The measurement of one or more observables can be considered to yield sample points which are in general fuzzy sets. Operationally these fuzzy sample points are the outcomes of calibration procedures undertaken to ensure the internal consistency of a scheme of measurement. By introducing generalized probability measures on σ-semifields of fuzzy events, one can view a quantum mechanical state as an ensemble of probability measures which specify the likelihood of occurrence of any specific fuzzy sample point at (...) some instant. These sample points are the possible outcomes of any infinitely rapid succession of measurements at that instant of any sequence of observables of the system. (shrink)

This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description (classical in the limited sense implied by the correspondence principle of Bohr) of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from (...) the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics. (shrink)

This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the (...) known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics. (shrink)

In this paper, we discuss the importance of measurement in quantum mechanics and the so-called measurement problem. Any quantum system can be described as a linear combination of eigenstates of an operator representing a physical quantity; this means that the system can be in a superposition of states that corresponds to different eigenvalues, i.e., different physical outcomes, each one incompatible with the others. The measurement process converts a state of superposition in a well-defined state. We (...) show that, if we describe the measurement by the standard laws of quantum mechanics, the system would preserve its state of superposition even on a macroscopic scale. Since this is not the case, we assume that a measurement does not obey to standard quantum mechanics, but to a new set of laws that form a “quantum measurement theory”. (shrink)

This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the (...) known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics. (shrink)

Determinism is established in quantum mechanics by tracing the probabilities in the Born rules back to the absolute (overall) phase constants of the wave functions and recognizing these phase constants as pseudorandom numbers. The reduction process (collapse) is independent of measurement. It occurs when two wavepackets overlap in ordinary space and satisfy a certain criterion, which depends on the phase constants of both wavepackets. Reduction means contraction of the wavepackets to the place of overlap. The measurement apparatus (...) fans out the incoming wavepacket into spatially separated eigenpackets of the chosen observable. When one of these eigenpackets together with a wavepacket located in the apparatus satisfy the criterion, the reduction associates the place of contraction with an eigenvalue of the observable. The theory is nonlocal and contextual. Keywords:. (shrink)

It is the purpose of this note to comment on some important problems which have been already vividly discussed by several authors. Besides the well known former discussions of Schrödinger and J. v. Neumann I should like to mention here especially H. Margenau's article, “Critical Points in Modern Physical Theory,” which strongly influenced my present discussion.

In the standard mathematical formulation of quantum mechanics, measurement is an additional, exceptional fundamental process rather than an often complex, but ordinary process which happens also to serve a particular epistemic function: during a measurement of one of its properties which is not already determined by a preceding measurement, a measured system, even if closed, is taken to change its state discontinuously rather than continuously as is usual. Many, including Bell, have been concerned about the fundamental (...) role thus given to measurement in the foundation of the theory. Others, including the early Bohr and Schwinger, have suggested that quantum mechanics naturally incorporates the unavoidable uncontrollable disturbance of physical state that accompanies any local measurement without the need for an exceptional fundamental process or a special measurement theory. Disturbance is unanalyzable for Bohr, but for Schwinger it is due to physical interactions’ being borne by fundamental particles having discrete properties and behavior which is beyond physical control. Here, Schwinger’s approach is distinguished from more well known treatments of measurement, with the conclusion that, unlike most, it does not suffer under Bell’s critique of quantum measurement. Finally, Schwinger’s critique of measurement theory is explicated as a call for a deeper investigation of measurement processes that requires the use of a theory of quantum fields. (shrink)

I have written extensively of the topic of this tutorial. But in order to reach a broad audience I have in many of my more recent works refrained from using equations. That approach makes those works accessible in principle both to readers who are repelled by equations, and also to quantum physicists who are sufficiently familiar with the details of the quantum theory of measurement to be able to fill in for themselves the omitted equations. However, that (...) approach means also that an important class of potential readers is not being optimally reached. This class consists of persons having an engineering or mathematical background, and possessing perhaps even some familiarity with classical physics, but who have little knowledge of quantum mechanics. (shrink)

It is argued that the measurement problem reduces to the problem of modeling quasi-classical systems in a modified quantum mechanics with superselection rules. A measurement theorem is proved, demonstrating, on the basis of a principle for selecting the quantities of a system that are determinate (i.e., have values) in a given state, that after a suitable interaction between a systemS and a quasi-classical systemM, essentially only the quantity measured in the interaction and the indicator quantity ofM are (...) determinate. The theorem justifies interpreting the noncommutative algebra of observables of a quantum mechanical system as an algebra of “beables,” in Bell's sense. (shrink)

We examine, in the context of the Einstein-Podolsky-Rosen-Bohm gedankenexperiment, problems associated with state reduction and with nonlocal influences according to different interpretations of quantum mechanics, when attempts are made to apply these interpretations in the relativistic domain. We begin by considering the significance of retrodiction within four different interpretations of quantum mechanics, and show that three of these interpretations, if applied in a relativistic context, can lead to ambiguities in their description of a process. We consider ways of (...) dealing with these ambiguities, in particular focussing on the “preferred frame” hypothesis. We then re-examine an argument involving nonlocal measurements which claimed that the preferred frame hypothesis is not tenable, and show that this argument does not in fact necessitate a rejection of the preferred frame. We then suggest that, to avoid confusion, the preferred frame could be extended to cover unitary interactions as well as state reductions. We conclude with a brief examination of a proposal that state reduction should take effect across the backward light cone of a measurement event. (shrink)

A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer's information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with (...) the projection postulate being a noncommutative generalization of conditional probability. This view clarifies many problems surrounding the interpretation of quantum mechanics, particularly problems relating to the measuring process. (shrink)

A quantum mechanical model of a counter monitoring the decay of an unstable microsystem is constructed. Detailed investigation of the time evolution of this model shows that the counter behaves essentially classically; i.e., its discharges may be considered as objective, observer-independent events. The possible relevance of this result for the physical interpretation of quantum mechanics is discussed.

We investigate the problem of “wave packet reduction” in quantum mechanics by solving the Schrödinger equation for a system composed of a model measuring apparatusM interacting with a microscopic objects. The “instrument” is intended to be somewhat more realistic than others previously proposed, but at the same time still simple enough to lead to an explicit solution for the time-dependent density matrix. It turns out that,practically, everything happens as if the wave packet reduction had occurred. This is a consequence (...) of the fact that the apparatus is made up of a very large number of microsystems interacting withs. More precisely, our model shows that the “macroscopic size” of a measuring apparatus can lead by itself to a density matrix for the systemM + s which is physically equivalent to the density matrix of a statistical mixture corresponding to the reduced wave packet. (shrink)

We review the notion of complementarity of observables in quantum mechanics, as formulated and studied by Paul Busch and his colleagues over the years. In addition, we provide further clarification on the operational meaning of the concept, and present several characterisations of complementarity—some of which new—in a unified manner, as a consequence of a basic factorisation lemma for quantum effects. We work out several applications, including the canonical cases of position–momentum, position–energy, number–phase, as well as periodic observables relevant (...) to spatial interferometry. We close the paper with some considerations of complementarity in a noisy setting, focusing especially on the case of convolutions of position and momentum, which was a recurring topic in Paul’s work on operational formulation of quantum measurements and central to his philosophy of unsharp reality. (shrink)

It is well known that successive observations of the instantaneous state of a decaying system lead to a modified decay law. In the limit of infinitely frequent observations, the modified lifetime becomes infinite (“Zeno's paradox”). We study here the behavior of decaying systems under continuous rather than successive observations. Such continuous observation is achieved by a permanent coupling of the decaying system to a counter, which is sufficiently sensitive to the presence of the decay products. For two explicitly soluble models (...) we obtain a result very similar to Zeno's paradox: The observation again strongly modifies the decay law, and prevents the decay completely in the limit of a perfect (i.e., infinitely sensitive) counter. Like Zeno's paradox, however, this “watchdog effect” is not very likely to be detected in actual experiments, e.g., with radioactive nuclei. (shrink)

The semantics underlying the propositional structure of Hilbert space quantum mechanics involves an inherent ambiguity concerning the impossibility of assigning definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. Although the preceding Kochen-Specker result forbids a global, absolute assignment of truth values to quantum mechanical propositions, it does not exclude ones that are contextual. In this respect, the Bub-Clifton “uniqueness theorem” is utilized for arguing that truth-value definiteness is consistently restored (...) with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a suitable “preferred” observable. It is suggested that the most natural choice of the latter, especially for confronting the problem of truth valuation in quantum mechanics, results in the determinateness of the observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The resulting account of truth is compatible with a realist conception of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. (shrink)

We attempt to clarify the main conceptual issues in approaches to ‘objectification’ or ‘measurement’ in quantum mechanics which are based on superselection rules. Such approaches venture to derive the emergence of classical ‘reality’ relative to a class of observers; those believing that the classical world exists intrinsically and absolutely are advised against reading this paper. The prototype approach (K. Hepp, Helv. Phys. Acta45 (1972), 237–248) where superselection sectors are assumed in the state space of the apparatus is shown (...) to be untenable. Instead, one should couple system and apparatus to an environment, and postulate superselection rules for the latter. These are motivated by the locality of any observer or other (actual or virtual) monitoring system. In this way ‘environmental’ solutions to the measurement problem (H.D. Zeh, Found. Phys.1 (1970), 69–76; W. H. Zurek, Phys. Rev.D26 (1982), 1862–1880 and Progr. Theor. Phys.89 (1993), 281–312) become consistent and acceptable, too. Points of contact with the modal interpretation are briefly discussed. We propose a minimal value attribution to observables in theories with superselection rules, in which only central observables have properties. In particular, the eigenvector-eigenvalue link is dropped. This is mainly motivated by Ockham's razor. (shrink)

The problem of simultaneous measurement of incompatible observables in quantum mechanics is studied on the one hand from the viewpoint of an axiomatic treatment of quantum mechanics and on the other hand starting from a theory of measurement. It is argued that it is precisely such a theory of measurement that should provide a meaning to the axiomatically introduced concepts, especially to the concept of observable. Defining an observable as a class of measurement procedures (...) yielding a certain prescribed result for the probability distribution of the set of values of some quantity (to be described by the set of eigenvalues of some Hermitian operator), this notion is extended to joint probability distributions of incompatible observables. It is shown that such an extension is possible on the basis of a theory of measurement, under the proviso that in simultaneously measuring such observables there is a disturbance of the measurement results of the one observable, caused by the presence of the measuring instrument of the other observable. This has as a consequence that the joint probability distribution cannot obey the marginal distribution laws usually imposed. This result is of great importance in exposing quantum mechanics as an axiomatized theory, since overlooking it seems to prohibit an axiomatic description of simultaneous measurement of incompatible observables by quantum mechanics. (shrink)

We study the conservation of energy, or lack thereof, when measurements are performed in quantum mechanics. The expectation value of the Hamiltonian of a system changes when wave functions collapse in accordance with the standard textbook treatment of quantum measurement, but one might imagine that the change in energy is compensated by the measuring apparatus or environment. We show that this is not true; the change in the energy of a state after measurement can be arbitrarily (...) large, independent of the physical measurement process. In Everettian quantum theory, while the expectation value of the Hamiltonian is conserved for the wave function of the universe, it is not constant within individual worlds. It should therefore be possible to experimentally measure violations of conservation of energy, and we suggest an experimental protocol for doing so. (shrink)

The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case (...) of “unitary” qubits. The converse interpretation of any qubits as referring to a certain physical quantity implies its generalization to non-Hermitian operators, thus neither unitary, nor conserving energy. Their physical sense, speaking loosely, consists in exchanging temporal moments therefore being implemented out of the space-time “screen”. “Dark matter” and “dark energy” can be explained by the same generalization of “quantity” to non-Hermitian operators only secondarily projected on the pseudo-Riemannian space-time “screen” of general relativity according to Einstein's “Mach’s principle” and his field equation. (shrink)

The “observer” in physics has always referred to someone who stands on the outside of a system looking in. In this paper an “inside observer” is defined, and an experiment is proposed that tests a given formulation of the problem of measurement in quantum mechanics.

It is shown that there exist observablesA and Borel setsE such that the procedure “measureA and give as output the number 1 (0) if theA measurement outcome is (is not) inE” does not correspond to a measurement of the proposition observable ℰA(E) usually assigned to such procedures. This result is discussed in terms of limitations on choice powers of observers.

Position probabilities play a privileged role in the interpretation of quantum mechanics. The standard interpretation has it that |Ψ | 2 represents the probability that the system is at the location r. Use of these probabilities, however, creates tremendous conceptual difficulties. It forces us either to adopt a non-standard logic, or to be saddled with an intractable measurement problem. This paper proposes that we try to eliminate position probabilities, and instead to interpret quantum mechanics through the use (...) of energy transition probabilities. Energy transitions, unlike particle positions, either occur, or they do not. Their probabilities are unproblematic, and they do not require either a deviant logic or a nonclassical probability structure. They are thus good candidates to serve as the fundamental interpreted quantity of the quantum theory. (shrink)

The formal time symmetry of the quantum measurement process is extensively discussed. Then, the origin of the alleged association between a fixed temporal direction and quantum measurements is investigated. It is shown that some features of such an association might arise from epistemological rather than purely physical assumptions. In particular, it is brought out that a sequence of statements bearing on quantum measurements may display intrinsic asymmetric properties, irrespective of the location of corresponding measurements in time (...) t of the Schrodinger equation. The situation of an observer performing two measurements in two opposite directions of t is eventually investigated. Essential differences are found between two descriptions of this situation: the internal one (taking only into account what is recorded in the observer's memory) and the external one (whereby the observer is considered as a quantum system ruled by the Schrodinger equation). Finally, a method allowing several observers to establish a correspondence between their memory sizes is analyzed. The most important facts that usually lead to the associating of a preferential temporal direction with quantum measurements may be inferred from this correspondence. (shrink)

Of the many ways of getting at the core of the weirdnesses in quantum mechanics, there’s one which traces back to Schrödinger’s seminal 1935 paper, and has to do with the apparent fuzzy nature of the reality described by the formalism through the wavefunction $$\psi$$ ψ. This issue, which I will be calling the Determinacy Problem, is distinct from the standard measurement problem of quantum mechanics, despite Schrödinger himself ends up conflating the two. I will argue that (...) the Determinacy Problem is an exquisitely philosophical problem, for as it is standard when facing any phenomenon which appears to have indeterminate or fuzzy characteristics, the solutions available are to either blame the deficiencies of our language, or our lack of knowledge, or to blame the world itself. These three attitudes can already be found in the literature on quantum mechanics, either explicitly or implicitly, and they appear to motivate three very distinct research programs: high-dimensional realism, primitive ontology, and quantum indeterminacy. (shrink)

The philosophy of quantum mechanics has often been conceived by physicists as a collection of dogmas concerning what can be measured, observed and known. To this branch of dialectics the present paper does not attempt to contribute, chiefly because it is written from the conviction that no part of science, nor any philosophy, can safely predict what may be feasible or knowable. Rather, this brief essay endeavors to expose the epistemology of quantum physics in a way which allows (...) it to be recognized as an extension of the ordinary processes of cognition, as the continuation of a line which starts in sensory perception, leads straight through the methods of classical physics into quantum mechanics and shows no signs of terminating even there. (shrink)

Recent advantages in experimental quantum physics call for a careful reconsideration of the measurement process in quantum mechanics. In this paper we describe the structure of the ideal measurements and their status among the repeatable measurements. Then we provide an exhaustive account of the interrelations between repeatability and the apparently weaker notions of value reproducible or first- kind measurements. We demonstrate the close link between repeatable measurements and discrete observables and show how the ensuing measurement limitations (...) for continuous observables can be lifted in a way that is in full accordance with actual experimental practice. We present examples of almost repeatable measurements of continuous observables and some realistic models of weakly disturbing measurements. (shrink)

A striking characteristic of contemporary science is its emphasis upon probability. This is especially notable in quantum mechanics.There is a respect in which probability is the same for all scientific theories. Verifiability requires that any theory predict certain numbers which can be compared with the numbers gained by actual operations of measuring. In actual practice these numbers, which we shall term theoretical measurables and operative measurables respectively, never correspond. It becomes necessary, therefore, for the scientist to specify when the (...) deviation between them is such that verification occurs. These specifications are defined by the theory of errors in which the concept of probability has an essential place and a specific meaning. But the theory of errors is the same for all applications; hence, probability as defined by the theory of errors is the same for all scientific theories. (shrink)

State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under which it is performed. Each context provides a viewpoint of the quantum system being measured. This gives only a partial picture of the system which may be distorted and in order to obtain a total accurate picture, various contexts need (...) to be employed. We first discuss some basic definitions and results concerning quantum channels. We briefly describe the relationship between this work and ontological models that form the basis for contextuality studies. We then consider properties of channels and contexts. For example, we show that the set of sharp channels can be given a natural partial order in which contexts are the smallest elements. We also study properties of channel maps. The last section considers mutually unbiased contexts. These are related to mutually unbiased bases which have a large current literature. Finally, we connect them to completely random channel maps. (shrink)

Decoherence results from the dissipative interaction between a quantum system and its environment. As the system and environment become entangled, the reduced density operator describing the system "decoheres" into a mixture (with the interference terms damped out). This formal result prompts some to exclaim that the measurement problem is solved. I will scrutinize this claim by examining how modal and relative-state interpretations can use decoherence. Although decoherence cannot rescue these interpretations from general metaphysical difficulties, decoherence may help these (...) interpretations to pick out a preferred basis. I will explore whether decoherence solves nagging technical problems associated with selecting a preferred basis. (shrink)

SummaryThe following two questions are examined: 1o Do the unobservable parameters possess precise, though unknown, values ? 2o If these unobservable values were known, would it be possible to make precise predictions of the reults of later measurements ?The answer is shown to be negative; the questions, therefore, are not meaningless, being capable of a falsification. The inquiry leads to the establishment of a principle of anomaly, more precisely speaking, of causal anomaly, which is to be added to Heisenberg's principle (...) of indeterminacy. This principle states that the principle of action by contact is violated whenever definite values are assigned to the unobserved quantities, i. e., when an exhaustive interpretation of quantum mechanics is used. The two most important exhaustive interpretations are given by the corpuscle and the wave interpretation; each leads to causal anomalies, though for different places.The causal anomalies can be eliminated by the use of a restrictive interpretation, which separates statements about unobserved quantities, as a third propositional class, from true or false statements. Bohr and Heisenberg have called such statements meaningless, without being able to eliminate them completely; these statements arte thus merely shifted into the metalanguage. In another version of the restrictive interpretation such statements are assigned a third truth value, the value indeterminate, and quantum mechanics is then presented in the form of a three‐valued logic.The inquiry is carried through without the presupposition of any philosophical conception; every interpretation is examined with respect to the consequences to which it leads. ‐ H. R.'. (shrink)

Metaphysical underdetermination arises when we are not able to decide, through purely theoretical criteria, between competing interpretations of scientific theories with different metaphysical commitments. This is the case in which non-relativistic quantum mechanics (QM) finds itself in. Among several available interpretations, there is the one that states that the interaction with the conscious mind of a human observer causes a change in the dynamics of quantum objects undergoing from indefinite to definite states. In this paper, we argue that (...) there seems to be also a metaphysical underdetermination concerning London and Bauer’s theory of measurement between two methods of phenomenological reduction: the eidetic and the transcendental approaches. Recently, Steven French argued that both methods can be combined in order to interpret London and Bauer’s formalism. However, in this paper we argue that the eidetic one is the only viable phenomenological way to interpret this particular theory of measurement in QM based on the formalism presented by London and Bauer, hence breaking this phenomenological underdetermination. (shrink)

It is explained why quantum mechanics applies principally to single systems and not to ensembles. A thorough analysis of thought-experiments shows clearly that irreversibility is connected with the storing of information rather than with the act of measurement. In order to avoid paradoxes one has to admit that the wave function does not represent the state of the system in itself, but information acquired in consequence of a complete measurement. The meaning of the time-energy uncertainty relation for (...) stable systems is discussed. (shrink)

The monistic worldview aims at a uniform description of nature based on scientific models. Quantum physical systems are mutually part of the other quantum physical systems. An aperture distributes the subsystems and the wave front in all possible ways. The system only takes one of the possible paths, as measurements show. Conclusion from Bell's theorem: Before the quantum physical measurement, there is no point-like location in the universe where all the information that explains the measurement (...) is available. Distributed information is possible. Movement of the particle and measuring process are deterministic. The oscillation between location uncertainty and momentum uncertainty leads photons to determine their own location at short intervals. The uncertainty principle focuses the systems. The fields of the surrounding matter influence the location of the new formation. The effect of all fields is based on a common mechanism. (shrink)

It is demonstrated that neither the arguments leading to inconsistencies in the description of quantum-mechanical measurement nor those “explaining” the process of measurement by means of thermodynamical statistics are valid. Instead, it is argued that the probability interpretation is compatible with an objective interpretation of the wave function.

I consider to what extent the phenomenon of interference precludes the possibility of attributing simultaneously determinate values to noncommuting observables, and I show that, while all observables can in principle be taken as simultaneously determinate, it suffices to take a suitable privileged observable as determinate to solve the measurement problem.

Heisenberg'sgendanken experiments in quantum mechanics have given rise to a widespread belief that the indeterminacy relations holding for the variables of a quantal system can be explained quasiclassically in terms of a disturbance suffered by the system in interaction with a quantal measurement, or state preparation, agent. There are a number of criticisms of this doctrine in the literature, which are critically examined in this article and found to be ininconclusive, the chief error being the conflation of this (...) disturbance with the projection postulate. We present a critique of the disturbance theory based on the fact that the required disturbance will in general depend on the interaction time of the system and state-preparer. This point is exploited in the construction of a spin-interaction model which acts as a counterexample to the disturbance doctrine, while remaining faithful to the spirit of Heisenberg'sgedanken experiments. Several consequences of this result are discussed. (shrink)

The objectivity is a basic requirement for the measurements in the classical world, namely, different observers must reach a consensus on their measurement results, so that they believe that the object exists “objectively” since whoever measures it obtains the same result. We find that this simple requirement of objectivity indeed imposes an important constraint upon quantum measurements, i.e., if two or more observers could reach a consensus on their quantum measurement results, their measurement basis must (...) be orthogonal vector sets. This naturally explains why quantum measurements are based on orthogonal vector basis, which is proposed as one of the axioms in textbooks of quantum mechanics. The role of the macroscopicality of the observers in an objective measurement is discussed, which supports the belief that macroscopicality is a characteristic of classicality. (shrink)

In the Copenhagen interpretation the Heisenberg inequality ΔQΔP≥ℏ/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 operator-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 uncertainty in quantum mechanics are discussed. (shrink)

This paper examines the problem of the interpretation of mixtures in quantum mechanics, presenting a survey of the philosophical debate between the ignorance interpretation (IgI) and the instrumentalist approach. By defining specific procedures for preparing and analyzing mixed beams of polarized light, we show that an important argument in defense of the IgI is not valid: differently prepared but equivalent mixtures cannot be distinguished by measuring particle fluctuations. We present an alternative argument, based on an experiment to test whether (...) the process of mixing is reversible or not. The expected result of this thought-experiment favors a weak version of the IgI. (shrink)

A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. We were also able to obtain the classical interpretation of the quantum-mechanical law of addition of probabilities by introducing a number of new notions. The principle of “local equity” assumes the transaction (...) completed (regardless of the result) of the states of transaction partners are not changed in connection with the reception of new information on proposed offers or adopted decisions (consent or refusal of the transaction). However it has no relation to the paradoxes of quantum theory connected with non-local interaction of entangled states. In the economic systems the mechanism of entangling has a classical interpretation, while the quantum-mechanical formalism of the description of states appears as a result of idealization of the selection mechanism in the proprietor's consciousness. (shrink)

We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result (...) is to be interpreted as the statistically inferred state of the original system rather than the state of the system after measurement. The phenomenon of “reduction of states” appears in this light as a consequence of incomplete information rather than the physical interaction between measured system and measuring instrument. (shrink)

Prevailing theories of consciousness may be characterized as either a physicalist view of mind with material building blocks that grow in complexity unto an emergent conscious experience, or as a dualistic model in which mind-body interaction is taken as the interface of conscious intent and unconscious bodily processing. Roger Penrose supports a model of consciousness that goes beyond dualism by adding a third domain [19]. The Three World model describes interconnected yet independent aspects of consciousness: Physical, Mental & Platonic. These (...) three worlds are grounded in the three axioms of quantum mechanics: measurement, superposition and entanglement. The Mental World corresponds to the superposition principle in which all possible future realities are superposed as potentials before a choice is made. The superposition is analogous to the choices we make everyday. In the Physical World, the measurement principles states that the quantum system must collapse the superposed possibilities into a single actuality. The most peculiar phenomenon in quantum mechanics is entanglement. Quantum systems may be entangled in a timeless and spaceless way such that they will still be connected despite separation in space or time. The Platonic World is akin to entanglement, because mathematics and conceptual forms are unchanging regardless of space or time. Finally, a new model called Fractal Trialism is proposed which describes how there is a nested trialism within each of the three worlds in order to elaborate their interconnectedness. This model describes digital computers, quantum computers and shared experience. Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}. (shrink)

The present paper discusses the problem of quantum-mechanical properties of a subject’s consciousness. The model of generalized economic measurements is used for the analysis. Two types of such measurements are analyzed – transactions and technologies. Algebraic ratios between the technology-type measurements allow making their analogy with slit experiments in physics. It has been shown that the description of results of such measurements is possible both in classical and in quantum formalism of calculation of probabilities. Thus, the quantum-mechanical (...) formalism of the description of states appears as a result of idealization of the selection mechanism in the proprietor's consciousness. (shrink)