Cambridge University Press eBooks

Locality and incompleteness

Guido Bacciagaluppi, Antony Valentini

Published Oct 22, 2009• 0 citations

Abstract

Einstein's 1927 argument for incompleteness A huge literature arose out of the famous ‘EPR’ paper by Einstein, Podolsky and Rosen (1935), entitled ‘Can quantum-mechanical description of physical reality be considered complete?’. The EPR paper argued, on the basis of (among other things) the absence of action at a distance, that quantum theory must be incomplete. It is less well-known that a much simpler argument, leading to the same conclusion, was presented by Einstein eight years earlier in the general discussion at the fifth Solvay conference (pp. 440ff.). Einstein compares and contrasts two views about the nature of the wave function ψ , for the specific case of a single electron. According to view I, ψ represents an ensemble (or ‘cloud’) of electrons, while according to view II, ψ is a complete description of an individual electron. Einstein argues that view II is incompatible with locality, and that to avoid this, in addition to ψ there should exist a localised particle (along the lines of de Broglie's theory). Thus, according to this reasoning, if one assumes locality, then quantum theory (as normally understood today) is incomplete. The conclusion of Einstein's argument in 1927 is the same as that of EPR in 1935, even if the form of the argument is rather different. Einstein considers electrons striking a screen with a small hole that diffracts the electron wave, which on the far side of the screen spreads out uniformly in all directions and strikes a photographic film in the shape of a hemisphere with large radius (see Einstein's figure, p. 440).

DOI: 10.1017/cbo9781139194983.008

Related papers

PBR theorem and Einstein's quantum hole argument

Galina Weinstein

Upon reading Einstein's views on quantum incompleteness in publications or in his correspondence after 1935 (the EPR paradox), one gets a very intense feeling of deja-vu. Einstein presents a quantum hole argument, which somewhat reminds of the hole argument in his 1914 "Entwurf" theory of general relativity. PBR write in their paper, "An important step towards the derivation of our result is the idea that the quantum state is physical if distinct quantum states correspond to non-overlapping distributions for [physical states]". PBR then conclude, "The general notion that two distinct quantum states may describe the same state of reality, however, has a long history. For example, in a letter to Schrödinger containing a variant of the famous EPR (Einstein-Podolsky-Rosen) argument", and they refer to Einstein's quantum hole argument. This short paper discusses the PBR theorem, and the connection between the PBR argument and Einstein's argument and solution.

arXiv:1301.7526Jan 31, 20130 citations

On quantum mechanics self-consistency: EPR incompleteness claims require no extraneous concepts beyond the theory's plain formalism for refutation

D. F. Orsini, L. R. N. Oliveira, M. G. E. da Luz

From a phenomenological and experimental viewpoint, quantum mechanics is remarkably successful in explaining effects and processes in the microscopic world. Recently, however, a growing body of literature has revisited the theory's own formal foundations, specifically addressing issues of self-consistency and completeness. As a major historical example of these foundational challenges, the Einstein-Podolsky-Rosen (EPR) argument famously claimed that the theory is incomplete. While many valid criticisms and refutations of the EPR logic exist, they generally rely on a combination of technical results and conceptual objections to EPR's interpretive assumptions, thus transcending the plain quantum framework itself. Motivated by these trends of examining the theory's structural limits, here we revisit the EPR argument. Focusing on elements essential to the EPR reasoning, we first analyze general quantum correlations for EPR states: (i) the fact that their observables are always associated with non-commuting operators, and (ii) the nature of the correlated information obtained through measurement. From these two points alone, and relying strictly on the core rules of quantum mechanics, we demonstrate how to overturn the alleged EPR incompleteness without invoking any extraneous propositions. Consequently, we show that the standard formalism alone suffices to resolve such type of skepticism regarding the theory's physical reach. This offers, at least in a paradigmatic instance, a powerful indication of a structurally well-founded, self-consistent quantum theory.

quant-pharXiv:2608.10006Aug 11, 20260 citations

Relativity, Quantum Mechanics and EPR

Robert K. Clifton, Constantine Pagonis, Itamar Pitowsky

The Einstein-Podolsky-Rosen argument for the incompleteness of quantum mechanics involves two assumptions: one about locality and the other about when it is legitimate to infer the existence of an element-of-reality. Using one simple thought experiment, we argue that quantum predictions and the relativity of simultaneity require that both these assumptions fail, whether or not quantum mechanics is complete. EPR’s (1935) argument for the incompleteness of QM turns upon the following sufficient condition: “If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.“ EPR apply this condition in a case where knowledge gained from measuring one quantum system allows one to predict with certainty a value for a physical quantity on another.

PSA Proceedings of the Biennial Meeting of the Philosophy of Science AssociationJan 1, 199228 citations

The Einstein–Podolsky–Rosen experiment and nonlocality

Peter Holland

Assessment of Einstein's argument Is quantum mechanics complete and local … It was observed in §1.4 that Einstein's method of criticizing the orthodox view of quantum theory was to focus on examples whose special characteristics could be used to show that adherence to the completeness assumption compels one to adopt ‘unnatural theoretical interpretations’. It was a way not of disproving the conventional interpretation by attempting to locate in it some logical flaw, but of pushing it into a corner that in Einstein's view no one would seriously want to inhabit. The paper of Einstein, Podolsky & Rosen (EPR) (1935) is the most famous component of this programme and the purpose of this chapter is to analyse the extent to which the arguments presented in it are compatible with the quantum theory of motion. From contemporaneous correspondence it appears that the EPR paper was written by Podolsky and that Einstein did not consider that the point which was really troubling him had been made explicit (Fine, 1986, Chap. 3). According to Einstein's accounts, EPR had the following purpose: to show that if one believes the wavefunction exhausts all the statements that can be meaningfully asserted about a physical system, then one must also accept that the real physical state of the system depends on what befalls another system with which it has previously interacted, no matter how far apart the two systems may become.

Cambridge University Press eBooksMay 13, 19931 citation

Einstein’s boxes

Travis Norsen

At the 1927 Solvay conference, Albert Einstein presented a thought experiment intended to demonstrate the incompleteness of the quantum mechanical description of reality. In the following years, the experiment was modified by Einstein, de Broglie, and several other commentators into a simple scenario involving the splitting in half of the wave function of a single particle in a box. This paper collects together several formulations of this thought experiment from the literature, analyzes and assesses it from the point of view of the Einstein–Bohr debates, the EPR dilemma, and Bell’s theorem, and argues for “Einstein’s Boxes” taking its rightful place alongside similar but historically better known quantum mechanical thought experiments such as EPR and Schrödinger’s Cat.

arXiv:quant-ph/0404016American Journal of PhysicsJan 13, 200572 citations

Bell’s theorem and local reality

Jim Baggott

Abstract If we reject the ‘spooky’ action at a distance that seems to be required in the Copenhagen interpretation of quantum theory, and which is highlighted by the EPR thought experiment, we must accept the EPR argument that the theory is somehow incomplete. In essence, this involves the rejection of the first postulate of quantum theory: the state of a quantum mechanical system is not completely described by the wave function or state vector.Einstein had hinted at a statistical interpretation. In his opinion, the squares of the wave functions or state vectors of quantum theory represented statistical probabilities obtained by averaging over a large number of real particles. The Copenhagen interpretation of the EPR experiment insists that the reality of the physical states that can be measured is defined by the nature of the interaction between two quantum particles and the nature of the experimental arrangement. A completely deterministic, locally real version of quantum theory demands that the physical states of the particles be established at the moment of their interaction and that the particles separate as individually real entities in those physical states. The physical states of the particles are prescribed by the physics of their interaction and independent of how we choose to set up the measuring instrument, and so no reference to the nature of the latter is necessary, except to define how the independently real particles interact with it. The instrument thus probes an observer-independent reality.

Nov 6, 20030 citations