An Approach to Measurement in Quantum Mechanics

Peter Renkel

The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it is desirable to build a bridge from CM to QM. This paper presents a generalization of CM to QM. It starts from the generalization of a point-like object and naturally arrives at the quantum state vector of quantum systems in the complex valued Hilbert space, its time evolution and quantum representation of a measurement apparatus of any size. Each time, when generalization is performed, there is a possibility to develop new theory giving up most simple generalizations. It is shown that a measurement apparatus is a special case of a general quantum object. An example of a measurement apparatus of an intermediate size is considered in the end.

Gordon Reece

Ken Krechmer

Abstract This paper is a response to the EPR paper titled: "Can quantum-mechanical description of physical reality be considered complete?", published in Physical Review in 1935. A quantum-mechanical (QM) measure function describes a distribution of local results, while each experimental measurement process produces one result as exact as allowed by a measuring apparatus calibrated to a non-local unit standard. Repeating experimental measurements produces a Gaussian distribution of measurement results. These QM and experimental measurement result distributions can be compared. To compare a QM measure function describing a distribution of eigenvectors to a distribution of repetitive experimental measurement results, it is necessary to determine, by calibration, the precision of the eigenvectors to the same standard as the experimental results, because each eigenvector evidences uncertainty relative to a standard. When the calibration process is recognized as formal as well as empirical, QM measure function and experimental measurement process results are unified.

Alexey N. Rubtsov

Alexey N. Rubtsov

Jürg Fröhlich, Alessandro Pizzo

This note starts with a recapitulation of what people call the ``Measurement Problem'' of Quantum Mechanics (QM). The dissipative nature of the quantum-mechanical time-evolution of averages of states over large ensembles of identical isolated systems consisting of matter interacting with the radiation field is discussed and shown to correspond to a stochastic time-evolution of states of individual systems. The importance of dissipation for the successful completion of measurements is highlighted. To conclude, a solution of the ``Measurement Problem'' is sketched in an idealized model of a double-slit experiment.