I Relativity of simultaneity doubt

[italicus]

No, it is not your word against mine. Both of our words are equally valid. That is what it means for something to be a convention. My word does not invalidate yours and yours does not invalidate mine.
I am not sure what you have against conventions. You do realize that, for example, the electron being negative is a convention, right? And that if we decided to do it we could switch to positive electrons tomorrow. And if we got tired of revising old textbooks then we could switch back to negative electrons.

I have nothing against conventions. I am sufficiently open-minded.

Nothing in nature requires us to choose one convention or the other. We can simply agree to it because we choose to.

Yes, nature does’t care of human conventions, nature makes its way , “ Finchè il Sole risplenderà sulle sciagure umane - Ugo Foscolo, I Sepolcri” . Ever read ?

There is no more to the one-way speed of light than there is to choosing a negative charge on the electron. It is a convention. No more.

Sorry, I respect you point of view but I don’t share it. When Einstein took the invariance of c (in SR at least) as a “postulate”, he implicitly assumed that the speed was the same in all directions, that is “isotropic". On this second postulate, together with the principle of relativity, extended to e.m. laws (which are already relativistic , as everybody knows) he built his theory. But it was also implicit in his assumptions that the one-way speed of light was always the same, because on this he based the synchronisation of two clocks.
Do you define this “a convention” , like that on negative or positive definition of electrical charges? In my opinion , it is a great deal more than a convention.

 

[Dale]

Sorry, I respect you point of view but I don’t share it. When Einstein took the invariance of c (in SR at least) as a “postulate”, he implicitly assumed that the speed was the same in all directions, that is “isotropic". On this second postulate, together with the principle of relativity, extended to e.m. laws (which are already relativistic , as everybody knows) he built his theory. But it was also implicit in his assumptions that the one-way speed of light was always the same, because on this he based the synchronisation of two clocks

I am not sure what part of what you said there is incompatible with the one way speed of light being a convention. Do you think a postulate is forbidden from asserting some convention? Or do you think that once a convention is asserted by postulate that nobody else is permitted to use a different convention?

In any case, the fact that the one way speed of light is a convention is well established. It was proven by Reichenbach several decades ago, and it is also quite clear by using tensors and arbitrary coordinate charts in flat spacetime.

 

[italicus]

I am not sure what part of what you said there is incompatible with the one way speed of light being a convention. Do you think a postulate is forbidden from asserting some convention? Or do you think that once a convention is asserted by postulate that nobody else is permitted to use a different convention?

Short answer : 1) No; 2)No.
But we are sliding into metaphysic , or philosophy (which is worse).

In any case, the fact that the one way speed of light is a convention is well established. It was proven by Reichenbach several decades ago, and it is also quite clear by using tensors and arbitrary coordinate charts in flat spacetime.

Please avoid me to carry out research, and link a paper by Reichenbach: I remember of it, but don’t want to get bored looking for...

 

[Dale]

Short answer : 1) No; 2)No.
But we are sliding into metaphysic , or philosophy (which is worse).

Then I honestly have no idea what your objection is. You said that you disagreed and then made a bunch of statements about Einstein’s second postulate that didn’t clearly explain why you disagreed. The only two possibilities I could see from what you wrote weren’t it. So please explain clearly your disagreement.

The identification of specific concepts or quantities as conventional or not is hardly philosophy. The value of a conventional quantity may be a matter of philosophy or preference, but whether or not a quantity is conventional is not.

Please avoid me to carry out research, and link a paper by Reichenbach: I remember of it, but don’t want to get bored looking for...

I will dig one up for you. But it is easier to see this by learning about tensors, coordinate charts, and manifolds. So I will also post a reference for Sean Carroll’s GR notes which I would recommend over Reichenbach’s work.

 

[Dale]

link a paper by Reichenbach:

Here is Reichenbach’s original 1924 book: https://books.google.com/books/about/Axiomatization_of_the_Theory_of_Relativi.html?id=OztALUF8EMoC but I don’t actually use it.

This paper is a much broader overview: https://www.sciencedirect.com/science/article/abs/pii/S0370157397000513?via=ihub

It describes many different approaches that are equivalent but I just use Reichenbach’s name since he has priority. Note, this is paywalled but there are non paywalled versions on the web that I won’t link to directly.

Also, the Wikipedia page is decent and has good references: https://en.wikipedia.org/wiki/One-w...ansformations_with_anisotropic_one-way_speeds

Finally, as I said, I recommend actually learning this through the tensor approach. You can get what you need for that from the first two chapters of Carroll's Lecture Notes on General Relativity: https://arxiv.org/abs/gr-qc/9712019

 

[vanhees71]

I will dig one up for you. But it is easier to see this by learning about tensors, coordinate charts, and manifolds. So I will also post a reference for Sean Carroll’s GR notes which I would recommend over Reichenbach’s work.

I'm pretty sure it's much better spent time to study Carroll's GR notes than any work by Reichenbach:

https://arxiv.org/abs/gr-qc/9712019

 

[Dale]

I'm pretty sure it's much better spent time to study Carroll's GR notes than any work by Reichenbach:

Me too. After Reichenbach you will have a direct answer to a question that is completely useless outside of internet discussions. After Carroll (chapters 1 and 2) you will have an indirect answer to the same question plus a really important conceptual tool for a unified understanding of SR that can serve as a springboard for future studies of GR.

 

[italicus]

Thank you for the links. I already knew and studied Carroll and his GR notes, but this doesn’t matter.

Since my post #131, we have been discussing about the one-way speed of light, whether its constancy is a “convention” as you say, or a necessary condition that Einstein was compelled to adopt, in order to do watch synchronisation, starting from the postulate of the invariance of c wrt any inertial observer.
In the article from Wikipedia , there are further readings, among which three articles from Mathpages. This one (conventional wisdom) :

https://www.mathpages.com/rr/s4-05/4-05.htm

reports the following (in the paragraph where the author speaks of Einstein and Solovine reading the book by Poincaré ) :

Indeed we find in Einstein's 1905 paper on special relativity the statement:
A time common to A and B can now be determined by establishing by definition that the time needed for the light to travel from A to B is equal to the time it needs to travel from B to A.
He later wrote that this is “neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity”.

This is just my point : Einstein was someway “forced” to adopt the invariance of the one-way speed of light, in order to be able to make watch synchronisation and arrive at a definition od simultaneity. So, to me this is not a "convention” , if I have well understood your idea of convention (e.g. : names of electrical charges). It's a need, deriving from the postulate of invariance.

But maybe in the end we are saying the same thing, only with different words. The article from Wikipedia speaks of “convention” , but has this word the same meaning given by you, in this contest?

Although the average speed over a two-way path can be measured, the one-way speed in one direction or the other is undefined (and not simply unknown), unless one can define what is "the same time" in two different locations. To measure the time that the light has taken to travel from one place to another it is necessary to know the start and finish times as measured on the same time scale. This requires either two synchronized clocks, one at the start and one at the finish, or some means of sending a signal instantaneously from the start to the finish. No instantaneous means of transmitting information is known. Thus the measured value of the average one-way speed is dependent on the method used to synchronize the start and finish clocks. This is a matter of convention. The Lorentz transformation is defined such that the one-way speed of light will be measured to be independent of the inertial frame chosen.[8]

 

[Dale]

whether its constancy is a “convention” as you say, or a necessary condition that Einstein was compelled to adopt, in order to do watch synchronisation, starting from the postulate of the invariance of c wrt any inertial observer.

The one way speed of light and the synchronization convention are the same convention. Either one uniquely determines the other. Together they are a single convention.

establishing by definition

In other words, it’s a convention.

a stipulation which I can make of my own freewill

This is literally the definition of a convention. How can you possibly claim that this reference supports the exact opposite conclusion?

Einstein was someway “forced” to adopt the invariance of the one-way speed of light, in order to be able to make watch synchronisation and arrive at a definition od simultaneity

Again, they are two sides of the same convention. One determines the other.

So, to me this is not a "convention” , if I have well understood your idea of convention (e.g. : names of electrical charges). It's a need, deriving from the postulate of invariance.

The second postulate itself is the convention in question.

the one-way speed in one direction or the other is undefined (and not simply unknown), unless one can define what is "the same time" in two different locations

Do you not see that this is explaining that the one way speed and the synchronization are tied together?

Thus the measured value of the average one-way speed is dependent on the method used to synchronize the start and finish clocks. This is a matter of convention.

And here it literally uses the word convention.

. I already knew and studied Carroll and his GR notes

Then this should be easy. Consider a worldline $x^{\mu}(\lambda)$ and any coordinate system with a timelike coordinate $x^0=t$. Then the one way speed of anything, including light, is defined as the spacelike part of $$\frac{dx^{\mu}}{dt}$$ This quantity is clearly coordinate dependent and coordinates are a matter of convention. Therefore the one way speed of anything is a matter of convention.

 

[italicus]

Taken from Mathpages article (words by Einstein) :
“...a stipulation which I can make of my own freewill..."

Answered by Dale :
This is literally the definition of a convention. How can you possibly claim that this reference supports the exact opposite conclusion?

My comment:
How can you possibly claim that "a stipulation made of my own freewill” is a convention? IT is a unilateral decision. A convention is to be made between two or more people, no? And accepted!
Einstein didn’t ask anybody (as far as I know, of course) and took that decision. Peer-review didn’t exist at that time, I think.
Anyway , I think we have gone OT a great deal. I hope the OP will excuse me.

Now my watch and my circadian cycle tell me to go to sleep. Buona notte.

 

[PeterDonis]

A convention is to be made between two or more people

You're quibbling. The point is not whether the word "convention" is the best word to describe what is being discussed; if you don't like that word, fine, pick another one. It won't change the key point that what you are doing has no physical content; it's just picking a particular way of describing what is happening. Whether you call the act of picking a particular way of describing what is happening a "convention" or a "stipulation which I can make of my own freewill" is irrelevant. Either way it still has no physical content.

 

[PAllen]

Taken from Mathpages article (words by Einstein) :
“...a stipulation which I can make of my own freewill..."

Answered by Dale :
This is literally the definition of a convention. How can you possibly claim that this reference supports the exact opposite conclusion?

My comment:
How can you possibly claim that "a stipulation made of my own freewill” is a convention? IT is a unilateral decision. A convention is to be made between two or more people, no? And accepted!
Einstein didn’t ask anybody (as far as I know, of course) and took that decision. Peer-review didn’t exist at that time, I think.
Anyway , I think we have gone OT a great deal. I hope the OP will excuse me.

Now my watch and my circadian cycle tell me to go to sleep. Buona notte.

This is a totally weird definition of convention. A convention is something not required by physical law, generally where there alternative choices that can be made. @Dale gave the example of whether to call the charge of the electron positive or negative. This is a unilateral choice you can make. No one else has to agree with you. Of course, for ease of communication it is better for many people to adopt the same convention, which has happened with the charge convention and one way speed of light. However, an example of a convention with no clear consensus is metric sign convention - mostly plus, or mostly minus. This is pretty much split, so every paper has to declare their choice.

 

[Dale]

IT is a unilateral decision. A convention is to be made between two or more people, no?

Scientifically the salient point is that it is not a property of nature, it is a human decision. The number of persons is a trivial and scientifically irrelevant detail.

Please re-read the above discussion recognizing that this is a scientific forum and hence the word “convention” is being used in its scientific context: as a statement that the thing in question is not a fact of nature but something that can be decided arbitrarily by humans. Let me know if you still disagree with my claim given that understanding.

 

[italicus]

This is my opinion.
The invariance of the one way speed of light, from A to B and from B to A , was assumed by Einstein as a property of nature ; the underlying reason was to explain the synchronization of watches. Maybe I am wrong? Maybe.

As far as concerns all my previous post, take for good post #30 (I haven’t checked the number) , where I put a Minkowski diagram regarding train, embankment, light strikes in A and B, which are simoultaneous for M on the embankment but aren’t so for M’ on the train: for him, event B happens before event A. This is a consequence of the second postulate.
Ignore the others even if some of them are good, I hope.
Dale, coordinates are conventional, no doubt.
Dale, I know where I am. Excuse me for having abused of your time. Me too have spent a lot of mine.I wish a nice day to all of you.

 

[cianfa72]

The one way speed of light and the synchronization convention are the same convention. Either one uniquely determines the other. Together they are a single convention.

So, the standard Minkowski coordinates in flat spacetime does represent actually a convention: namely the Einstein synchronization convention or that's the same that one-way (coordinate) speed of light in that frame is the universal constant c.

 

[vanhees71]

I think the paper quoted above by @Dale is a gem. Indeed, most GR textbooks do not emphasize enough the gauge-theoretical foundation of GR, i.e., the fact that what's called "general covariance" is a local gauge symmetry, and it shows that coordinates themselves have a priori no physical meaning as the four-potential of the electromagnetic field doesn't have a direct physical meaning but only gauge-invariant quantities derived from it.

In SR you can as well introduce arbitrary "curvilinear coordinates" in the same sense as you can introduce arbitrary "curvilinear coordinates" in Euclidean geometry. Per se they also don't have a specific meaning but only the geometric properties expressed by them. In SR the introduction of such generalized coordinates can also correspond to the use of a different "coordinate time" and thus also a different "synchronization convention" than the standard convention a la Einstein, which leads to the most simple "natural coordinates" based on a Minkowski-orthonormal basis, i.e., global inertial reference frames.

In GR you don't have such global inertial reference frames since the Poincare invariance is made a local gauge symmetry, which is the other more physics inclined approach to GR, also leading to the extension of standard GR to Einstein-Cartan theory as soon as fields with spin are involved. I think it's worthwhile not only to study the usually emphasized geometrical point of view but also this gauge-symmetry approach, because it avoids a lot of quibbles concerning the meaning of coordinates.

 

[cianfa72]

I think the paper quoted above by @Dale is a gem.

Sorry, which is the paper you are talking of ?

 

[vanhees71]

This one:

https://doi.org/10.1016/S0370-1573(97)00051-3

 

[Dale]

So, the standard Minkowski coordinates in flat spacetime does represent actually a convention: namely the Einstein synchronization convention or that's the same that one-way (coordinate) speed of light in that frame is the universal constant c.

Yes. What Reichenbach did was to show that all of the observable results of any experiment could be obtained using an alternate synchronization. He used an approach where the anisotropy in the one way speed of light was characterized by a parameter $\epsilon$ that describes the degree of anisotropy and a vector that describes the direction of anisotropy. Einstein’s convention is the same as Reichenbach’s with $\epsilon=0.5$.

He showed that the one way speed of light depends on $\epsilon$, but no experimental predictions do. Therefore no experiment can be used to determine $\epsilon$ and hence its value is a matter of convention. So if any value is convention then $\epsilon=0.5$ is also convention, which is Einstein’s synchronization

 

[Dale]

I think it's worthwhile not only to study the usually emphasized geometrical point of view but also this gauge-symmetry approach, because it avoids a lot of quibbles concerning the meaning of coordinates.

Plus it ties relativity into some of the other major approaches of physics. It puts gauge symmetries at the center of all modern physics. Conversely, bringing tensors to QFT brings the geometrical tools of GR to all of modern physics. So the exchange of powerful mathematical tools goes both ways. To me that is rather satisfying.

 

[Dale]

This is my opinion.
The invariance of the one way speed of light, from A to B and from B to A , was assumed by Einstein as a property of nature

I think that Einstein’s own opinion on what he was assuming is probably the most relevant opinion:

“That light requires the same time to traverse the path A -> M as for the path B -> M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity.”

https://einsteinpapers.press.princeton.edu/vol6-trans/284

He pretty clearly was under the belief that what he was doing was setting a convention, not describing a physical property of nature. Reichenbach later proved that his belief was correct.

 

[vanhees71]

Plus it ties relativity into some of the other major approaches of physics. It puts gauge symmetries at the center of all modern physics. Conversely, bringing tensors to QFT brings the geometrical tools of GR to all of modern physics. So the exchange of powerful mathematical tools goes both ways. To me that is rather satisfying.

In some sense there is also not such a difference in the two approaches to GR. In some sense most of the conceptual understanding of all of physics is using symmetry principles, and this is, as was worked out already in the 19th century by Riemann and further in Klein's Erlanger Programm, after all the modern approach to geometry in a wide sense.

 

[cianfa72]

So if any value is convention then $\epsilon=0.5$ is also convention, which is Einstein’s synchronization

Suppose to choose $\epsilon=0.2$ which is not Einstein's synchronization. Then in SR the standard inertial coordinate chart is not Minkowski and the metric is not in the standard form $s^2=x^2 + y^2 + z^2 - (ct)^2$, right ?

 

[jbriggs444]

Given a spacetime coordinate system, the unaccelerated paths are well defined. Any other path has some accelerations. So the concept of acceleration is not relative to any other object, it is defined by the spacetime coordinate system.

The concept of coordinate acceleration is defined by a coordinate system.
The concept of proper acceleration is invariant.

 

[FactChecker]

The concept of coordinate acceleration is defined by a coordinate system.
The concept of proper acceleration is invariant.

Yes, I should have been more careful. There is a difference between the strictly mathematical detection of coordinate acceleration versus the physics concept of proper acceleration. The point I was trying to make is that even putting blinders on and only considering the mathematics of the coordinate system, one can define acceleration without reference to motion versus other objects. Or is that still too naive?

EDIT: I think I am still being too naive. It seems that proper acceleration is can also be defined strictly mathematically with no reference to anything beyond the coordinate systems. (https://en.wikipedia.org/wiki/Proper_acceleration )

 

[Nugatory]

Yes, I should have been more careful. There is a difference between the strictly mathematical detection of coordinate acceleration versus the physics concept of proper acceleration. The point I was trying to make is that even putting blinders on and only considering the mathematics of the coordinate system, one can define acceleration without reference to motion versus other objects. Or is that still too naive?

One can define coordinate acceleration without reference to any other objects. In fact, we can make the coordinate acceleration come out to be any value we want just choosing coordinates that produce that value. There's no need for any other object (although when we are considering only a single object it would be perverse to choose coordinates in which its velocity and coordinate acceleration are non-zero).

It seems that proper acceleration is can also be defined strictly mathematically with no reference to anything beyond the coordinate systems. (https://en.wikipedia.org/wiki/Proper_acceleration )

Whereas proper acceleration is defined physically by the reading of an accelerometer and mathematically by the deviation from a geodesic worldline - neither definition has anything to do with coordinates and both will come out the same no matter what coordinates we choose.

 

[Dale]

Suppose to choose $\epsilon=0.2$ which is not Einstein's synchronization. Then in SR the standard inertial coordinate chart is not Minkowski and the metric is not in the standard form $s^2=x^2 + y^2 + z^2 - (ct)^2$, right ?

Yes, that is correct. The metric would be: $$ ds^2 = - dt^2 -2 \kappa \ dx \ dt + (1-\kappa^2) dx^2 + dy^2 + dz^2 $$ where $\kappa = 2 \epsilon -1$ so in your case $\kappa = -0.6$

If you go through the trouble you should be able to show that this metric is still flat spacetime (assuming I made no mistake). The curvature is zero, but this is not the metric of a standard inertial frame.

 

[FactChecker]

Whereas proper acceleration is defined ... mathematically by the deviation from a geodesic worldline - neither definition has anything to do with coordinates and both will come out the same no matter what coordinates we choose.

I stand corrected. I guess that a geodesic worldline exists agnostic of the choice of a coordinate system (if any) to specify it.

 

[PeterDonis]

I guess that a geodesic worldline exists agnostic of the choice of a coordinate system (if any) to specify it.

Exactly.

 

[bhobba]

I still think the whole issue is most easily resolved by Landau's definition of an inertial frame, i.e. it is a frame where the laws of physics are the same at any point, direction or instant of time. This means whatever laws govern the speed of light, they are the same regardless of orientation. So one way light speed is the same regardless of direction - which is exactly what Maxwell's equations say. If there were an aether, it would play havoc with the value of that definition as part of the POR, i.e. the laws of physics are the same in any inertial frame. That would be because there would be only one inertial frame - the one where the aether is at rest - all other frames moving at constant velocity relative to that frame would have an aether 'wind' breaking isotropy. And since classical mechanics, when analysed carefully, depends on the POR (as done in Landau's Mechanics), it would pose problems for even classical physics. IMHO what Einstein did was what was necessary to put even classical mechanics on a firm footing.

Indeed measuring the one-way speed of light is an issue in experimentally determining if a frame is inertial. But we know no frame is strictly inertial (except maybe locally), although frames in interstellar space are thought to be very close.

Thanks
Bill