'Proving' the Constancy of the Speed of Light

Most recent answer: 02/03/2012

why speed of light is constant in any inertial frame?is its experimental or theoritical proof?explain plz...
- nafis akhter (age 22)
Hi Nafis,

The notion of "proof" in a field like mathematics simply doesn't exist in physics. In mathematics, certain "facts" can be definitively shown to be true. Such is not the case in physics or any other science; it is fundamentally against the philosophy of science.

"The test of all knowledge is experiment. Experiment is the sole judge of scientific 'truth'". -Richard Feynman

Einstein arrived at his theory of special relativity by guessing that the speed of light is constant in all inertial frames. He did not "prove" it with mathematics anywhere, that would be impossible.

From this assumption, Einstein was able to form his theory of special relativity. In addition to a constant speed of light, special relativity predicts other phenomenon that can be tested with experiments. Additionally, the groundwork of special relativity has enabled the development of nearly every modern theory of physics, predicting all sorts phenomenon that Einstein could have scarcely imagined in 1905.

Why do we readily accept a constant speed of light as "truth"? Simply because, as far as we can tell, it seems to be true. We've never been able to perform an experiment that conclusively shows that the speed of light isn't constant in every inertial frame. Nor have we been able to conduct an experiment that contradicts the other predictions from Einstein's theory  (in a weak gravitational field). This is what some would call "empirical proof" (empirical is just a fancy word describing information found from evidence and observation), though I've never been fond of that term, since it isn't a proof at all.

If we ever do find good evidence that contradicts a constant speed of light, then we would no longer accept the notion to be true. This is how science progresses. Before Einstein came along the world did mostly fine with classical Galilean relativity. And, as far as they could tell, it was the truth! Only as our experiments became more advanced were we able to see that it only holds true given constraints, and that new theories were needed.

Matt J.

It's worth noting that just because a theory isn't exactly consistent with modern experiments, doesn't mean it's not useful. For example, many things we deal with on earth can be dealt with just fine using classical mechanics, not accounting for relativistic effects. We know that it is technically not the best model we have, but the effect is so small that we can get along just fine with our old models. However, in systems like the Global Positioning System, we cannot get away with using old physics. When we want to model things that are more "extreme" (e.g. satellites orbiting the earth) we must use our more accurate models.

(published on 02/03/2012)

Follow-Up #1: relative speeds

So far as I can tell, scientists do not understand why the speed of light is a constant in the sense of "Of course! It must be so." If I´m travelling in a space ship and I measure the relative speed of a space ship passing me in the same direction, I´ll get exactly the answer that I would expect - but if it´s a photon that´s passing me I will not get the answer I´d expect - I´ll always get the same answer, irrespective of my own speed. Please inform whether this is something bizarre that has been shown to be so, but no-one can actually explain how it´s possible or whether there is, in fact, an "Of course!" involved.
- Robert (age 52)
It's not really true that the relative speed of the ship passing you will be exactly what you'd expect from common sense. Say your velocity relative to something (maybe the Sun) is u. Say that the velocity of the other ship in that frame is v, for simplicity along the same direction. Common sense would say that the velocity of the other ship in your frame would be v-u. In fact it's (v-u)/(1-uv/c2).

Notice that if you're traveling at almost the same speed in the same direction (as judged by the Sun) this comes out very close to (u-v) since uv/c2 is very small. If, however, the other ship is traveling at c (maybe it's just a blip of light) it just comes out to be c again. So the behavior of light and of other objects all falls in the same framework, not with separate rules for each.

I wouldn't say that there's an "of course" involved, at least for most of us, but the whole framework can be derived from the assumption that there is some finite speed limit.

Mike W.

The theory also correctly predicts the results of a gazillion experiments that have been performed from the Michelson-Morley experiment to the recent results from Fermilab and the LHC.


(published on 07/27/2012)

Follow-Up #2: Experiments on special relativity

Tell me please at least one experiment to prove constancy of speed of light and one real experiment showing time dilation (not the Hafelle - Keating one) whose results were wrong. Let us discuss.
- Shabsigh

On the frame-independent speed, obviously there was the old Michelson-Morley experiment. Versions have been repeated, always confirming the frame-independence, with dramatically improved accuracy. See .

The time-dilation effects are also confirmed by an enormous variety of experiments. These range from the famous old muon lifetime effects () to the rates of all clocks on satellites.  

We've got some older answers on this:  .

More fundamentally, the relativistic framework, based on the hypothesis of a universal speed limit, has been cranking out predictions for over a hundred years now for all sorts of diverse effects- what the rules for new forces will be, how magnetic an electron spin is, what the connection is between spin and particle statistics, how to focus an electron microscope,..... . Some of these are qualitative predictions (spin-statistics) others quantitative to spectacular accuracy (electron spin magnetism). 

There seems to be something about these ideas that bothers you. Perhaps we could give a more focussed answer if we knew more what your objection was. Surely it's not just that the first version of one particular experiment had fairly large experimental error bars.

Mike W.

(published on 01/19/2015)