geordief

Invariance of the speed of light

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geordief    53

This has been verified experimentally and it seems that any effect exhibiting this invariance and a finite speed could be used to derive the Lorentz Transformations.

 

Is there any way of showing that this invariance and finite speed must be the case or does one just accept observations as they are and proceed from there?

 

https://books.google.ie/books?id=WTfnBwAAQBAJ&pg=PA44&dq=Rindler++speed+limit+cosmology&hl=en&sa=X&redir_esc=y#v=onepage&q=28.2&f=false

 

page 43

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geordief    53

Not clear what you are asking, can you try again?

Can the invariance of the speed of light (or any other effect) be proven other than experimentally?

 

Is it ,as apparently was the case with Einstein , a "given" or can it be shown that it corresponds to certain (even more) fundamental requirements?

 

I don't want to disprove (since it is experimentally true apparently) it but would be interested if it might be shown from first principles(which I doubt by the way -but still live in hope)

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zztop    11
Posted (edited)

Can the invariance of the speed of light (or any other effect) be proven other than experimentally?

 

There are derivations of SR that do not use the axiom of light speed constancy, these papers actually derive this from the principle of relativity PLUS the outcome of the Michelson-Morley experiment.

Edited by zztop

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StringJunky    1504

AFAIK Einstein postulated light as c then investigated the effects of assuming that on the other parameters affected by it; it is an axiom.

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Klaynos    721

Experiments are all that can provide evidence in science.

 

The speed of light being constant is a result of electromagnetism, Maxwell's theory is relativistic. The evidence that this theory is correct is overwhelming and some simple experiments e.G flowing charge having a magnetic effect, can be easily shown with a wire and compuss at home.

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geordief    53
Posted (edited)

Not quite what I asked,I think

@zztop

.It was specifically the frame invariance of lightI was wondering about-whether that could be derived from other postulates.

 

I think the answer is no but am really just scratching an itch, I suppose.

Edited by geordief

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swansont    6213

Not quite what I asked,I think

 

.It was specifically the frame invariance of lightI was wondering about-whether that could be derived from other postulates.

 

I think the answer is no but am really just scratching an itch, I suppose.

 

 

The invariance is present in Maxwell's equations. That they work (there is a wave equation you can formulate from them) is evidence that c is invariant. If it weren't, you wouldn't have EM waves as a solution when there was relative motion of the source and receiver. Relativity is an extension of this applied to kinematics, which is why the paper is entitled "On the Electrodynamics of Moving Bodies"

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zztop    11

Not quite what I asked,I think

@zztop

.It was specifically the frame invariance of lightI was wondering about-whether that could be derived from other postulates.

 

I think the answer is no but am really just scratching an itch, I suppose.

I answered your question exactly. The answer is not "no", it is "yes". Not only that the speed light is invariant and equal to "c" in vacuum in inertial frames, it can ALSO be PROVEN that it is invariant and equal to "c" in uniformly accelerated frames and in uniformly rotating frames. These are very advanced subjects in relativity.

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geordief    53
Posted (edited)

I answered your question exactly. The answer is not "no", it is "yes". Not only that the speed light is invariant and equal to "c" in vacuum in inertial frames, it can ALSO be PROVEN that it is invariant and equal to "c" in uniformly accelerated frames and in uniformly rotating frames. These are very advanced subjects in relativity.

You would not have a link to where I might find that proof, would you?

The invariance is present in Maxwell's equations. That they work (there is a wave equation you can formulate from them) is evidence that c is invariant. If it weren't, you wouldn't have EM waves as a solution when there was relative motion of the source and receiver. Relativity is an extension of this applied to kinematics, which is why the paper is entitled "On the Electrodynamics of Moving Bodies"

Yes I think I have heard that but have not so far been able to go onto it myself at"first hand".Perhaps that is also what zztop is getting at. Edited by geordief

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zztop    11
Posted (edited)

You would not have a link to where I might find that proof, would you?

 

Sure, here is the earliest one: https://en.wikipedia.org/wiki/History_of_Lorentz_transformations#Ignatowski_.281910.29

There are many more:

 

L ́evy-Leblond, J.M. (1976). One more derivation of the Lorentz transformation.
American Journal of Physics, 44, 271-277
Mermin, N. D. (1984). Relativity without light.American Journal of Physics,52, 119-124
Mitvalsky, V. (1966). Special relativity without the postulate of constancy of light,American Journal of Physics, 34, 825
Pal, Palash B, (2003). Nothing but relativity.European Journal of Physics, 24,315-319
Pauli, W. (1958).Theory of Relativity, (Pergamon, Oxford)
Schwartz, H. M. (1984). Deduction of the general Lorentz transformations from a set of necessary assumptions.American Journal of Physics, 52(4), 346-350
Schwartz, M. (1987). Principles of electrodynamics. Dover, New York
Sela, O., Tamir, B., Dolev, S. and Elitzur, A.C. (2009). Can special relativity be derived from Galilean mechanics alone?Foundations of Physics, 39,499-509
Edited by zztop

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Delta1212    894

AFAIK Einstein postulated light as c then investigated the effects of assuming that on the other parameters affected by it; it is an axiom.

I'm not sure that postulated is quite the right term. It falls out of Maxwell's equations, but nobody had fully worked through all of the implications of that before Einstein did.

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StringJunky    1504

I'm not sure that postulated is quite the right term. It falls out of Maxwell's equations, but nobody had fully worked through all of the implications of that before Einstein did.

Right.

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hoola    10
Posted (edited)

while the speed of light is fixed, doesn't the hawking radiation emitted at the end of a black hole's life supposedly exceed C as a result of the uncertainty principle?

Edited by hoola

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Mordred    893

no Hawking radiation occurs outside the EH and the particles do not exceed c

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hoola    10
Posted (edited)

This was discussed in the hawking radiation lectures of 2015. I don't remember who said it, or which lecture, but it did seem pretty unbelievable...the reason given, as I recall was that as the position of the hawking radiation source is more defineable as it shrinks, the velocity becomes less defineable (uncertainty principle), and that is why the radiation increases as the hole shrinks down towards zero size. I will go back over them (Utube) and find out and provide that info.

Edited by hoola

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MigL    511

No, Mordred is right, Hawking Radiation increases as the BH shrinks because the 'temperature' of the BH increases.

 

IIRC the Lorentz transforms were introduced in the late 1800s and were originally proposed as an explanation for the M-M experiment, long before Einstein's great year of 1905.

These transforms were also used by Poincare, who came close to beating Einstein to Special Relativity; but it was Einstein who proposed the invariance of c to explain the application of the transforms.

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hoola    10
Posted (edited)

ok, but what is the proposed explanation of that evaporation temperature increase, if not via the uncertainty principle of position vs. momentum allowing particle speeds to exceed C?

Edited by hoola

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Janus    687

ok, but what is the proposed explanation of that evaporation temperature increase, if not via the uncertainty principle of position vs. momentum allowing particle speeds to exceed C?

A increase in momentum via the uncertainty principle does not lead to particles exceeding c. It increases the momentum and thus the kinetic energy of the particles created, and thus the temperature, because temperature is a measure of the average kinetic energy. But since both kinetic energy and momentum approaches infinity as the speed of the particle approaches c, they can increase without bound without the particle's speed ever exceeding c.

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hoola    10

thank you janus, this seems to settle the issue of why the temp increases.

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Tim88    30

This has been verified experimentally and it seems that any effect exhibiting this invariance and a finite speed could be used to derive the Lorentz Transformations.

 

Is there any way of showing that this invariance and finite speed must be the case or does one just accept observations as they are and proceed from there?

 

https://books.google.ie/books?id=WTfnBwAAQBAJ&pg=PA44&dq=Rindler++speed+limit+cosmology&hl=en&sa=X&redir_esc=y#v=onepage&q=28.2&f=false

 

page 43

p.43 is not visible for me in your link.

Anyway, it has been shown that if you assume the validity of Maxwell's equations for a single reference system as well as the validity of the conservation laws (energy, momentum), the relativity principle follows - which implies invariance and limit speed.

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mistermack    36

Isn't it because of time dilation that the speed of light is a constant?

If you accept that two different observers travelling relative to each other experience different elapsed time, for the same measurement, then even though they observe different distances, they also measure different elapsed time.

 

And because the speed of light is intimately involved in the time dilation, the difference in distance is always exactly negated by the difference in time elapsed. So the ratio of distance over time for light has to be the same for both observers.

 

I'm not a mathematician, but if you have the formulae for time dilation, can't you prove that any and every observer will always get the same value for the speed of light?

 

Of course, you're then making assumptions for time dilation, or going on the experimental results I guess.

One way or another, you have to propose something first, and then verify it with experiments.

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swansont    6213

Isn't it because of time dilation that the speed of light is a constant?

 

 

 

c being invariant means that length and time are relative.

 

It might be possible to come up with some sort of time variation without c being invariant, so it does not necessarily follow that time dilation would imply invariance of c. (But we don't observe that.)

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geordief    53

Is it possible to highlight the salient feature in Maxwell's mathematics that mean that the invariance of c "jumps out of them" ?

 

Does this invariance "jump out" only in the final equations or can it be seen to be introduced as the maths proceeds earlier on in the working?

 

Does Maxwell base his maths on experimental observation and is there an aspect to these observations that would lead one to say that this particular observation implied necessarily that the speed of propagation of the wave would be the same no matter whether the observer was in relative motion wrt the experimental setup?

Edited by geordief

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Strange    2490

Is it possible to highlight the salient feature in Maxwell's mathematics that mean that the invariance of c "jumps out of them" ?

 

Does this invariance "jump out" only in the final equations or can it be seen to be introduced as the maths proceeds earlier on in the working?

 

 

This is a really good video (yes, I don't say that very often) that explains how the speed of light falls out of Maxwell's equations.

 

Note that the equations don't include anything about the position or the speed of the "things" generating or interacting with the electric or magnetic fields. So the equations are the same wherever you are and whatever your state of motion (Galilean relativity).

 

 

 

Does Maxwell base his maths on experimental observation and is there an aspect to these observations that would lead one to say that this particular observation implied necessarily that the speed of propagation of the wave would be the same no matter whether the observer was in relative motion wrt the experimental setup?

 

The equations were mainly based on Faraday's experiments. (Faraday was apparently a bit miffed that Maxwell "mathematised" them.)

Edited by Strange

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