c = sqrt(1/ε0 µ0) ≈ 3 × 10^8 ms ^−1
In the above equation, ε0 and µ0 are the electrical permittivity & magnetic permeability of empty space. When you plug in their values, you get approximately 300000 km/s . An interesting thing in the above equation is that 1 , µ0 and ε0 are invariants (constants). Their values, by definition, will remain unchanged in every frame of reference. Since the speed of light is derived from constants only, it is invariant as well. It cannot change, ever. This is completely counter-intuitive as nothing else in nature behaves like this. Isn’t motion always relative to something? That’s what Galilean relativity is based on. That’s what Newton assumed in his theory. An absolute light speed would mean that people travelling towards and away from a light source at 0.5c will still measure light speed as c . This was one reason why Maxwell’s theory did not generate sufficient interest upon publication.
In 1905, Einstein, using the prior work done by Lorentz and Henri Poincare, managed to successfully argue that the reason c remains invariant is because space & time are not invariant as was previously thought.
Speed = distance(space)/time
. If light speed is constant, then space & time must shrink/stretch in lockstep so that light speed remains constant.
Time flows at different rates depending on several factors and space shrinks/stretches accordingly. An observer in one reference frame will have a local version of space & time, different from an observer in a different reference frame. When they both compute the speed of light, their local space/time equation will always return c .
Hence gravity appears to slow down light, when in fact light is always travelling at c . Its just that the longer distance it is travelling due to curved spacetime might not be apparent to an observer, and so the observer might feel that light is slowing down when it travelling near, say, the Sun or any other sizeable mass.
If light speed is a constant, why does light travel slower in glass than in vacuum?
Light takes more time to travel through denser media like glass than in vacuum, not because it slows down, but because it gets absorbed and re-emitted by the electrons in the glass as well as gets scattered by glass atoms. The absorption/re-emission takes time. The scattering increases the path length. The net result is, the path light takes in glass is never the shortest path. It zig-zags all over the glass, and by the time it comes out, a lot of time has passed. To an observer timing it, it would appear that it slowed down. But whenever it was travelling in glass, it was always moving at c . Note that light can travel only in the empty space between glass atoms and as we know, its speed in empty space is c.
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