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Can you explain why the momentum vector must be constant in magnitude?


There isn’t really a “why”, other than the need to match observed reality.

We know from observations that light moves at a constant speed, even when the observer is moving near the speed of light, and we know that this observation is true regardless of your frame of reference.

In order for physics to remain consistent while accounting for the constant speed of light, other things need to flex between the two reference frames: namely, time (time dilation) and length (Lorentz contraction).


> light moves at a constant speed

While in the same medium, right?

The speed of light is a universal constant in a vacuum, like the vacuum of space. However, light can* slow down slightly when it passes through an absorbing medium, like water (225,000 kilometers per second = 140,000 miles per second) or glass (200,000 kilometers per second = 124,000 miles per second).*

https://www.space.com/15830-light-speed.html#section-speed-o...


Light propagation in a medium is a quite different thing from light in vacuum.

For example, the speed of light in a medium is not the "speed limit" of things in the same medium, and particles in it can actually move faster than light: https://en.wikipedia.org/wiki/Cherenkov_radiation

In other words, the speed of light in vacuum plays a special role in both a vacuum and a medium.


In other words, "to make the math work out". That's kinda what I was poking at, trying to understand if that is some fundamental truth or if it is the result of some underlying mechanism that is more fundamental.


No, and if you could you would win a Nobel prize.

But a century of experimental and observational data proves that it is.

At this point it's generally just taken as a fact that the speed of light is constant for all observers. The explanation given above falls out as a direct mathematical consequence.


to hear Lenny Susskind say it, "light moves at the speed of light"




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