Undergrad Relativity of simultaneity doubt

[ergospherical]

@LBoy more generally in a curved spacetime, the ability to synchronise clocks via the Einstein-Poincaré simultaneity criterion reduces to the condition that $\displaystyle{\oint} \dfrac{g_{0i}}{g_{00}} dx^i = 0$ around any closed curve, where $i$ runs over $1,2,3$.

[You can show it by starting with the same idea in #113 about sending and receiving light signals, except now writing the metric as $g = g_{ij} dx^i dx^j + 2g_{0i} dx^0 dx^i + g_{00} dx^0 dx^0$ and solving for the zeroes of $g$ w.r.t. $dx^0$; these are the times of emission and reception]

 

[cianfa72]

Radar coordinates are defined by assuming that the second postulate holds even for a non-inertial observer.

I read the paper. Aboout your claim above I think the point is just that we are assuming that in the (t,x) inertial frame the radar signal sent from non-inertial (proper) accelerating observer's worldline has the same equation $x=\pm t$.

Btw, I believe in Figure 4 $u$ and $v$ axes are actually reversed.

 

[Dale]

Btw, I believe in Figure 4 $u$ and $v$ axes are actually reversed.

No, I think those are correct. You can get the $u$ axis by setting $v=0$ which gives the line $y=x$ as shown in the figure.

 

[cianfa72]

No, I think those are correct. You can get the $u$ axis by setting $v=0$ which gives the line $y=x$ as shown in the figure.

Sorry you're right I confused them. What about my claim above about radar signals ? Is it actually the same as yours ? Thank you.

 

[Dale]

Sorry you're right I confused them. What about my claim above about radar signals ? Is it actually the same as yours ? Thank you.

I don’t know. I didn’t really understand the point you were trying to make there. Could you rephrase, perhaps?

 

[cianfa72]

Could you rephrase, perhaps?

Surely. You said that radar coordinates definition assumes the second postulate holds even for non-inertial observers. Second postulate is about the invariant one-way speed of light, right ?

 

[Dale]

Surely. You said that radar coordinates definition assumes the second postulate holds even for non-inertial observers. Second postulate is about the invariant one-way speed of light, right ?

Yes, that is correct.

 

[cianfa72]

Yes, that is correct.

So the assumption is that the one-way coordinate speed of light even for non-inertial observers is always the same c.

 

[Dale]

So the assumption is that the one-way coordinate speed of light even for non-inertial observers is always the same c.

Yes. I think that the only time a speed is not a coordinate speed is when it is the relative speed in a collision. But in any case, that is what I had in mind here.

 

[PAllen]

The Minkowski diagram (Italicus post 30) shows that the two signal reception events by OT and OE are not "colocated at the same event", we are dealing with two different events: OE receives a lightning strike signal, and OT receives two signals. These events are separated both temporally and spatially.

My point was simply that in the initial post where I raised this, you were apparently disputing the claim that two observers colocated at the same event but with relative motion must either both receive two signals or neither. They cannot disagree about such things. The post you were criticizing made no claim about non-colocated observations.

The second issue I have is the existence of simultaneity of events (what you call, I believe, modeling simultaneity). Here I use a mathematical definition: events are simultaneous to an observer if they are orthogonal to its time vector in Minkowski space. And maybe it's just a matter of name (you used the term "convention") but to me it's not a convention, in a simple SR model the straight line, plane or R3 containing simultaneity events are precisely defined for the observer.I s here something more to that?

A mathematical definition is not physical unless it can be observed. By causality in SR, nothing about a spacelike separated event can be observed, in any way. Thus simultaneity is inherently not physical in SR. Further, SR in no way requires you to use standard Minkowski coordinates (let alone a particular choice of these), and any choice of coordinates is convention not physics. The world does not care how you label things. The only physical relation between distant events in SR is that either one is in the causal future of the other, or not. In SR (but not GR, in general), a non-causal relation means the events can be connected by a unique spacelike geodesic.
[edit: as an example, consider the following book:

https://www.amazon.com/dp/3642372759/?tag=pfamazon01-20

standard Minkowski coordinates and the Lorentz transform are not even introduced until all the essential physics of SR is developed in a coordinate free manner. And simultaneity is introduced as convention.]

 

[italicus]

@Dale
As far as I know, the problem of the one-way speed of light has not been solved yet. The constancy of c in vacuum, in any inertial reference frame, is a “postulate “ assumed by Einstein, and is valid in SR only, where you can imagine inertial reference frames extended without limits. His sincronisation of clocks is based on forth and back light signals , and has been criticized by Reichenbach and others.
But in GR the situation is different. It is impossibile to have r.f. extended to the infinite. One of the formulations of the equivalence principle is this : “ In every point of ST you can put an inertial rf. , that is a local frame in “free fall”, abandoned to gravity, in which the laws of physics are those of SR”.
In GR you cannot compare a vector “here “ to a very far vector “there “ , unless you don’t carry the first near the second.
Wolfgang Pauli said very clearly: we cannot say nothing about the speed of light very far from us.
The same J.H. Wheeler used to say: Physics is easy only locally.
There are a lot of works about the one way speed of light problem , it seems that even recently , by means of GPS clocks signals, an anysotropy in c value has been found.
Are you sure that time flow is the same here and in a galaxy 100 millions yl far? I am not so sure.
but in SR a uniform lattice of sticks and synchronized watches is supposed all over ST, have a look at paragraph 2.6of the book “ Spacetime physics “ by Taylor and Wheeler.

But I am not an expert verified scientist, feel free to correct what I have written, where necessary.

 

[cianfa72]

@Dale
As far as I know, the problem of the one-way speed of light has not been solved yet. The constancy of c in vacuum, in any inertial reference frame, is a “postulate “ assumed by Einstein, and is valid in SR only, where you can imagine inertial reference frames extended without limits. His syncronization of clocks is based on forth and back light signals , and has been criticized by Reichenbach and others.

Btw, it can be proven that the constancy of one-way speed of light follows (logically) from the universal speed of light over closed paths -- https://arxiv.org/pdf/gr-qc/0211091.pdf

 

[vanhees71]

A tangent space is a local construction. The only definition of simultaneity that would make any sense in GR is that two events have the same timelike coordinate. And that is manifestly a coordinate-dependent definition.

In GR all there is are local observations, i.e., spacetime-point coincidences. This was in fact a pretty much debated point in the 8-10 years from Einstein's first approaches till the final version of GR has been found. To discuss "simultaneity" one has to refer to some coordinate time, and it's thus even more conventional than in SR, where you have at least a preferred global simultaneity convention already formulated in Einstein's 1905 paper using the two-way speed of light with the "light clock" to synchronize a continuum of clocks at rest within an inertial reference frame. Already for accelerated observers in you only have a local definition of simultaneity. An illuminating example that you cannot have a global definition of simultaneity or clock synchronization are observers on a rigidly rotating disk:

https://en.wikipedia.org/wiki/Born_coordinates

 

[Dale]

Btw, it can be proven that the constancy of one-way speed of light follows (logically) from the universal speed of light over closed paths -- https://arxiv.org/pdf/gr-qc/0211091.pdf

Be careful. You are overstating the claim made in that paper. The actual claim is that the universal speed of light over closed paths (ie the two way speed of light) implies the possibility of a one-way speed of light synchronization convention. It is an “existence” proof not a “uniqueness” proof. It does not exclude other synchronization conventions.

Also, it is better to cite the arxiv abstract page instead of the pdf: https://arxiv.org/abs/gr-qc/0211091

 

[Dale]

As far as I know, the problem of the one-way speed of light has not been solved yet.

I am not sure what you mean. I don’t know what problem there is. The one way speed of light is a convention to choose, not a problem to solve.

As far as I can tell the only problem is that people think it can be measured. But that is an education problem.

 

[cianfa72]

Be careful. You are overstating the claim made in that paper. The actual claim is that the universal speed of light over closed paths (ie the two way speed of light) implies the possibility of a one-way speed of light synchronization convention. It is an “existence” proof not a “uniqueness” proof. It does not exclude other synchronization conventions.

ok got it. Basically it proves that -- under the hypothesis of constant universal speed of light over closed paths -- we can define a synchronization convention such that all clocks at rest each other can be consistently Einstein synchronized and the one-way speed of light results to be the invariant constant c.

 

[cianfa72]

Just a point about what we said above: the proof in the Minguzzi/Macdonald paper assumes clocks at rest each other.

How can we actually define 'mutually at rest' if not using again light signals over closed paths ? (i.e. defining two clocks as at rest each other if the round-trip time of a light signal exchanged between them does not change).

 

[italicus]

I am not sure what you mean. I don’t know what problem there is. The one way speed of light is a convention to choose, not a problem to solve.

As far as I can tell the only problem is that people think it can be measured. But that is an education problem.

The following article is one of a lot, that can be found on the web:

https://www.intechopen.com/chapters/39778#B14

Furthermore, have a look at paragraph 84 , chapter X , of Landau-Lifshitz “classical theory of fields” , for distances and time intervals in GR.

The problem is that, if the light speed from A to B is different wrt that from B to A, the Einstein sincronization is no longer possible. The cited author concludes that the Lorentz transforms aren’t correct, and should be replaced by others. I hope I have read the article in the right way.

 

[weirdoguy]

The following article is one of a lot, that can be found on the web:

Sorry, but this author is not a physicist. In one of his papers he writes:

Einstein's equivalence principle, the idea underpinning the general theory of relativity (GTR), is examined and shown to be invalid. As a result, GTR collapses and can no longer be considered a viable physical theory.

which is nonsense. Check your sources, please. For physicists there is no problem with one way speed of light. For others - well, not everyone understands relativity. That's their problem

 

[italicus]

Sorry, but this author is not a physicist. In one of his papers he writes:
which is nonsense. Check your sources, please. For physicists there is no problem with one way speed of light. For others - well, not everyone understands relativity. That's their problem

Thank you for the information, I didn’t really check the source, sorry . But I wish to inform you that professor Franco Selleri, cited in the article, was (he died some years ago) a well-known physicist, taught physics and relativity in many universities, wrote a lot of books and articles and made a lot of conferences all over the world. You can check his profile on the Internet.
For him, that understood relativity very well, the one-way speed of light was a problem.

Anyway, this doesn’t mean that I reject relativity , on the contrary! But there are some unsolved problems.

 

[jbriggs444]

Franco Selleri, cited in the article

Citing someone in an article demonstrates neither that they agree with you nor that you are both right.

Einstein has said many times that he agrees with me on that. :-)

 

[Dale]

The problem is that, if the light speed from A to B is different wrt that from B to A, the Einstein sincronization is no longer possible.

Sure. But again, it is a matter of convention. So if you choose to use the convention that it is not different then Einstein synchronization is possible. That is the point of it being a convention. Conventions are things that you can decide, according to your preferences. I don't see how that is a problem.

The cited author concludes that the Lorentz transforms aren’t correct, and should be replaced by others. I hope I have read the article in the right way.

Note that the cited article is not a peer-reviewed paper. It is a self-published paper.

I am sure that the author tried to get this published and was rejected. It is based on an elementary misunderstanding of the Sagnac effect, so it would have been correctly dismissed.

professor Franco Selleri, cited in the article, was (he died some years ago) a well-known physicist, taught physics and relativity in many universities, wrote a lot of books and articles and made a lot of conferences all over the world. You can check his profile on the Internet.
For him, that understood relativity very well, the one-way speed of light was a problem.

Do you have a paper from him then that identifies this as a problem? The fact that a known scientist is cited by a fringe author doesn't mean the known scientist actually agrees with the fringe author.

But there are some unsolved problems.

If there are, this (the one way speed of light) is not one of them. It is a convention so you are free to adopt the convention of isotropy or not, as you wish.

 

[italicus]

Sure. But again, it is a matter of convention. So if you choose to use the convention that it is not different then Einstein synchronization is possible. That is the point of it being a convention. Conventions are things that you can decide, according to your preferences. I don't see how that is a problem.

For the sake of simplicity, and a greater clarity, could you explain better ? I have said this:

"the light speed from A to B is different wrt that from B to A"

so, how do you sincronize “a la Einstein” two clocks ?

 

[Dale]

Just a point about what we said above: the proof in the Minguzzi/Macdonald paper assumes clocks at rest each other.

How can we actually define 'mutually at rest' if not using again light signals over closed paths ? (i.e. defining two clocks as at rest each other if the round-trip time of a light signal exchanged between them does not change).

Good point. But I think that the starting point of the proof is actually stronger than that. Not only does the two-way speed need to be constant, it should also be equal to c. Of course, to make that meaningful would require using previous definitions of the meter where this is not tautological, but hopefully that is not too controversial.

 

[Dale]

For the sake of simplicity, and a greater clarity, could you explain better ? I have said this:

"the light speed from A to B is different wrt that from B to A"

so, how do you sincronize “a la Einstein” two clocks ?

Sure: You say "the light speed from A to B is different wrt that from B to A".

And since the one way speed of light is a convention then regardless of what you say, I can still say "the light speed from A to B is the same as that from B to A".

Therefore while you cannot use Einstein synchronization I can.

And tomorrow we can switch conventions if we like and I will stop using Einstein synchronization and you will start using it. That is what it means for it to be a convention. It is a completely arbitrary matter of choice to use whichever convention we prefer for whatever reason we prefer it.

 

[vanhees71]

Of course all "practical" metrology finally depends on our present knowledge. From our present theoretical point of view the fundamental "limiting speed" of relativistic physics is not necessarily the speed of light in a vacuum. There is not even a fundamental principle in the Standard Model of elementary-particle physics "guaranteeing" that this is necessarily the case. So after all we have to empirically test that hypothesis that indeed the speed of light in a vacuum is identical with the "limiting speed". The current status of this empirical test is expressed as an upper limit of the photon mass being $10^{-18} \; \text{eV}$. That's why we believe it is safe to use light (em. waves) for clock synchronization. Even if the photon mass is non-zero with this upper limit it's FAPP impossible to observe it.

For more along these lines, see

https://www.desy.de/user/projects/Physics/Relativity/SpeedOfLight/speed_of_light.html

and links therein.

It's also an interesting fact that the current practical limitation of clock synchronization on Earth is rather the still not accurate knowledge about the gravitational field of the Earth, i.e., the accuracy of most modern time measuring (with all kinds of quantum optical tools like frequency combs etc) is higher than our ability to take the gravitational effects of the Earth's gravitational field on time accurately into account.

 

[italicus]

Sure: You say "the light speed from A to B is different wrt that from B to A".

And since the one way speed of light is a convention then regardless of what you say, I can still say "the light speed from A to B is the same as that from B to A".

Therefore while you cannot use Einstein synchronization I can.

And tomorrow we can switch conventions if we like and I must stop using Einstein synchronization and you can start using it. That is what it means for it to be a convention. It is a completely arbitrary matter of choice to use whichever choice we prefer for whatever reason we prefer it.

But this is simply “ your word against mine” ! Is this a convention , on which a science can be founded? Scientists should agree on basic principles, otherwise it would be an anarchy! Changing idea from one day to the other isn’t good for science...

In the meantime, I have found an interesting article on the one-way question, which gives an idea on the reason why it isn’t really a problem :

https://spaceaustralia.com/news/one-way-speed-light

but of course this is their idea.

 

[Dale]

But this is simply “ your word against mine” !

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.

Is this a convention , on which a science can be founded? Scientists should agree on basic principles, otherwise it would be an anarchy! Changing idea from one day to the other isn’t good for science...

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

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.

 

[PeterDonis]

I have found an interesting article on the one-way question

This is not a peer-reviewed paper. Please do not cite invalid references.

 

[cianfa72]

Good point. But I think that the starting point of the proof is actually stronger than that. Not only does the two-way speed need to be constant, it should also be equal to c. Of course, to make that meaningful would require using previous definitions of the meter where this is not tautological, but hopefully that is not too controversial.

ok, so...in what 'sense' two clocks are defined as at rest each other ? Assuming that the two-way speed of light is constant and equal to $c$ over a closed path, then the distance between clocks A e B does not change (i.e. they are defined as at rest each other) iff the time interval $\Delta t$ measured for instance by clock A between the point in time light signal is sent from it and the point in time is received back from B does not change.

$\Delta t = 2AB/c$