# Constancy of speed of light

In a particular derivation of the Lorentz transformation, as illustrated in $\textbf{Relativity, Gravitation and Cosmology , Robert A Lambourne }$ (p. 21) one of the key elements is the constancy of light.

So if $S$ and $S'$ are two inertial frames, with $S'$ moving with a constant velocity $V$ with respect to $S$, then in $S$ we have $c = \frac{x}{t}$ and in $S'$ we have $c = \frac{x'}{t'}$ even though $S'$ is moving with respect to $S$.

My question is, what is this constancy of the speed of light based upon, other than it allowing for a simplification in the coordinate transformation? Was this experimentally confirmed?

The consequence of this leads to many strange postulates, such as the classic "moving clock runs slower".

• The constancy of the speed of light is essentially derived from Maxwell's equations as far as I'm aware. It isn't possible to verify the speed of light in a frame moving close to it, as we obviously cannot go that fast. I'd recommend further research. Jun 26, 2017 at 6:34
• See the Michelson-Morley experiment.
– Robert Israel
Jun 26, 2017 at 6:38
• Yes, the constant speed of light has been experimentally confirmed witch the Mechelson Morley experiment. Wrong stack exchange though. Jun 26, 2017 at 6:39

The form of the Lorentz transformation (i.e. that the group of transformations between inertial frames is the Lorentz group) with the speed $c$ as a free parameter follows from very basic symmetry assumptions about the universe. I discuss these further here.
In particular, in a universe with the above symmetries hold and where the value of $c$ is finite, it is readily deduced that anything moving at $c$ relative to some inertial observer is seen to be moving at $c$ relative to all inertial observers. Therefore, the observation of anything with this invariant speed behavior confirms experimentally the above theory.
The Michelson-Morley experiment famously succeeded in doing this, thus establishing experimentally that there is indeed an invariant speed $c$, and that light moves at this speed for all observers (or at least does so to an extremely good approximation). Modern versions of the Michelson-Morley experiment (using resonant interferometers rather like small versions of the LIGO ones) show that the change in the speed of light $\Delta c_L$ wrought by the addition of the Earth's motion is of the is of the order of $\Delta c_L/c_L<10^{-15}$. Incidentally, this also shows that light must be mediated by a massless particle (or again, one with exquisitely small mass).
Another property of this invariant speed is that, if a particle has nonzero mass, as we push harder and harder giving it higher and higher kinetic energy, its speed relative to us must asymptote to $c$. This is exactly what we observe in particle accelerators. In the LHC experiments, for example, we can treat all the collided particles - protons - as being massless, because their energy is thousands of times their rest energy (proton rest mass $\approx 1 {\rm GeV}$, LHC proton total energy $\approx 7{\rm TeV}$). It's not as accurate a way as the Michelson-Morely experiment to confirm the invariant speed's existence, but it is in some ways more intuitive and compelling.