A Model for a Quantum-Mechanical Measurement

Anton Amann

Pier A. Mello, Lars M. Johansen, Moises Martinez-Mares +1 more

Many textbooks on Quantum Mechanics are not very precise as to the meaning of making a measurement: as a consequence, they frequently make assertions which are not based on a dynamical description of the measurement process. A model proposed by von Neumann allows a dynamical description of measurement in Quantum Mechanics, including the measuring instrument in the formalism.In this article we apply von Neumann’s model to illustrate the measurement of an observable by means of a measuring instrument and show how various results, which are sometimens postulated without a dynamical basis, actually emerge.We also investigate the more complex, intriguing and fundamental problem of two successive measurements in Quantum Mechanics, extending von Neumann’s model to two measuring instruments. We present a description which allows obtaining, in a unified way, various results that have been given in the literature.

Eugene Paul Wigner

Henry Margenau

Jiří Souček

In this study we introduce and describe in details the hybrid-epistemic model for quantum mechanics. The main differences with respect to the standard model are following: (1) the measurement process is considered as an internal process inside quantum mechanics, i.e. it does not make a part of axioms and (2) the process of the observation of the state of the individual measuring system is introduced into axioms. The intrinsic measurement process is described in two variants (simplified and generalized). Our model contains hybrid, epistemic and hybrid-epistemic systems. Each hybrid system contains a unique orthogonal base composed from homogeneous (i.e. ontic) states. We show that in our model the measurement problem is consistently solvable. Our model represents the rational compromise between the Bohr’s view (the ontic model) and the Einstein’s view (the epistemic model).

Agung Budiyono

We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system.