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

[Dale]

Since a different synchronization convention means a different system of coordinates, wouldn't the second postulate just need to be reformulated accordingly?

That wouldn’t be merely a reformulation in my view. In my view a reformulation is a different way of expressing the same thing. This would be a different thing.

 

[Orodruin]

I would answer in the negative and cite Einstein’s 2nd postulate in doing so.

All I am saying is that the case can be made for both. You can also take Newton’s view that an inertial frame is a frame such that an inertial system is any system in which an object will be in constant rectilinear motion unless acted upon by a force, which is the original meaning. Of course, Newton never imagined mixing space and time.

I am also not too fond of teaching SR based on Einstein’s postulates. They were formulated almost 120 years ago and the theory as well as didactics have evolved during this time. However, the same type of parroting appears in essentially every textbook on modern physics. I’ll mention them, then move on to discuss how they relate to geometry and from there on out the focus is on spacetime geometry. Using light clocks and similar with the postulates to derive things like time dilation just creates more confusion than it’s worth. But that is my 5 cents…

 

[Sagittarius A-Star]

I would answer in the negative and cite Einstein’s 2nd postulate in doing so.

I don't think, that Einstein used his 2nd postulate to define the term "inertial frame". I am even not sure, if he considered non-orthonormal coordinates. In 1916, he restricted his two postulates to a "co-ordinate system K be so chosen that when referred to it the physical laws hold in their simplest forms".

§ 1. Remarks on the Special Relativity Theory.
The special relativity theory rests on the following postulate which also holds valid for the Galileo-Newtonian mechanics.

If a co-ordinate system K be so chosen that when referred to it the physical laws hold in their simplest forms, these laws would be also valid when referred to another system of co-ordinates K′ which is subjected to an uniform translational motion relative to K. We call this postulate "The Special Relativity Principle".
...
The Special Relativity Theory does not differ from the classical mechanics through the assumption of this postulate, but only through the postulate of the constancy of light-velocity in vacuum which, when combined with the special relativity postulate, gives in a well-known way, the relativity of synchronism as well as the Lorentz transformation, with all the relations between moving rigid bodies and clocks.

Source (see A 1.1):
https://en.wikisource.org/wiki/The_...§_1._Remarks_on_the_Special_Relativity_Theory

 

[Dale]

I don't think, that Einstein used his 2nd postulate to define the term "inertial frame".

Einstein didn't do that, but the usual modern formulation of his 2nd postulate is explicitly in terms of inertial frames. E.g. on Wikipedia https://en.wikipedia.org/wiki/Postulates_of_special_relativity#Postulates_of_special_relativity
"As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c ..."

 

[Herman Trivilino]

Yes, you are right. I should've said, "Two clocks at the same location and at rest relative to each other can run at the same speed but if one shows 10 o'clock when the other shows 10:15, they are not synchronized."

And if they're co-located you can't use them to measure the speed of a beam of light that moves from one clock to the other. I thought that measuring the one-way speed of light was your main concern?

 

[Hill]

And if they're co-located you can't use them to measure the speed of a beam of light that moves from one clock to the other. I thought that measuring the one-way speed of light was your main concern?

I didn't express any concern. The OP question was if synchronization as used in SR requires the clocks to show the same time or them running at the same rate is enough. I answer that they have to show the same time to be called synchronized in SR. I didn't notice anything regarding measuring the one-way speed of light in this thread.

 

[Dale]

I didn't notice anything regarding measuring the one-way speed of light in this thread.

It is in the OP

When reading about the one way speed of light, I think it's fair to say that most potential methods to obtain this …

 

[Sagittarius A-Star]

"As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c ..."

Such measurements can only use the two-way speed of light to check the definition of 1 meter. And what means "in" any inertial frame?

In the following quote, "free-float frames" does not exclude non-orthonormal coordinate systems.

3.3 WHAT IS THE SAME IN DIFFERENT FRAMES
..
One basic physical constant appears in the laws of electromagnetism: the speed of light in a vacuum, c = 299,792,458 meters per second. According to the Principle of Relativity, this value must be the same in all free-float frames in uniform relative motion. Has observation checked this conclusion? Yes

Source:
https://www.eftaylor.com/spacetimephysics/03_chapter3.pdf

A reference frame is said to be an “inertial” or “free-float” or “Lorentz” reference frame in a certain region of space and time when, throughout that region of spacetime — and within some specified accuracy — every free test particle initially at rest with respect to that frame remains at rest, and every free test particle initially in motion with respect to that frame continues its motion without change in speed or in direction

Source:
https://www.eftaylor.com/spacetimephysics/02_chapter2.pdf

 

[PeterDonis]

In the following quote, "free-float frames" does not exclude non-orthonormal coordinate systems.

Yes, it does, because it says the speed of light is $c$ in all such frames. In a non-orthonormal coordinate system, the speed of light will not always be $c$; it will depend on direction.

 

[PeterDonis]

Such measurements can only use the two-way speed of light

The quotes you give do not restrict "the speed of light" to two-way measurements.

 

[Sagittarius A-Star]

Yes, it does, because it says the speed of light is $c$ in all such frames. In a non-orthonormal coordinate system, the speed of light will not always be $c$; it will depend on direction.

They don't say explicitly "One-way-coordinate speed". The two-way-speed of light does not depend on direction in a non-orthonormal coordinate system. And they refer to observations.

The quotes you give do not restrict "the speed of light" to two-way measurements.

The one-way speed cannot be observed.

 

[Dale]

They don't say explicitly "One-way-coordinate speed".

They don’t have to. That is what the word “speed” means by itself.

 

[Ibix]

Apart from anything else, if the derivation meant something other than an isotropic one-way speed of light, the result would not be the usual Lorentz transforms. It'd be something that, in matrix form, looks like $S\Lambda S^{-1}$, where $\Lambda$ is the Lorentz transforms and $S$ is the Jacobean matrix transforming from the usual orthonormal coordinates to the skewed coordinates you get from a non-isotropic one way speed of light.

 

[Sagittarius A-Star]

They don’t have to. That is what the word “speed” means by itself.

Yes, but if they had, that would have been more specific and clear. In the cited chapter 2, they use “inertial frame” and “free-float frame” as synonyms.

 

[Orodruin]

Einstein didn't do that, but the usual modern formulation of his 2nd postulate is explicitly in terms of inertial frames. E.g. on Wikipedia https://en.wikipedia.org/wiki/Postulates_of_special_relativity#Postulates_of_special_relativity
"As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c ..."

... the most trustable source of information on the internet after ChatGPT ...

 

[Dale]

... the most trustable source of information on the internet after ChatGPT ...

Wikipedia is generally pretty good. Not perfect but good. It is particularly good at getting the standard or common view of things.

 

[Orodruin]

Wikipedia is generally pretty good. Not perfect but good. It is particularly good at getting the standard or common view of things.

The common view is not always what is desirable. Just look at ChatGPT, which essentially learns from the common view (although it is on a different level of wrong). Care is needed particularly in advanced subjects.

 

[Dale]

The common view is not always what is desirable.

No, but that is specifically what I cited it for. I said “the usual modern formulation” which is precisely what Wikipedia best represents.

I know there is a lot of Wikipedia antagonism in the community, not just here but elsewhere too. I am not persuaded. Wikipedia is a tool and like any tool it has imperfections but it is useful for some tasks and not useful for others. I assert that it is useful specifically for the purpose for which I used it in this thread.

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.

 

[Herman Trivilino]

I didn't notice anything regarding measuring the one-way speed of light in this thread.

Sorry. I had you confused with the OP. My apologies.

 

[Orodruin]

No, but that is specifically what I cited it for. I said “the usual modern formulation” which is precisely what Wikipedia best represents.

I know there is a lot of Wikipedia antagonism in the community, not just here but elsewhere too. I am not persuaded. Wikipedia is a tool and like any tool it has imperfections but it is useful for some tasks and not useful for others. I assert that it is useful specifically for the purpose for which I used it in this thread.

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 think you will be hard pressed to find any source that discusses oblique coordinates, whether calling them inertial or not - and for obvious reasons. They are simply not very useful. I will repeat however that oblique coordinates would satisfy the requirements on an inertial coordinate system as specified by Newton's first law, the original meaning.* That it is has become common to equate inertial frames to Minkowski frames is not very surprising as it tends to be the only type of frame one considers in most treatments of SR. Einstein, however, did not mention the words "inertial frame" at all in the 1905 paper.

* Of note is that the Galilean transformation - being linear - of course does specify a set of oblique coordinates on Minkowski space (assuming that either the primed or unprimed coordinates belong to a Minkowski frame). Of course, we do not use such coordinates for obvious reasons.

 

[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.