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Mechanism for Time Reparametrization Symmetry Breaking in Spinor Gravity Coupled to Long-Range Spinor Particles

Eiji Konishi

Published Jan 27, 2016• 0 citations
OpenAlex

Abstract

We propose a mechanism for time reparametrization symmetry breaking in canonical gravity. We consider a model of spinor gravity, based on Sen's reformulation of canonical gravity as a spin system, with one additional long-range self-interacting massive spinor particle that is coupled to spinor gravity. The symmetry breaking is identified with the origin of the quantum mechanical non-unitary evolution. A part of our approach to deriving non-unitary time-dependent processes of wave functions follows the Diosi-Penrose argument on gravity's role in quantum state reduction.

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We propose a mechanism for time reparametrization symmetry breaking in canonical gravity. We consider a model of spinor gravity, based on Sen's reformulation of canonical gravity as a spin system, with one additional long-range self-interacting massive spinor particle that is coupled to spinor gravity. The symmetry breaking is identified with the origin of the quantum mechanical non-unitary evolution. A part of our approach to deriving non-unitary time-dependent processes of wave functions follows the Diosi-Penrose argument on gravity's role in quantum state reduction.
We propose a mechanism for system-induced spontaneous time reparametrization symmetry breaking in canonical gravity. We consider a model of extended canonical gravity, based on Sen's spinorial expression of the spatial-diffeomorphism-gauge independent part of the shift vector, with one additional long-range self-interacting massive spin-1/21/21/2 particle whose spin is coupled to Sen's spinor in the Hamiltonian. This additional particle plays the role of creating the system-induced time reparametrization invariant potential. We use this potential to break time reparametrization symmetry spontaneously. We identify the symmetry breaking with the origin of the quantum energy measurement processes in the ensemble interpretation of quantum mechanics. Our theory uses a novel interpretation of quantum mechanics with respect to quantum mechanical position uncertainties of particles. The spatial-diffeomorphism-gauge independent part of the shift vector is attributed to this novel interpretation of quantum mechanics.
We propose a mechanism for system-induced spontaneous time reparametrization symmetry breaking in canonical gravity. We consider a model of extended canonical gravity, based on Sen's spinorial expression of the spatial-diffeomorphism-gauge independent part of the shift vector, with one additional long-range self-interacting massive spin-1/21/21/2 particle whose spin is coupled to Sen's spinor in the Hamiltonian. This additional particle plays the role of creating the system-induced time reparametrization invariant potential. We use this potential to break time reparametrization symmetry spontaneously. We identify the symmetry breaking with the origin of the quantum energy measurement processes in the ensemble interpretation of quantum mechanics. Our theory uses a novel interpretation of quantum mechanics with respect to quantum mechanical position uncertainties of particles. The spatial-diffeomorphism-gauge independent part of the shift vector is attributed to this novel interpretation of quantum mechanics.
Modern, state-of-the-art nanomechanical devices are capable of creating spatial superpositions that are massive enough to begin to experimentally access the quantum to classical crossover, and thus force us to consider the possible ways in which the usual quantum dynamics may be affected. One recent theoretical proposal describes the crossover from unitary quantum mechanics to classical dynamics as a form of spontaneous symmetry breaking. Here, we propose a specific experimental set-up capable of identifying the source of unitarity breaking in such a mechanism. The experiment is aimed specifically at clarifying the role played by gravity, and distinguishes the resulting dynamics from that suggested by alternative scenarios for the quantum to classical crossover. We give both a theoretical description of the expected dynamics, and a discussion of the involved experimental parameter values and the proposed experimental protocol.
A Lorentz invariant model for gravity-induced quantum state reduction is presented, which is mainly developed from Penrose's argument that the time translation operator in a superposition of macroscopic states is ill-defined. The problem to define a Lorentz invariant stochastic dynamics for the wave-function is solved by assuming that the stochastic time flow is running orthogonal to the deterministic, unitary time evolution inside the four-dimensional space-time, which makes the direction of causality independent from the chosen reference frame. This new view allows to accept Bell's position on the implication of quantum non-locality on relativity, without having to give up the Lorentz invariance of the specified dynamics. It is shown that it is possible to formulate on the basis of this new view a meaningful physical model. The model is also checked for possible higher order effects, which provide new starting points for experimental research.
A new approach to wavefunction collapse is prepared by an analysis of semiclassical gravity. The fact that, in semiclassical gravity, superposed states must share a common classical spacetime geometry, even if they prefer (according to general relativity) differently curved spacetimes, leads to energy increases of the states, when their mass distributions are different. If one interprets these energy increases divided by Planck's constant as decay rates of the states, one obtains the lifetimes of superpositions according to the Diosi-Penrose criterion and reduction probabilities according to Born's rule. The derivation of Born's rule for two-state superpositions can be adapted to the typical quantum mechanical experiments with the help of a common property of these experiments. It is that they lead to never more than two different mass distributions at one location referring e.g. to the cases that a particle "is", or "is not", detected at the location. From the characteristic energy of the Diosi-Penrose criterion, an action is constructed whose relativistic generalisation becomes obvious by a decomposition of the Einstein-Hilbert action to the superposed states. In Part 2, semiclassical gravity is enhanced to the so-called Dynamical Spacetime approach to wavefunction collapse, which leads to a physical mechanism for collapse.
We study the effects of self gravity on the quantum state of a massive and static particle that initially contains quantum coherence between two positions. We employ linearized quantum gravity to obtain the self-interacting dynamics of the particle mediated by gravitons, and find that the effective evolution of the particle's state can be viewed as a quantum channel composed of a unitary, dephasing, depolarizing, and erasure part. Depolarization drives the state towards maximal mixedness while depolarization and dephasing decrease its quantum coherence. Crucially, the intrinsic diffusion and dephasing timescales of the problem determine a relation between the mass and size of the particle that naturally identifies the transition between its classical and quantum regime. Our work therefore provides an explanation for the observational difference between the quantum behavior of small and light systems and the classical behavior of larger and heavier ones.