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The speed limit is built into the structure of Minkowski spacetime
All points (x,y,z,t) in Minkowski space obeys the equation
with constant.
Suppose we have a particle whose motion accelerating along the x axis, i.e. then
Differentiating, we get an expression for velocity
Clearly as , x'(t) approaches .
It turns out that is the square of mass, and indeed if it equals 0—every massless particle always moves at lightspeed.
A particle with mass, with a speed below c can't accelerate beyond c. This can be proven.
Consider . Clearly this has to change sign if a particle is to surpass c. To change sign smoothly we must have for some . Then
which can only be satisfied if but if then is . Therefore a massive particle can never accelerate beyond speed c if its speed is less than c, or fall below c if its speed is greater. In fact, Minkowski spacetime does allow for particles that always faster than c, such particles are called Tachyons and have never been observed.
While our universe seems to be consistent with having local Minkowski structure, it is just a model and can't be proven absolutely. But the speed limit is a natural and inevitable consequence of it.
TLDR: Current models of the universe have a speed limit built into spacetime structure which explain why you can't move faster than light.
