Yes, agreed.PAllen said:What is important is that events being connected by a spacelike geodesic no longer guarantees that one is not in the causal future of the other.
That was for cases where issues like the presence of closed timelike curves do not apply. In spacetimes where CTCs are present, as @PAllen has pointed out, the fact that two events are connected by a spacelike geodesic does not imply that there is no causal curve (timelike or lightlike) connecting them. So one's intuitive picture of what "spacelike separation" means doesn't even work in such a spacetime.cianfa72 said:Some thead ago we said it is "better" to employ geodesics only (not just generic curves) in order to define the separation type for a couple of events.
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.PAllen said:Are you possibly confused by 'see' versus 'model'? If two detectors are colocated at some moment (present at the same event), irrespective of their relative state of motion, it is physically impossible and absurd to claim that one receives two signals at that event and the other does not.
PAllen said:How you model simultaneity of the distant emission events is a separate question and is fundamentally one of convention, not physics. Frame dependent is not enough of a statement to capture the issue. More precisely, the only invariant statements that can be made about distinct events is whether one is in the causal future, past, or neither (acausal, "possibly now") from the other. The only further statement that can be made is that if two observers use the same convention meeting certain properties (e.g. the Einstein convention) for assigning simultaneity to spacelike separated events, and one is in motion relative to the other, then they will disagree on simultaneity assignment. But simultaneity of distinct events is never an observable, per se.
It is definitely a convention. In fact, I think there are at least 3 conventions used here:LBoy said: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?
I think this definition is not fundamentally different from mine. Before PAllen answers I would like to know your view on the issue of simultaneity: convention or physical reality? Because I admit I don't understand this argument.vanhees71 said:I'd define the simultaneity of events wrt. an observer in a frame-independent way by: two events with spacetime fourvectors ##x## and ##y## are simultaneous wrt. an observer with four-velcity ##u## if ##u \cdot (x-y)=0##.
It's definitely convention. Take the example where there are two aliens on a planet in the Andromeda galaxy, about 2 million light years from Earth. To simplify things let's assume their planet and the Earth are actually at rest relative to each other.LBoy said:I think this definition is not fundamentally different from mine. Before PAllen answers I would like to know your view on the issue of simultaneity: convention or physical reality? Because I admit I don't understand this argument.
Oh yes, 1 and 2 are pretty obvious, using non-inertial observers is beyond my question, the question concerns only the third point: defining simultaneity for a choosen observer is not a convention, it is a precise term (mathematical and physical too - imho) for this chosen observer.Dale said:It is definitely a convention. In fact, I think there are at least 3 conventions used here:
First, it is a convention to say that the one-way speed of light is c. This convention has been extensively investigated by Reichenbach and others. Second, it is a convention to use inertial observers. With non-inertial observers the simultaneity
I disagree. It is indeed a convention as shown most clearly by Reichenbach. It is clearly a completely standard convention, but nonetheless a convention.LBoy said:defining simultaneity for a choosen observer is not a convention
Yes, they are obvious, but they are still conventions. A convention doesn’t cease being a convention just because it is obvious.LBoy said:Oh yes, 1 and 2 are pretty obvious
Dale said:Yes, they are obvious, but they are still conventions. A convention doesn’t cease being a convention just because it is obvious.
Dale said:In what way can you specify simultaneity for a chosen observer without using all three conventions?
vanhees71 said:To define simultaneity of spatially distant events you need a clock-synchronization convention. The one used by Einstein in his famous pape
Can you elaborate this point, please ? Thanks.Dale said:With non-inertial observers the simultaneity defined by using the first convention is not even momentarily the same as for momentarily co-moving inertial observers.
Looking for simultaneity to be physically meaningful is a dead end, in any case, if you wish to study GR.LBoy said:I would like to think that simultaneity is something that is independent of a clock synchronization procedure, like a real and physical measure (or maybe rather a feature of a space time for a choosen observer) with a precise definition (mathematical), regardless of the clock-synchronization procedure. It "is there" as a feature regardless if we can measure it or not.
Not a doubt here, eventually it can be preciselly defined locally in a tangent space at a point, but physically I think this has no sense (although there is a local "similarity" between a tangent space and a R4 "space-time" with cartesian coordinates, but this makes less and less physical sense anyway as the curvature of spacetime increases...)PeroK said:Looking for simultaneity to be physically meaningful is a dead end, in any case, if you wish to study GR.
Yes. This is radar-coordinates which can be applied for non-inertial observers. Radar coordinates are defined by assuming that the second postulate holds even for a non-inertial observer. So for every event the observer sends a radar signal out and gets a radar echo back. The distance to the event is the difference in time (echo - emission) divided by two and the time of the event is the sum divided by two.cianfa72 said:Can you elaborate this point, please ? Thanks.
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.LBoy said:Not a doubt here, eventually it can be preciselly defined locally in a tangent space at a point, but physically I think this has no sense (although there is a local "similarity" between a tangent space and a R4 "space-time" with cartesian coordinates, but this makes less and less physical sense anyway as the curvature of spacetime increases...)
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##.Dale said:Radar coordinates are defined by assuming that the second postulate holds even for a non-inertial observer.
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 said:Btw, I believe in Figure 4 ##u## and ##v## axes are actually reversed.
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 said: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.
I don’t know. I didn’t really understand the point you were trying to make there. Could you rephrase, perhaps?cianfa72 said:Sorry you're right I confused them. What about my claim above about radar signals ? Is it actually the same as yours ? Thank you.
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 said:Could you rephrase, perhaps?
Yes, that is correct.cianfa72 said: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 ?
So the assumption is that the one-way coordinate speed of light even for non-inertial observers is always the same c.Dale said:Yes, that is correct.
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.cianfa72 said:So the assumption is that the one-way coordinate speed of light even for non-inertial observers is always the same c.
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.LBoy said: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.
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.LBoy said: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?
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.pdfitalicus said:@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.
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:PeroK said: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.
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.cianfa72 said: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
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.italicus said:As far as I know, the problem of the one-way speed of light has not been solved yet.
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.Dale said: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.
The following article is one of a lot, that can be found on the web:Dale said: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.
italicus said:The following article is one of a lot, that can be found on the web:
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.
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.weirdoguy said: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![]()
Citing someone in an article demonstrates neither that they agree with you nor that you are both right.italicus said:Franco Selleri, cited in the article
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.italicus said: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.
Note that the cited article is not a peer-reviewed paper. It is a self-published paper.italicus said: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.
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.italicus said: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.
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 said:But there are some unsolved problems.
For the sake of simplicity, and a greater clarity, could you explain better ? I have said this:Dale said: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.
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.cianfa72 said: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).
Sure: You say "the light speed from A to B is different wrt that from B to A".italicus said: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 ?
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...Dale said: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.
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.italicus said:But this is simply “ your word against 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. Nothing in nature requires us to choose one convention or the other. We can simply agree to it because we choose to.italicus said: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...
This is not a peer-reviewed paper. Please do not cite invalid references.italicus said:I have found an interesting article on the one-way question
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.Dale said: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.