show that the velocity of light is invariant ?
Answers
The physical speed of light is invariant with respect to any reference frame and depends on medium where light propagates through the refractive index. cS is the “speed relativistic” of light and it depends on the speed v. The relativistic speed of light is covariant with respect to moving reference frames.
Answer:
The speed of light in a vacuum was predicted to be 299792458299792458 m/s by James Clerk Maxwell in 1865 (at the time this value had an uncertainty associated with it).
This value is a function of the system of units arbitrarily chosen to describe reality.
It came out of Maxwell's equations for electromagnetism from which a standard wave equation can be derived.
The velocity of these “electromagnetic waves” was defined from invariant quantities which describe the propensity of the vacuum to accept electric and magnetic fields: the electric and magnetic constants, ϵ0ϵ0 and μ0μ0.
These quantities are necessarily the same in all reference frames otherwise the laws of physics would change whether or not you are moving. Since this is not what we observe, they are constant.
Therefore, given that this “wave speed” is given by
1ϵ0μ0√1ϵ0μ0,
it is equally frame invariant.
Once this speed was calculated and it was seen to be the same as the measured speed of light, it was deduced that light is, in fact, an electromagnetic wave.
After this, the invariant speed which underpinned electromagnetism (and, as it turned out, all forces) was called “the speed of light”.
Albert Einstein subsequently used this speed invariance to develop his special theory of relativity in 1905 and it is seen today as a fundamental constant of nature.