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arXiv:quant-ph/0701001

Can quantum-mechanical description of physical reality be considered incomplete?

Gilles Brassard A, André Allan Méthot

Published Dec 30, 2006• 3 citations
arXivHTMLPDF

Abstract

In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proof that the EPR argument was fatally flawed. The modest purpose of our paper is to give a critical analysis of the original EPR paper and point out its logical shortcomings in a way that could have been done 70 years ago, with no need to wait for Bell's theorem. We also present an overview of Bohr's response in the interest of showing how it failed to address the gist of the EPR argument.

DOI
10.48550/arxiv.quant-ph/0701001

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In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proof that the EPR argument was fatally flawed. The modest purpose of our paper is to give a critical analysis of the original EPR paper and point out its logical shortcomings in a way that could have been done 70 years ago, with no need to wait for Bell's theorem. We also present an overview of Bohr's response in the interest of showing how it failed to address the gist of the EPR argument.
In loving memory of Asher Peres, we discuss a most important and influential paper written in 1935 by his thesis supervisor and mentor Nathan Rosen, together with Albert Einstein and Boris Podolsky. In that paper, the trio known as EPR questioned the completeness of quantum mechanics. The authors argued that the then-new theory should not be considered final because they believed it incapable of describing physical reality. The epic battle between Einstein and Bohr intensified following the latter's response later the same year. Three decades elapsed before John S. Bell gave a devastating proof that the EPR argument was fatally flawed. The modest purpose of our paper is to give a critical analysis of the original EPR paper and point out its logical shortcomings in a way that could have been done 70 years ago, with no need to wait for Bell's theorem. We also present an overview of Bohr's response in the interest of showing how it failed to address the gist of the EPR argument.
The third round of the Bohr-Einstein debate was conducted by way of the journals rather than in person. Five years after Bohr’s victory at the Sixth Solvay Conference, Einstein, working with two younger colleagues, Boris Podolsky and Nathan Rosen, finally achieved a sharp formulation of the argument that quantum mechanics is an incomplete description of reality. They published in the American journal The Physical Review , in 1935. As one expects in a paper bearing Einstein’s name, the argument is simple but very clever. An improvement by Schrödinger speeds up the exposition. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This study posits that Bohr failed to defend the completeness of the quantum mechanical description of physical reality against Einstein–Podolsky–Rosen’s (EPR) paper. Although there are many papers in the literature that focus on Bohr’s argument in his reply to the EPR paper, the purpose of the current paper is not to clarify Bohr’s argument. Instead, I contend that regardless of which interpretation of Bohr’s argument is correct, his defense of the quantum mechanical description of physical reality remained incomplete. For example, a recent trend in studies of Bohr’s work is to suggest he considered the wave-function description to be epistemic. However, such an interpretation cannot be used to defend the completeness of the quantum mechanical description.
When it was first put forward, special relativity struck many people as counterintuitive and possibly inconsistent, as we saw when we considered the twin paradox in Chapter 17. Quantum mechanics had a similar effect, only to a much greater and longer lasting degree, from the time of its inception in the mid 1920s until the present. This reaction to quantum theory was not confined to an initial confusion that often accompanies a new subject, but remained a life-long puzzle for Einstein, to mention only the most prominent opponent of what he took to be the reigning orthodoxy. In this chapter we study a famous attempt by Einstein and two of his colleagues to show that quantum mechanics was, if not logically inconsistent, then at least an incomplete theory. This charge of incompleteness is just that raised by Schrödinger's cat paradox (Section 21.4). THE EPR PARADOX In 1935 Einstein, Boris Podolsky (1896–1966) and Nathan Rosen (1909–1995) (hereafter referred to as EPR) published a paper titled ‘Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?’. They take as their criterion for the completeness of a theory that it contains terms corresponding to every relevant entity found in reality. For example, in the classical description of a system, such as a planet going around the sun, there are symbols representing the position r , the momentum p and so forth for the various parts of the system.
The first round of the Einstein–Bohr debates took place when Einstein challenged Bohr’s principle of complementarity at the Solvay conference in 1927 and Bohr successfully defended it. The most serious challenge, however, came in 1935 when a paper by Einstein, Podolsky, and Rosen (EPR) argued that quantum mechanics was incomplete through a gedanken experiment motivating an approach based on hidden variables. In this chapter, EPR’s arguments about the incompleteness of quantum mechanics and Bohr’s reply to them are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and was nothing that Einstein would have expected. Bell’s inequality and the subsequent Bell-CHSH inequality, that are satisfied by all theories based on the “self-evident truths” of reality and locality are discussed. The startling results that quantum mechanics violates Bell’s inequality and the experimental results are in agreement with the prediction of quantum mechanics are presented.