Consider the scenario where you measure the time it takes for light to travel to the left 10 meters and to the right 10 meters. Both measurements will take the same time, even though we are moving through space at crazy speeds. This must mean that light is not moving relative to "space" as a whole. What does it move relative to? The light emitter? If so, try shooting two beams of light 10 meters from the wall. The first time the emitter is stationary; the second time it is moving at 100 m/s. Am I mistaken in thinking that it would hit the wall slightly faster? Wouldn't this light be moving faster than the light emitted from the stationary source?
Am I mistaken in thinking that it would hit the wall slightly faster?
THE insight of relativity is that this is not true. No matter whose clocks and rulers you use, you will always measure the speed of light (in vacuum) to be the same.
This has as a consequence the fact that lengths and times are not as absolute as was once thought. If you are looking at a ruler that is moving relative to you, then that ruler will appear to be shorter (along the direction it's moving); and a moving clock will appear to be slower.
This must mean that light is not moving relative to "space" as a whole.
Relativity does away with the idea of absolute space and instead all velocities are relative to some object or frame of reference (hence relativity).
According to the intuitive Galilean velocity addition formula, velocities add linearly.
If an object has velocity $u$ in the frame of reference $O$ and $O$ has velocity $v$ in the frame of reference $O'$, the object has velocity $u' = u + v$ in the $O'$ frame.
But, what if $u$ is infinite? Since $\infty + v = \infty$, an object with infinite velocity relative to some frame of reference has infinite velocity relative to any frame of reference with relative velocity $v$; infinite speed would be an invariant speed.
In the context of special relativity, $c$ is, in a certain sense, like the infinite speed in the context of Galilean relativity; $c$ is an invariant speed. In SR, if a particle has speed $c$ in a frame of reference, it has speed $c$ in any frame of reference.
In fact, if one replaces $c$ with $\infty$ in the Lorentz transformations, one recovers the Galilean transformations.
In this sense, the Lorentz transformations are more general and, in fact, one can derive the form of the Lorentz transformations with just the principle of relativity leaving the determination of the invariant speed as a matter of empirical verification.
We deduce the most general space-time transformation laws consistent with the principle of relativity. Thus, our result contains the results of both Galilean and Einsteinian relativity. The velocity addition law comes as a bi-product [sic] of this analysis. We also argue why Galilean and Einsteinian versions are the only possible embodiments of the principle of relativity.
What is the speed of light relative to?
It is relative to you and all other objects, in direction and measure.
As mentioned by physicist Brian Greene in his book The Elegant Universe, see The_Elegant_Universe-B.Greene.pdf Motion Through Space-Time pages 26 and 27, all objects are constantly on the move within Space-Time at the speed of light.
This common constant motion of all objects in Space-Time, and the rotation that occurs if they change their direction of travel within that Space-Time environment, changes the measurement instruments in such a manner that the speed of light is always measured as being the speed of light no matter what direction you are traveling in within the environment of Space-Time, thus in turn no matter what percentage of your constant motion(c) is across space only(v).