Synchronization free of Contradiction: 1905 Paper

[bahamagreen]

TL;DR Summary

I must be missing some of the implicit assumptions among the explicit ones presented.

1905 paper, looks to me like:

Postulates:
- principle of relativity
- definite velocity of c

Definition of inertial frame coordinate system
- using rigid rods to identify position of A at rest WRT to the IFR coordinates

Seems clear that rigid rods may be used to identify the place of other points at rest WRT the IRF coordinates.

Mentions a point moving WRT to the IRF coordinates, raises issue of time.

Uses the phrase "time value indication", so seems the time issue is not rate of time? However, he emphasizes that the distance itself is a problem? Leading up through the "A time", "B time", and "Common time", does he not believe that all points at rest in the system have the same rate of time?

The procedure with A and B
- disregards relative motion between A and B
- assumes one trial
- assumes (see below)
A->B =B->A
if A->B = A->C then also = B->C

But seems that he can't know if B is in relative motion to A, the rigid rod measure that would verify rest WRT to the IRF is forgone and light reflection path duration is used, but mustn't duration A to B and B to A be equal whether there is relative motion or not? Doesn't it require additional tests to verify longitudinal rest? Won't constant lateral motion be hidden even with multiple tests measuring only reflection path duration?

The whole thing is a combination of explicit and implicit ideas and assumptions; what are the implicit assumptions I am missing or misreading? Is there a clearer presentation that addresses these kinds of question?

 

[Dale]

Is there a clearer presentation that addresses these kinds of question?

Yes. The seminal works are rarely the best place to learn because there is typically a lack of clarity early on and often there are many false starts or other mistakes.

I would recommend starting with a modern dedicated textbook on the topic. Modern authors have had the advantage of a century of development to clarify and refine the concepts and presentation.

 

[Orodruin]

If you want to learn relativity you should not read the 1905 paper, you should be reading a modern textbook. Reading original research papers is generally not a good way to learn something.

 

[Ibix]

The reason that original relativity papers aren't the best to read is that they are written for an audience of experts in late 19th century physics. And they are part of a dialog between said experts, not teaching material. For a fundamental paper, Einstein's 1905 paper is easy to read, essentially because it's a conversation starter in a new topic. But it's still written for people with different background and training to you, and translated from German to boot.

Get a modern textbook.

 

[bahamagreen]

Of course you all anticipate that my questions arise because the next section places clocks on the ends of the rod AB moving with respect to the system at rest, having those moving clocks indicating the time values of local at rest clocks using the synchronization process. His original example synch process didn't quite exclude synching of clocks in relative motion, but we will know later that relative motion alters mutually observed clock rates...

Is there somewhere on the web that you feel lays out the foundation well with regard to the details of assumptions, definitions, and procedures?

 

[pervect]

Of course you all anticipate that my questions arise because the next section places clocks on the ends of the rod AB moving with respect to the system at rest, having those moving clocks indicating the time values of local at rest clocks using the synchronization process. His original example synch process didn't quite exclude synching of clocks in relative motion, but we will know later that relative motion alters mutually observed clock rates...

Is there somewhere on the web that you feel lays out the foundation well with regard to the details of assumptions, definitions, and procedures?

I'm not quite sure what your question is. If it's about the usual, the relativity of simultaneity,
you could try Scherr's paper, "The challenge of changing deeply held student beliefs about the relativity of simultaneity", but it might be too advanced.

I'm also not sure how well it works for students - I recommend it occasionally, but haven't had much feedback on it. So I'm fearing that it's not being read, or if it is , it's not being appreciated.

http://www.physics.umd.edu/perg/papers/scherr/ScherrAJP2.pdf

On the general subject of learning relativity, I am rather partial to Bondi's treatment in "Relativity and common sense", which should be available on the WWW if you look for it. I think it's in the public domain nowadays, but I'm not confident enough to post a link.

That's a pretty basic treatment, for a more advanced treatment that will lead to GR< I'd recommend something like "Spacetime physics", by Taylor. There are a few chapters of an earlier edition that available on the web, but not the whole book, and not the latest edition.

The author's webiste, with the first chapter, is at http://www.eftaylor.com/download.html

 

[Mister T]

His original example synch process didn't quite exclude synching of clocks in relative motion, but we will know later that relative motion alters mutually observed clock rates...

But unless you understand how distant clocks are synchronized you can not understand how the observed dilation of clock rates can be mutual.

 

[PeroK]

Of course you all anticipate that my questions arise because the next section places clocks on the ends of the rod AB moving with respect to the system at rest, having those moving clocks indicating the time values of local at rest clocks using the synchronization process. His original example synch process didn't quite exclude synching of clocks in relative motion, but we will know later that relative motion alters mutually observed clock rates...

Is there somewhere on the web that you feel lays out the foundation well with regard to the details of assumptions, definitions, and procedures?

There's also the first chapter of Morin's book on SR online:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

 

[Orodruin]

Based on your title, it seems you are looking to find some way of synchronizing clocks that does not depend on the observer. If so you will be very disappointed because it cannot be done. Simultaneity of events that are not co-located in relativity will at best be an arbitrary convention. Typically, this arbitrary convention is constructed by the introduction of some coordinate system (similar to how Einstein introduced his inertial coordinates) and calling events that have the same ”time” coordinate simultaneous. However, since coordinates are arbitrary, any such definition of simultaneity will be arbitrary. Mathematically this is no stranger than having different x-axes in Euclidean space depending om how you rotate your coordinate system. What you can ask if is this is a better description of Nature than the absolute time of Galilean spacetime. Empirical evidence strongly suggests it is.

 

[bahamagreen]

Based on your title, it seems you are looking to find some way of synchronizing clocks that does not depend on the observer. If so you will be very disappointed because it cannot be done. Simultaneity of events that are not co-located in relativity will at best be an arbitrary convention. Typically, this arbitrary convention is constructed by the introduction of some coordinate system (similar to how Einstein introduced his inertial coordinates) and calling events that have the same ”time” coordinate simultaneous. However, since coordinates are arbitrary, any such definition of simultaneity will be arbitrary. Mathematically this is no stranger than having different x-axes in Euclidean space depending om how you rotate your coordinate system. What you can ask if is this is a better description of Nature than the absolute time of Galilean spacetime. Empirical evidence strongly suggests it is.

My title just shows the part of the 1905 paper about which I'm asking, not suggesting losing the observer.

I think I understand how distant clocks at rest wrt to an IFR are synchronized. What I am not understanding is how that process is extended to collocated clocks in relative motion.

What I am thinking about:

- do clocks at rest wrt to an IFR share the same rate of time? (I think yes)
- does the synch process between such rest clocks ensure that A->B = B->A and if A->B = A->C then also = B->C ? (think yes)

- do clocks in relative motion wrt to an IFR share the same rate of time? (I think, no)
- does the scope of the synch process extend to include clocks in relative motion? (I would think no, the reflexive and associative relations not holding)

- if all that is so, how are the clocks on the ends of the moving AB rod synchronized with the clocks at rest wrt to the IFR? (back to wondering if sharing the same time rate is necessary for synchronization even if the momentary time value indications are matched).

Somehow, the presentation seems to have skipped ahead of me following along the assumptions and implicit steps; the synchronization process is described as without contradiction (which means to me that his example definition should stand well being applied in his next example, but I'm not seeing how the moving rod end clocks can synch to the IFR rest clocks if synchronization assumes "same time rate" as well as "momentary same time indication". Synchronized clocks stay synchronous until something changes, right? Doesn't that mean not only do their time indications match, but also their rates of time?

 

[PeroK]

- if all that is so, how are the clocks on the ends of the moving AB rod synchronized with the clocks at rest wrt to the IFR? (back to wondering if sharing the same time rate is necessary for synchronization even if the momentary time value indications are matched).

In the final analysis, if you are not prepared to get a modern text and learn from a source designed to teach SR to someone like you, then you have only yourself to blame for not understanding this stuff.

The clocks in the rest frame are synchronised wrt each other (in the rest frame) and the clocks in the moving frame are synchronised with each other (in the moving frame). But, they are not all synchronised in either frame. That is the heart of the relativity of simultaneity.

In the moving frame the rest clocks are out of sync; and, in the rest frame the moving clocks are out of sync.

 

[PeterDonis]

What I am not understanding is how that process is extended to collocated clocks in relative motion.

It isn't. Any clock synchronization process only applies to clocks at rest relative to each other.

 

[bahamagreen]

OK, that's what I have been thinking, too.

Section 2 presents the moving rod AB wrt the "stationary system".
Let me show you the problematic paragraph - tenth paragraph of section 2, regarding the clocks placed on the ends of the moving rod AB...

"We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the "time of the stationary system" at the places where they happen to be. These clocks are therefore "synchronous in the stationary system".

I read this as synchronizing the moving clocks on the ends of the rod with the instantaneously collocated unmoving clocks of the stationary system.

 

[PeroK]

OK, that's what I have been thinking, too.

Section 2 presents the moving rod AB wrt the "stationary system".
Let me show you the problematic paragraph - tenth paragraph of section 2, regarding the clocks placed on the ends of the moving rod AB...

"We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the "time of the stationary system" at the places where they happen to be. These clocks are therefore "synchronous in the stationary system".

I read this as synchronizing the moving clocks on the ends of the rod with the instantaneously collocated unmoving clocks of the stationary system.

What he's doing is keeping the moving clocks in sync with the local time in the stationary frame and then, in the next paragraph, showing that they are not synchronised in the moving frame.

You could imagine these moving clocks continually being updated from local clocks in the rest frame.

It's a slightly cumbersome approach compared to a more modern treatment. It's wordy and has no diagrams as well.

 

[PeterDonis]

I read this as synchronizing the moving clocks on the ends of the rod with the instantaneously collocated unmoving clocks of the stationary system.

"Synchronizing" in the sense of "continually forcibly resetting the clocks", yes. But this is not what Einstein uses the term "clock synchronization" to mean in other places. In other places, he uses that term to mean a one-time process in which spatially separated clocks that are at rest relative to each other are synchronized by exchanging light signals. (This process is often called "Einstein clock synchronization" in the literature since Einstein was the first to describe it.)

 

[bahamagreen]

That's all kind of what I've been thing, too.

What remains is the justification for the process between the moving and rest clocks. He is careful to describe the process between clocks at rest, but then applies that concept to relatively moving clocks.

Since we will learn later that clocks in relative motion don't share the same rate, how does that not confound the process of matching the time values of the moving and at rest clocks?

 

[Orodruin]

That's all kind of what I've been thing, too.

What remains is the justification for the process between the moving and rest clocks. He is careful to describe the process between clocks at rest, but then applies that concept to relatively moving clocks.

Since we will learn later that clocks in relative motion don't share the same rate, how does that not confound the process of matching the time values of the moving and at rest clocks?

You neer match moving clocks to rest clocks. What is moving and at reat depends on the frame. What you can do is to synchronize clocks that are at relative rest to each other.

 

[PeroK]

Since we will learn later that clocks in relative motion don't share the same rate, how does that not confound the process of matching the time values of the moving and at rest clocks?

It is a clumsy process. Every time you pass a rest clock you have to adjust your clock. These days you could do it by updating the moving clock from a time signal from the local rest clock.

 

[PeterDonis]

then applies that concept to relatively moving clocks

No, he doesn't. As I said, when he uses the term "synchronization" in relation to relatively moving clocks, he is not talking about the same process as he is when he uses the term "synchronization" in relation to clocks at rest relative to each other. They are different concepts, different processes. It's unfortunate that he used the same word for both, but it's much too late to fix that now.

 

[Orodruin]

They are different concepts, different processes. It's unfortunate that he used the same word for both, but it's much too late to fix that now.

Again underlining the advice to get a modern textbook.

 

[bahamagreen]

"We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the "time of the stationary system" at the places where they happen to be. These clocks are therefore "synchronous in the stationary system".

I see relatively moving clocks' time value indications being matched to the indications of clocks at rest.
Whether this process is proper Einstein clock synchronization or not, the result is that the clocks instantaneously match their time value indications, but do not share the same time rates... perhaps he is doing this because this kind of continuous updated time value indication matching is all he needs to move forward - that the differential rates of the clocks involved are of no concern to what he is setting up to show?

edit update: I'm behind in the responses...

If the section 2 process is different, why does he just decree it rather than defining it like earlier where he is so careful. In the original definition it is clear that rest clocks share the same time rate and the process matches the time indication values. In the section 2 process, it seems clear that the time rates of relatively moving clocks will not match, even if they may match their time value indications for an instant.

It looks to me that the same process itself may be used in both the case of relatively moving and at rest clocks; just that the only result that will be consistent in both cases will be the instantaneous time value indications, not the assumption of matched time rates.

I'm looking through the references provided; have not found examination this yet.

 

[PeroK]

 

[PeterDonis]

If the section 2 process is different, why does he just decree it rather than defining it like earlier where he is so careful.

Who knows? We can't ask Einstein because he's been dead for more than half a century.

You have already been given the best advice we can give you: learn from a modern textbook.

Thread closed.

 

[Dale]

I read this as synchronizing the moving clocks on the ends of the rod with the instantaneously collocated unmoving clocks of the stationary system.

Yes, you read that correctly. This is one specific reason to learn this material from a more modern source. What he is doing is valid but confusing. I would recommend learning the material elsewhere first and then coming back to the seminal paper later.

Edit: I see I am a bit late to the party :)