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AIP conference proceedings

The Problem of Locality and a Relational Interpretation of the Wave Function

Thomas Filk A

Published Jan 1, 2006• 2 citations
Publisher

Abstract

It is argued that many of the so‐called “mysteries” of quantum mechanics like the “particle‐wave duality” or the “spooky action at a distance” loose their weirdness if space itself, the “embedding” of quantum objects into space, and the entanglement among quantum objects are interpreted as relational concepts. Extended to space‐time, this approach may allow for a new interpretation of Haag’s localization of events.

DOI
10.1063/1.2158733

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Relational interpretation of the wave function and a possible way around Bell's theorem

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The famous ``spooky action at a distance'' in the EPR-szenario is shown to be a local interaction, once entanglement is interpreted as a kind of ``nearest neighbor'' relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the ``nearest neighbor'' relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, ``position'' becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the ``weird'' aspects, like the particle-wave duality, the non-locality of entanglement, or the ``mystery'' of the double-slit experiment, disappear. Furthermore, this picture cirumvents the restrictions set by Bell's inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics.

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Abstract For about a century, physicists have been debating over the behavior of particles on a microscopic scale. Although the principle of the wave-particle duality is accepted in the scientific community, many experiments with puzzling results are still challenging quantum mechanics until now, such as the double slit experiment, entanglement, interferences of a single electron, or delayed choice quantum eraser. In this article, we shall bring forth explanations for some of these experiments. Unlike standard quantum mechanics (SQM) built by Schr¨odinger1 and P.Dirac2 which considers that the wave function is an abstract mathematical tool, our model takes up the concept of the pilot wave once initiated by physicists De Broglie and D.Bohm,3 who suggested that the wave associated to a quantum object has a real existence and that it is not simply a wave of probability. We shall discuss how this old-new conception of reality renders quantum mechanics ultimately less mysterious than it seems.

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It is argued that many of the so‐called “mysteries” of quantum mechanics like the “particle‐wave duality” or the “spooky action at a distance” loose their weirdness if space itself, the “embedding” of quantum objects into space, and the entanglement among quantum objects are interpreted as relational concepts. Extended to space‐time, this approach may allow for a new interpretation of Haag’s localization of events.
The famous ``spooky action at a distance'' in the EPR-szenario is shown to be a local interaction, once entanglement is interpreted as a kind of ``nearest neighbor'' relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the ``nearest neighbor'' relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, ``position'' becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the ``weird'' aspects, like the particle-wave duality, the non-locality of entanglement, or the ``mystery'' of the double-slit experiment, disappear. Furthermore, this picture cirumvents the restrictions set by Bell's inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics.
The paper demonstrates that the non-locality and non-reality of the quantum world are \ndirect consequences of the concept of uncertainty. It is also shown that the analysis of \nstates in the phase space entails the operator formalism of wave mechanics. While being \nwell known that the uncertainty principle is a consequence of the commutation rules of \noperators, the paper shows that the reverse path is also possible; i.e. the uncertainty \nequations entails themselves the operators and wave equations of energy and momen- \ntum. The same theoretical approach has been eventually extended to infer significant \nresults of the special relativity.
Abstract Initially proposed by Hugh Everett III as the “theory of the universal wave function,” the many worlds interpretation has since been developed and refined into one of the most influential ways of giving meaning to quantum mechanics. This volume explores the idea that if one adopts the many worlds interpretation, then one can avoid what Einstein called “spooky action at a distance,” the non-locality that is supposed to be a consequence of quantum entanglement according to other approaches. The essays in this volume articulate a clear and defensible formulation of the argument from locality for preferring the many worlds interpretation of quantum mechanics over its rivals and evaluate it. They question in what sense those in quantum foundations should care about locality, in particular, whether and how an interpretation of quantum mechanics must avoid action at a distance in order to maintain consistency with special relativity. Finally, these essays assess whether the many worlds theory needs a particular metaphysical or mathematical interpretation in order to achieve the aim of providing a local interpretation of quantum mechanics.
This chapter focuses the concepts of entanglement and non-locality. Quantum mechanics has yet another mystery—one that occurs as a consequence of superposition states involving two or more particles or two or more beams of photons. This is referred to as entanglement, also known as non-separability. The existence of entangled states is allowed, and even mandated, by quantum mechanics, and this leads us into yet another mystery: non-locality. It demonstrates how subatomic particles can be put into entangled states which reveal strange correlation effects—the effects being the essence of entanglement. It discusses the EPR argument, from the 1935 paper by Einstein, Boris Podolsky, and Nathan Rosen; the polarization states of photons; Bell's theorem; and the Hardy–Jordan argument.
Abstract So, where do we go from here? It is apparent from the last two chapters that nature denies us the easy way out. The clear experimental demonstration of quantum entanglement rules out the idea of local hidden variables, one of the simpler solutions to the conceptual problems of quantum theory. For the time being at least, we are forced to live with the consequences of entanglement, non-locality, and ‘spooky’ action at a distance. This might make some of us uncomfortable, but there is no solace in the Copenhagen interpretation, which does not provide us with any answers and is still regarded by many to be no interpretation at all. And, lest we forget, there remain the problems of interpreting the meaning of quantum probability and the collapse of the wave function. Even those who adhere to the Copenhagen view tend to put aside or disregard the conceptual difficulties that these issues raise as they analyse the results from the latest particle-accelerator experiment. This is not a very satisfactory situation.
Abstract For about a century, physicists have been debating over the behavior of particles on a microscopic scale. Although the principle of the wave-particle duality is accepted in the scientific community, many experiments with puzzling results are still challenging quantum mechanics until now, such as the double slit experiment, entanglement, interferences of a single electron, or delayed choice quantum eraser. In this article, we shall bring forth explanations for some of these experiments. Unlike standard quantum mechanics (SQM) built by Schr¨odinger1 and P.Dirac2 which considers that the wave function is an abstract mathematical tool, our model takes up the concept of the pilot wave once initiated by physicists De Broglie and D.Bohm,3 who suggested that the wave associated to a quantum object has a real existence and that it is not simply a wave of probability. We shall discuss how this old-new conception of reality renders quantum mechanics ultimately less mysterious than it seems.