concepts from modern textbooks rather than from the seminal works.

the issue I am having is with the fact that the events in question (the light signals being registered by the moving clocks) is physically not the same events that are associated with it in the stationary frame. In the latter the timings are obtained by associating with the events the times of the corresponding stationary clocks that happen to be at the location where the paths of the moving clocks and the light signal as defined by clocks/detectors in the stationary frame intersect. If you do this however, you should also associate the velocities c-v and c+v in the timing equations of the stationary frame with the speed of light in the moving frame, which obviously would contradict the postulate of the invariance of c.

(emphasis added, see below)

OK, this seems more like a substantive concern rather than a complaint about Einstein's presentation. It would be best to avoid constantly referencing his presentation, since it makes it seem like your intent is merely an objection to his description.

The bolded part of your comments is wrong, and may be the source of the confusion. An event is a frame-invariant geometric object. It is a "point" in spacetime. An event in one frame is indeed physically the same event as in any other frame. The only difference is the different coordinates that different frames will use to label the same event. The events are physically the same events in all frames. The coordinates assigned to each event is what varies.

Given a single event (which is physically the same event in one frame as in all other frames) there is a function which allows you to determine the coordinates in a second frame given the coordinates in the first frame. This function is called the coordinate transformation. The relativity of simultaneity is simply the fact that the transformation between inertial frames (aka the Lorentz transform) allows events which share the same time coordinate in one frame to have different time coordinates in another frame.

 

[A.T.]

An event in one frame is indeed physically the same event as in any other frame. The only difference is the different coordinates that different frames will use to label the same event.

As already explained in post #15.

 

[Fantasist]

At the time that Einstein wrote it there was no established convention. Nobody else had recognized that clock synchronization required a convention. That is one reason that it is generally better to learn scientific concepts from modern textbooks rather than from the seminal works.

We are discussing this because of issues that are usually not addressed in textbooks (not in that detail anyway). So there is really little choice other than occasionally having to refer back to the original text where the concepts were developed. The different notations and conventions there may initially be a source of confusion, but lastly I think they only help to clarify the issue.

An event is a frame-invariant geometric object. It is a "point" in spacetime.

Yes, as a mathematical idealization/abstraction.

An event in one frame is indeed physically the same event as in any other frame.

Events can only be defined through their physical detection, and each detection is a separate event on its own, not only for detectors belonging to different reference frame but even the same frame. It is only through educated guesses that you assign a common event as a cause to the detection events. But these educated guesses are not a priori correct. You could have for instance by coincidence (or design) a sequence of detector events that only mimic a common causal event without actually one being there.

 

[Dale]

Yes, as a mathematical idealization/abstraction.

Certainly. The same as with any mathematical quantity in any good theory of physics.

Events can only be defined through their physical detection, and each detection is a separate event on its own, not only for detectors belonging to different reference frame but even the same frame. It is only through educated guesses that you assign a common event as a cause to the detection events. But these educated guesses are not a priori correct. You could have for instance by coincidence (or design) a sequence of detector events that only mimic a common causal event without actually one being there

Certainly we can make mistakes in our experiments. I don't see how that is relevant.

If you are talking about relativity (which is what we do here) then you are talking about a theory in which all physical objects and events are mathematically represented by frame invariant geometric objects which simply are labeled with different coordinates in different frames. Neither the geometrical objects nor the physical things they represent "belong" to a reference frame.

Your "issue" that you describe above is not an issue with SR. It is an issue that arises only because of your incorrect understanding of what an event is in SR. This is why it isn't in standard SR textbooks.

 

[A.T.]

each detection is a separate event on its own

If two physical events coincide in one frame, then they coincide in all frames and can be considered one event.

detectors belonging to different reference frame

All detectors exist in all reference frames.