Document Type


Publication Date



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 rst 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 nally 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 nite 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.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Contemporary Physics, volume 57, in 2016 following peer review. The definitive publisher-authenticated version is available online at DOI: 10.1080/00107514.2015.1063233.

Peer Reviewed



Taylor & Francis



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.