Derivation of Relativistic Causality from Quantum Mechanics

Quantum mechanics includes a phenomenon known as quantum entanglement. It is famous that in the last century, Einstein called quantum entanglement a 'spooky action at a distance,' expressing his distrust of quantum mechanics. For example, the quantum state of two entangled particles shared between the Earth and a distant star changes instantaneously upon the measurement of the particle on Earth. Because this state change occurs instantaneously, including the particle at the distant star, Einstein called it a 'spooky' phenomenon that appeared to violate relativistic causality.

However, in the 21st century, not only has the existence of quantum entanglement been confirmed by experiments, but our theoretical understanding has also advanced. Quantum entanglement is by no means a 'spooky action at a distance' in quantum mechanics; rather, it can be naturally understood as a property of quantum mechanics as an operational theory that satisfies relativity.

For instance, if Alice measures one of the quantum systems in an entangled state, the overall quantum state changes instantaneously, but that change is only for Alice, who knows the result of the measurement; the change in the quantum state has not yet occurred for Bob, an observer at a remote location who holds the other entangled quantum system. The quantum state for Bob changes only after the information about the measurement result arrives. Quantum mechanics is not some kind of realistic theory, but merely a form of information theory. Quantum states and wave functions are nothing more than collections of information contained within the probability distributions of physical quantities, and they may differ for each observer.

Therefore, quantum entanglement does not represent the non-locality of quantum mechanics. Since it is perfectly consistent with relativity, quantum entanglement is neither spooky nor anything of the sort.

It is clear that quantum mechanics is not a 'non-local theory' as Einstein suggested, but rather an extremely local theory. One piece of evidence for this is information causality. This information causality is an interesting property satisfied by quantum mechanics, which was pointed out in the following paper [1].

[1] M. Pawłowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter,
and M. Żukowski, Nature 461, 1101 (2009)

I also covered this information causality in Chapter 15 of my book, 'Introduction to Modern Quantum Mechanics'.

Let M be an arbitrary natural number. When Alice sends an M-bit message to Bob, the amount of information Bob can know about Alice's data from that message does not exceed M bits; this property is information causality. This can be classified as a strong property within relativistic causality. (As an example of weak relativistic causality, the no-signaling condition is known. Please also refer to Chapter 15 of my book mentioned above for this.) And quantum mechanics is a theory that satisfies not only the no-signaling condition but also strictly this information causality.

There is an interesting point here. The no-signaling condition and information causality are derived solely from the framework of quantum mechanics without assuming relativity. Even if, historically, relativity had been discovered after quantum mechanics, this information causality could have been found before relativity was established. This is highly non-trivial. Although quantum mechanics was not constructed based on the theory of relativity, as a result, quantum mechanics inherently contains the relativistic causal structure of spacetime. This profound fact also strongly supports the 'It From Qbit' idea, which suggests that quantum information gives rise to the emergence of spacetime.