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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Disentanglement of quantum wave functions: Answer to ‘‘Comment on ‘Unified dynamics for microscopic and macroscopic systems’ ’’

G. C. Ghirardi, A. Rimini, T. Weber

Published Nov 15, 1987• 98 citations
Publisher

Abstract

It is shown that the assumption of a stochastic localization process for the quantum wave function is essentially different from the suppression of coherence over macroscopic distances arising from the interaction with the environment and allows for a conceptually complete derivation of the classical behavior of macroscopic bodies.
DOI
10.1103/physrevd.36.3287

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An explicit model allowing a unified description of microscopic and macroscopic systems is exhibited. First, a modified quantum dynamics for the description of macroscopic objects is constructed and it is shown that it forbids the occurrence of linear superpositions of states localized in far-away spatial regions and induces an evolution agreeing with classical mechanics. This dynamics also allows a description of the evolution in terms of trajectories. To set up a unified description of all physical phenomena, a modification of the dynamics, with respect to the standard Hamiltonian one, is then postulated also for microscopic systems. It is shown that one can consistently deduce from it the previously considered dynamics for the center of mass of macroscopic systems. Choosing in an appropriate way the parameters of the so-obtained model one can show that both the standard quantum theory for microscopic objects and the classical behavior for macroscopic objects can all be derived in a consistent way. In the case of a macroscopic system one can obtain, by means of appropriate approximations, a description of the evolution in terms of a phase-space density distribution obeying a Fokker-Planck diffusion equation. The model also provides the basis for a conceptually appealing description of quantum measurement.
One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.
I argue that conventional estimates of the criterion for classical behavior of a macroscopic body are incorrect in most circumstances,because they do not take into account the locality of interactions, which characterizes the behavior of all systems described approximately by local quantum field theory. The deviations from classical behavior of a macroscopic body, except for those that can be described as classical uncertainties in the initial values of macroscopic variables,are {\it exponentially} small as a function of the volume of the macro-system in microscopic units. Conventional estimates are correct only when the internal degrees of freedom of the macrosystem are in their ground state, and the classical motion of collective coordinates is adiabatic. Otherwise, the system acts as its own environment and washes out quantum phase correlations between different classical states of its collective coordinates. I suggest that it is likely that we can only achieve meso-scopic superpositions, for systems which have topological variables, and for which we can couple to those variables without exciting phonons.
We discuss and clarify the concept of dephasing in the many-Hilbert-space approach to the quantum measurement problem. We argue that the phase randomization provoked by a detecting macroscopic device is responsible for the loss of quantum coherence, and that the ``collapse of the wave function'' is to be regarded as a statistical process for the accumulated distribution over many events. In stressing the fundamental differences between our approach and the Copenhagen interpretation, we counter the objections put forward by Johnston [preceding Comment, Phys. Rev. A 48, 2497 (1993)], whose standpoint is essentially similar to the Copenhagen one.
A brief review is given of the present state of an approach to consistency between basic quantum mechanics and a unique macroscopic reality, with no assumption of branching in the state of the universe. The main new idea consists in the recognition of local properties in the growth and transport of entanglement between a macroscopic measuring quantum system and a microscopic measured one. Moving waves of entanglement from the environment arise then and carry external phases, affecting significantly the state of the measuring device. These "predecoherence" waves perturb randomly the growth of other waves, which carry entanglement with the measured system. The outcome of these wave interactions could generate random fluctuations in the quantum probabilities of different measurement channels, which could lead in turn to a collapse mechanism satisfying Born's probability rule, according to earlier works by Nelson and Pearle. A necessary randomness in the environment remains however unexplained and some suggestions regarding algorithmic complexity of the wave functions in a large quantum system e are made along that direction.
I argue that conventional estimates of the criterion for classical behavior of a macroscopic body are incorrect, because they do not take into account the locality of interactions, which characterizes the behavior of all systems described approximately by local quantum field theory. Black holes are the only localized objects which do not have such a description. The deviations from classical behavior of a macroscopic body, except for those which can be described as classical uncertainties in the initial values of macroscopic variables,are {\it exponentially} small as a function of the volume of the macro-system in microscopic units.