Quantum principle of relativity

Abstract

Quantum mechanics is an incredibly successful theory and yet the statistical nature of its predictions is hard to accept and has been the subject of numerous debates. The notion of inherent randomness, something that happens without any cause, goes against our rational understanding of reality. To add to the puzzle, randomness that appears in non-relativistic quantum theory tacitly respects relativity, for example, it makes instantaneous signalling impossible. Here, we argue that this is because the special theory of relativity can itself account for such a random behaviour. We show that the full mathematical structure of the Lorentz transformation, the one which includes the superluminal part, implies the emergence of non-deterministic dynamics, together with complex probability amplitudes and multiple trajectories. This indicates that the connections between the two seemingly different theories are deeper and more subtle than previously thought.