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arXiv:1205.3892

A survey on uncertainty relations and quantum measurements

Spiridon Dumitru

Published May 17, 2012• 3 citations

Abstract

This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is revealed to be grounded on six basic precepts. But one finds that all the respective precepts are discredited by insurmountable deficiencies. So, in regard to UR, the alluded philosophy discloses oneself to be an unjustified mythology. Then UR appear either as short-lived historical conventions or as simple and limited mathematical formulas, without any essential significance for physics. Such a finding reinforces the Dirac's prediction that UR "`in their present form will not survive in the physics of future"'. The noted facets of UR motivate reconsiderations of associated debates on QMS. Mainly one reveals that, properly, UR have not any essential connection with genuine descriptions of QMS. For such descriptions, it is necessary that, mathematically, the quantum observables to be considered as random variables. The measuring scenarios with a single sampling, such are wave function collapse or Schrodinger's cat thought experiment, are revealed as being useless exercises. We propose to describe QMS as transmission processes for stochastic data. Note that the above-announced revaluation of UR and QMS philosophy does not disturb in any way the practical framework of the usual quantum mechanics.

DOI: 10.48550/arxiv.1205.3892

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Discussions on uncertainty relations (UR) and quantum measurements (QMS) persisted until nowadays in publications about quantum mechanics (QM). They originate mainly from the conventional interpretation of UR (CIUR). In the most of the QM literarure, it is underestimated the fact that, over the years, a lot of deficiencies regarding CIUR were signaled. As a rule the alluded deficiencies were remarked disparately and discussed as punctual and non-essential questions. Here we approach an investigation of the mentioned deficiencies collected in a conclusive ensemble. Subsequently we expose a reconsideration of the major problems referring to UR and QMS. We reveal that all the basic presumption of CIUR are troubled by insurmountable deficiencies which require the indubitable failure of CIUR and its necessary abandonment. Therefore the UR must be deprived of their statute of crucial pieces for physics. So, the aboriginal versions of UR appear as being in postures of either (i) thought-experimental fictions or (ii) simple QM formulae and, any other versions of them, have no connection with the QMS. Then the QMS must be viewed as an additional subject comparatively with the usual questions of QM. For a theoretical description of QMS we propose an informationtransmission model, in which the quantum observables are considered as random variables. Our approach directs to natural solutions and simplifications for many problems regarding UR and QMS.

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This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is revealed to be grounded on six basic precepts. But one finds that all the respective precepts are discredited by insurmountable deficiencies. So, in regard to UR, the alluded philosophy discloses oneself to be an unjustified mythology. Then UR appear either as short-lived historical conventions or as simple and limited mathematical formulas, without any essential significance for physics. Such a finding reinforces the Dirac's prediction that UR "`in their present form will not survive in the physics of future"'. The noted facets of UR motivate reconsiderations of associated debates on QMS. Mainly one reveals that, properly, UR have not any essential connection with genuine descriptions of QMS. For such descriptions, it is necessary that, mathematically, the quantum observables to be considered as random variables. The measuring scenarios with a single sampling, such are wave function collapse or Schrodinger's cat thought experiment, are revealed as being useless exercises. We propose to describe QMS as transmission processes for stochastic data. Note that the above-announced revaluation of UR and QMS philosophy does not disturb in any way the practical framework of the usual quantum mechanics.

Discussions on uncertainty relations (UR) and quantum measurements (QMS) persisted until nowadays in publications about quantum mechanics (QM). They originate mainly from the conventional interpretation of UR (CIUR). In the most of the QM literarure, it is underestimated the fact that, over the years, a lot of deficiencies regarding CIUR were signaled. As a rule the alluded deficiencies were remarked disparately and discussed as punctual and non-essential questions. Here we approach an investigation of the mentioned deficiencies collected in a conclusive ensemble. Subsequently we expose a reconsideration of the major problems referring to UR and QMS. We reveal that all the basic presumption of CIUR are troubled by insurmountable deficiencies which require the indubitable failure of CIUR and its necessary abandonment. Therefore the UR must be deprived of their statute of crucial pieces for physics. So, the aboriginal versions of UR appear as being in postures of either (i) thought-experimental fictions or (ii) simple QM formulae and, any other versions of them, have no connection with the QMS. Then the QMS must be viewed as an additional subject comparatively with the usual questions of QM. For a theoretical description of QMS we propose an informationtransmission model, in which the quantum observables are considered as random variables. Our approach directs to natural solutions and simplifications for many problems regarding UR and QMS.

Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective shortcomings disclose veridic and unavoidable facts which require the abandonment of the mentioned interpretation. So the primitive uncertainty relations appear as being either thought fictions or fluctuations formulae. Subsequently we reveal that the conventional approaches of quantum measurements are grounded on incorrect premises. We propose a new approach in which : (i) the quantum observables are considered as generalized stochastic variables, (ii) the view is focused only on the pre-existent state of the measured system, without any interest for the collapse of the respective state, (iii) a measurement is described as an input-output transformation which modify the probability density and current but preserve the expressions of the operators. The measuring uncertainties are evaluated as changes in the probabilistic estimators of observables. Related to different observables we do not find reasons of principle neither for uncertainties-connections nor for measuring compatibility/incompatibility.

It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The new approach regards QMS as a statistical samplings (but not as simple detection acts) and their description as a distinct task, independent of actual procedures of quantum mechanics. A QMS is described by means of transformations of probability density and probability current, from intrinsic into recorded readings. The quantum observables appear as random variables, described by usual operators and valuable through probabilistic numerical parameters (mean values, correlations and standard deviations). The values of the respective parameters are not the same in the two mentioned readings. Then the measurement uncertainties (errors) are described by means of the changes in the alluded values. The new QMS approach is illustrated through an one-dimensional example.

The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new approach are set forth. The quantum measurements, regarded experimentally as statistical samplings, are described theoretically by means of linear integral transforms of quantum probability density and current, from intrinsic into recorded readings. Accordingly, the quantum observables appear as random variables, valuable, in both readings, through probabilistic numerical parameters (characteristics). The measurements uncertainties (errors) are described by means of the intrinsic-recorded changes for the alluded parameters or for the informational entropies. The present approach, together with other author's investigations, give a natural and unified reconsideration of primary problems of Heisenberg's relations and quantum measurements. The respective reconsideration can offer some nontrivial elements for an expected re-examination of some disputed subsequent questions regarding the foundations and interpretation of quantum mechanics.

The disputed question of uncertainty relations (UR) on a circle is regarded as a particular element of a more general problem which refers to the quantum description of angular observables

L_z

and

ϕ

. The improvised

L_z-ϕ

UR are found to be affected by unsourmontable shortcomings. Also in contradiction with a largely accepted belief it is proved that the usual procedures of quantum mechanics are accurately applicable for the

L_z-ϕ

pair. The applicability regards both the known circular motions and the less known non-circular rotational motions. The presented facts contribute as arguments to the following indubitable conclusions: (i) the traditional interpretation of UR must be denied as an incorrect doctrine, (ii) for a natural physical consideration of the the

L_z-ϕ

pair the results from the usual quantum mechanics are sufficient while the improvised

L_z-ϕ

UR must be rejected as senseless formulas and (iii) the descriptions of quantum measurements have to be done in a framework which is distinct and additional in respect with the usual quantum mechanics.