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NeuroQuantology

Quantum State Reduction by a Physical Interaction Between the States and its Perspective for Biology

Garrelt Quandt-Wiese

Published Mar 2, 2009• 2 citations
Publisher

Abstract

A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented, which bases only the idea that quantum state reduction has its origin in a physical interaction between the states. The model is explicitly worked out for the hypothesis of gravity-induced quantum state reduction. It agrees for typical quantum mechanical experiments with the projection postulate and predicts regimes in which other behaviour could be observed. For verification a feasible quantum-optical experiment is proposed. An outlook on the possible role of state reduction for biology is given by exemplarily discussing mutation effects of bacteria.

DOI
10.14704/nq.2009.7.2.231

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A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented, which bases only the idea that quantum state reduction has its origin in a physical interaction between the states. The model is explicitly worked out for the hypothesis of gravity-induced quantum state reduction. It agrees for typical quantum mechanical experiments with the projection postulate and predicts regimes in which other behaviour could be observed. For verification a feasible quantum-optical experiment is proposed. An outlook on the possible role of state reduction for biology is given by exemplarily discussing mutation effects of bacteria.
A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented. The approach bases only the idea that quantum state reduction has its origin in a mutual physical interaction between the states. The model is explicitly worked out for the gravitational reduction hypothesis of Diosi and Penrose. It agrees for typical quantum mechanical experiments with the projection postulate and predicts regimes in which other behavior could be observed. An outlook is given, how the new effects can possibly become of interest for biology. For verification a feasible quantum optical experiment is proposed. The approach is analyzed from the view point of quantum non-locality in concrete its consequences for signalling.
This article focuses on the approach to biology in terms of quantum mechanics. Quantum biology is a hypothesis that allows experimental verification, and pretends to be a further refinement of the known gene-centric model. The state of the species is represented as the state vector in the Hilbert space, so that the evolution of this vector is described by means of quantum mechanics. Experimental verification of this hypothesis is based on the accuracy of quantum theory and the ability to quickly gather statistics when working with populations of bacteria. The positive result of such experiment would allow to apply to the living computational methods of quantum theory, which has not yet go beyond the particular ''quantum effects''.
We analyze Penrose's ideas concerning the role of gravity in the quantum-mechanical state reduction from the perspective of analogue-gravity models. We first review a line of work which argues that it is not enough to find a satisfactory quantization scheme for gravity in the description of a matter-gravity system. Instead of that; the standard rules of quantum mechanics as they are actually applied to matter systems need to be modified when the gravitational interaction is relevant. Among these ideas we focus on Penrose's argument for the absence of macroscopic quantum superpositions. He argues that such phenomenon has its roots in the idiosyncratic aspects of gravity, which become relevant just when the system is macroscopic and hence able to generate a sufficiently strong gravitational field, and not in the environmental decoherence. We then present an analogue model consisting of a Bose-Einstein condensate in a double well potential, where it is possible to build states that would correspond to putative superpositions of spacetimes. Such configurations are unstable and the source of instability from a microscopic point of view can be related to the abscence of a well-defined causal structure in the effective geometric description. We also discuss some additional lessons that can be taken from these instabilities.
It is well known, that the causal Schrödinger evolution of a quantum state is not compatible with the reduction postulate, even when decoherence is taken into account. The violation of the causal evolution, introduced by the standard reduction postulate distinguishes certain systems (as the measurement devices), whose states are very close to statistical mixtures (as the ones resulting from the process of decoherence). In these systems, this violation has not any observable effect. In arbitrary quantum systems, the transition from the initial density matrix to a diagonal matrix predicted by the standard reduction postulate, would lead to a complete breakdown of the Schrödinger evolution, and consequently would destroy all the predictive power of quantum mechanics. What we show here, is that there is a modified version of the postulate that allows to treat all the quantum mechanical systems on equal footing. The standard reduction postulate may be considered as a good approximation, useful for practical purposes, of this modified version which is consistent with the Schrödinger evolution and via decoherence with the experimental results. Within this approach, the physical role played by the reduction postulate is as a tool for the computation of relative probabilities and consequently for the determination of the probabilities of consistent histories.
Inspired by an ontic view of the wavefunction in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates. We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states. Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.
Abstract Inspired by an ontic view of the wave function in quantum mechanics and motivated by the universal interaction of gravity, we discuss a possible gravity implication in the state collapse mechanism. Concretely, we investigate the stability of the spatial superposition of a massive quantum state under the gravity effect. In this context, we argue that the stability of the spatially superposed state , depends on its gravitational self-energy originating from the effective mass density distribution through the spatially localized eigenstates . We reveal that the gravitational self-interaction between the different spacetime curvatures created by the eigenstate effective masses leads to the reduction of the superposed state to one of the possible localized states . Among others, we discuss such a gravity-driven state reduction. Then, we approach the corresponding collapse time and the induced effective electric current in the case of a charged state, as well as the possible detection aspects.