Defining the observable φ canonically conjugate to the number observable N has long been an open problem in quantum theory. The problem stems from the fact that N is bounded from below. In a previous work we have shown how to define the absolute phase observable Φ≡|φ| by suitably restricting the Hilbert space of x and p like variables. Here we show that also from the classical point of view, there is no rigorous definition for the (...) phase even though it's absolute value is well defined. (shrink)

Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity represented by the limit $\hbar \rightarrow 0$ (...) : when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system becomes equivalent to the description of an ensemble of classical trajectories on phase space weighted by their corresponding probabilities. (shrink)

We approach the relationship between classical and quantum theories in a new way, which allows both to be expressed in the same mathematical language, in terms of a matrix algebra in a phase space. This makes clear not only the similarities of the two theories, but also certain essential differences, and lays a foundation for understanding their relationship. We use the Wigner-Moyal transformation as a change of representation in phase space, and we avoid the problem of (...) “negative probabilities” by regarding the solutions of our equations as constants of the motion, rather than as statistical weight factors. We show a close relationship of our work to that of Prigogine and his group. We bring in a new nonnegative probability function, and we propose extensions of the theory to cover thermodynamic processes involving entropy changes, as well as the usual reversible processes. (shrink)

We analyze phase-space approaches to relativistic quantum mechanics from the viewpoint of the causal interpretation. In particular, we discuss the canonical phase space associated with stochastic quantization, its relation to Hilbert space, and the Wigner-Moyal formalism. We then consider the nature of Feynman paths, and the problem of nonlocality, and conclude that a perfectly consistent relativistically covariant interpretation of quantum mechanics which retains the notion of particle trajectory is possible.

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random fluctuations (...) of the perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented. (shrink)

The problem of initializing phase in a quantum computing system is considered. The initialization of phases is a problem when the system is initially present in a superposition state as well as in the application of the quantum gate transformations, since each gate will introduce phase uncertainty. The accumulation of these random phases will reduce the effectiveness of the recently proposed quantum computing schemes. The paper also presents general observations on the nonlocal nature (...) of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or phase-flip or both. It is argued that these codes cannot directly solve the initialization problem of quantum computing. (shrink)

A century after the advent of quantum mechanics and general relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion of relativistic locality include the Bell’s inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava–Lifshitz gravity. Here, we explore a recent proposal for a “real ensemble” non-local description of quantum (...) mechanics, in which “particles” can copy each others’ observable values AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has quantum mechanics as a fixed point, where all particles with the same values for a given observable have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per value of the observable, as well as systematic deviations from quantum mechanics, decay as \ time)\, where \. Interestingly, this convergence is controlled by the absolute value of energy, suggesting a possible connection to gravitational physics. Finally, we discuss different issues related to this theory, as well as potential novel applications for the spectrum of primordial cosmological perturbations and the cosmological constant problem. (shrink)

In the early phase of the new history of physics that emerged at about 1970 and was pioneered by John Heilbron, Thomas Kuhn, Paul Forman, and others, the quantum and atomic theories of the first three decades of the twentieth century played a central role. Since then, interest in the area has continued, but for the last few decades at a slower rate. While other areas of the new physics—such as the general theory of relativity—have attracted much attention, (...) only relatively little has been written about the quantum revolution. Given this situation, Suman Seth’s comprehensive and innovative Crafting the Quantum is a welcome publication that provides the field with fresh blood and new perspectives. The title derives from a letter to Einstein of January 1922, in which Arnold Sommerfeld wrote that “I can only advance the craft of the quantum, you have to make its philosophy.” In spite of its title, Seth’s book is neither restricted to the new quantum theory nor to Sommerfeld’s role in the tr. (shrink)

This paper discusses the problem of finding and defining chaos in quantum mechanics. While chaotic time evolution appears to be ubiquitous in classical mechanics, it is apparently absent in quantum mechanics in part because for a bound, isolated quantum system, the evolution of its state is multiply periodic. This has led a number of investigators to search for semiclassical signatures of chaos. Here I am concerned with the status of semiclassical mechanics as a distinct third theory (...) of the asymptotic domain between classical and quantum mechanics. I discuss in some detail the meaning of such crucial locutions as the " classical counterpart to a quantum system " and a quantum system ' s " underlying classical motion ". A proper elucidation of these concepts requires a semiclassical association between phase space surfaces and wave - functions. This significance of this association is discussed in some detail. (shrink)

J. S. Bell's argument that only “nonlocal” hidden variable theories can reproduce the quantum statistical correlations of the singlet spin state in the case of two separated spin-1/2 particles is examined in terms of Wigner's formulation. It is shown that a similar argument applies to a single spin-1/2 particle, and that the exclusion of hidden variables depends on an obviously untenable assumption concerning conditional probabilities. The problem of completeness is discussed briefly, and the grounds for rejecting a (...) class='Hi'>phase-space reconstruction of the quantum statistics are clarified. (shrink)

Symmetries are introduced into the convexity approach to physics. This allows one to make connections between classical and quantum theories by exploiting the properties of quantum mechanics on phase space. The measurement problem is discussed and many of the known no-go theorems are shown not to apply. Finally, hidden variable theories exhibiting these physical symmetries are shown to have a certain required group structure, if they exist at all.

According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well‐known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be “taken seriously.” This article takes singularities seriously and (...) analyzes their role by using the well‐known distinction between data and phenomena , in an attempt to better understand the origin of the puzzle. *Received April 2009; revised July 2009. †To contact the author, please write to: University of Cambridge, Department of History and Philosophy of Science, Free School Lane, Cambridge CB2 3RH, United Kingdom; e‐mail: [email protected]. (shrink)

We give a common mathematical characterization of relevant stochastic evolution schemes built up in the literatute to attack the quantum measurement problem. This characterization is based on two hypotheses, namely, (i) the trace conservation with probability one and (ii) the existence of a complex phase determining a linear support for the stochastic process driving the random evolution.

Recently we have studied quantum mechanics of bounded operators with a discrete spectrum. In particular, we derived an expression for the commutator[Q, P] of two bounded operators whose spectrum is discrete, and we showed that in the limit of a continuous spectrum the commutator becomes the standard one of Heisenberg. In this paper we show that the angular momentum operator and the phase operator satisfy the new commutation relation. We also briefly discuss the problem of the canonical (...) phase operator conjugate to the number operator. (shrink)

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (“states” of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a “general syntax of relativized conceptualization” where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be (...) qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie,Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965). (shrink)

Almost all of the entropy in the universe is in the form of Bekenstein–Hawking (BH) entropy of super-massive black holes. This entropy, if it satisfies Boltzmann’s equation S=logN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=\log \mathcal{N}$$\end{document}, hence represents almost all the accessible phase space of the Universe, somehow associated to objects which themselves fill out a very small fraction of ordinary three-dimensional space. Although time scales are very long, it is believed that black holes will eventually evaporate (...) by emitting Hawking radiation, which is thermal when counted mode by mode. A pure quantum state collapsing to a black hole will hence eventually re-emerge as a state with strictly positive entropy, which constitutes the famous black hole information paradox. Expanding on a remark by Hawking we posit that BH entropy is a thermodynamic entropy, which must be distinguished from information-theoretic entropy. The paradox can then be explained by information return in Hawking radiation. The novel perspective advanced here is that if BH entropy counts the number of accessible physical states in a quantum black hole, then the paradox can be seen as an instance of the fundamental problem of statistical mechanics. We suggest a specific analogy to the increase of the entropy in a solvation process. We further show that the huge phase volume (N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{N}$$\end{document}), which must be made available to the universe in a gravitational collapse, cannot originate from the entanglement between ordinary matter and/or radiation inside and outside the black hole. We argue that, instead, the quantum degrees of freedom of the gravitational field must get activated near the singularity, resulting in a final state of the ‘entangled entanglement’ form involving both matter and gravity. (shrink)

The stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed. It leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents. The resulting particle propagators are used in the formulation of stochastic geometries underlying a concept of quantum spacetime that is operationally based on stochastically extended quantum test particles. The epistemological implications of the intrinsic stochasticity of such quantum spacetime frameworks for microcausality, the EPR (...) paradox, etc., are discussed. (shrink)

In quantum mechanics, the state of an individual particle (or system) is unobservable, i.e., it cannot be determined experimentally, even in principle. However, the notion of “measuring a state” is meaningful if it refers to anensemble of similarly prepared particles, i.e., the question may be addressed: Is it possible to determine experimentally the state operator (density matrix) into which a given preparation procedure puts particles. After reviewing the previous work on this problem, we give simple procedures, in the (...) line of Lamb's operational interpretation of quantum mechanics, for measuring a translational state operator (whether pure or mixed), via its Wigner function. These procedures closely parallel methods that might be used in classical mechanics to determine a true phase space probability distribution; thus, the Wigner function simulates such a distribution not only formally, but operationally also. There is no way to determine what the wave function (or state vector) of a system is—if arbitrarily given, there is no way to “measure” its wave function. Clearly, such a measurement would have to result in afunction of several variables, not in a relatively small set ofnumbers .... In order to verify the [quantum] theory in its generality, at least a succession of two measurements are needed. There is in general no way to determine the original state of the system, but having produced a definite state by a first measurement, the probabilities of the outcomes of a second measurement are then given by the theory.E. P. Wigner(1). (shrink)

The present work is motivated by recent experiments aimed to measure the propagation velocity of bound electromagnetic field that reveal no retardation in the absence of EM radiation. We show how these findings can be incorporated into the mathematical structure of special relativity theory that allows us to reconsider some selected problems of classical and quantum electrodynamics. In particular, we come to the conclusion that the total four-momentum for a classical system “particles plus fields” ought to be a present (...) state function of moving charges if EM radiation is negligible. In quantum domain, we analyze novel definition of the momentum operator recently suggested in the study of quantum phase effects. It implies that bound EM field energy and momentum are to be present state functions, too. Being in agreement with reported experiments, these conclusions suggest the necessity to carry out more precise experimental verifications for additional and independent determination of propagation properties of bound EM fields. A scheme of a possible experiment on this subject is also proposed. (shrink)

The paper addresses a problem for the unification of quantum physics with the new Aristotelianism: the identification of the members of the category of substance. I outline briefly the role that substance plays in Aristotelian metaphysics, leading to the postulating of the Tiling Constraint. I then turn to the question of which entities in quantum physics can qualify as Aristotelian substances. I offer an answer: the theory of thermal substances, and I construct a fivefold case for thermal (...) substances, based on the irreversibility of time, the definition of thermodynamic concepts, spontaneous symmetry breaking, phase transitions, and chemical form. (shrink)

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, (...) I believe, that we consider how space itself relates to reality, and how other so-called "spaces" used in physics relate to reality. In chapter 2, I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the "property view" of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter 3, prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman. In chapter 4, some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the "measurement problem" of quantum mechanics: this problem and its proposed solution are the primary subjects of chapter 4. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber. Finally, in chapters 5 and 6, I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time. (shrink)

Schwinger’s algebra of microscopic measurement, with the associated complex field of transformation functions, is shown to provide the foundation for a discrete quantum phase space of known type, equipped with a Wigner function and a star product. Discrete position and momentum variables label points in the phase space, each taking \(N\) distinct values, where \(N\) is any chosen prime number. Because of the direct physical interpretation of the measurement symbols, the phase space structure is thereby related (...) to definite experimental configurations. (shrink)

This paper presents the results of optical interferometry experiments in which the phase of photons in one arm of a Mach-Zehnder interferometer is modified by applying a transverse constriction. An equivalent quantum interferometry experiment using neutron de Broglie waves is discussed in which the observed phase shift is in the spirit of the force-free phase shift of the Aharonov-Bohm effects. In the optical experiments the experimental results are in excellent agreement with predictions.

We suggest a new answer to this intriguing question and argue that the answer may have implications for the solutions to the measurement problem. The main basis of our analysis is the doctrine of psychophysical supervenience. First of all, based on this doctrine, we argue that an observer in a quantum superposition or a quantum observer has a definite conscious experience, which is neither disjunctive nor illusive. The inconsistency of this result with the bare theory is further (...) analyzed, and it is shown that an appropriate use of the strategy of analyzing the disposition of an observer to answer a particular question also leads to the same result. Next, we argue that this new result seems to disfavor Everett's and Bohm's approaches to quantum mechanics when considering the doctrine of psychophysical supervenience. This suggests that dynamical collapse theories are in the right direction to solve the measurement problem. Thirdly, we analyze the concrete content of the conscious experience of a quantum observer. It is argued that the mental content of a quantum observer is related to both the amplitude and relative phase of each branch of the superposition she is physically in, and it is composed of the mental content corresponding to every branch of the superposition. In addition, we argue that when assuming the modulus squared of the amplitude of each branch determines the vividness of the mental content corresponding to the branch, the structured tails problem of dynamical collapse theories can be solved. (shrink)

The integrodifferential equations satisfied by the statistical frequency functions for physical systems undergoing stochastic transitions are derived by application of a causality principle and selection rules to the Markov chain equations. The result equations can be viewed as generalizations of the diffusion equation, but, unlike the latter, they have a direct bearing onactive transport problems in biophysics andcondensation aggregation problems of astrophysics and phase transition theory. Simple specific examples of the effects of severe selection rules, such as the relaxational (...) Boltzmann transport equation and the diffusion equation, are also given. Finally, partial differential equations for the probability amplitudes of quantum mechanics are derived, usingunitarity instead of causality, and a selection rule is applied directly to obtain ageneralization of the Dirac equation in which infinite transitions between states arenot allowed. (shrink)

I will give a broad overview of what has become the standard paradigm in cosmology. I will describe the relational notion of time that is often used in cosmological calculations and discuss how the local nature of Einstein's equations allows us to translate this notion into statements about `initial' data. Classically this relates our local definition of time to a quasi-local region of a particular spatial slice, however incorporating quantum theory comes at the expense of losing this locality entirely. (...) This occurs due to the presence of two, apparently distinct, issues: Seemingly classical issues to do with the infinite spatial volume of the universe and Quantum field theory issues, which revolve around trying to apply renormalization in cosmology. Following the ‘cosmological principle’ - an extension of the ‘Copernicus principle’ - that physics at every point in our universe should look the same, we are lead to the modern view of cosmology. This procedure is reasonably well understood for an exactly homogeneous universe, however the inclusions of small perturbations over this homogeneity leads to many interpretational/ conceptual difficulties. For example, in an infinite universe perturbations can be arbitrarily close to homogeneous. To any observer, such a perturbation would appear to be a simple rescaling of the homogenous background and hence, physically, would not be considered an inhomogeneous perturbation at all. However, any attempt to choose the physically relevant scale at which perturbations should be considered homogeneous will break the cosmological principle i.e. it will make the resulting physics observer dependent. It amounts to `putting the perturbations in a box' and a delicate practical issue is that the universe is not static, hence the scale of the box will be time dependent. Thus what appears ‘physically homogeneous’ to an observer at one time will not appear so at another. This issue is brought to the forefront by considering the canonical version of the theory. The phase space formulation of General Relativity, just as for any other theory, contains the shadow of the underlying quantum theory. This means that, although the formulation is still classical, many of the subtleties that are present in the quantum theory are already apparent. In the cosmological context the infinite spatial volume renders almost all expressions formal or ill-defined. In order to proceed, we must restrict our attention to a cosmology that has some finite spatial extent, on which our relational notion of time is everywhere definable. In particular, this would constrain the permissible data outside our `observable universe'. This difficulty is an IR or large scale issues in cosmology, however in addition there are UV or short scale problems that need to be tackled. There are the usual problems of renormalization, which are further complicated by the fact that the universe is not static. In the cosmological setting this leads to new IR problems which again prevent one from taking the spatial extent of the universe to infinity. The physical relevance of this problem, the consequence for defining a time variable, and the distinction of homogeneous and inhomogeneous IR issues will be discussed. (shrink)

We consider a stochastic process which is described by a continuous-time Markov chain on only short time-scales and constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of the Markov chain is given and the conserved quantities are known to exist, but not explicitly given. To study the stochastic dynamics we propose to use the principle of stationary entropy production. Then the problem can be transformed into a variational problem for (...) a suitably defined “action” and with time-dependent Lagrange multipliers. We show that the stochastic dynamics can be described by a Schrödinger equation, with Lagrange multipliers playing the role of phases, whenever the transition matrix is symmetric or the detailed balance condition is satisfied, the system is not too far from the equilibrium and the number of the conserved quantities is large. (shrink)

A publication by Professor Margenau is always of interest to persons concerned with philosophy of science. This is especially true, however, of his recently published book, The Nature of Physical Reality; for this book, dealing with basic epistemological problems arising from the development of modern quantum mechanics, is the most comprehensive and most systematic formulation of its author's philosophical position and is at the same time conceived as a “challenge” to “uncritical realism, unadorned operationalism, and radical empiricism”—to points of (...) view, that is, which Professor Margenau regards as “outmoded and in disharmony with the successful phases of contemporary physics”. (shrink)

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry. The geometry also plays an important role in foundations of quantum mechanics and quantum information. In this work we discuss a geometric framework for mixed quantum states represented by density matrices, where the quantum phase space of density matrices is equipped with a symplectic structure, an almost complex structure, (...) and a compatible Riemannian metric. This compatible triple allow us to investigate arbitrary quantum systems. We will also discuss some applications of the geometric framework. (shrink)

I discuss the question: Is it possible to prepare, by purely thermodynamic means, an ensemble described by a quantum state having a definite phase relation between two component states which have never been in direct contact? Resolution of this question requires us to take explicit account of the nature of the correlations between the system and its thermal environment.

The quantum measurement problem and various unsuccessful attempts to resolve it are reviewed. A suggestion by Diosi and Penrose for the half-life of the quantum superposition of two Newtonian gravitational fields is generalized to an arbitrary quantum superposition of relativistic, but weak, gravitational fields. The nature of the “collapse” process of the wave function is examined.

The quantum corrections related to the ideal gas model often considered are those associated to the bosonic or fermionic nature of particles. However, in this work, other kinds of corrections related to the quantum nature of phase space are highlighted. These corrections are introduced as improvements in the expression of the partition function of an ideal gas. Then corrected thermodynamics properties of the ideal gas are deduced. Both the non-relativistic quantum and relativistic quantum cases are (...) considered. It is shown that the corrections in the non-relativistic quantum case may be particularly useful to describe the deviation from the Maxwell–Boltzmann model at low temperature and/or in confined space. These corrections can be considered as including the description of quantum size and shape effects. For the relativistic quantum case, the corrections could be relevant for confined space and when the thermal energy of each particle is comparable to their rest energy. The corrections appear mainly as modifications in the thermodynamic equation of state and in the expressions of the partition function and thermodynamic functions like entropy, internal energy and free energy. Expressions corresponding to the Maxwell–Boltzmann model are shown to be asymptotic limits of the corrected expressions. (shrink)

This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics.In it, I aim to review, in a way accessible to foundationally interested physicists as well as physics-informed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don't advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence (...) theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the "traditional" formulation of the problem. (shrink)

A modified Beltrametti-Cassinelli-Lahti model of the measurement apparatus that satisfies both the probability reproducibility condition and the objectification requirement is constructed. Only measurements on microsystems are considered. The cluster separability forms a basis for the first working hypothesis: the current version of quantum mechanics leaves open what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. The second working hypothesis is that (...) registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This implies that the separation status of a microsystem changes during both preparation and registration. A new rule that specifies what happens when these changes occur and that guarantees the objectification is formulated and discussed. A part of our result has certain similarities with ‘collapse of the wave function’. (shrink)

Based on the exactly solvable case of a harmonic oscillator, we show that the direct correspondence between the Bohr-Sommerfeld phase of semiclassical quantum mechanics and the topological phase of Aharonov and Anandan is restricted to the case of a coherent state. For other Gaussian wave packets the geometric quantum phase strongly depends on the amount of squeezing.

The integration of recent work on decoherence into a so-called modal interpretation offers a promising new approach to the measurement problem in quantum mechanics. In this paper I explain and develop this approach in the context of the interactive interpretation presented in Healey (1989). I begin by questioning a number of assumptions which are standardly made in setting up the measurement problem, and I conclude that no satisfactory solution can afford to ignore the influence of the environment. (...) Further, I argue that there are good reasons to believe that on a modal interpretation environmental interactions rapidly ensure that a quantummechanically describable apparatus indeed records a definite result following a measurement interaction. (shrink)

The aim of this paper is to give a systematic account of the so-called “measurement problem” in the frame of the standard interpretation of quantum mechanics. It is argued that there is not one but five distinct formulations of this problem. Each of them depends on what is assumed to be a “satisfactory” description of the measurement process in the frame of the standard interpretation. Moreover, the paper points out that each of these formulations refers not to (...) a unique problem, but to a set of sub-problems. (shrink)

`Quantum theory' is not a single physical theory but a framework in which many different concrete theories fit. As such, a solution to the quantum measurement problem ought to provide a recipe to interpret each such concrete theory, in a mutually consistent way. But with the exception of the Everett interpretation, the mainextant solutions either try to make sense of the abstract framework as if it were concrete, or else interpret one particular quantum theory under the (...) fiction that it is fundamental and exact. In either case, these approaches are unable to help themselves to the very theory-laden, level-relative ways in which quantum theory makes contact with experiment in mainstream physics, and so are committed to major revisionary projects which have not been carried out even in outline. As such, only the Everett interpretation is currently suited to make sense of quantum physics as we find it. (shrink)

The Genetic Algorithm (GA) and Simulated Annealing (SA), two techniques for global optimization, were applied to a reduced (simplified) form of the phase problem (RPP) in computational crystallography. Results were compared with those of "enhanced pair flipping" (EPF), a more elaborate problem-specific algorithm incorporating local and global searches. Not surprisingly, EPF did better than the GA or SA approaches, but the existence of GA and SA techniques more advanced than those used in this study suggest that these (...) techniques still hold promise for phase problem applications. The RPP is, furthermore, an excellent test problem for such global optimization methods. (shrink)

Can there be `peaceful coexistence' between quantum theory and special relativity? Thirty years ago, Shimony hoped that isolating the culprit in proofs of Bell inequalities as Outcome Independence would secure such peaceful coexistence: or, if not secure it, at least show a way---maybe the best or only way---to secure it. In this paper, I begin by being sceptical of Shimony's approach, urging that we need a relativistic solution to the quantum measurement problem. Then I analyse Outcome Independence (...) in Kent's realist one-world Lorentz-invariant interpretation of quantum theory. Then I consider Shimony's other condition, Parameter Independence, both in Kent's proposal and more generally, in the light of recent remarkable theorems by Colbeck, Renner and Leegwater. For both Outcome Independence and Parameter Independence, there is a striking analogy with the situation in pilot-wave theory. Finally, I will suggest that these recent theorems make some kind of peaceful coexistence mandatory for someone who, like Shimony, endorses Parameter Independence. (shrink)

According to orthodox quantum mechanics, state vectors change in two incompatible ways: "deterministically" in accordance with Schroedinger's time-dependent equation, and probabilistically if and only if a measurement is made. It is argued here that the problem of measurement arises because the precise mutually exclusive conditions for these two types of transitions to occur are not specified within orthodox quantum mechanics. Fundamentally, this is due to an inevitable ambiguity in the notion of "meawurement" itself. Hence, if the (...) class='Hi'>problem of measurement is to be resolved, a new, fully objective version of quantjm mechanics needs to be developed which does not incorporate the notion of measurement in its basic postuolates at all. (shrink)

The different versions of the Kochen-Specker Theorem show that quantum mechanics cannot be supplemented by hidden variables given two constraints. These results are generally interpreted as showing that QM is complete in the following way. A QM system S has only those values of observables for which the state yields probability 1. For all other probabilities S adopts a value during the measurement interaction. But this interpretation is fundamentally problematic. In fact it cannot yield a general and coherent interpretation (...) of the trace formula. I present an argument to this effect, discuss a possible objection and sketch implications. (shrink)

A generic non-conservative force, applied to an interferometer particle for a period in the past and then turned off, leaves stationary phase and fringe shifts in the now force-free interferometer. Both Aharonov-Bohm and Aharonov-Casher topological phase and fringe shifts can be created in this way. The specific sources of the non-conservative forces behind Aharonov-Bohm and Aharonov-Casher stationary fringe shifts are, respectively, Faraday induction fields and Maxwell displacement currents, now off.

In a recent article entitled “The problem of molecular structure just is the measurement problem”, Alexander Franklin and Vanessa Seifert argue that insofar as the quantum measurement problem is solved, the problems of molecular structure are resolved as well. The purpose of the present article is to show that such a claim is too optimistic. Although the solution of the quantum measurement problem is relevant to how the problem of molecular structure is faced, (...) such a solution is not sufficient to account for the structure of molecules as understood in the field of chemistry. (shrink)