Abstract
This chapter offers an analysis of Bohr’s exchanges with Einstein concerning the completeness and locality of quantum mechanics, most especially Einstein, Podolsky, and Rosen’s article and Bohr’s reply, both published under the same title—“Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”—in 1935. EPR’s article introduced a thought experiment, the EPR experiment, and offered a particular argument concerning it, EPR’s argument (to be distinguished from the EPR experiment), which led EPR to conclude that quantum mechanics is incomplete, or else nonlocal, in the sense of entailing instantaneous physical connections between events, connections forbidden by relativity. These conclusions were questioned by Bohr in his reply, which offers a different analysis of the EPR experiment and derives different conclusions concerning its meaning and implications. While important for Bohr and Einstein (and a few others at the time), the EPR experiment and the Bohr–Einstein exchange concerning it had been somewhat marginal to the debate concerning quantum theory, until Bell’s and related theorems discovered in the 1960s and then the experimental findings associated with these theorems. These developments have brought the EPR experiment to center stage of this debate, indeed largely defined now by the key questions posed by the experiment, especially those concerning the locality of quantum phenomena and quantum mechanics.
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Notes
- 1.
It is not possible, within the scope of this study, to offer a close reading of Bohr’s reply itself, which would be necessary in order to make the strongest possible case for my claim. I do, however, offer such a reading in (Plotnitsky 2009, pp. 279–312).
- 2.
As throughout this study, I use the term “local” in the sense of compatibility with (special) relativity. One encounters a number of conceptions of locality or nonlocality in the discussions of the EPR-type experiments. Other terms, such as nonseparability, are used and are given various meanings in turn. Some of these meanings are compatible with my argument in this chapter, while others would require further qualifications. These qualifications, however, are not essential for my argument, which only involves locality in the sense just defined.
- 3.
Here and throughout his reply, Bohr uses the term phenomena in its conventional sense, rather than in his special sense, introduced later. Accordingly, in this chapter I shall use the term in this conventional sense as well, unless specified otherwise.
- 4.
Some commentators do attribute to Bohr, including in his post-EPR thinking, the view that “measurement reveals the objective, preexisting value of an observable” (Murdoch 1977, p. 107). This view is problematic in the present reading of Bohr, and I do not think that Murdoch offers sufficient support for his claim.
- 5.
There has been much debate concerning Bell’s theorem and related findings: how tight these arguments are, what they actually demonstrate, and so forth. The subject has generated an immense body of literature, reflecting a great multitude of views, as have EPR’s article and Bohr’s reply, whether in their own right, or in the context of Bell’s theorem, which renewed attentions to both papers. For some instructive exchanges concerning EPR’s article and Bohr’s reply, see (Mehra and Rechenberg 2001, vol 6, part 2, pp. 713–759). For reasonably representative selections of articles on Bell’s theorem, see (Cushing and McMullen 1989), (Kafatos 1989), and (Ellis and Amati 2000). Bell’s own work is assembled in (Bell 2004). See (Shimony 2004) and (Held 2006) for helpful introductions to, respectively, Bell’s and the Kochen–Specker theorems. It is sometimes argued that Bell’s theorem or the EPR-type experiments imply the nonlocality of quantum phenomena. I shall not try to counter these contentions here, although, in my view, Bell’s theorem and these experiments only allow for the possibility of nonlocality, which, however, is in conflict with the experimental evidence, thus far confirming relativity. Apart from the fact that these contentions have no significant bearings on our understanding of Bohr’s argumentation, they represent a minority view, albeit a vocal minority. My understanding of Bell’s theorem, stated here, is consistent with that of many commentators. See, for example, Mermin’s essays on the subject collected in (Mermin 1990) or his argument in (Mermin 1998), (Gottfried 2000), (Peres 1993), (Bertlmann and Zeilinger 2002), and (Zeilinger et al. 2005).
- 6.
Since they allow for attributing some (but not all) properties to a quantum object at the time of measurement, Bell’s and the Kochen–Specker theorems only require the epistemology of the type Bohr adopts in his reply. They do not entail Bohr’s ultimate epistemology, which is, however, consistent with both theorems.
- 7.
As I noted, unlike the Bell-Bohm version of the EPR experiment for spin, the original experiment proposed by EPR, dealing with continuous variables, cannot be physically realized, since the EPR entangled quantum state is non-normalizable. This fact, however, does not affect the fundamentals of the case, which can be considered in terms of the corresponding idealized experiment. Cf., Bohr’s comment on this point (Bohr 1935, p. 698, n.). There are experiments that statistically approximate the idealized entangled state constructed by EPR.
- 8.
By “states” I mean here the mathematical entities (vectors in Hilbert spaces) that, accompanied by other elements of the formalism and appropriate rules, such as Born’s rule, enable our predictions concerning the outcome of quantum experiments. One of the main questions in the debate concerning quantum mechanics is whether quantum states in this sense in fact correspond to some actual physical entities or “elements of physical reality.” In Bohr’s view, they do not.
- 9.
For a detailed reading of Bohr’s argument, see (Plotnitsky 2009, pp. 279–312).
- 10.
These considerations bear on the question of counterfactual statements in considering quantum phenomena. This question, also germane to Bell’s and the Kochen–Specker theorems, is beyond my scope here. See the works cited in Note 5, especially (Mermin 1990) and (Peres 1993).
- 11.
The argument given here could be transferred to Bohm’s version of the EPR experiment and spin variables. In this case, too, any assignment of the alternative spin-related quantity to the same quantum object becomes impossible, once one such quantity is assigned. An assignment of the other would require an alternative type of measurement, mutually exclusive with the first, on the first object of a given pair, and hence another fully identically behaving EPR-Bohm pair, which is, again, not possible. Only statistical correlations between such assignments are possible (cf., Mermin 1990, pp. 107–108). The argument concerning locality given in the next section could be transferred to the case of discrete variables as well.
- 12.
Ideally, one would need a proper reading of Bohr’s discussion leading to this elaboration, which cannot be offered here, but, see, again (Plotnitsky 2009, pp. 279–312). However, the logic of Bohr’s argument, explained above is sufficient to explicate Bohr’s main meaning.
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© 2013 Arkady Plotnitsky
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Plotnitsky, A. (2013). 1935. “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”: The EPR Experiment and Complementarity. In: Niels Bohr and Complementarity. SpringerBriefs in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4517-3_8
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