Michael B. Mensky

Reality in quantum mechanics, Extended Everett Concept, and consciousness

Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer’s consciousness into the quantum theory of measurements. Most naturally, this is achieved in the framework of Everett’s “many-world interpretation” of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains the classical character of the alternatives and unusual manifestations of consciousness arising “at the edge of consciousness” (i.e., in sleep or trance) when its access to “other alternative classical realities” (other Everett’s worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent, while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence the probabilities of alternatives (which is consistent in case of infinitely many Everett’s worlds), EEC explains free will, “probabilistic miracles” (observing low-probability events), and decreasing entropy in the sphere of life.

Optimal monitoring of position in nonlinear quantum systems

We discuss a model of repeated measurements of position in a quantum system which is monitored for a finite amount of time with a finite instrumental error. In this framework we recover the optimum monitoring of a harmonic oscillator proposed in the case of an instantaneous collapse of the wave function into an infinite-accuracy measurement result. We also establish numerically the existence of an optimal measurement strategy in the case of a nonlinear system. This optimal strategy is completely defined by the spectral properties of the nonlinear system.

Quantum Zeno effect in the decay onto an unstable level

Abstract Under certain assumptions it is shown that the decay of level 2 of a three-level system onto level 1 is slowed down because of the further decay of level 1 onto level 0. It is argued that this phenomenon may be interpreted as a consequence of the quantum Zeno effect. The reason why this may be possible is that the second decay (or accompanying photon radiation) may be considered as a sign of the transition 2→1 so that during the first transition the system is under continuous observation.

Finite resolution of time in continuous measurements: phenomenology and the model

Abstract The definition of the quantum corridor describing monitoring a quantum observable in the framework of the phenomenological restricted-path-integrals approach is generalized for the case of finite resolution of time. The resulting evolution of the continuously measured system cannot be presented by a differential equation. Monitoring position of a quantum particle is considered then with the help of a model taking into account finite resolution in measurement of time. The results based on the model are shown to coincide with those of the phenomenological approach.

Physical model for monitoring the position of a quantum particle

Abstract A simple model for continuously measuring the position of a quantum particle is considered and compared with the phenomenological path-integral approach. The model contains a net of quantum oscillators having a finite range of interaction with the particle. Tracing out the variables of the measuring oscillators, one obtains a density matrix for the particle undergoing the influence of the continuous measurement. This density matrix coincides with that obtained earlier with the help of the path-integral method.

Continuous quantum monitoring of position of nonlinear oscillators

Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to nonlinear oscillators with use of numerical computations to evaluate quantum limitations for monitoring position in such a class of systems.

HOW TO VISUALIZE A QUANTUM TRANSITION OF A SINGLE ATOM

Abstract The previously proposed visualization of Rabi oscillations of a single atom by a continuous fuzzy measurement of energy is specified for the case of a single transition between levels caused by a π-pulse of a driving field. An analysis in the framework of the restricted-path-integral approach (which reduces effectively to a Schrodinger equation with a complex Hamiltonian) shows that the measurement gives reliable information about the system evolution, but the probability of the transition becomes less than unity. In addition an experimental setup is proposed for continuously monitoring the state of an atom by observation of electrons scattered by it. It is shown how this setup realizes a continuous fuzzy measurement of the atom energy.

Measurability of electromagnetic field: model and path integral methods

Abstract The problem of the measurability of the electromagnetic field is investigated: (i) in the framework of the abstract restricted-path-integral method, and (ii) by explecitly accounting the action of the field onto the meter and its back reaction. The sense of the previously obtained results as well as of the classical results of Bohr and Rosenfeld is made clear. The restricted-path-integral method with integration over field configurations is shown to give an estimation on the measurability of the field by any device not deforming the measured field (in the process of measurement) more than by the measurement error. Such a method of measurement is necessary for the control of the field in electronic devices.

Group-theoretical structure of quantum continuous measurements

Abstract The group-theoretical structure of continuous measurements is investigated in the framework of the path-integral phenomenological theory of quantum continuous measurements. The “transversal” group transforming alternative measurement results (outputs) into each other and the “longitudinal” semigroup describing the evolution of a quantum system subject to continuous measurement are introduced as well as their unification in a single semigroup. The resulting group-theoretical scheme generalizes the scheme describing the evolution of a nonrelativistic particle in an external field.

Decoherence in continuous measurements: From models to phenomenology

Decoherence is the name for the complex of phenomena leading to appearance of classical features of quantum systems. In the present paper decoherence in continuous measurements is analyzed with the help of restricted path integrals (RPI) and (equivalently in simple cases) complex Hamiltonians. A continuous measurement results in a readout giving information in the classical form on the evolution of the measured quantum system. The quantum features of the system reveal themselves in the variation of possible measurement readouts. For example, the monitoring energy of a multi-level system may visualize a transition between levels as a process evolving in time but with an unavoidable quantum noise. Decoherence of a continuously measured system is completely determined by the measurement readout, i.e., by the information recorded in its environment. It is shown that the ideology of RPI makes the Feynman version of quantum mechanics closed, contrary to the conventional operator form of quantum mechanics which needs quantum theory of measurement as a necessary additional part.