# Can the constancy of the speed of light in vacuum be derived from a deeper theory?

Einstein's second postulate of special relativity is:

The speed of light in vacuum takes the same value ($c$) for any observer in an inertial frame of reference.

I know there is a lot of experimental evidence for this statement, but has it every been proven (theoretically) to be the result of another ("deeper"?) theory, that does not take it as a postulate?

• – ACuriousMind Mar 24 '16 at 18:00
• @ACuriousMind In the sense that the answer to that question also answers this one (with "No, there is not")? – Danu Mar 24 '16 at 18:14
• @Danu "Why is X the case?" and "Can X be derived from a deeper theory?" seem to me to be pretty much the same question. The only way physics ever answers why questions for axioms is by providing a deeper theory in which they are not axioms anymore, but derived. – ACuriousMind Mar 24 '16 at 18:16
• @ACuriousMind Hmm, I'm not so sure. You're excluding the option of having competing theories. – Danu Mar 24 '16 at 18:17
• I don't know about deeper, but the idea came from an earlier theory. Maxwell predicted the existence of electro-magnetic waves that, according to his theory, would always be observed to have the same speed regardless of the relative motion of the observer and the source. Einstein's theory is the culmination of work by several physicists who wanted to reconcile Maxwell's prediction with the so-called principle of relativity---the idea that the laws of physics should be the same for every observer regardless of the observer's motion or location. – Solomon Slow Mar 24 '16 at 19:29

The "deeper theory" is that the universe is causal. In a causal universe there must be a maximum speed for communication; experiment teaches us that this is the speed of light.

It is possible to frame the axioms of Special Relativity in terms of causality; you will find papers and books on the various axiomatic approaches primarily in the philosophy of science/mathematical literature.

This has been discussed in Is causality a formalised concept in physics? and elsewhere.

• Well, Galilean relativity is causal, so it's not quite as simple as this – tfb Mar 24 '16 at 18:43
• Only if there is a maximum speed that everyone agrees upon. – Peter Diehr Mar 24 '16 at 18:47
• I don't think so. I think it's causal but clearly hopeless (ie no electromagnetism) – tfb Mar 24 '16 at 18:49
• See also Do we know why there is a speed limit in our Universe? A Galilean Universe would have a global notion of causality, but not a local initial-value formulation. – Michael Seifert Mar 24 '16 at 19:14
• @PeterDiehr: Oh sorry, I may be confused about the definition of 'causal': I'd assumed it meant that there's a partial ordering of events, which is true for Galilean relativity, but if you additionally require that no two distinct events are equivalent under the partial order you get something which is not true for Galilean relativity, and that's probably what 'causal' means. Sorry! – tfb Mar 24 '16 at 20:07

Can the constancy of the speed of light be derived from a deeper theory?

You can't derive it from a "deeper theory", but yes, you can understand why this postulate holds good.

Einstein's second postulate of special relativity is: The speed of light takes the same value ($c$) for any observer in an inertial frame of reference.

Yes. The Michelson-Morley experiment came up with a null result, so Einstein got his thinking cap on and set some groundrules, and the result was special relativity. There was a bit of an issue in that he didn't acknowledge some of the other relativity guys such a Voigt, Fitzgerald, Lorentz, Poincare, but such is life.

I know there is a lot of experimental evidence for this statement, but has it every been proven (theoretically) to be the result of another ("deeper"?) theory, that does not take it as a postulate?

Like I was saying, it hasn't been proven to be the result of a different theory, but IMHO a lot of relativists know that it's because of the wave nature of matter. See http://arxiv.org/abs/0705.4507 by Magueijo and Moffat where you can read this:

"Following Ellis, let us first consider c as the speed of the photon. Can c vary? Could such a variation be measured? As correctly pointed out by Ellis, within the current protocol for measuring time and space the answer is no. The unit of time is defined by an oscillating system or the frequency of an atomic transition, and the unit of space is defined in terms of the distance travelled by light in the unit of time. We therefore have a situation akin to saying that the speed of light is “one light-year per year”, i.e. its constancy has become a tautology or a definition".

The local speed of light is always measured to be the same because we use the local motion of light to define the second and the metre, and we then use them to measure the local speed of light. It's circular, it's a tautology. Note however that whilst the local speed of light is always measured to be the same, a gravitational field is a place where the speed of light is spatially variable. Einstein said this repeatedly from 1908, but there are some cargo-cult issues in that not many people know about it. This example is from 1920, see the second paragraph:

There's other examples from other years, such as this one from 1915: ""the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned". There's also examples from authors such as Shapiro:

Also see this PhysicsFAQ article by editor Don Koks:

"Einstein talked about the speed of light changing in his new theory. In the English translation of his 1920 book "Relativity: the special and general theory" he wrote: "according to the general theory of relativity, the law of the constancy of the velocity [Einstein clearly means speed here, since velocity (a vector) is not in keeping with the rest of his sentence] of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity [speed] of propagation of light varies with position." This difference in speeds is precisely that referred to above by ceiling and floor observers."

I rather think Robert Close explains the deeper meaning rather well in The Other meaning of Special Relativity. Note that it's not some other deeper theory, it's a matter of understanding the evidence of things like pair production and electron diffraction. It's a matter of understanding why special relativity works. it's because of the wave nature of matter. When you and your rods and clocks are made out of waves, you always measure the local wave speed to be the same, because you calibrate those rods and clocks using those waves.

• This answer concludes that one needs quantum physics (wave-particle duality) to understand the constancy of the speed of light. That's an extremely confused and non-mainstream view. – Danu Apr 9 '16 at 17:23