No Return to Classical Reality

TL;DR

This paper reviews fundamental quantum phenomena that fundamentally defy classical explanation, emphasizing recent theorems like Hardy's and Pusey--Barrett--Rudolph's that establish the inherently quantum nature of reality.

Contribution

It synthesizes key results demonstrating that quantum mechanics cannot be reduced to classical physics, highlighting recent theorems that deepen our understanding of quantum foundations.

Findings

Quantum phenomena such as randomness, interference, and noncommutativity cannot be explained classically.

Bell's theorem and recent results show the intrinsic non-classical nature of quantum correlations.

Hardy's theorem and Pusey--Barrett--Rudolph theorem establish the objective reality of the wave-function.

Abstract

At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of Nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by first granting quite a broad notion of classicality, describe a range of quantum phenomena (such as randomness, discreteness, the indistinguishability of states, measurement-uncertainty, measurement-disturbance, complementarity, noncommutativity, interference, the no-cloning theorem, and the collapse of the wave-packet) that do fall under its liberal scope, and then finally describe some aspects of quantum physics that can never admit a classical understanding -- the intrinsically quantum mechanical aspects of Nature. The most famous of these is Bell's theorem, but we also review two more recent results in this area. Firstly, Hardy's theorem shows that even a finite dimensional quantum system must contain an infinite amount of information, and secondly, the Pusey--Barrett--Rudolph theorem shows that the wave-function must be an objective property of an individual quantum system. Besides being of foundational interest, results of this sort now find surprising practical applications in areas such as quantum information science and the simulation of quantum systems.