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Philosophy of Science

Quantum Reference Frames in the Context of EPR

Michael Dickson

Published Dec 1, 2004• 6 citations
Publisher

Abstract

Taking a cue from Bohr's use of the notion of a reference frame in his reply to EPR's argument against the completeness (and consistency) of standard quantum theory, this paper presents an analysis ofthe role of reference frames in the situation considered by EPR, using a quantum-theoretical account of physical reference frames based on the work of Mackey, and Aharonov and Kaufherr. That analysis appears to justify at least some crucial aspects of a Bohrian reply to EPR.

DOI
10.1086/425939

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Taking a cue from Bohr's use of the notion of a reference frame in his reply to EPR's argument against the completeness (and consistency) of standard quantum theory, this paper presents an analysis ofthe role of reference frames in the situation considered by EPR, using a quantum-theoretical account of physical reference frames based on the work of Mackey, and Aharonov and Kaufherr. That analysis appears to justify at least some crucial aspects of a Bohrian reply to EPR.
After summarising a previously given analysis of Bohr's reply to Einstein, Podolsky and Rosen (EPR), this chapter endorses the claim made by Everett himself that Everettian quantum mechanics `in a certain sense bridges the positions of Einstein and Bohr'. On the one hand, it shows how Everett's theory provides a reconstruction of Bohr's viewpoint of complementarity as applied to the EPR case and a justi�cation of his criticism of EPR's `criterion of reality'. On the other hand, it includes a notion of physical reality that is independent of any observational context, and suggests a remaining shortcoming of Bohr's reply.
Recent work on Bohr's reply to EPR has helped improve our understanding of Bohr's reply, but further work is needed. In this paper I do two things towards that end. First, I make some elementary points about EPR's argument, which help to clear the air of some minor criticisms of Bohr's reply. Second, I argue that Bohr's thought experiment is a reasonable realization of EPR's argument, and I briefly suggest how to understand that experiment. I finish with a brief remark about Bohm's version of the experiment, and its relation to Bohr's.
The topic of quantum reference frames (QRFs) has attracted a great deal of attention in the recent literature. Potentially, the correct description of such frames is important for both the technological applications of quantum mechanics and for its foundations, including the search for a future theory of quantum gravity. In this letter, we point out potential inconsistencies in the mainstream approach to this subject and propose an alternative definition that avoids these problems. Crucially, we reject the notion that transformations between QRFs can be represented by unitary operators and explain the clear physical reasons for this. An experimental protocol, capable of empirically distinguishing between competing definitions of the term, is also proposed. The implications of the new model, for uncertainty relations, spacetime symmetries, gauge symmetries, the quantisation of gravity, and other foundational issues are discussed, and possible directions for future work in this field are considered.
The concept of a reference frame has been a part of the physical formalism since the early days of physics. The reference frame was always understood as a physical system with respect to which states of other physical systems are described. With the adoption of quantum theory, our understanding of physical systems has fundamentally changed, yet we still rely on classical systems for the definition of reference frames. If we acknowledge the fact that all systems are quantum mechanical, including reference frames, then we have to be able to describe quantum systems relative to other quantum systems. \n \nIn this thesis we develop a framework for integrating quantum reference frames into the formalism of quantum mechanics. We show how the description of states and measurements has to be refined in order to account for the quantum nature of the reference frame. Initially, we study the implications of the new description with a quantum reference frame associated with a generic compact group. Then, we apply the same approach to the study of relativistic quantum reference frames associated with the Poincaré group, which is not compact. \n \nOur findings for the generic compact group include an analysis of how well a quantum system defines a frame of reference for other systems. Also in the generic case we analyze the effects of a measurement on a quantum reference frame. In the relativistic case we first find how the massive representations of the Poincaré group decompose into irreducible representations. This is a key problem in the analysis of quantum reference frames. Finally, we analyze a relativistic quantum reference frame that is used for measuring the total momentum. We will show how the relativistic measurements of total momentum should be described with respect to a quantum reference frame. We will also show how these measurements affect the quantum reference frame.
This chapter introduces in more comprehensive fashion than elsewhere in the literature the interesting role of Heisenberg in the EPR debate. Although we have already published an analysis of Heisenberg’s posthumously published draft response to EPR, only now are we able to situate this excellent primary source in its fullest context, by contributing a chapter describing, for example, Heisenberg’s thinking prior to EPR about interacting systems and hidden variables, the crucial role of Grete Hermann for Heisenberg’s thinking about separability, completeness and observational context, and describing the correspondence between Heisenberg and Bohr discussing Heisenberg’s manuscript.