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arXiv:1605.06022 · International Journal of Modern Physics D

Quantum nonlocality and the end of classical spacetime

Shreya Banerjee, Sayantani Bera, Tejinder P. Singh

Published Jul 28, 2016• 9 citations
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Abstract

Quantum nonlocal correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in quantum theory. There should exist a reformulation of quantum theory which does not refer to classical time. Such a reformulation is obtained by suggesting that spacetime is fundamentally noncommutative. Quantum theory without classical time is the equilibrium statistical thermodynamics of the underlying noncommutative relativity. Stochastic fluctuations about equilibrium give rise to the classical limit and ordinary spacetime geometry. However, measurement on an entangled state can be correctly described only in the underlying noncommutative spacetime, where there is no causality violation, nor a spooky action at a distance.

DOI
10.1142/s0218271816440053

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Quantum nonlocal correlations and the acausal, spooky action at a distance suggest a discord between quantum theory and special relativity. We propose a resolution for this discord by first observing that there is a problem of time in quantum theory. There should exist a reformulation of quantum theory which does not refer to classical time. Such a reformulation is obtained by suggesting that spacetime is fundamentally noncommutative. Quantum theory without classical time is the equilibrium statistical thermodynamics of the underlying noncommutative relativity. Stochastic fluctuations about equilibrium give rise to the classical limit and ordinary spacetime geometry. However, measurement on an entangled state can be correctly described only in the underlying noncommutative spacetime, where there is no causality violation, nor a spooky action at a distance.
Collapse models possibly suggest the need for a better understanding of the structure of space-time. We argue that physical space, and space-time, are emergent features of the Universe, which arise as a result of dynamical collapse of the wave function. The starting point for this argument is the observation that classical time is external to quantum theory, and there ought to exist an equivalent reformulation which does not refer to classical time. We propose such a reformulation, based on a non-commutative special relativity. In the spirit of Trace Dynamics, the reformulation is arrived at, as a statistical thermodynamics of an underlying classical dynamics in which matter and non-commuting space-time degrees of freedom are matrices obeying arbitrary commutation relations. Inevitable statistical fluctuations around equilibrium can explain the emergence of classical matter fields and classical space-time, in the limit in which the universe is dominated by macroscopic objects. The underlying non-commutative structure of space-time also helps understand better the peculiar nature of quantum non-locality, where the effect of wave-function collapse in entangled systems is felt across space-like separations.
Abstract Quantum entanglement is the most famous nonlocal phenomenon in modern physics, and its instantaneous ultra-distance correlation has puzzled physicists for nearly a century. Einstein referred to this effect as “spooky action at a distance”, because it seemingly violates the local causality and light-speed limit of general relativity. Traditional physical theories can only describe entanglement through mathematical wave functions but cannot explain its fundamental physical origin. Based on the three-dimensional time quantization unified field theory, this paper proposes a novel physical mechanism for quantum entanglement. The instantaneous synchronization of entangled particles does not rely on spatial signal transmission, but originates from the shared coupling of the fluctuating time dimension. Quantum systems can bypass classical spatial restrictions through time-dimensional resonance, perfectly explaining quantum nonlocality without violating relativistic rules. This study fundamentally resolves the core contradiction between quantum mechanics and general relativity, reveals the essential nature of entanglement, and completes the systematic theoretical verification of the three-dimensional time unified field framework. AI Usage Note: All theoretical ideas, mathematical derivations and conclusions are independently created by the author. Generative AI was only used for linguistic polishing of sentences. The author takes full responsibility for all content.
The concept of nonlocality and its role in the violation of Bell's inequalities are discussed.A weaker nonlocality is revealed in comparison with Albert Einstein's ``Spooky Action at a Distance'' and at the same time does not contradict the principles of the special theory of relativity (STR).A correlation statistical experiment with the violation of the Clauser±Horne±Shimony± Holt inequality in STR is described, in which weak nonlocality is manifested.The correlation in such an experiment propagates with infinite speed in the proper frame of reference of the measuring device.
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such classical matter fields, quantum mechanics should be formulated without reference to a classical time. If such a new formulation exists, it follows as a consequence that standard linear quantum mechanics is a limiting case of an underlying non-linear quantum theory. A possible approach to the new formulation is through the use of noncommuting spacetime coordinates in noncommutative differential geometry. Here, the non-linear theory is described by a non-linear Schrodinger equation which belongs to the Doebner-Goldin class of equations, discovered some years ago. This mass-dependent non-linearity is significant when particle masses are comparable to Planck mass, and negligible otherwise. Such a nonlinearity is in principle detectable through experimental tests of quantum mechanics for mesoscopic systems, and is a valuable empirical probe of theories of quantum gravity. We also briefly remark on the possible connection our approach could have with loop quantum gravity and string theory.
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime. Therefore such basic notions in quantum information theory as qubit, channel, composite systems and entangled states should be formulated in space and time. In this paper some basic notions of quantum information theory are considered from the point of view of quantum field theory and general relativity. It is pointed out an important fact that in quantum field theory there is a statistical dependence between two regions in spacetime even if they are spacelike separated. A classical probabilistic representation for a family of correlation functions in quantum field theory is obtained. A noncommutative generalization of von Neumann`s spectral theorem is discussed. We suggest a new physical principle describing a relation between the mathematical formalism of Hilbert space and quantum physical phenomena which goes beyond the superselection rules. Entangled states and the change of state associated with the measurement process in space and time are discussed including the black hole and the cosmological spacetime. It is shown that any reasonable state in relativistic quantum field theory becomes disentangled at large spacelike distances if one makes local observations. As a result a violation of Bell`s inequalities can be observed without inconsistency with principles of relativistic quantum theory only if the distance between detectors is rather small. We suggest a further experimental study of entangled states in spacetime by studying the dependence of the correlation functions on the distance between detectors.