Preparation and measurement: two independent sources of uncertainty in quantum mechanics

In the Copenhagen interpretation the Heisenberg uncertainty relation is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint measurement of incompatible observables. This interpretation has already been criticized by Ballentine a long time ago, and has recently been challenged in an experimental way. These criticisms can be substantiated by using the generalized formalism of positive operator-valued measures, from which a new inequality can be derived, precisely illustrating the Copenhagen concept of complementarity. The different roles of preparation and measurement in creating uncertainty in quantum mechanics are discussed.Comment: latex, 18 pages, 4 eps figure

Interpretations of quantum mechanics, and interpretations of violation of Bell's inequality

The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and empiricist interpretations of the mathematical formalism of quantum mechanics, iii) the distinction between measurement and preparation. It will be demonstrated that an interpretation of violation of Bell's inequality by quantum mechanics as evidence of non-locality of the quantum world is a consequence of a particular choice between these alternatives. Also a distinction must be drawn between two forms of realism, viz. a) realist interpretations of quantum mechanics, b) the possibility of hidden-variables (sub-quantum) theories.Comment: LATeX, 20 pages, 4 figures, to be published in Proceedings of the International Conference on Foundations of Probability and Physics, Vaxjo, 27 Nov. -1 Dec. 200

From Copenhagen to neo-Copenhagen interpretation

Positive and negative features of the Copenhagen interpretation are discussed. As positive features can be mentioned its pragmatism and its awareness of the crucial role of measurement. However, the main part of the contribution is devoted to the negative features, to wit, its pragmatism (once again), its confounding of preparation and measurement, its classical account of measurement, its completeness claims, the ambiguity of its notion of correspondence, its confused notion of complementarity. It is demonstrated how confusions and paradoxes stemming from the negative features of the Copenhagen interpretation can be dealt with in an amended interpretation, to be referred to as `neo-Copenhagen interpretation', in which the role of the measuring instrument is taken seriously by recognizing the quantum mechanical character of its interaction with the microscopic object. The ensuing necessity of extending the notion of a quantum mechanical observable from the Hermitian operator of the standard formalism to the positive operator-valued measure of a generalized formalism is demonstrated to yield a sound mathematical basis for a transition from the Copenhagen contextualistic-realist interpretation to the neo-Copenhagen empiricist one. Applications to the uncertainty relations and to the Bell inequalities are briefly discussed.Comment: To be published in the Proceedings of the Conference: Quantum Theory - 4, Reconsideration of Foundations, V\"axj\"o, June 11-16, 200

Physical modalities in musculoskeletal disorders: evidence-based?

Učinkovitost različitih fizikalnih modaliteta koji se primjenjuju u liječenju i rehabilitaciji mišićnokoštanih poremećaja je još uvijek dvojbena. Unatoč poznatim fiziološkim učincima kliničkih podataka o učinkovitosti mnogih tehnika koje se rabe u okviru elektroterapije nema ili su nedostatni. Zbog toga za specifične intervencije često ne možemo dati kliničke preporuke. Zbog tih razočaravajućih rezultata temeljenih na dokazima istraživanja iz područja elektroterapije belgijska vlada je odlučila ne nadoknađivati većinu terapija iz ovoga područja. Vrlo je malo intervencija za mišićnokoštane poremećaje s dobrim odnosnom rizika i dobrobiti za koje je dokazana jasna učinkovitost u randomiziranim kliničkim istraživanjima. Većina studija o niskofrekventnim, srednjefrekvennim i visokofrekventnim strujama pokazala je nedostatak kliničkih znanstvenih dokaza, što je u suprotnosti s njihovom čestom uporabom u cijeloj Europi. Primjena ovih terapija zahtijeva daljnju evaluaciju. Problem većine studija je nedostatak praktične uniformnosti. Dvostruko slijepe studije nisu uvijek moguće, a niti dijagnoza nije uvijek sasvim jasna. Stoga postoji potreba za objektivnijim kliničkim strategijama. Također treba relativizirati neke od rezultata, jer kada nema jasnih dokaza za specifično liječenje, to ne znači da ono ne djeluje.A variety of physical modalities are applied in the treatment and rehabilitation of musculoskeletal disorders, but the efficacy of these passive interventions is still controversial. Despite the well-known physiological effects, there are either no clinical data or there is insufficient clinical information on the effectiveness of many techniques used in electrotherapy. As a consequence, we are often unable to make clinical recommendation regarding specific interventions. Because of these often disappointing results based on evidence-based research in electrotherapy, the Belgian government has decided not to reimburse a large number of treatments in this sector. Interventions that have been demonstrated effective through clear evidence in randomised clinical trials and with a good risk-benefit ratio are rather limited as far as musculoskeletal disorders are concerned. Most studies on low-frequency, medium-frequency (including interferential current) and high-frequency currents show the lack of clinical scientific evidence, which is in contrast with the frequent use of electrotherapy all over Europe. The application of these therapies should be further evaluated. The problem in most studies is the lack of practical uniformity (parameters, frequency, duration, etc.). Double-blind studies are not always possible and the diagnosis is not always very clear. Therefore, there is a need for more objective clinical strategies. We should also relativise some of the results because when there is no clear evidence for a specific treatment, it does not mean that this therapy does not work

Von Neumann-Lueders projection, and its applicability to EPR experiments

Notwithstanding it is well known that von Neumann's projection postulate is inapplicable to most realistic measurement procedures, it keeps haunting the foundations of quantum mechanics. In particular its applicability to EPR experiments is often assumed. In the present contribution this problem is considered from the point of view of a quantum mechanical theory of measurement, allowing a treatment of projection in EPR experiments as a special case of conditional preparation. The conditions are spelled out under which the postulate may be applicable.Comment: 5 pages, 1 figur

Information in neutron interference experiments

Wigner measures are calculated for a number of neutron interference experiments that can be interpreted as joint nonideal measurements of path and interference. It is demonstrated that the Wigner measure need not be influenced by fluctuations, thus showing that fluctuations need not diminish the information content of the experiment. A measurement is proposed yielding complete information on the incoming neutron state.</p

On the relation between the Einstein-Podolsky-Rosen paradox and the problem of nonlocality in quantum mechanics

The EPR problem is studied both from an instrumentalistic and from a realistic point of view. Bohr's reply to the EPR paper is analyzed and demonstrated to be not completely representative of Bohr's general views on the possibility of defining properties of a microscopic object. A more faithful Bohrian answer would not have led Einstein to the conclusion that Bohr's completeness claim of quantum mechanics implies nonlocality. The projection postulate, already denounced in 1936 by Margenau as the source of the EPR paradox, is found to be also at the origin of the nonlocality conundrum. Its unobservability in EPR-like experiments is demonstrated, thus showing the redundancy of the idea of nonlocality in the instrumentalist interpretation of quantum mechanics. It is argued that also from a realist point of view there is no reason to assume nonlocality. The relevance of Bohm's quantum potential and of Bell's inequalities with respect to the (non)locality problem is discussed.</p

Preparation and Measurement:Two Independent Sources of Uncertainty in Quantum Mechanics

In the Copenhagen interpretation the Heisenberg inequality ΔQ ΔP ≥ h/2 is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint measurement of incompatible observables. This interpretation was criticized a long time ago and has recently been challenged in an experimental way. These criticisms can be substantiated by using the generalized formalism of positive operato-valued measures, from which an inequality, different from the Heisenberg inequality, can be derived, precisely illustrating the Copenhagen concept of complementarity. The different roles of preparation and measurement in creating uncertainly in quantum mechanics are discussed.</p