The invariance of the speed of light is not only a hypothesis?

[zoltrix]

hello

Einstein assumed the invariance of the speed of light as an hyphotesis, while I was told that :
"The speed of light need not have been postulated as an invariant."
in other words
the invariance of the speed of light could have been proven even regardless of the special relativity
is it true ?
if so, why and how ?

 

[Ibix]

Not exactly. There are various so-called "one postulate" derivations of relativity that do not assume anything about the speed of light. They lead to the conclusion that there are only two systems of physics that respect the principle of relativity, one with no invariant speed (Newtonian physics) and one with an unspecified finite invariant speed (Einstein's relativity). You then need to do an experiment to determine whether you are in a Newtonian or Einsteinian universe and, in the latter case, to determine what the invariant speed is.

So no, you can't prove the invariance of the speed of light. But you don't need to postulate it - you just need to check if there is an invariant speed or not once your theorising has narrowed your theoretical choices down to two.

 

[Nugatory]

while I was told…

Told by whom? You will get better and more helpful answers if we have the context.

 

[zoltrix]

a friend of mine quoting : Landau and Minkowiski

 

[Sagittarius A-Star]

"The speed of light need not have been postulated as an invariant."

As @Ibix mentioned, there exist derivations of the Lorentz transformation, that work with weaker assumptions than the 2^nd SR postulate.

One example is "Nothing but Relativity" from Palash B. Pal. The assumptions are listed in there:
https://arxiv.org/abs/physics/0302045

The following derivation contains less complex calculations. Newton's "absolute time" could be ruled-out by a time-dilation experiment.
https://www.physicsforums.com/threa...rom-commutative-velocity-composition.1017275/

 

[FactChecker]

there are only two systems of physics that respect the principle of relativity, one with no invariant speed (Newtonian physics) and one with an unspecified finite invariant speed (Einstein's relativity). You then need to do an experiment to determine whether you are in a Newtonian or Einsteinian universe and, in the latter case, to determine what the invariant speed is.

In Newtonian physics, would there be an atom bomb, and would GPS work as it does incorporating corrections for relativity? Can we consider those as well-established, commonly known proofs of the Einsteinian universe?

 

[PeterDonis]

In Newtonian physics, would there be an atom bomb

"Atom bomb" is really a misnomer since the reactions in question are nuclear reactions. It's not clear that the question of whether nuclear reactions would exist if Newtonian physics were exactly correct has an answer, since the strong interaction, which is the relevant one for the nuclear reactions in question, was not even known until well after relativity was discovered, so nobody ever tried to build a Newtonian model of it and test it to see what it predicted.

would GPS work as it does incorporating corrections for relativity?

No. This one is clear since we know that Newtonian physics does not predict either of the effects (time dilation due to relative motion or time dilation due to differences in gravitational potential) that are corrected for in GPS.

 

[Ibix]

In Newtonian physics, would there be an atom bomb, and would GPS work as it does incorporating corrections for relativity? Can we consider those as well-established, commonly known proofs of the Einsteinian universe?

I don't think there's any workable explanation for those phenomena within Newtonian physics, no. Alternatively Maxwell's equations are invariant under Lorentz transform but not Galilean, or particle accelerators never push anything above $c$ no matter how hard they try. There are a lot of hints.

 

[PeterDonis]

I don't think there's any workable explanation for those phenomena within Newtonian physics, no.

As I noted in post #7, it's hard to say anything about this for nuclear reactions because nobody has ever tried to build a Newtonian explanation for them.

For the GPS corrections, we know there is not a workable explanation within Newtonian physics, because, as I noted in post #7, we already know what Newtonian physics predicts, or more to the point does not predict, for this case.

 

[Halc]

the invariance of the speed of light could have been proven even regardless of the special relativity
is it true ?

It is false actually. There are alternative theories (I. Schmelzer comes to mind) that don't take any of the premises of special relativity, and come to a valid interpretation of most physics. That one is an absolutist theory in which light only moves at c relative to a (absolutely) stationary observer. Such absolute interpretations of special relativity have been around since before SR (Lorentz Ether Theory), but the Schmelzer one goes so far as to complete the generalization, something which nobody every did in the 20th century AFAIK.

I does have a falsification test. Jump into what Einstein calls a black hole (they don't exist according to Schmelzer). If you can cross the event horizon and still live (your watch says a time after Schmelzer says it would have stopped), you've falsified Schmelzer, but of course you cannot report this finding to anybody on the outside. Kind of like proving there is an afterlife: You need to die to do it, and then you cannot publish.

PS
Sentences are initiated with a capital letter and terminated with a period or some such punctuation. Adhering to these grammatical standards helps other take your posts more seriously.

 

[PeterDonis]

There are alternative theories (I. Schmelzer comes to mind) that don't take any of the premises of special relativity, and come to a valid interpretation of most physics. That one is an absolutist theory in which light only moves at c relative to a (absolutely) stationary observer. Such absolute interpretations of special relativity have been around since before SR (Lorentz Ether Theory), but the Schmelzer one goes so far as to complete the generalization

Please note that discussion of LET is off topic here. Discussion of Schmelzer's theories, while not strictly speaking off topic, has already been beaten to death in enough previous PF threads that there is no point in continuing it here.

As far as actual observations go, none of these "alternatives" are distinguishable from standard SR.

 

[Halc]

As far as actual observations go, none of these "alternatives" are distinguishable from standard SR.

Well that's kind of the point then, isn't it.
Einstein assumed the invariant speed of light precisely because it wouldn't need to be an assumption if it could be demonstrated. The predicted observations are what matter, not the metaphysics behind it. Einstein made the simplest metaphysical assumption and the entire theory fell into place from that. No alternative assumptions have churned out mathematics as simple and elegant as those that derive from the simplest premises.
To the OP, the invariant speed of light cannot be proven by Einstein's theory since using a theory that assumes it to prove it would be begging. The only way to prove the invariance is to assume it varies, and then drive that assumption to self-contradiction. That has not been done to my knowledge.

 

[PeterDonis]

Einstein assumed the invariant speed of light precisely because it wouldn't need to be an assumption if it could be demonstrated.

No. Einstein took the invariant speed of light as a postulate when he derived SR because it already had been experimentally demonstrated, and he therefore did not have to produce any argument to justify it. Einstein was perfectly familiar with the Michelson-Morley experiment and its result. He was also perfectly familiar with attempts by other physicists to explain the result. He took all that into account before writing and publishing his 1905 paper on SR.

the invariant speed of light cannot be proven by Einstein's theory since using a theory that assumes it to prove it would be begging.

As far as SR derived the way Einstein derived it, that is correct. However, that is not the only way to derive SR. An alternative is the derivations referred to by @Ibix in post #2, which start from other assumptions (basically the principle of relativity and the homogeneity and isotropy of space) and reach the conclusion that there must either be no invariant speed, or some finite invariant speed--or more precisely, that the laws of physics must be either Galilean invariant or Lorentz invariant. We still have to rely on experiments to rule out the Galilean invariant case (by ruling out Newtonian mechanics), but we don't have to just assume a finite invariant speed from scratch with no supporting argument.

Another alternative would be to take Maxwell's Equations as given and derive from the Lorentz invariance of those equations the prediction that electromagnetic radiation in vacuum will have a finite invariant speed.

The only way to prove the invariance is to assume it varies, and then drive that assumption to self-contradiction.

If we disallow bringing in any other considerations, yes, that would be true. But we don't have to disallow them. See above.

 

[Dale]

To the OP, the invariant speed of light cannot be proven by Einstein's theory since using a theory that assumes it to prove it would be begging. The only way to prove the invariance is to assume it varies, and then drive that assumption to self-contradiction.

Well, you can always do experiments too. In the scientific method that is also “proof”.

 

[externo]

No. Einstein took the invariant speed of light as a postulate when he derived SR because it already had been experimentally demonstrated, and he therefore did not have to produce any argument to justify it. Einstein was perfectly familiar with the Michelson-Morley experiment and its result.

This is false. Einstein postulate of the invariant speed of light is not experimentally demonstrated.

 

[Dale]

This is false. Einstein postulate of the invariant speed of light is not experimentally demonstrated.

I think you are confusing the invariance of the speed of light, which is experimentally demonstrated, versus the one way speed of light, which is just an arbitrary synchronization convention and hence does not need experimental demonstration

 

[externo]

What has been demonstrated is the invariance on a round trip, not on a one-way trip. However, Einstein's postulate says that the speed is invariant in a one-way trip as well, so that it is not an arbitrary convention only, but the core of his theory.

 

[Sagittarius A-Star]

What has been demonstrated is the invariance on a round trip, not on a one-way trip. However, Einstein's postulate says that the speed is invariant in a one-way trip as well, so that it is not an arbitrary convention only, but the core of his theory.

Einstein referenced his postulates to standard inertial coordinate systems. Those have per definition a time coordinate, that is defined based on the Einstein clock synchronization. This is based on the definition, that the one-way speed is isotropic.

 

[externo]

This is based on the definition, that the one-way speed is isotropic.

So it's a definition, so it's not experimentally demonstrated.

 

[Dale]

What has been demonstrated is the invariance on a round trip, not on a one-way trip. However, Einstein's postulate says that the speed is invariant in a one-way trip as well, so that it is not an arbitrary convention only, but the core of his theory.

Only the two-way speed needs experimental confirmation (and as @PeterDonis said, it was confirmed before SR). The one-way speed does not need experimental confirmation, it can simply be chosen by convention. Einstein was clear from the beginning that it is only an arbitrary convention. It seems that you have been misled by another bad source on this point

 

[externo]

The one-way speed does not need experimental confirmation, it can simply be chosen by convention. Einstein was clear from the beginning that it is only an arbitrary convention.

In this case, the physical contraction of objects is only a convention too, since it only appears if we assume the definition of the isotropy of the speed of light.

That being said, given very reasonable and desirable assumptions there are only two mathematically consistent models (Newtonian and Einsteinian) and the Newtonian model is not compatible with GPS and other things.

There is another model: LET

 

[Dale]

In this case, the physical contraction of objects is only a convention too, since it only appears if we assume the definition of the isotropy of the speed of light.

Sure. That doesn’t bother me. Does it bother you?

There is another model: LET

It isn’t a different model from a mathematical perspective, just philosophically

 

[Motore]

There is another model: LET

And there is no need to complicate things.

Remember that without adopting a simultaneity convenction the one way speed of light can never be experimentally determined.

 

[externo]

Sure. That doesn’t bother me. Does it bother you?

Well, yes, because this contraction must be real so that the ladder can pass through the barn door etc...
The contraction must be real for Michelson's experiment to give its result...

Remember that without adopting a simultaneity convenction the one way speed of light can never be experimentally determined.

But logic tells us that the speed should not be the same in both directions. Why deny logic?

 

[Ibix]

Well, yes, because this contraction must be real so that the ladder can pass through the barn door etc...

If you assume a different synchronisation convention you get different length contraction. Or possibly no length contraction, but your different synchronisation convention means that the doors aren't shut simultaneously so it doesn't matter that the rod doesn't fit.

But logic tells us that the speed should not be the same in both directions.

What logic tells you that?

 

[Dale]

Well, yes, because this contraction must be real so that the ladder can pass through the barn door etc.

This is incorrect. It can fit through the barn door regardless of the convention you choose.

But logic tells us that the speed should not be the same in both directions.

It does not.

 

[externo]

This is incorrect. It can fit through the barn door regardless of the convention you choose.

The contraction must be real for Michelson's experiment to give its result...

What logic?

Well, it is logical to think that the light travels faster relative to you when it is going to meet you than when it is running after you.

 

[Ibix]

The contraction must be real for Michelson's experiment to give its result...

No - if you use a different synchronisation convention you have different velocities and lengths and timings, but you still get a null result. You should probably try doing the maths.

Well, it is logical to think that the light travels faster relative to you when it is going to meet you than when it is running after you.

That is logical if you assume Galilean relativity, yes. Why do you make that assumption? Especially since it's known to be a bad one?

 

[externo]

No - if you use a different synchronisation convention you have different velocities and lengths and timings, but you still get a null result. You should probably try doing the maths.

I have trouble understanding this. What other synchronization can we choose?

 

[Dale]

The contraction must be real for Michelson's experiment to give its result.

The word “real” is not well defined. So this is literally a meaningless claim.

If you actually formulate a meaningful claim you will find that there is no issue: The measured invariance of the two-way speed of light leads to all of the measured relativistic results, and the one-way speed is purely a matter of convention

I have trouble understanding this. What other synchronization can we choose?

E.g. Anderson’s convention or Reichenbach’s convention. I personally prefer Anderson’s, but Reichenbach’s is more widely known

 

[Sagittarius A-Star]

I have trouble understanding this. What other synchronization can we choose?

Here is an example:
https://www.mathpages.com/home/kmath229/kmath229.htm

 

[externo]

That is logical if you assume Galilean relativity, yes. Why do you make that assumption? Especially since it's known to be a bad one?

I'm not making any assumptions, it's the reality of the closing speed, which is something that can be verified experimentally. Why make other assumptions? You are the one making assumptions, not me. I don't understand where Einstein's synchronization convention comes from.

The word “real” is not well defined. So this is literally a meaningless claim.

The real is that which has practical consequences and which does not depend on a convention

 

[Sagittarius A-Star]

I'm not making any assumptions, it's the reality of the closing speed, which is something that can be verified experimentally.

The closing speed between two moving objects is a calculated quantity.

Assume as reference a standard inertial coordinate system, as defined in SR.

A light pulse moves with speed $c$ in positive x direction and an object A moves with constant speed $v$ in negative x direction towards the light pulse. The calculated closing speed is $c+v$.

If you transform the speed of the light pulse into the rest frame of object $A$, then you get the speed $c$.

 

[externo]

I am surprised by your assertions of the non-reality of length contraction. The electric field of an electron really contracts at high speed, it is not a convention.

Assume as reference a standard inertial coordinate system, as defined in SR.

Why would I make such an assumption? This assumption contains in itself the isotropy of the speed of light as a postulate.

 

[Sagittarius A-Star]

Why would I make such an assumption? This assumption contains in itself the isotropy of the speed of light as a postulate.

If I would define the one-way speed as non-isotropic, then the transformation formula would become more complicated, without added value:
https://en.wikipedia.org/wiki/One-w...ansformations_with_anisotropic_one-way_speeds

See also:

The basic principle of clock synchronization is to ensure that the coordinate description of physics is as symmetric as the physics itself. For example, bullets shot off by the same gun at any point and in any direction should always have the same coordinate velocity dr/dt .

Source:
http://www.scholarpedia.org/article...nematics#Galilean_and_Lorentz_transformations