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Journal of Modern Physics

Quantum Effects from a Simple Card Game

Allen D. Allen

Published Jan 1, 2014• 0 citations
Publisher

Abstract

A well-known, classical conundrum, which is related to conditional probability, has heretofore only been used for games and puzzles.It is shown here, both empirically and formally, that the counterintuitive phenomenon in question has consequences that are far more profound, especially for physics.A simple card game the reader can play at home demonstrates the counterintuitive phenomenon, and shows how it gives rise to hidden variables.These variables are "hidden" in the sense that they belong to the past and no longer exist.A formal proof shows that the results are due to the duration of what can be thought of as a gambler's bet, without loss of generalization.The bet is over when it is won or lost, analogous to the collapse of a wave function.In the meantime, new and empowering information does not change the original probabilities.A related thought experiment involving a pregnant woman demonstrates that macroscopic systems do not always have states that are completely intrinsic.Rather, the state of a macroscopic system may depend upon how the experiment is set up and how the system is measured even though no wave functions are involved.This obviously mitigates the chasm between the quantum mechanical and the classical.

DOI
10.4236/jmp.2014.518195

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A well-known, classical conundrum, which is related to conditional probability, has heretofore only been used for games and puzzles.It is shown here, both empirically and formally, that the counterintuitive phenomenon in question has consequences that are far more profound, especially for physics.A simple card game the reader can play at home demonstrates the counterintuitive phenomenon, and shows how it gives rise to hidden variables.These variables are "hidden" in the sense that they belong to the past and no longer exist.A formal proof shows that the results are due to the duration of what can be thought of as a gambler's bet, without loss of generalization.The bet is over when it is won or lost, analogous to the collapse of a wave function.In the meantime, new and empowering information does not change the original probabilities.A related thought experiment involving a pregnant woman demonstrates that macroscopic systems do not always have states that are completely intrinsic.Rather, the state of a macroscopic system may depend upon how the experiment is set up and how the system is measured even though no wave functions are involved.This obviously mitigates the chasm between the quantum mechanical and the classical.
Causality and the relativity of simultaneity seem at odds with the apparently sudden, acausal state-vector changes ("collapses") characteristic of quantum phenomena. The problem of how physical phenomena can be causally determined, have the probabilities predicted by quantum theory, and be consistent with special relativity appears to be solved by the assumption, essentially the same as one first used by Aharonov, Bergmann, and Lebowitz to address a different problem, that the "initial" and "final" state vectors of a phenomenon or observation, along with certain other state vectors, all represent the system's state at all times. Each member of such an aggregate of state vectors is postulated to represent a different aspect of a physical state rather than a state, so that most of the state vectors in effect constitute a set of nonlocal hidden variables. Various implications of this assumption are illustrated through several physical situations. Among the results is a somewhat surprising resolution of a paradox in a three-spin Greenberger-Horne-Zeilinger experiment (a "three-particle EPR" experiment), which involves a logical consequence that differs from familiar ideas of quantum physics that has no practical experimental consequence, and the prediction of new experimental phenomena related to the Zou-Wang-Mandel superposed-idler system. The potential value of the concepts described as heuristics for new predictions and for developing physical intuition by clarifying the interrelation and coherence of physical principles that would otherwise seem contradictory is briefly discussed.
Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present six such properties and a Venn diagram of how they are related. With two existence theorems and three no-go theorems (EPR, Bell, and Kochen-Specker), we show which properties of empirically equivalent hidden-variable models are possible and which are not. Formally, our treatment relies only on classical probability models, and physical phenomena are used only to motivate which models to choose.
An interpretation of quantum mechanics involving multiple dimensions is proposed, as well as a thought experiment that in principle if performed correctly could either prove or disprove quantum randomness. All outcomes, of a particle’s wave function manifest but manifest in more than three dimensions, and when the wave function collapses, we see the outcome of the wave function, which only exist in three dimensions. Furthermore, a particle is a much larger object, and exists physically as a wave across more than three dimensions and our best description of this is the Schrodinger wave, because it only describes it in three dimensions. We cannot observe the particle as a wave because it is spread out as an object in which most of it exists in more than three dimensions, but when we observe the part or outcome of a wave function that does exist in three dimensions, which is when collapse occurs it leads to particle like properties, due to not being able to interact with the rest of the wave because it is confined to just interacting on a three dimensional scale because we are observing it in three dimensions. Furthermore we cannot observe the part of the wave function that exists in more than three dimensions, in three dimensions because of the principle that in order to observe an object in it's entirety it needs to be observed in all of it's dimensions. Strange phenomenon in quantum mechanics such as tunneling, can be explained by saying that there is a probability of finding the part of wave function that exists in three dimensions on the other side of the barrier, which has travelled over that barrier classically and the probability of it travelling over the barrier decreases expontentially to the width of the barrier increasing. Whether the quantum world is random, or is determined by non-local hidden variables, can be determined by a simple deductive thought experiment as outlined in this article.
Looking at conditional probability from the right perspective allows one to avoid classic paradoxical aspects of quantum mechanics. We discuss, as an elementary analogue of quan-tum states, a classical example (an urn of unknown composition) with similar (putative) paradoxical situ-ations, despite the fact that there is no quantum effect to which they could be ascribed. A crucial feature is that we look at them from an epis-temic point of view and not from the viewpoint of a (seemingly) ontologi-cal reality.
Quantum entanglement is widely regarded as the most puzzling phenomenon in quantum mechanics---two particles, no matter how far apart, appear to instantly determine each other's state upon measurement. For a century, this has been interpreted as "nonlocal correlation" or "spooky action at a distance", yet none of these interpretations have answered a fundamental question: What is the physical carrier of the correlation? This paper offers a simple answer using Time Field Theory (TFT): Entanglement is not the transmission of information, but the inevitable geometric consequence of conservation laws. In TFT, spacetime is governed by strict conservation laws---local intrinsic total velocity conservation and spacetime flux conservation together form the underlying logic of the theory. An entangled photon pair emerges from the ground state of the background time field, and their total phase is locked by the conservation law: the two photons combined must return to the original ground state, because the default setting of the universe allows nothing to be created or lost without constraint. Measurement merely "reads out" this pre-written result. No information transfer is needed, because a conservation law is not a signal---it is the default constraint of the cosmic background. This interpretation requires no wave-function collapse, no postulate of nonlocality, no hidden variables, and no "observer trigger". It is simply an inevitable corollary of the strict conservation laws that permeate TFT. The mystery of entanglement is not a riddle of nature, but a consequence of asking the wrong question---we have always thought something was being transmitted, when in fact nothing is. This is the 12th paper in the Time Field Theory (TFT) series.