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arXiv:1201.1799

Analogs of wave function reduction, quantum entanglement and EPR experiment in classical physics of spacetimes with time machines

Ilya A. Ovid’ko

Published Jan 5, 2012• 0 citations
arXivHTMLPDF

Abstract

It is theoretically revealed that, in classical physics of spacetimes with wormholes, there are analogs of wave function reduction events, quantum entanglement and Einstein-Podolsky-Rosen (EPR) experiment. Within the suggested approach, wormholes are specified by a typical microscopic radius of their mouths, and this causes the size effect in operation of wormhole-based time machines (closed timelike curves; CTCs). For geometric reasons, classical solid balls in a spacetime with a wormhole are divided into the two categories: small and large balls whose traverse through wormholes is permitted and forbidden, respectively. Evolutions of small balls on CTCs can be self-inconsistent (or, in other terms, inconsistent with conventional causality), in which case there is an uncertainty in their behaviors. In contrast, evolutions of large solid balls are always unambiguous. In the situation where small balls can be absorbed by large balls, uncertain behaviors of small balls transform into unambiguous evolutions of large balls in the logical way analogous to that of a quantum measurement - wave function reduction - event. Also, within the suggested approach operating with classical balls in spacetimes with wormholes, analogs of quantum entanglement and EPR experiment are defined and theoretically described.

DOI
10.48550/arxiv.1201.1799

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It is theoretically revealed that, in classical physics of spacetimes with wormholes, there are analogs of wave function reduction events, quantum entanglement and Einstein-Podolsky-Rosen (EPR) experiment. Within the suggested approach, wormholes are specified by a typical microscopic radius of their mouths, and this causes the size effect in operation of wormhole-based time machines (closed timelike curves; CTCs). For geometric reasons, classical solid balls in a spacetime with a wormhole are divided into the two categories: small and large balls whose traverse through wormholes is permitted and forbidden, respectively. Evolutions of small balls on CTCs can be self-inconsistent (or, in other terms, inconsistent with conventional causality), in which case there is an uncertainty in their behaviors. In contrast, evolutions of large solid balls are always unambiguous. In the situation where small balls can be absorbed by large balls, uncertain behaviors of small balls transform into unambiguous evolutions of large balls in the logical way analogous to that of a quantum measurement - wave function reduction - event. Also, within the suggested approach operating with classical balls in spacetimes with wormholes, analogs of quantum entanglement and EPR experiment are defined and theoretically described.
We consider the two-particle wave function of an Einstein-Podolsky-Rosen system, given by a two-dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In this way an effective metric, which is analogous to a black hole metric in some limited region, is obtained in one case and a particular metric with singularities appears in the other case, opening the possibility, following Holland, of interpreting the EPR correlations as being originated by an effective wormhole geometry, through which the physical signals can propagate.
When backward time travel through wormholes is taken into account, classical physics loses its determinism and allows simulation of some quantum behaviours. We show how it is possible to simulate a non-local wavefunction reduction-type effect, i.e. we present a mechanical analogy for the collapse of the wavefunction of an entangled state of two removed particles. This situation can be seen as the simplest EPR situation, i.e. the situation where there is just one direction to measure along the spin (or the correlated properties). We present no rigorous results here, just a different point of view about something that is generally thought to be impossible: modelling a quantum indeterministic and non-local behaviour with a mechanical system.
If spacetime is built out of quantum bits, does the shape of space depend on how the bits are entangled? The ER=EPR\mathrm{ER}=\mathrm{EPR}ER=EPR conjecture relates the entanglement entropy of a collection of black holes to the cross sectional area of Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and Cadney-Linden-Winter inequalities. These are nontrivial properties of entanglement entropy, so this is evidence for ER=EPR\mathrm{ER}=\mathrm{EPR}ER=EPR. We further show that the entanglement entropy associated with classical ER bridges has nonpositive tripartite information. This is not a property of entanglement entropy, in general. For example, the entangled four qubit pure state ∣GHZ4⟩=(∣0000⟩+∣1111⟩)/2|GH{Z}_{4}⟩=(|0000⟩+|1111⟩)/\sqrt{2}∣GHZ4​⟩=(∣0000⟩+∣1111⟩)/2​ has positive tripartite information, so this state cannot be described by a classical ER bridge. Large black holes with massive amounts of entanglement between them can fail to have a classical ER bridge if they are built out of ∣GHZ4⟩|GH{Z}_{4}⟩∣GHZ4​⟩ states. States with nonpositive tripartite information are called monogamous. We conclude that classical ER bridges require monogamous EPR correlations.
*Special Relativity places severe constraints on any possibility for faster-than-light (FTL) phenomenon. There are four hopes for FTL; warp drive via General Relativity Theory (GRT), wormholes via GRT, tachyons, and quantum mechanics. This talk focuses on why quantum mechanics makes the list. The nonlocal nature of matter demonstrates correlations between distant events that cannot be explained by current concepts of causality. For two classical events to be correlated, either one causes the other, or both possess a common cause in their past light cones. Neither kind of causality can explain the correlations observed in entangled quantum systems. Reality seems to support a third mysterious type of causality, with an essential spacelike nature, but direct spacelike causality should be impossible as it would lead to temporal paradox. The two concepts of classical causality, timelike causes and common cause, are presented along with a review of the EPR experiment showing that something like spacelike causality exists between the distant parts of an entangled quantum system. Bell’s Inequality shows that the EPR correlations cannot be attributed to common causes. Gisin’s EPR-Relativity experiment shows that timelike causes cannot explain the EPR correlations either. The metaphor of Quantum Tic-Tac-Toe is used to show a third type of causality applicable only to quantum situations. This third type of causality is an indirect spacelike cause acting through multiple classical realities, permitting FTL but prohibiting temporal paradox. I. Introduction HIS paper considers the issue of causality in entangled quantum systems. The Background section reviews the two classical notions of causality, EPR type entanglements, and Special Relativity. The Common Cause section reviews Bell’s Inequality theorem and shows how this type of causality cannot explain the correlations seen in entangled systems. The Einsteinian Causality section reviews Gisin’s experiment demonstrating that time-like causality cannot explain these correlations either. Gisin’s conclusion is that quantum systems support a new mysterious 3 rd type of causality. The Quantum Causality section introduces a situation in Quantum Tic-Tac-Toe that exhibits this same kind of causality
The EPR paradox, showing the incompatibility between causality and quantum mechanics, leads, especially after Bell's theorem and the experiments based on it, to a deep crisis of the causality principle. A complete redefinition of the entanglement concept, based on the impossibility of violation of conservation laws and on the generalization to a 5-dimensional space, leads to the recovery of the classical and fundamental idea for the physics of causality. The absolute validity of conservation laws, induces moreover, in the cases where they would be otherwise violated, topology changes which make possible "tunneling processes" (like wormholes in astrophysics) which connect separate spacetimes. It can be shown that such a phenomenon is a-luminal , opening the door, without overcoming light speed, to a conceivable time-machine.
Closed timelike curves (CTCs) are non-intuitive theoretical solutions of general relativity field equations. The main paradox associated with the physical existence of CTCs, the so-called grandfather paradox, can be satisfactorily solved by a quantum model named Deutsch-CTC. An outstanding theoretical result that has been demonstrated in the Deutsch-CTC model is the computational equivalence of a classical and a quantum computer in the presence of a CTC. In this article, in order to explore the possible implications for the foundations of quantum mechanics of that equivalence, a fundamental particle is modelled as a classical-like system supplemented with an information space in which a randomizer and a classical Turing machine are stored. The particle could then generate quantum behavior in real time in case it was controlled by a classical algorithm coding the rules of quantum mechanics and, in addition, a logical circuit simulating a CTC was present on its information space. The conditions that, through the action of evolution under natural selection, might produce a population of such particles with both elements on their information spaces from initial sheer random behavior are analyzed.