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ON EPR PARADOX AND MATTERWAVE IN EUCLIDEAN RELATIVITY

Vu B Ho

Published Jan 1, 2018• 0 citations
Publisher

Abstract

: In our previous works, we showed that the Einstein-Podolsky-Rosen (EPR) paradox could be resolved by constructing a Euclidean relativity that not only leads to the same results obtained from Einstein general relativity but also permits an instantaneous transmission of interaction. However, there still remains the question about the nature of these physical fields and their mathematical formulations if they exist. In this work we show that it is possible to formulate Euclidean relativistic field equations similar Dirac equation from a general system of linear first order partial differential equation. Since the speeds of the Euclidean relativistic fields have no upper values, they can be used to rectify the quantum entanglement in quantum mechanics.

DOI
10.13140/rg.2.2.35711.71849

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: In our previous works, we showed that the Einstein-Podolsky-Rosen (EPR) paradox could be resolved by constructing a Euclidean relativity that not only leads to the same results obtained from Einstein general relativity but also permits an instantaneous transmission of interaction. However, there still remains the question about the nature of these physical fields and their mathematical formulations if they exist. In this work we show that it is possible to formulate Euclidean relativistic field equations similar Dirac equation from a general system of linear first order partial differential equation. Since the speeds of the Euclidean relativistic fields have no upper values, they can be used to rectify the quantum entanglement in quantum mechanics.
Recent experimental results have shown a violation of Bell’s inequalities, which are a mathematical formulation of Einstein-Podolsky-Rosen (EPR) paradox. The violation leads to the conclusion that there are no local hidden variable theories that underlie quantum mechanics. However, the Bell’s inequalities do not rule out the possibility to construct non-local hidden variable theories that comply with quantum mechanics, in particular, a theory of special and general relativity that permits an instantaneous transmission of interaction. In this work we show that a special relativity with a Euclidean metric that allows not only local interactions but also interactions that can be transmitted instantaneously can be constructed and, furthermore, such special relativity can also be generalised to formulate a general theory of relativity that leads to the same experimental results as Einstein theory of general relativity. We also show that it is possible to formulate Dirac-like relativistic wave equations in this Euclidean relativity with either real mass or imaginary mass, which suggests that the proper mass of a quantum particle may be defined in terms of a differential operator that is associated with a spacetime substructure of the particle.
In this work we discuss the nature of Maxwell and Dirac field by examining the mathematical structures of the subfields that are coupled to form these two physical fields. We show that while Maxwell and Dirac field are hyperbolic fields which are described by wave equations the subfields are elliptic fields which are described by elliptic equations. Therefore, it is reasonable to suggest that the subfields are more fundamental and should be used to represent quantum particles in stable states with invariant physical properties. Furthermore, since the subfields are described by elliptic equations therefore they comply with the Euclidean relativity rather than the pseudo-Euclidean relativity as Maxwell and Dirac fields do, and this results in profound implications such as if quantum particles possess physical properties that are represented by subfields which are described by elliptic equations, hence acting in accordance with the Euclidean relativity, then they can be used to explain physical phenomena that require physical transmissions with speeds greater than the speed of light in vacuum, such as the Einstein-Podosky-Rosen paradox in quantum entanglement. As a further discussion, we also show that it is possible to formulate a Dirac-like elliptic field that complies with the Euclidean relativity.
The Einstein-Podolsky-Rosen (EPR) paradox was enunciated in 1935 and since then it has made a lot of ink flow. Being a subtle result, it has also been largely misunderstood. Indeed, if questioned about its solution, many physicists will still affirm today that the paradox has been solved by the Bell-test experimental results, which have shown that entangled states are real. However, this remains a wrong view, as the validity of the EPR ex-absurdum reasoning is independent from the Bell-test experiments, and the possible structural shortcomings it evidenced cannot be eliminated. These were correctly identified by the Belgian physicist Diederik Aerts, in the eighties of last century, and are about the inability of the quantum formalism to describe separate physical systems. The purpose of the present article is to bring Aerts' overlooked result to the attention again of the physics' community, explaining its content and implications.
The famous EPR paradox shows that if we describe quantum particles in the usual way -- by their wave functions -- then we get the following seeming contradiction. If we entangle the states of the two particles, then move them far away from each other, and measure the state of the first particle, then the state of the second particle immediately changes -- which contradicts to special relativity, according to which such immediate-action-at-a-distance is not possible. It is known that, from the physical viewpoint, this is not a real paradox: if we measure any property of the second particle, the results will not change whether we perform the measurement on the first particle or not. What the above argument shows is that the usual wave function description of a quantum state does not always adequately describe the corresponding physics. In this paper, we propose a new, more physically adequate description of a quantum state, a description in which there is no EPR paradox: measurements performed at the first particle does not change the state of the remote second one.
Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.