arXiv subjects
Publications and source records attributed to Warren Leffler.
We analyze the property of locality with respect to the framework for quantum mechanics based on the path integral formalism. As is well known, this framework makes the same experimental predictions as does the one based on a separable Hilbert space and the Schrödinger equation.
We construct a space of ideal elements (particles and their paths) to analyze certain aspects of quantum physics. The particles are taken from a model of particle interaction first described by David Deutsch (based on a different but related framework, that of MWI), and the paths are based on Richard Feynman's path-integral formulation of quantum mechanics. By combining the two systems we develop a new approach to quantum mechanics that eliminates various quantum paradoxes.
Bell's theorem rests on the following fundamental condition for a local system: P(a,b|alpha, beta, lambda)= P(a|alpha, lambda)P(b|beta, lambda). Here a and b are the outcomes respectively for measurements alpha on one side, and beta on the other, of an experiment involving two entangled particles traveling in opposite directions from a source. The parameter lambda (the set of "hidden variables") represents a more complete description of the joint state of the two particles. Because of lambda, the joint probability of detection is now dependent only on lambda and the local measurement setting of alpha; similarly for the other side and the setting beta. From this equation John Bell derived a simple inequality that is violated by the predictions of quantum mechanics, which is generally taken to imply that quantum mechanics is a nonlocal theory. But, by combining Richard Feynman's formulation of quantum mechanics with a model of particle interaction described by David Deutsch, we develop a system (the "space of all paths," SP) that (1) is immediately seen to replicate the predictions of quantum mechanics, (2) has a single outcome for each quantum event (unlike MWI on which it is partly based), and (3) contains the set lambda of hidden variables consisting of all possible paths from the source to the detectors on each side of the two-particle experiment. However, the set lambda is nonmeasurable, and therefore the above equation is meaningless in SP.
In this paper we identify a hidden premise in Bell's theorem: measurability of the underlying space. But our system (the space of all paths, SP) is not measurable, although it replicates the predictions of standard quantum mechanics. Using it we present three counterexamples to Bell's theorem and also show why Bell-like arguments for more than two particles cannot be carried out in this model. Moreover, we show that the result places severe constraints on possible viable interpretations of quantum mechanics: Either an interpretation must in some form represent a quantum system in terms of all paths within the system or, alternatively, the interpretation must harbor "action at a distance".
This paper implements in a simple but rigorous fashion a model of particle interaction involving all paths within a quantum system, both for configuration space and for spin. The model, which we call the space of all paths, leads to a locally explicable conceptual framework for quantum mechanics. Using it we present two counterexamples to Bell's theorem. Moreover, we show that the result places severe constraints on possible viable interpretations of quantum mechanics: Either an interpretation must in some form represent a quantum system in terms of all paths within the system or, alternatively, the interpretation must harbor "action at a distance." We take action-at-a-distance as a reductio ad absurdum argument for our framework for quantum foundations, since any mechanism in which causal effects can operate instantaneously across vast distances would be completely unknown and magical, a near absurdity.
We explore the consequences of denying the "emptiness of paths not taken," EPNT, a premise of Bernstein, Greenberger, Horne, and Zeilinger in their paper titled, Bell theorem without inequalities. Carrying out the negation of EPNT leads to the concept of a "shadow stream." Streams are essentially particle implementations of the path amplitudes in Feynman's formulation of quantum mechanics, resulting in a simple and consistent extension of the standard postulates for quantum mechanics. Following up on the negation of EPNT using shadow streams, we analyze the experimental outcomes in a standard two-particle interferometer. The result is a simple counterexample to Bell's theorem in position/momentum space.
This paper explores the consequences of denying the "emptiness of paths not taken," EPNT, premise of Bernstein, Greenberger, Horne, and Zeilinger (BGHZ) in their paper titled, Bell theorem without inequalities.[ ] Carrying out the negation of EPNT leads to the concept of a "shadow stream." Streams are essentially particle implementations of the paths in Feynman path-integrals, resulting in a simple and consistent extension of the standard axioms for quantum mechanics. The construct provides elegant resolutions of single- and multi-particle interference paradoxes. Moreover, combining the argument of this paper with that of BGHZ shows that there are just two choices for quantum foundations: interpretations closely similar to the present one or those that harbor instantaneous action at a distance.