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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum measurement: a bridge to classical physics

Gérard G. Emch

Published Aug 5, 2003• 1 citation
Publisher

Abstract

In light of the lessons learned in the last 35 years from the quantum statistical mechanics description of phase transitions, I argue that the dichotomy in the evolution of quantum systems proposed by von Neumann, and pursued by Wigner in spite of the Einstein--Bohr criticisms on the attendent lack of resolution in terms of classical reality, fails to take into account the middle term suggested by the existence of superselection rules, Wigner's own discovery (with Wightmann and Wick). I claim that the part of the measurement problem concerned with the stable transfer of microscopic information to macroscopic physics can be treated entirely within the framework of a deterministic, conservative evolution of the joint system, i.e. without requiring the type of evolution von Neumann proposed besides that governed by the Schroedinger equation. I sustain this claim with the use of an exactly solvable model akin to the x-y model of statistical mechanics and involving its thermodynamical limit.

DOI
10.1117/12.488674

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In light of the lessons learned in the last 35 years from the quantum statistical mechanics description of phase transitions, I argue that the dichotomy in the evolution of quantum systems proposed by von Neumann, and pursued by Wigner in spite of the Einstein--Bohr criticisms on the attendent lack of resolution in terms of classical reality, fails to take into account the middle term suggested by the existence of superselection rules, Wigner's own discovery (with Wightmann and Wick). I claim that the part of the measurement problem concerned with the stable transfer of microscopic information to macroscopic physics can be treated entirely within the framework of a deterministic, conservative evolution of the joint system, i.e. without requiring the type of evolution von Neumann proposed besides that governed by the Schroedinger equation. I sustain this claim with the use of an exactly solvable model akin to the x-y model of statistical mechanics and involving its thermodynamical limit.
A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place for quantum phenomenology such as events. The development of quantum measurement theory, initiated by von Neumann, and Bell's conceptual critics of hidden variable theories indicated a possibility for resolution of this crisis. This can be done by divorcing the algebra of the dynamical generators and an extended algebra of the potential (quantum) and the actual (classical) observables. The latter, called beables, form the center of the algebra of all observables, as the only visible (macroscopic) observables must be compatible with any hidden (microscopic) observable. It is shown that within this approach quantum causality can be rehabilitated within an extended quantum mechanics (eventum mechanics) in the form of a superselection rule for compatibility of the consistent histories with the statistically predictable future. The application of this rule in the form of the nondemolition principle leads to the statistical inference of the von Neumann projection postulate, and also to the more general quantum information dynamics for instantaneous events, spontaneous localizations (i.e. quantum jumps), and state diffusions (i.e. continuous trajectories). This gives a dynamical solution, in the form of a Dirac boundary value problem and reduced filtering equations, of the notorious decoherence and measurement problems which was tackled unsuccessfully by many famous mathematicians and physicists starting with von Neumann, Schroedinger and Bohr.
We present a complete, mathematically rigorous, and observer-free resolution of the quantum measurement problem. Building entirely on the axiomatic framework established in the preceding work, which derives the Born rule exclusively from unitary dynamics, uniqueness of classical records, unitary invariance, and ergodic stability, we show that the entire measurement process is governed by a single deterministic law: unitary evolution. The apparent wavefunction collapse is not a physical process but an effective description of the emergence of a unique dynamically stable classical record under decoherence and unique ergodicity. No auxiliary postulates, collapse mechanisms, or observer-dependent inputs are required. We explain the origin of definite measurement outcomes, the emergence of objective probability, the elimination of quantum-classical duality, and provide a fully consistent resolution of the Wigner’s friend paradox. The framework reproduces all experimental predictions of quantum mechanics without contradictions and establishes a unified, self-contained foundation for quantum measurement theory. This work constitutes the first complete, minimal, and mathematically closed solution to the quantum measurement problem.
We implement Feynman's suggestion that the only missing notion needed for the puzzle of Quantum Measurement is the statistical mechanics of amplifying apparatus. We define a thermodynamic limit of quantum amplifiers which is a classically describable system in the sense of Bohr, and define macroscopic pointer variables for the limit system. Then we derive the probabilities of Quantum Measurement from the deterministic Schroedinger equation by the usual techniques of Classical Statistical Mechanics.
This paper presents the measurement problem from the point of view of the thermal interpretation of quantum physics introduced in Part II. The measurement of a Hermitian quantity AAA is regarded as giving an uncertain value approximating the q-expectation ⟨A⟩\langle A\rangle⟨A⟩ rather than (as tradition wanted to have it) as an exact revelation of an eigenvalue of AAA. Single observations of microscopic systems are (except under special circumstances) very uncertain measurements only. The thermal interpretation * treats detection events as a statistical measurement of particle beam intensity. * claims that the particle concept is only asymptotically valid, under conditions where particles are essentially free. * claims that the unmodeled environment influences the results enough to cause all randomness in quantum physics. * allows one to derive Born's rule for scattering and in the limit of ideal measurements; but in general, only part of Born's rule holds exactly: Whenever a quantity A with zero uncertainty is measured exactly, its value is an eigenvalue of A. * has no explicit collapse -- the latter emerges approximately in non-isolated subsystems. * gives a valid interpretation of systems modeled by a quantum-classical dynamics. * explains the peculiar features of the Copenhagen interpretation (lacking realism between measurements) and the minimal statistical interpretation (lacking realism for the single case) where these interpretations apply -- in the microscopic domain. The thermal interpretation is an interpretation of quantum physics that is in principle refutable by theoretical arguments leading to a negative answer to a number of open issues collected at the end of the paper, since there is plenty of experimental evidence for each of the points mentioned there.
In the mid-19th century, both the laws of mechanics and thermodynamics were known, and both appeared fundamental. This was changed by Boltzmann and Gibbs, who showed that thermodynamics can be *derived*, by applying mechanics to very large systems, and making simple statistical assumptions about their behavior. Similarly, when Quantum Mechanics (QM) was first discovered, it appeared to require two sets of postulates: one about the deterministic evolution of wavefunctions, and another about the probabilistic measurement process. Here again, the latter is derivable from the former: by applying unitary evolution to large systems (apparatuses, observers and environment), and making simple assumptions about their behavior, one can derive all the features of quantum measurement. We set out to demonstrate this claim, using a simple and explicit model of a quantum experiment, which we hope will be clear and compelling to the average physicist.