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Quantum Field Theory Motivated Model for the Einstein, Podolsky, Rosen (EPR) Experiment

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Quantum Field Theory Motivated Model for the Einstein, Podolsky, Rosen (EPR) Experiment Canadian Journal of Physics Quantum Field Theory Motivated Model for the Einstein, Podolsky, Rosen (EPR) Experiment Journal: Canadian Journal of Physics Manuscript ID cjp-2019-0537.R2 Manuscript Type:ForPoint Reviewof View Only Date Submitted by the 12-Mar-2020 Author: Complete List of Authors: Schatten, Kenneth; a.i. Solutions, Inc., Physics Research Jacobs, V.J.; Naval Research Laboratory Quantum Field Theory, Electron Dressing, EPR, Einstein, Podolsky and Keyword: Rosen Experiment, Probabilistic Is the invited manuscript for consideration in a Special Not applicable (regular submission) Issue? : © The Author(s) or their Institution(s) Page 1 of 11 Canadian Journal of Physics Quantum Field Theory Motivated Model for the Einstein, Podolsky, Rosen (EPR) Experiment For ReviewKenneth H. Schatten* Only NASA/GSFC Greenbelt, MD 20771 *now at: ai-Solutions, Inc. Lanham, MD 20706 and Verne L. Jacobs Center for Computational Materials Science, Code 6390, Materials Science and Technology Division, Naval Research Laboratory, Washington, D. C. 20375-5345 1 © The Author(s) or their Institution(s) Canadian Journal of Physics Page 2 of 11 Abstract Bell deduced the nature and form of “nonlocal hidden variables” that could yield the unusual pattern of responses in the paradoxical Bohm (B-EPR) version of the Einstein, Podolsky, Rosen (EPR) experiment. We consider that Quantum Field Theory (QFT)allows for the existence of Bell’s hidden variables in the “dressing” of free electrons that may explain the EPR experimental results. Specifically, the dressing of free electrons can convey random vector information. Motivated by this, we use a random vector paradigm (RVP) to explore how well a Monte Carlo computer program compares with the experimental B-EPR statistics. In this algorithm, the random vector provides a unique fingerprint that allows these charged leptons to bear unique responses when their spin is read by Stern-Gerlach detectors. The program’s numerical results compare well with Bell’s experimental summary. This work offers the opportunity to consider that virtual particles play a role in understanding the origins of QM’s unique entanglement andFor probabilistic Review behaviors. Only 1. Introduction Einstein, Podolsky and Rosen [1] (EPR) considered that non-commuting quantities (e.g. momentum and position) could be simultaneously measured by observing these properties on two particles simultaneously released from a common source. This suggested to these authors that both properties were based in local reality. The current paper focuses on David Bohm’s [2] (B-EPR) version of the EPR experiment, that was more amenable to experimental testing. In the B-EPR experiment, two spin ½ particles, an electron and a positron, are formed from an initial zero spin state in this generic EPR experiment. To conserve spin, each particle must provide a deterministic opposite spin from the other when the Stern-Gerlach(SG) detectors have a collinear orientation. Thus, if one measures spin UP (+), the other measures spin DOWN (-), and for any other opposite orientation, e.g., RIGHT, LEFT, etc. Non-collinear orientations, however, reveal differing stochastic behaviors. For example, when the detectors are oriented orthogonally, the particles’ spins are randomly distributed: half correlated (+ + or - -) and half anti-correlated (+ - or - +). Mixed statistics of differing amounts occur for other relative orientation angles. How deterministic and probabilistic properties can both exist within these charged particles is an integral component of what has been called the “EPR paradox.” Bell [3] was the first to deduce a commonality to these puzzling experiments. From his deep insight and thoughtful interpretation of the B-EPR experiments, he showed that “non- local hidden variables” could be required to provide the unusual Stern-Gerlach detector responses. Yet, the subject still remains shrouded in mystery because his hidden variables were counter-intuitive, requiring what was called “non-local,” “action at a distance,” and even “spooky” behavior, seemingly violating relativity. Further important steps followed, one by CHSH [4], who provided a more complete account of the degree to which non- 2 © The Author(s) or their Institution(s) Page 3 of 11 Canadian Journal of Physics locality needed to be involved with generalized EPR experiments. Even now, in the 21st century, we have not really answered the question posed by EPR, as to whether quantum mechanics is “complete.” This phrasing essentially indicates that one needs to have a mechanism that determines where each particle goes. Yet despite a probabilistic view, Quantum Field Theory [5] (QFT) has shown itself to be the best physical theory we have to date, calculating atomic properties with a precision from 12-14 significant digits. To set the stage for how we employ QFT to allow the electrons and positrons (e&p) used in the EPR experiment, we need to examine their QFT structure. Eq.(1) shows the difference between the bare electron and the QFT free electron,[5] the latter being a “dressed” electron, after Lindgren.[6] This equation indicates that a free electron (solid line at left) can be represented as the sum of a bare electron, dashed line, plus its dressing, consisting of the sum of all possible virtual photons, etc., that the electron can withdraw from the vacuum, corresponding to the remainderFor Reviewof the equation. Each Only sub-graph in Eq. (1) represents an integral equation in QFT. Previously, we developed a random vector model [7] following Bell’s methodology that provided the QM statistics. This was a mathematical construct that showing that Bell’s methodology worked, however, these electrons lacked any physical attribute beyond the tightly bound electron containing 3 sets of 2x2 Pauli spin-matrices that appeared insufficient to allow sufficient hidden variables to be encoded onto these electrons, and result in the Bell statistics. A richer source of encoded information is needed to provide the B-EPR experimental results, as required by Bell’s non-local statistics. More recently, Tommasini [8] argued for a statistical interpretation of Quantum Field Theory (QFT) that would support reconciliation of locality and causality. On the subject of the statistical interpretation of the electrons used in the B-EPR experiment, we should keep in mind that e&p belong to the class of particles called leptons and also are Fermions, meaning they obey Fermi-Dirac statistics, namely unlike Bosons, no two can exist in the same quantum state. In this paper, we develop a QFT paradigm wherein free electron dressings contain virtual particles and examine their ability, within the EPR experiment, to provide the Bell statistics. Virtual photons play an important role in physics; for example their exchange between an electron and the nucleus is the force that holds atoms together. The use of QFT here is solely limited to providing motivation for a random vector paradigm (RVP) to free electrons 3 © The Author(s) or their Institution(s) Canadian Journal of Physics Page 4 of 11 and positrons (e&p). This random vector paradigm simply describes free e&p to contain virtual particles in their dressings, represented with vector properties. This RVP can serve as Bell’s hidden variables in the B-EPR experiment. This shall enable the development of a Monte Carlo computer program for testing the B-EPR statistics with. In effect, the virtual particles, most commonly virtual photons here, are embedded onto free electrons. They may then be viewed as carriers of information that allow these leptons to have unique, deterministic responses when viewed by the Stern-Gerlach Detectors (SGDs) within these B- EPR experiments. Each particle’s “deterministic response” would be coupled to their mirror twin particle taking part at a distant location of the B-EPR experiment. An electron’s dressing in QFT is needed by free e&p, for without this, these charged particles would radiate energy into space. The dressing shields the electron by inhibiting it from radiating energy. Without this, the electron might not have the energy to escape its bound state. Rather, itFor would lose Review energy by Bremsstrahlung Only radiation into space, and hence would be unable to transition from its bound state. It is important to point out that, owing to conservation laws and the requirement of zero radiative emission from a free electron, whatever conserved properties the dressing retains (e.g. spin, energy,, etc.), the free e&p also possesses. Hence the particular properties gathered from the vacuum acquired as the bound leptons becomes free, remain attached to these free particles. This remains so, generally, until the free particles interact with matter. This paper offers a more detailed account of free electron properties within the B-EPR experiment than is typically considered. Let us briefly describe how Stern-Gerlach Detectors (SGDs) work. Electrons, for example, are attached to neutral silver atoms to create a beam of neutral particles that pass through the SGD. The SGDs have a strong magnetic field gradient in a direction perpendicular to the beam and detector axis. This field gradient provides a force in the direction of the field gradient, dependent upon the electron’s spin in that direction. This separates the particles along the field gradient direction by amounts dependent upon the spin component or components in that direction. Since electrons have spin 1/2 the beam splits up into two separate beams, spin UP and spin DOWN. In our RVP, we employ a single random vector (RV) to model each electron’s dressing. For this paper, our usage allows free electrons a greater degree of determinism than the 3 sets of 2x2 Pauli spin matrices provides for tightly bound electrons. In the B-EPR experiment, free electrons have their spin gauged by Stern-Gerlach(SG) detectors [9]. 4 © The Author(s) or their Institution(s) Page 5 of 11 Canadian Journal of Physics For Review Only Figure 1. In the B-EPR experiment, a positron, p, and an electron, e, emanate from a Zero- Spin State located at X.
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