I Clock Synchronisation -- Do clock speeds go out of synch?

[Sagittarius A-Star]

If you have some other source that captures “the usual modern formulation”, such as a meta-analysis or a survey of many scientists or authors, then present it. Trying guilt-by-association with ChatGPT is unconvincing.

I found a short survey and a citation of Edwards in Wikipedia, which includes "two (inertial) coordinate systems". I cannot check if the citation, including "inertial", is correct because the cited paper is not freely available online:

For instance, Edwards replaced Einstein's postulate that the one-way speed of light is constant when measured in an inertial frame with the postulate:

The two-way speed of light in a vacuum as measured in two (inertial) coordinate systems moving with constant relative velocity is the same regardless of any assumptions regarding the one-way speed.[47]​

Source:
https://en.wikipedia.org/wiki/One-w...ansformations_with_anisotropic_one-way_speeds

Abstract of cited paper [47]:
https://pubs.aip.org/aapt/ajp/artic...-in-Anisotropic-Space?redirectedFrom=fulltext

 

[Dale]

I found a short survey and a citation of Edwards in Wikipedia, which includes "two (inertial) coordinate systems". I cannot check if the citation, including "inertial", is correct because the cited paper is not freely available online:Source:
https://en.wikipedia.org/wiki/One-w...ansformations_with_anisotropic_one-way_speeds

Abstract of cited paper [47]:
https://pubs.aip.org/aapt/ajp/artic...-in-Anisotropic-Space?redirectedFrom=fulltext

I didn’t see any survey, just Edwards. I see no indication whatsoever that the common usage of the term “inertial frame” includes anisotropic synchronization conventions.

That it is has become common to equate inertial frames to Minkowski frames is not very surprising

That is all I am claiming.

Using another convention than the common one is liable to bring confusion, as I mentioned back on the previous page. I never claimed that nobody does it, just that it is a source of confusion and I recommend against it. I hold to that position.

As far as I can tell there are at least three modern meanings of the term “inertial frame”:

1) Newton’s 1st law holds. Non-interacting objects move in a straight line at constant speed.

2) The laws of physics have their simplest form.

3) The two postulates hold. Equivalently, the metric is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$

These are not equivalent. 1) implies that the transformation between inertial frames is any affine transformation. 2) simply makes me uncomfortable because I feel that the simplest form is in terms of differential forms or tensors which gets rid of the concept of frames entirely. So 3) is my preference and recommendation, particularly since it is the common modern view. Using one of the other definitions is not wrong, per se, but does invite miscommunication.

 

[Sagittarius A-Star]

I didn’t see any survey, just Edwards.

Sorry that I didn't link to that subtopic directly: "Inertial frames and dynamics". From there, the document [24] is linked to (The author writes: "I thank John Stachel and Ronald Anderson for discussions and helpful comments. I also thank Hans Ohanian and Michel Janssen for their useful comments"):
https://web.archive.org/web/2012090...aam829/1/m/Relativity_files/Conventions-1.pdf
But I didn't find that very useful.

I see no indication whatsoever that the common usage of the term “inertial frame” includes anisotropic synchronization conventions.

If true, then the 2^nd postulate in most SR books tacitly assumes Einstein-synchronization and is therefore not a valid argument against deviate for the "non-orthonormal inertial coordinate-system" from the standard terminology and re-formulate the 2^nd postulate and LT according to Edwards.

As far as I can tell there are at least three modern meanings of the term “inertial frame”:

1) Newton’s 1st law holds. Non-interacting objects move in a straight line at constant speed.

2) The laws of physics have their simplest form.

3) The two postulates hold. Equivalently, the metric is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$

I prefer (1) because in common language "inertial" means something physical, while the synchronization convention is something mathematical.

See also:

In classical physics and special relativity, an inertial frame of reference (also called inertial space, or Galilean reference frame) is a frame of reference not undergoing any acceleration. It is a frame in which an isolated physical object—an object with zero net force acting on it—is perceived to move with a constant velocity or, equivalently, it is a frame of reference in which Newton's first law of motion holds.[1] All inertial frames are in a state of constant, rectilinear motion with respect to one another; in other words, an accelerometer moving with any of them would detect zero acceleration.

Source:
https://en.wikipedia.org/wiki/Inertial_frame_of_reference

Using one of the other definitions is not wrong, per se, but does invite miscommunication.

I think that common SR books invite miscommunication and misunderstanding if they deviate from common language (see above) and use "inertial frame" instead of specifically "orthonormal inertial coordinate system" when applying the usual LT.

Einstein avoided this by using for a good reason the complicated formulation according to option (2).

 

[Ibix]

1) Newton’s 1st law holds. Non-interacting objects move in a straight line at constant speed.

2) The laws of physics have their simplest form.

3) The two postulates hold. Equivalently, the metric is $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$

These are not equivalent. 1) implies that the transformation between inertial frames is any affine transformation. 2) simply makes me uncomfortable because I feel that the simplest form is in terms of differential forms or tensors which gets rid of the concept of frames entirely. So 3) is my preference and recommendation, particularly since it is the common modern view. Using one of the other definitions is not wrong, per se, but does invite miscommunication.

(1), plus an assumption of isotropy works, includes both Galilean and Einsteinian relativity, and enforces orthogonal coordinates in the latter case. (3) excludes Galilean relativity. I'm not sure if that was your intent or not.

 

[Adrian59]

I think that the clock that has moved will necessarily lag.

IF they were initially synchronized, yes.

They both moved relative to others frame of reference, as phinds pointed out in in #14.

 

[Hill]

They both moved relative to others frame of reference, as phinds pointed out in in #14.

Yes, of course. And in each frame of reference, the one that moves in that frame of reference lags relative to the one that is at rest in that frame of reference.

 

[Dale]

I prefer (1) because in common language "inertial" means something physical, while the synchronization convention is something mathematical.

There is also the consequence that taking only 1) violates 2). The laws of physics no longer have their simplest form when written in terms of the coordinates. Straight lines at constant speed also constrain the synchronization convention, so I don’t think that specific distinction is as stark as you suggest.

I think that common SR books invite miscommunication and misunderstanding if they deviate from common language (see above)

That is a fair criticism. Unfortunately, the same word does have different meanings in different fields of study. This inevitably does lead to misunderstanding for students. I think this is unavoidable because the differing meanings are so entrenched in each separate field.

In a relativity context I would recommend 3) to avoid miscommunication, but in a Newtonian context I would recommend using a Newtonian meaning for the same reason.

Einstein avoided this by using for a good reason the complicated formulation according to option (2).

Einstein didn’t have a choice. The modern relativistic definitions didn’t exist before he developed relativity. A seminal author gets the first word on the theory that bears their name, but they do not have the last word.

If true, then the 2nd postulate in most SR books tacitly assumes Einstein-synchronization

Not tacitly, but explicitly and deliberately.

and is therefore not a valid argument against …

Of course it is valid. Definitions are tautologically valid by definition.

 

[Sagittarius A-Star]

Straight lines at constant speed also constrain the synchronization convention, so I don’t think that specific distinction is as stark as you suggest.

Yes. I did not formulate this correctly. Such a constraint is contained in Rindler's SR book in the definition of "inertial frame":

Do you agree, that this definition of "inertial frame" can be fulfilled by a clock synchronization based on anisotropic one-way-speed of light?

Do you think, that Rindler's following conclusion from the 2^nd postulate contradicts the definition in the above scan?

Rindler didn't mention here, that the MM experiment tested only the direction-independence of the two-way-speed of light.

 

[Dale]

Do you agree, that this definition of "inertial frame" can be fulfilled by a clock synchronization based on anisotropic one-way-speed of light?

It allows anisotropic OWSOL conventions that are spatially and temporally homogenous, but it forbids spatially or temporally varying OWSOL conventions. That is the mathematical restriction I was referring to above. Your objection to 3) on the grounds of it being “something mathematical” rather than physical applies to 1) also.

 

[Dale]

(3) excludes Galilean relativity. I'm not sure if that was your intent or not

Yes, that is intentional, particularly in the metric-based version which is my preference.