You always hear this phrase if you watch something about astrophysics ‘Nothing can move faster than light’. But speed is only relative. How can this be true if speed can only be experienced/measured relative to something else?
In: Physics
Hey mate, I defend for my Ph.D. in physics in a month. This explanation is not ELI5 but, unfortunately, it doesn’t seem like the more elementary explanations are really that, explanations. Rather… just kind of rehashing different ways of saying “yup that’s just how it is.” So a little more detail may be needed.
The paradox seems to arise because of how you’re used to looking at relative velocities. If you’re driving in a car, someone looks like they’re going backwards to you at the same speed that you’re going forward to them. And if you introduce a third object, moving at half your speed in the same direction, then you see it as moving backwards at half of your speed while the ground observer sees it as moving forward at half your speed.
This type of shifting between different points of view (reference frames), where you can just add or subtract velocity differences, is what’s called a [Galilean Transformation](https://en.wikipedia.org/wiki/Galilean_transformation) and does a good job at describing different the points of view as we humans perceive them. To us also, the differences in velocity between us and other things we see from day to day is extremely small compared to the speed of light. So the difference in the effects between light appearing to move a bit slower or faster in different frames (what a Galilean transformation prescribes) versus light actually always being the same speed, are extremely small.
But it just so happens that some people [1](https://en.wikipedia.org/wiki/James_Clerk_Maxwell) [2](https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment) from ~1850-1900ish figured out that light should actually appear to always be moving at *exactly* the speed of light in any frame, not just approximately. This obviously contradicts the Galilean transformation since the simple addition of velocities between frames isn’t satisfied anymore.
The ability to mathematically shift between different points of view without changing the underlying reality is called symmetry. Its the same idea that if you rotate a ball it looks the same all around. Galilean transformation is a form of symmetry. It was found that there’s another form of symmetry for changing frames of reference called a [Lorentz transformation](https://en.wikipedia.org/wiki/Lorentz_transformation). The Lorentz transformation functions very similarly to the Galilean transformation when things are moving slowly relative to each other when compared to the speed of light. But it also doesn’t break down when account for light having to always be the same speed in every reference frame.
Since the Lorentz transformation accurately describes reality, its differences with the Galilean transformation have implications on the way that we have to frame our physical interpretation of the world. Among other things, it implies that the coordinates of length can expand and contract as seen in different reference frames, and that the concept of time, which was formerly thought to be a distinct entity, must be treated similarly to position. In other words, time is, in some ways, a ‘fourth spatial dimension’, and just like space under the Lorentz transformation, it can “shrink” and “expand” and observers may “rotate” towards and away from the “time” axis, just like you can turn left and right when you walk. Consequently, the paradox of the speed of light seeming to be the same to all observers is accommodated by the notions of space and time changing for observers to preserve the speed of light from every point of view.
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