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On the Consequences of a Probabilistic Space-Time Continuum

Mustafa A. Khan

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

ABSTRACT: In this article I propose the following: (1) Probability is an intrinsic property of the space-time continuum similar to the spatial dimensions and time. (2) This probability space has certain specific characteristics. (3) The probability space is affected by matter just as the other dimensions of space-time continuum. (4) The effect of matter on the probability space is of a specific characteristic. (5) This effect of matter on the probability space can be tested in a simple experiment using modern technology and thereby prove/disprove it's existence. (6) If the existence of the probability space is proved, then certain profound consequences follow which have both theoretical and practical implications.

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ABSTRACT: In this article I propose the following: (1) Probability is an intrinsic property of the space-time continuum similar to the spatial dimensions and time. (2) This probability space has certain specific characteristics. (3) The probability space is affected by matter just as the other dimensions of space-time continuum. (4) The effect of matter on the probability space is of a specific characteristic. (5) This effect of matter on the probability space can be tested in a simple experiment using modern technology and thereby prove/disprove it's existence. (6) If the existence of the probability space is proved, then certain profound consequences follow which have both theoretical and practical implications.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and interpretations depend on the probability space adopted. Some other recent works have also shown that generalized measurements may allow to further exploit the statistics of Bell-like tests. Following these ideas, in this work we show that one and the same experimental arrangement can provide a practical scheme valid for two very different probability spaces. Moreover, we show that this allows the introduction of novel Bell tests that are not possible in more standard approaches.
We propose that quantum entanglement occurs because the fundamental particles, such as electrons, quarks, and photons, simultaneously experience both the 4th real spatial dimension in R4 as well as the time dimension in (3 + 1)-D spacetime. Consequently, the entangled particles can never become separated in the 4th spatial dimension no matter how far they have moved apart in the other 3 spatial dimensions. Because the quark and lepton families represent specific different discrete symmetry binary subgroups of SU(2), we can establish that the quantum states of the fundamental particles are defined in 4 spatial dimensions, so there is then no need for a spacetime communication from one detector (or particle) to inform the other detector (or particle) of the physical state of the first detected entangled particle. A clever experiment needs to determine whether the fundamental particles actually experience a 4th spatial dimension, and if so, whether they experience the 4th spatial dimension as the time dimension simultaneously. Apparently, if a Casimir-like test reveals that virtual particles have a non-zero mass, there are claims that a 4th spatial dimension does not exist.
In this paper, we generalize a previous relativistic -dimensional model for two mass-less Dirac particles with contact interactions to the N -particle case. Our model is based on the notion of a multi-time wave function which, according to Dirac, is the central object in a relativistic multi-particle quantum theory in the Schrödinger picture. Consequently, we achieve a manifestly Lorentz invariant formulation on configuration space–time. Our model is constructed to be compatible with antisymmetry and probability conservation in a relativistic sense. On the mathematical side, we further develop the method of multi-time characteristics and show that uniqueness of solutions follows from probability conservation. We prove that the model is interacting and outline how one can understand the interaction as effectively given by a -potential at equal times. Finally, we answer the question of whether Lorentz invariant and probability-conserving dynamics can also be obtained when the particles are confined in a region with a non-zero minimal space-like distance, a question relevant for an extension to higher dimensions.