Is there a thought experiment to show that the speed of light is constant?

[somega]

I know the amazing thought experiment by Albert Einstein with the two light clocks.
(The observer at the train station has a light clock and the person in the train.)

It's amazing because you can even deduce the formula to calculate how fast the clock in the train goes.

But this experiment requires the knowledge that the speed of light is constant.
(So I personally would never have come to this thought experiment.)

I wonder if there is another thought experiment that shows that the speed of light is constant?

 

[Ibix]

No - the invariance of the speed of light is an axiom of relativity. That is, it's something we assume, and justify by the success of the resulting predictions.

It is possible to start from just the principle of relativity and the assumption that space is homogeneous and isotropic (i.e., there are no special directions or points in space) and show that the only two systems of physics consistent with this are Newtonian physics and Relativity. You still have to go and do an experiment to see which is correct, but you don't need to assume the existence of an invariant speed.

Note that there's a difference between "invariant" (the same in all frames of reference) and "constant" (doesn't change over time), although many sources are sloppy about this distinction (including me, occasionally). The important thing about lightspeed here is its invariance, not its constancy.

 

[Orodruin]

I wonder if there is another thought experiment that shows that the speed of light is constant?

You can never show anything with a thought experiment. You can only use thought experiments to try to understand a theory. For actually understanding how the world works you need actual experiments.

 

[Nugatory]

I wonder if there is another thought experiment that shows that the speed of light is constant?

As the posts above say, there is no way that a thought experiment can prove that the speed of light is teh same for all observers (or prove anything else, for that matter).

The closest we can come is a suggestion from Einstein: imagine that you could travel alongside a flash of light, moving at the same speed as the light. There's some discussion here: https://www.nytimes.com/2015/11/01/opinion/sunday/the-light-beam-rider.html

 

[pervect]

I know the amazing thought experiment by Albert Einstein with the two light clocks.
(The observer at the train station has a light clock and the person in the train.)

It's amazing because you can even deduce the formula to calculate how fast the clock in the train goes.

But this experiment requires the knowledge that the speed of light is constant.
(So I personally would never have come to this thought experiment.)

I wonder if there is another thought experiment that shows that the speed of light is constant?

I would say that it's not a matter for thought experiments, but actual experiments. It is logically possible that Newtonian physics with no speed limit is correct, but experiment shows that's not the way the world works.

One the easiest to understand (though not most accurate) experiments is given below. There's a peer reviewed paper on this, it's not only a youtube video, but I don't have a link for the paper.

 

[vanhees71]

Here's the link to the corresponding AJP paper:

https://doi.org/10.1119/1.1970770

Of course the motion of electrons in electromagnetic fields was investigated already around 1900, and it was one of the first confirmations of SRT. In the beginning the accuracy was insufficient to decide between the well-known predictions of SR (at this time misinterpreted as a dependence of mass on velocity) and other models based on a "deformable electron" by Abraham, but when the experiments got more accurate and higher-energy electrons became available, of course the decision was clearly that SR is the correct theory.

Today I would rather say that it is a question about the "photon mass", i.e., whether the electromagnetic field is really correctly described as a massless spin-1 field (and thus necessarily as a gauge field). Today the upper limit of the photon mass is $m_{\gamma} < 10^{-18} \text{eV}$.

 

[f todd baker]

The principle of relativity is that the laws of physics are the same in all inertial frames of reference. Maxwell's equations comprise a law of physics. Maxwell's equations unambiguously predict a wave which travels with speed c in vacuum and which depends only on two properties of empty space, the permittivity and permiability of free space. Therefore, c must be the speed of light in any inertial frame of reference.

 

[Nugatory]

Maxwell's equations unambiguously predict...

”Unambiguous” is a bit too strong of a statement. I’m comfortable asserting that by the end of the 29th century the ambiguity has been reduced to zero... but between 1865 and 1905 an entire generation of physicists felt otherwise. Maxwell’s laws are consistent with a different interpretation: the speed of light in vacuum is c in the rest frame of the ether but deviates slightly in other frames. It required experimental data to eliminate that interpretation of Maxwell’s laws.

 

[PeterDonis]

Maxwell’s laws are consistent with a different interpretation: the speed of light in vacuum is c in the rest frame of the ether but deviates slightly in other frames

I don't think this is correct as you state it. Maxwell's Equations themselves do say, unambiguously, that the speed of the waves they predict is Lorentz invariant (since the equations themselves are Lorentz invariant). They do not predict waves that have one speed in the ether rest frame and some other speed in a different frame. If you apply a Galilean transformation to Maxwell's Equations, you don't get Maxwell's Equations in the new frame.

In other words, if you believe, as many physicists at the end of the 19th century did, that the correct fundamental laws of physics are Galilean invariant (as opposed to Lorentz invariant), then what you have is not an "interpretation" of Maxwell's Equations. What you have is a theory that says that Maxwell's Equations are not the true fundamental laws of electromagnetism, but only approximations, valid in the ether rest frame and nearly valid in frames that have small velocities relative to the ether rest frame.

 

[f todd baker]

First I must agree that experimental verification is imperative; physics is, after all, supposed to describe the universe as it is, not as we would like it to be. Also, unambiguous is too strong. But I think you missed my point, that the constancy of the speed of light is a result of the principle of relativity. Only nonsense results if you try to apply Galilean transformation to Maxwell's equations, not just something which looks pretty much like the equations in our frame--impossible contradictions occur. Perhaps historically it was not believed that Maxwellian E&M were laws of physics or approximations somehow, but we all know how Lorenz found, empirically, the transformation which maintained the same form when applied to Maxwell's equations, so the failure of Galilean relativity for electromagnetism was recognized well before Einstein. I am not a historian of physics, but have learned these few facts over the years. Perhaps I should say that I consider experimental verification of the constancy of c as verifying the principle of relativity. I guess that philosophically I find a more general assertion (principle of relativity) about the universe to be lovelier than an ad hoc assertion (constancy of c).

 

[A.T.]

..., so the failure of Galilean relativity for electromagnetism was recognized well before Einstein...

I think one should differentiate between Galilean relativity and the Galilean transformation:

- Galilean Relativity is the concept that you can have a set of frames (called inertial frames) in which the fundamental laws are the same. This concept doesn't "fail" for electromagnetism, but is in fact part of Special Relativity, as the first postulate.

- Galilean transformation is a rule that tells you how to transform between different frames. This rule "fails" for electromagnetism and was therefore replaced by the Lorentz transformation.

 

[Ibix]

so the failure of Galilean relativity for electromagnetism was recognized well before Einstein

I don't think it was. My understanding is that prior to Einstein, the Lorentz transforms were interpreted as relating the "real" Galilean time to a time parameter used for electromagnetism. I'm not sure anyone completely worked out the implications of such a patchwork system of physics because Einstein rendered the idea moot.

 

[vanhees71]

I don't think this is correct as you state it. Maxwell's Equations themselves do say, unambiguously, that the speed of the waves they predict is Lorentz invariant (since the equations themselves are Lorentz invariant). They do not predict waves that have one speed in the ether rest frame and some other speed in a different frame. If you apply a Galilean transformation to Maxwell's Equations, you don't get Maxwell's Equations in the new frame.

In other words, if you believe, as many physicists at the end of the 19th century did, that the correct fundamental laws of physics are Galilean invariant (as opposed to Lorentz invariant), then what you have is not an "interpretation" of Maxwell's Equations. What you have is a theory that says that Maxwell's Equations are not the true fundamental laws of electromagnetism, but only approximations, valid in the ether rest frame and nearly valid in frames that have small velocities relative to the ether rest frame.

The other then by most physicists followed interpretation was rather that electromagnetic phenomena allow to define a preferred inertial frame of reference. This was not a big surprise then, because they believed that there must be an aether, i.e., some fluid-like entity (with admittedly very exotic mechanical properties) whose vibrational states are the electromagnetic waves, predicted by Maxwell's equations. The preferred reference frame was simply thought to be the aether restframe.

Now the difficulty was that this theory is, from the modern relativistic point of view, phenomenologically correct for all observations at order $\vec{\beta}=\vec{v}/c$, where $\vec{v}$ is the velocity of the reference frame you perform you experiment in against the aether restframe. Deviations occur only at the next order $\beta^2$, and that was difficult to achieve at the time. The most famous experiment overcoming this experimental challenge is the Michelson-Morley experiment, attempting to measure the "aether wind". Famously it failed to demonstrate the aether wind, and that's why it's considered as one of the first confirmations of the relativistic point of view, which essentially at this time meant that one has to adjust the Galilei-Newtonian spacetime model (of absolute space and time) with the Einstein-Minkowskian one, implying that electromagnetic phenomena cannot be used to define an absolute preferred inertial frame (the aether restframe) and that thus there is no fluid-like substance whose tension state give rise to the electromagnetic field but that the electromagnetic field is itself a fundamental entity.

 

[vanhees71]

I think one should differentiate between Galilean relativity and the Galilean transformation:

- Galilean Relativity is the concept that you can have a set of frames (called inertial frames) in which the fundamental laws are the same. This concept doesn't "fail" for electromagnetism, but is in fact part of Special Relativity, as the first postulate.

- Galilean transformation is a rule that tells you how to transform between different frames. This rule "fails" for electromagnetism and was therefore replaced by the Lorentz transformation.

Another great thing is that, assuming also the other symmetries of space and time (homogeneity of space and time, Euclidicity and thus isotropy of space for all inertial observers) to be true, the special principle of relativity only admits two transformation groups, the Galileo or the Lorentz transformations, the latter with some universal speed, which empirically is very likely to be the speed of electromagnetic waves (with light being just electromagnetic waves in a wavelengths range our eyes are sensitive to and in this sense nothing very special but just em. waves).

 

[vanhees71]

I don't think it was. My understanding is that prior to Einstein, the Lorentz transforms were interpreted as relating the "real" Galilean time to a time parameter used for electromagnetism. I'm not sure anyone completely worked out the implications of such a patchwork system of physics because Einstein rendered the idea moot.

Well, I think Poincare and particularly Lorentz had quite detailed ideas concerning this point of view, but we can be lucky that Einstein came up with his much more easy and (after Minkowski sorted out the math) elegant description.

 

[Frodo]

I always like to think about it like this.

Do an experiment to measure some fundamental constants.

1. Measure the permittivity of free space in a vacuum (also called the electric constant) - it is epsilon-nought, 8.854 x 10^-12 F/m

2. Measure the permeability of free space in a vacuum (also called the magnetic constant) - it is mu-nought, 4 x pi x 10^-7 H/m

3. Calculate c = 1 / SQRT(mu-nought x epsilon-nought) = speed of light.

Now, when you measured these two constants of nature you had no idea whether you were moving or not. But you effectively measured the value of c = speed of light.

Imagine another person, who is moving relative to you, doing the same experiment. He or she gets exactly the same values for mu-nought and epsilon-nought and so gets so gets exactly the same value for c = speed of light.

Why is c obtained from these values?

Because light is an electromagnetic phenomenon. epsilon-nought is a measure of the electrical nature of space. mu-nought is a measure of the magnetic nature of space. Conceptually it is easy to see that the speed of light is related to them.

It is one of the most beautiful things to come out of Maxwell's Equations.

 

[weirdoguy]

epsilon-nought is a measure of the electrical nature of space. mu-nought is a measure of the magnetic nature of space.

Actually they are just conversion factors used when we stick to SI units. They are not used in other systems of units.

 

[PeterDonis]

Measure the permittivity of free space in a vacuum

Measure the permeability of free space in a vacuum

Neither of these things are measureable. As @weirdoguy has pointed out, they are artifacts of a particular choice of units (SI units).