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The Devil is in the Detail

Karl Hess

Published Oct 22, 2014• 0 citations
Publisher

Abstract

When I took a first glance at Bell’s paper, I got the impression that all of Bell’s statements were mathematically straightforward and simply true for numbers and, therefore, a mathematically proven truth, a theorem for numbers, just as Tony’s equation was. Both Walter and I could not see why this theorem could be applied to the actual experiments. I realized that it would be a lot of work to understand the physical significance of Bell’s ideas, and I first had to convincemyself that it was reallyworthwhile.What I askedmyself was whether Bell’s ideas had any consequences for engineering and technology and not just for the esoteric questions related to the battle between Einstein and Bohr. While I still was fond of my childhood dream to make a contribution in mathematical physics, I had worked too long in areas of applied physics and engineering to attack a problem that had no applications in the foreseeable future.

DOI
10.1201/b16809-7

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When I took a first glance at Bell’s paper, I got the impression that all of Bell’s statements were mathematically straightforward and simply true for numbers and, therefore, a mathematically proven truth, a theorem for numbers, just as Tony’s equation was. Both Walter and I could not see why this theorem could be applied to the actual experiments. I realized that it would be a lot of work to understand the physical significance of Bell’s ideas, and I first had to convincemyself that it was reallyworthwhile.What I askedmyself was whether Bell’s ideas had any consequences for engineering and technology and not just for the esoteric questions related to the battle between Einstein and Bohr. While I still was fond of my childhood dream to make a contribution in mathematical physics, I had worked too long in areas of applied physics and engineering to attack a problem that had no applications in the foreseeable future.
This review is related to the Einstein-Bohr debate and to Einstein–Podolsky–Rosen’s (EPR) and Bohm’s (EPRB) Gedanken-experiments as well as their realization in actual experiments. I examine a significant number of papers, from my minority point of view and conclude that the well-known theorems of Bell and Clauser, Horne, Shimony and Holt (CHSH) deal with mathematical abstractions that have only a tenuous relation to quantum theory and the actual EPRB experiments. It is also shown that, therefore, Bell-CHSH cannot be used to assess the nature of quantum entanglement, nor can physical features of entanglement be used to prove Bell-CHSH. Their proofs are, among other factors, based on a statistical sampling argument that is invalid for general physical entities and processes and only applicable for finite “populations”; not for elements of physical reality that are linked, for example, to a time-like continuum. Bell-CHSH have, furthermore, neglected the subtleties of the theorem of Vorob’ev that includes their theorems as special cases. Vorob’ev found that certain combinatorial-topological cyclicities of classical random variables form a necessary and sufficient condition for the constraints that are now known as Bell-CHSH inequalities. These constraints, however, must not be linked to the observables of quantum theory nor to the actual EPRB experiments for a variety of reasons, including the existence of continuum-related variables and appropriate considerations of symmetry.
If you ask Google to search for “no quantum world,” you will get nearly 300 hits. They all give the following quotation (or recognizable corruptions of it): There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature. Over 90% of them attribute the statement to Niels Bohr, with phrases like “Bohr's dictum …,” “Bohr insisted that …,” “Bohr proclaimed …,” “Niels Bohr said, in a frequently quoted passage …,” “Niels Bohr wrote [my emphasis] …,” and even “Explain and evaluate Bohr's philosophy of quantum theory with reference to his assertion ….” Here is yet another example of the power of the internet to enrich our knowledge. There is only one problem. Bohr, who took writing very seriously indeed, never published such an assertion in any of his writings, although he repeatedly refined, reformulated, and often simply repeated his position on the philosophical foundations of the quantum theory. The statement actually comes from an essay by Aage Petersen, “The Philosophy of Niels Bohr” [1], which he published in the Bulletin of the Atomic Scientists shortly after Bohr's death. Petersen introduced the words with When asked whether the algorithm of quantum mechanics could be considered as somehow mirroring an underlying quantum world, Bohr would answer … So what may now be the most celebrated of all Bohr quotations on the nature of the quantum theory is at best an attempt by a close associate to characterize Bohr's general response to the highly problematic notion of a “quantum world,” written too late for Bohr to respond. When you ask Google to list only those pages that also mention the actual author of the words, Petersen, the number of hits drops from 286 to 18. The status of this “quotation” as hearsay is in danger of being lost. I'm particularly sensitive to this risk because in the 1980s I used to enjoy giving physics colloquia on Bell's theorem and its implications for our understanding of quantum mechanics. I was always fond of Petersen's recollection of what Bohr used to say, and I felt that his formulation captured something important about the situation revealed by Bell's theorem.
The rapid rise of quantum information For the last four chapters I have been describing what may be called the ‘fundamental’ or ‘foundational’ aspects of quantum theory. I have been explaining what happens when you penetrate deeper into the ideas of quantum theory than when you merely make use of it, when you try to understand its basic meaning and what, if true, it tells us about the physical nature of the Universe. As I said in Chapter 5, once Bohr had given his approach to these matters in his Como paper of 1927, general opinion was that his views were sacrosanct, and that no self-respecting physicist needed to return to discuss them further. It was Bell's great achievement to dent this complacency at least a little, and from the very end of the 1960s for the next quarter of a century or so, there were a few experimentalists keen to test the Bell inequalities with increasing stringency, and a few theoreticians with fresh ideas about how quantum theory should be interpreted. While it was generally admitted that Bell's work was a genuine and important contribution to our understanding of quantum theory, and eventually the ideas actually reached some of the textbooks, in the 1970s and 1980s the field was still very much a minority interest, and even those who found it interesting would scarcely have felt that it had, or was likely to have in the foreseeable future, practical application.