What is the quantum mechanical explanation for the speed limit of light?

Question

What is the quantum mechanical explanation for the speed limit of light? Does it arise from more fundamental principles?

Answer 1

So far as we know, there is no quantum mechanical reason for the speed of light $c$ to be an absolutely limit. The limiting speed is a consequence of special relativity, and the validity of special relativity has nothing to do with the validity of quantum mechanics. You can have a consistent non-quantum yet relativistic theory; or you can have a consistent nonrelativistic quantum theory. As it happens, the actual universe is both quantum and relativistic, but quantum mechanics does not necessitate relativity.

Answer 2

Standard quantum mechanics is not even compatible with relativity. If you try to calculate the probability of a particle being found at the time $t$ at the position $\mathbf{x}$, given that it was measured at $\mathbf{x}_0$ at the time $t_0$, you find that $$P(t,x)=\left(\frac{m}{2 \pi i (t-t_0)}\right)^{\frac{3}{2}} \exp \left(i m \frac{\left|\mathbf{x}-\mathbf{x}_{0}\right|^{2}}{2 (t-t_0)}\right)$$ which is non-zero everywhere, implying that you can find the particle anywhere in the universe.

As you can see, there is no limiting speed.