# How can we show that the speed of light is really constant in all reference frames?

I had a debate with a friend who cannot believe that the speed of light is constant.

He said something like: so what if in the Michelson-experiment the moving apparatus simply added a constant velocity to those photons. So even if you are on a train, if you throw a ball two perpendicular directions at the same speed towards walls that have the same distance from you, they will bounce back and get back to you at the same so this experiment doesn't really prove that the speed of light is really constant at any reference frame per se.

Although I understand special relativity. I find his point quite hard to refute. Especially since in quantum mechanics we saw that light is made of particles again not waves. So I'm inconfident if I can begin with EM waves relative to the lab frame.

Are there other experiments and observations that confirm $c$ is really constant in all reference frames and there is no "slow" and "fast" light? So he who haven't really got the point of SR can see it?

• Request: when you select an answer, present it to your friend and report back whether you were able to change his mind. Humans are notorious for holding on to loved misbeliefs! – Carl Witthoft Jan 25 '15 at 13:10

You find this hard to refute because your friend is correct in one sense: the MM experiment did not prove Einstein's second postulate of relativity, namely that the speed of light is constant for all inertial observers.

Recall that the Michelson-Morley experiment was designed to detect motion relative to an aether, or material medium for light. If your experiment on an open train carriage measured the speed of sound, then you would indeed measure different speeds along and across the carriage. So the MM experiment cast serious doubt on the notion of an aether.

Now, it was well known that Maxwell's equations did not keep their form under Galilean transformations between inertial frames. This was thought to be fine because the notion of a medium for light was believed before the MM experiment, so that the wave equation for light should transform in the same way as the wave equation for sound between inertial frames.

So along comes Einstein and says, given there's no medium, let's see what happens to our physics if we assume that Maxwell's equations keep their form under a transformation between inertial frames. He postulated therefore that the speed of light would be measured to be the same for all inertial observers and concluded that (1) the transformation group was the Lorentz, not the Galilean group and (2) the time measured between two events would in general depend on the observer. (1) was already know at the time of Einstein's 1905 paper, (2) was radical.

So the MM experiment motivated the assumed Lorentz covariance of Maxwell's equations and thus the new relativity postulate that the speed of light would be measured to be the same by all inertial observers.

The second relativity postulate therefore comes into play only when we compare the light speed measured by different inertial observers. Someone observing a light source on your train would notice a very different transformation law from the approximate Galilean transformation law that would describe the ping-pong ball velocity transformation to an excellent approximation.

• "If your experiment on an open train carriage measured the speed of sound, then you would indeed measure different speeds along and across the carriage. So the MM experiment cast serious doubt on the notion of an aether." Wet, the thing is, the MM experiment did not separately measure the two speeds: "there" and "back". It measured there+back/2, i.e. the average. – bright magus Feb 3 '15 at 21:33
• @brightmagus Correct. But motion relative to the aether would still be seen. The Michelson interferometer is comparing delays (1) in the direction of and (2) at right angles to the putative aether wind. The aether theory foretold a difference that was not seen. An interferometer based on sound waves in motion relative to air would see a phase difference. – WetSavannaAnimal aka Rod Vance Feb 3 '15 at 22:19
• But would it or did it? (And air and sound are a little different.) Still, the conceptualization was wrong. In general, the points of view, of an external observer and the interferometer (stationary wrt. itself), are constantly mixed there. Also Feynman made the same mistake in "Six ... pieces" stating that "light moves at $c$" without saying wrt. to what. Everybody assumes now $c$ is wrt. to the aether, but the interferometr was moving wrt. to the aether itself, so the speed should be c-v and c+v (Feynman corrected the distances, but not the speeds). And this changes the whole math. – bright magus Feb 4 '15 at 13:03
• @brightmagus (1) "air and sound are a little different" and that's the whole point. Naturally they are different phenomena, but the MM experiment explicitly showed that their transformations are different, or at least gave strong experimental evidence for this. Whether or not you can tell the difference between there-and-back again $c$ and one-way $c$ is actually irrelevant here: the transformations still differ. Indeed SR is still consistent with experiment even though so far no experiment has succeeded in measuring one-way $c$ -we can only measure, so far, two way $c$. I don't know .... – WetSavannaAnimal aka Rod Vance Feb 5 '15 at 9:38
• @brightmagus ... whether you know of a different approach to relativity, and that is to simply see what happens to Galileo's relativity when one relaxes the assumption of absolute time. You still have something that is exactly the same in principle and method to Galileo's, but now you find that a whole family of transformations between inertial frames is allowed. In this treatment, $c$ becomes a parameter that defines which of this infinite family actually applies to our universe. It then falls to experiment to find out what value of $c$ applies to our universe. In this approach, $c$ is .... – WetSavannaAnimal aka Rod Vance Feb 5 '15 at 9:47

The easiest way would be to note that the speed of light can be measured by various apparatus, and that it is always measured to be the same (taking medium into account) regardless of its path relative to us.

In vacuum, light has never been measured to be moving faster or lesser than $c$, regardless of whether the Earth was moving towards, away, or perpendicular to it.

http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

http://en.wikibooks.org/wiki/Special_Relativity/Aether

• My friend's point is that if the source of light is on the Earth too, then of course the measured speed is $c$ relative to Earth. Can you cite an experiment where the source of light isn't Earth based? – Calmarius Jan 25 '15 at 13:06
• Would it help to point out that, sans special and general relativity, our space probes, GPS satellites, etc., wouldn't work? – Carl Witthoft Jan 25 '15 at 13:12
• There are vast numbers of experiments involving c and light from from non terrestial sources. Some of them directly led to Einstein developing SR. See here: math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html – iPherian Jan 25 '15 at 13:44
• One that jumps out at me is in 1810 by Francois Arago. Given that a ray of light will refract in glass based on the speed it was travelling and the properties of glass, if a glass prism be placed in a telescope, there should be a wide variety of different angles because the Earth is moving towards and away from all the different stars seen in the sky. However, only 1 angle of refraction was observed. And so the speed of light was observed to be the same regardless of whether one was moving towards or away from it. en.wikibooks.org/wiki/Special_Relativity/Aether. – iPherian Jan 25 '15 at 13:59
• In fact, it may interest you to know that, as far as I am aware, as of the Michelson-Morley experiment, people were no longer concerned with demonstrating the constant speed of light under inertial transformations. That had been known for several decades. Rather, and this part is quite a bit harder, Michelson and Morley were trying to prove whether or not this constancy was due to light travelling through an aether or not. – iPherian Jan 25 '15 at 14:13

Regarding the experiment mentioned with Francois Arago in 1810 measuring the speed of light when it hit the telescope, we are only measuring the speed of light once it hits earth's atmosphere. This does not tell us the speed of light out in space.

To test Lorentz invariance rigorously, one has to consider theoretical models where Lorentz invariance is violated that are not already ruled out. One can do that by considering the Standard Model and then adding terms that violate Lorentz invariance and studying the most general such model that is physically plausible. This has been done in this article where new predictions for experimental signatures of Lorentz invariance violations were made, such as:

• Quantitative predictions on vacuum Cherenkov radiation

• Decay of a high energy photon into a electron positron pair

• Decay of high energy muons into electrons and photons

• Stable high energy neutral pions due to the decay to two photons becoming kinematically forbidden

• Stable high energy neutrons while protons become unstable at high energies