# Talk:Einstein synchronisation

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## Untitled

If someone is going to create hr: (or sl:, ...) version: There's an article in Croation in the open access journal Prolegomeno on this subject:

Pjacobi 09:06, 8 November 2006 (UTC)

## Über die spezielle and die allgemeine Relativitätstheorie

I've read the book (in German) and I'm a bit confused which part of it supports this recent edit. To my best knowledge, and from a quick look into the online translation, in this book Einstein uses the midpoint-observer-method, which is of course completely equivalent to the back-and-forth-signal method. --Pjacobi 21:01, 9 November 2006 (UTC)

I've reverted for now. --Pjacobi 17:28, 12 November 2006 (UTC)

> [...] in this book Einstein uses the midpoint-observer-method
Sure. (As far as I can tell, Einstein didn't attach a name to the method; but observer M as "midpoint between" A and B plays a decisive role.)
> which is of course completely equivalent to the back-and-forth-signal method.
No -- these methods are inequivalent in several important ways (two of which had been indicated in the article):
1. They concern different notions.
The "midpoint-observer-method" itself is (merely) a method for deciding simultaneity of state pairs (and simultaneity is independent of appearance, labelling, or parametrization). In contrast, a determination about synchrony (i.e. both by the methods of 1905 and of 1917) requires the additional comparison of labels.
2. They have different requirements.
The synchrony definition of 1905 requires some particular real-valued parametrizations "$\tau$" (separately for the states of A and of B), while neither the simultaneity definition of 1917, nor the corresponding definition of synchrony require such parametrization (at least overtly). (In other words: only the latter method allows for instance to decide whether two given Floral clocks are in synchrony, or not. In this respect, the latter method is certainly superior to the former.)
3. They have different results.
Considering two clocks, A and B, moving at the periphery of a rotating disk (within a flat space). Using the synchrony definition of 1905 they may find having been synchronous at least for some suitable parametrizations "$\tau_{A}$" and "$\tau_{B}$". However, using the definition of 1917 (along with the definition of "midpoint" based on projective geometry), they already fail to find any simultaneous state pairs (and consequently cannot find having been synchronous at all, regardless of any parametrizations or labellings), because there cannot be found any observer as "midpoint M between" A and B to begin with; i.e. no observer M satisfies the conditions that
- Observer A finds two successive "back-and-forth-signal" intervals to and from observer M the same as one "back-and-forth-signal" interval to and from observer B,
- Observer B finds two successive "back-and-forth-signal" intervals to and from observer M the same as one "back-and-forth-signal" interval to and from observer A, and
- Observer M finds same "back-and-forth-signal" intervals to and from observer A and to and from observer B.
I'm not certain whether Einstein after Dec. of 1916 devised even further definitions of how to measure synchrony or of simultaneity (or whether he even was the first to develop the "midpoint-observer-method"), or whether afterwards he may again have reverted to the earlier definition. But the progress Einstein had made since 1905 ought to be recognized in any case. Frank W ~@) R 23:38, 12 November 2006
I'm still rather unclear what you are arguing here. Can you be so kind to state specifically which sentences in "Über die spezielle and die allgemeine Relativitätstheorie" you have in mind? Or what secondary sources you are using? --Pjacobi 08:07, 13 November 2006 (UTC)
> [...] Can you be so kind to state specifically which sentences in "Über die spezielle and die allgemeine Relativitätstheorie" you have in mind?
Why - certainly I can. (I'll quote the relevant passages of course from the English translation, which is also avaliable online; namely from Sect. 8, i.e. the reference that had been listed in the article):
$If the observer [...] placed at the midpoint M of the distance A B [...] perceives the two flashes of lightning at the same time, then they are simultaneous. We agreed already that (in your words) "Einstein uses the midpoint-observer-method". However, I note and emphasized in (1.) above that this method in itself is (merely) a method of defining simultaneity, not (yet) of synchrony. Moreover, I had indicated in (3.) above that the existence of a "midpoint between" two given observers is far from a trivial matter (nor is correspondingly the existence of a value of "distance between" two given observers, A and B). IIRC that's already sketched in Max Born's "Einstein's Theory of Relativity" (for instance; although there don't seem very many sources that even acknowledge Einstein's "use of the midpoint-observer-method" at all). Further on:$ [...] that clocks [...] are set in such a manner that the positions of their pointers are simultaneously [...] the same.
This unarguably (?) concludes the synchronisation definition under consideration, i.e. what I'd consider "Einstein's synchronisation definition of 1917". I note in (2.) that "positions of pointers" may be compared and judged "same" vs. "not same" regardless of some particular parametrizations "$\tau_{A}$" and "$\tau_{B}$" which are explicitly required by "Einstein's synchronisation definition of 1905" as sketched in the original article. Consequently the method of 1917 may allow to determine whether or not certain Floral clocks were in synchrony, while AFAIU the 1905 method doesn't allow such a determination at all.
(Also, as an aside and a matter of stylistic clarity, I wouldn't necessarily use the word "same" in reference to distinct items; such as referring to the more or less similar appearances of two distinct clocks; and "display state" would seem not as pedestrian as "position of pointer" ...). Frank W ~@) R 21:22, 13 November 2006 (UTC)
Thanks for clarifying. I have to think about it. --Pjacobi 08:47, 14 November 2006 (UTC)
Fine, thanks for giving it more thought for now. Even better: have (eventually) all interested W:Readers recognize and think about the issue, elaborate or correct as needed, or find their thoughts expressed already. (For instance, the thought of having the listing of sources start with the primary ones; which happen to be in chronological order as well.) I'll restore the article accordingly. Frank W ~@) R 20:52, 15 November 2006 (UTC)
In case you are still watching this talk page: I've reading some more sources (rather randomly choosen, by using these readily available), and would judge that Einstein later (sometimes) uses the midpoint observer method is primarily rooted in its simplicity. It does in addition makes less assumptions and achivieves arguebly more, but only withing context of even more general test theories. The philosophical debate about "Einstein synchronisation" centers about the conventionality of choosing $0 \le \alpha \le 1$ to 0,5. In this regard midpoint observer (or midpoint flash, which seems to be most popular introductory treatment) and the older back and forth method, are equivalent. In "midpont" methods α corresponds to the choice of the observer (flash) position.
Also there is an example of a widely used other synchronisation convention. The astronomical one which uses the backward lightcone of Earth (or an idealized "Earth" position) as surfaces of simultaneity. The 1987 Supernova is that one, whose light reached Earth in 1987.
Pjacobi 12:58, 4 December 2006 (UTC)

$In case you are still watching [...] In eny case there seems to be some need for discussion.$ [...] the midpoint observer method is primarily rooted in its simplicity.
Naming the distinguishing attribute of the midpoint observer method "its simplicity" might cause the wrong impression that a prescription such as "(choose some monotonous real-valued parametrization $\tau_{A}$) ... calculate $(\tau_{A2} + \tau_{A1}) / 2$, etc." were to be considered nevertheless a reasonable method, giving definite results.
More appropriately, the midpoint observer method should be primarily characterized as being "definite" or "sensible" or "reproducible", i.e. in distinction to indefinite/arbitrary or irreproducible prescriptions (such as "Einstein's earlier method" stated in the article without any selfstanding definition on how a suitable parametrization $\tau_{A}$ ought to be selected, say up to affine transformations).
(Also, I wouldn't consider the midpoint observer method itself particularly simple, in principle; especially not the underlying important determination, for a given pair of observers, A and B, which, if any, observer constitutes a "midpoint between" this pair.)
$[...] only withing context of even more general test theories. It is certainly indispensible to specify "theoretical context" in the sense of stating selfstanding definition (along with considering their consequences), especially when statements of order or equality are concerned (for instance whereever real numbers are assigned either as parameters or as result values) and whereever relations between several participants require mutual agreement (notably relations "between observer pairs" and even certain third parties). Therefore, not least, the two principal references ([Einstein1905] and [Einstein1917]) in the article, where axioms are indicated: [Einstein1905] (i.e. "the signal of clock 1, being reflected by clock 2 and arriving back at clock 1" referred to in the article): ∗ each observer can state signals, observe (and recognize) signals stated by others and observe (and recognize) echoes to own signals; ∗ each observer can order the own states (monotony with respect to this ordered set may be considered when choosing some suitable parametrization $\tau_{A}$); and [Einstein1917] ("If the observer perceives the two flashes of lighting at the same time ..."): ∗ each observer can distinguish whether observations were collected coincidently (in the same state) or successively (in distinct states). (Being rather self-evident, these axioms were recognized and their consequences considered by others as well, even prior to Dec. of 1916 for instance by Robb.) Since you're referring to the plural (theories) -- do they dispense with any of these (Einsteinian) observer-axioms? ... Also: Why "test theories"? What and how do you suppose might be tested by some particular choice of selfstanding definitions??$ The philosophical debate about "Einstein synchronisation" centers about the conventionality of choosing 0 \le \alpha \le 1 to 0,5.
Fascinating -- in as much as there is (presently) no mentioning of "\alpha" in the present article, much less a definition. Given the categorization of the present article, any inconsequential choices and debates might rather be segregated into Einstein synchronisation (Philosophy).
$[...] In "midpont" methods α corresponds to the choice of the observer (flash) position. Well - in (experimental) physics, the notion of "midpont" and, closely related, of "distance" (or the operators which define them as quantities) are considered rather definite (sensible, reproducible). Perhaps (though it may be a stretch and please correct me if I'm wrong (and the bit I've read of the "philosophical literature" in the article certainly doesn't hint at the following either)) you're denoting as "α" roughly the expression $(n_g * \beta( M, N ) + 1) / 2, ~ if ~ n_g > 1 ~ and ~ |\beta( M, N )| > 0$, where $n_g$ > 1 is the value of refractive index relevant to exchange of light signals, measured in a homogeneous region, and $\beta( M, N )$ is a ("directionally signed") number characterizing the speed measured between "midpoint observer M" and observer "N at rest in this homogeneous region" (i.e. roughly: who is unable to determine the value of $n_g$, while observer M can obtain it)? Note that, per definition (measuring procedure), $\beta( M, N ) < 1 / n_g$; and therefore, however, $0 < (n_g * \beta( M, N ) + 1) / 2< 1, ~ if ~ n_g > 1 ~ and ~ |\beta( M, N )| > 0$, different from your above inequality for α; and moreover, that this expression cannot even obtain the value "0.5". (Meanwhile I note that the article on Refractive index is presently woefully inadequate, especially concerning the definition/measurement of "refractive index" in homogenous regions.) Also, any particular value of $n_g * \beta( M, N )$ as evaluated from observational data collected from a particular experimental trial (as far as such a particular value can be obtained at all) is of course :::not::: a matter of choice, but an unambiguous consequence of the given data and the measurement operations being applied, as far as they are indeed unambiguous (definite, sensible, reproducible). Once the observational data is given, choice is limited to which quantity to evaluate (say, first), i.e. which measurement operator to apply (first).$ [...] In this regard midpoint observer [...] and the older back and forth method, are equivalent.
If the method of finding a value of α is arbitrarily "assuming/choosing", then it certainly doesn't have any relevance for the "midpoint procedure"; although appararently, the "back and forth method" (as currently represented in the article) involves likewise arbitrarily "assuming/choosing" some parametrization $\tau_{A}$.
If instead this concerns (the physics of) evaluating $n_g * \beta( M, N )$, which, as a measurement, is certainly required to be definite and thus depending on "Einstein's midpoint procedure of 1917", then the fact that the value "0.5" can't even be obtained seems rather more evidence for inequivalence.
$[...] midpoint observer (or midpoint flash, which seems to be most popular introductory treatment) These two partial procedures are certainly not alternative, but both required (among others) in the course of identifying some observer as "midpoint between" two given observers. As practically all introductory texts show (please refer to Fig. 1 of A. Einstein, Relativity. The Special and the General Theory, Sect. 9): the "flash procedure" alone, i.e. here the fact that M' (the "middle between" the two ends of the train) states a signal ("I'm meeting M, the middle between A and B") which is observed by both A and B does not imply that a subsequent "coincidence receiver procedure" is guaranteed to succeed. Instead (according to the prescribed setup), M' finds first the reflection from B, then the reflection from A. (That's sufficient to rule M' out from having constituted a "midpoint between" A and B throughout the experiment). On the other hand, both "flash procedure" and "coincidence receiver procedure" are found satisfied for M for each signal. (However, that's not sufficient to identify M as "midpoint between" A and B throughout the experiment; certain additional signal round trips to certain auxiliary observers need to be evaluated as well.)$ [...] Also there is an example of a widely used other synchronisation convention. The astronomical one which uses the backward lightcone of Earth (or an idealized "Earth" position) as surfaces of simultaneity. The 1987 Supernova is that one, whose light reached Earth in 1987.
Let me try a (somewhat abstract) example on my own to make sure I understand at what you're getting; for instance:
"Little Timmy saw the pulses of Pulsar_XYZ and the ticks of the_right_clock_in_Boulder coincidently; therefore little Timmy calls them synchronous."
That's both trivial and pointless (even [Einstein1905] is done dealing with this idea by paragraph six of the "Definition of Simultaneity").
The task is instead to come up with a measurement procedure, in application of which several distinct observers (foremost those who are directly involved, i.e. "Pulsar_XYZ" and "the_right_clock_in_Boulder", but moreover everyone else, including little Timmy) would be guaranteed to agree on the result. This alone is the basis on which real (unambiguous, definite, reproducible) number values are obtained in physics as result values; in this context, for instance: "the rate of Pulsar_XYZ was 1.0 (or: equal to) the rate of the_right_clock_in_Boulder". Frank W ~@) R 00:21, 29 December 2006 (UTC)

## The definition of synchronization is a nonsense

Following this article : a light signal is sent at time $\tau_1$ from clock 1 to clock 2 and immediately back, e.g. by means of a mirror. Its arrival time back at clock 1 is $\tau_2$. This synchronisation convention sets clock 2 so that the time of signal reflection is $\tau_1 + \tfrac{1}{2}(\tau_2 - \tau_1) = \tfrac{1}{2}(\tau_1 + \tau_2)$.

The relation above is always true whatever the values of $\tau_1,\tau_2$. — Preceding unsigned comment added by Liviusbarbatus (talkcontribs) 14:16, 5 October 2014 (UTC)

I think this article probably needs to explain a bit more clearly why Einstein synchronisation is a convention rather than a fact. There is more explanation in the article one-way speed of light. -- 14:39, 5 October 2014 (UTC)

The definition of synchronization in the article one-way speed of light is correct and equivalent to that of Einstein. But the definition in the article Einstein synchronization is clearly a nonsense, as explained above. — Preceding unsigned comment added by Liviusbarbatus (talkcontribs) 15:22, 5 October 2014 (UTC)

I've modified the wording in the article slightly, by introducing $\tau_3$. The equation you quote is intended as a definition of the value of $\tau_3$, not as a relationship between $\tau_1$ and $\tau_2$.-- 16:35, 5 October 2014 (UTC)

I don't agree with your correction. You must write the same relation already written in one-way speed of light, $\tau_2 = \tfrac{1}{2}(\tau_1 + \tau_3)$. This is equivalent to the Einstein definition in "On the Electrodynamics of moving bodies" which is $\tau_2 - \tau_1 = \tau_3 - \tau_2$

They are the same, with different notation. $\tau_1 = t_1; \tau_2 = t_3; \tau_3 = t_2$ -- 18:35, 5 October 2014 (UTC)