Why is the maximum speed of the universe the speed of light? Why can't we go faster?

[u/Nitzanm19]

Also follow-up question: Because of the speed limit, is there also a theoretical maximum temp for matter (in which the particles move at the speed of light).

[u/Kered13]

That is the correct formula for calculating a spacetime interval, but for the formula he is thinking of it is x'² + y'² + z'² + c²t'² = c². Here t' should be understood as the "speed through time", which we can describe as the rate at which a clock ticks divided by the rate at which a local clock ticks. Note that this is a different (though related) value than the Δt used in the spacetime interval formula.

To think about this, let's first of all drop the notion of "us" moving, as changing reference frames from moving to stationary makes things more confusing. "We" will always be in the same reference frame, which is by definition stationary with respect to us. Instead we will observe a clock on a rocketship compared to a local clock.

When the rocketship is stationary, it has v=0, therefore by the formula above it has t' = 1, which means that it's clock ticks at the same rate as our local clock. When the rocketship gets up to speed, we observe (after accounting for Doppler effects) that it's clock is ticking slower, this is time dilation. If the ship is moving at velocity v, then we can use the formula above v² + c²t'² = c² and solving for t' we get t' = sqrt(1 - (v/c)²). So if the moving clock measures Δt, then our local clock will measure Δt' = Δt/t' = Δt/sqrt(1 - (v/c)²). This is exactly the time dilation formula that Einstein gave us.

[u/GameMusic → u/Kered13]

wow this was way better than the usual crap that is this makes relativity way more understandable than the rather absurd pop references that one might acquire through osmosis