Collapse dynamics and Hilbert-space stochastic processes

Spontaneous collapse models of state vector reduction represent a possible solution to the quantum measurement problem. In the present paper we focus our attention on the Ghirardi–Rimini–Weber (GRW) theory and the corresponding continuous localisation models in the form of a Brownian-driven motion in Hilbert space. We consider experimental setups in which a single photon hits a beam splitter and is subsequently detected by photon detector(s), generating a superposition of photon-detector quantum states. Through a numerical approach we study the dependence of collapse times on the physical features of the superposition generated, including also the effect of a finite reaction time of the measuring apparatus. We find that collapse dynamics is sensitive to the number of detectors and the physical properties of the photon-detector quantum states superposition.

A Non-Critical String (Liouville) Approach to Brain Microtubules: State Vector Reduction, Memory Coding and Capacity

Microtubule (MT) networks, subneural paracrystalline cytoskeletal structures, seem to play a fundamental role in the neurons. We cast here the complicated MT dynamics in the form of a (1+1)-dimensional noncritical string theory, thus enabling us to provide a consistent quantum treatment of MTs, including enviromental friction effects. We suggest, thus, that the MTs are the microsites, in the brain, for the emergence of stable, macroscopic quantum coherent states, identifiable with the preconscious states. Quantum space-time effects, as described by noncritical string theory, trigger then an organized collapse of the coherent states down to a specific or conscious state. The whole process we estimate to take [Formula: see text], in excellent agreement with a plethora of experimental/observational findings. The microscopic arrow of time, endemic in noncritical string theory, and apparent here in the self-collapse process, provides a satisfactory and simple resolution to the age-old problem of how the, central to our feelings of awareness, sensation of the progression of time is generated. In addition, the complete integrability of the stringy model for MT we advocate in this work proves sufficient in providing a satisfactory solution to memory coding and capacity. Such features might turn out to be important for a model of the brain as a quantum computer.

A MODEL OF MEASUREMENT AS EVOLUTION DRIVEN BY BOTH PREVIOUS AND SUBSEQUENT CAUSES

The notion of the coexistence in the quantum framework of causality forward and backward in time, is used to develop a generalizazion of the conventional description of unitary evolutions, based on the assumption that evolutions are driven only by previous causes. Such a generalization is capable of describing basic aspects of state vector reduction.

A local deterministic model of quantum spin measurement

The conventional view, that Einstein was wrong to believe that quantum physics is local and deterministic, is challenged. A parametrized model, ' Q ' for the state vector evolution of spin-1/2 particles during measurement is developed. Q draws on recent work on ‘riddled basins’ in dynamical systems theory, and is local, determin­istic, nonlinear and time asymmetric. Moreover, the evolution of the state vector to one of two chaotic attractors (taken to represent observed spin states) is effectively uncomputable. Motivation for considering this model arises from speculations about the (time asymmetric and uncomputable) nature of quantum gravity, and the (nonlinear) role of gravity in quantum state vector reduction. Although the evolution of Q s state vector cannot be determined by a numerical algorithm, the probability that initial states in some given region of phase space will evolve to one of these attractors, is itself computable. These probabilities can be made to correspond to observed quantum spin probabilities. In an ensemble sense, the evolution of the state vector to an attractor can be described by a diffusive random walk process, suggesting that deterministic dynamics may underlie recent attempts to model state vector evolution by stochastic equations. Bell’s theorem and a version of the Bell-Kochen-Specker quantum entanglement paradox, as illustrated by Penrose’s ‘magic dodecahedra’, are discussed using Q as a model of quantum spin measurement. It is shown that in both cases, proving an inconsistency with locality demands the existence of definite truth values to certain counterfactual propositions. In Q these deterministic propositions are uncomputable, and no non-algorithmic mathematical solution is either known or suspected. Adapt­ing the mathematical formalist approach, the non-existence of definite truth values to such counterfactual propositions is posited. No inconsistency with experiment is found. As a result, it is claimed that Q is not constrained by Bell’s inequality, locality and determinism notwithstanding.