Measurement Problem

Quantum mechanics has always been regarded as, at best, puzzling, if not contradictory. The aim of the paper is to explore a particular approach to fundamental physical theories, the one based on the notion of primitive ontology. This approach, when applied to quantum mechanics, makes it a paradox-free theory.

I argue that Immanuel Kant's critical philosophy—in particular the doctrine of transcendental idealism which grounds it—is best understood as an `epistemic' or `metaphilosophical' doctrine. As such it aims to show how one may engage in the natural sciences and in metaphysics under the restriction that certain conditions are imposed on our cognition of objects. Underlying Kant's doctrine, however, is an ontological posit, of a sort, regarding the fundamental nature of our cognition. This posit, sometimes called the `discursivity thesis', while considered (...) to be completely obvious and uncontroversial by some, has nevertheless been denied by thinkers both before and after Kant. One such thinker is Jakob Friedrich Fries, an early neo-Kantian thinker who, despite his rejection of discursivity, also advocated for a metaphilosophical understanding of critical philosophy. As I will explain, a consequence for Fries of the denial of discursivity is a radical reconceptualisation of the method of critical philosophy; whereas this method is a priori for Kant, for Fries it is in general empirical. I discuss these issues in the context of quantum theory, and I focus in particular on the views of the physicist Niels Bohr and the Neo-Friesian philosopher Grete Hermann. I argue that Bohr's understanding of quantum mechanics can be seen as a natural extension of an orthodox Kantian viewpoint in the face of the challenges posed by quantum theory, and I compare this with the extension of Friesian philosophy that is represented by Hermann's view. (shrink)

Some variants of quantum theory theorize dogmatic "unimodal" states-of-being, and are based on hodge-podge classical-quantum language. They are based on ontic syntax, but pragmatic semantics. This error was termed semantic inconsistency [1]. Measurement seems to be central problem of these theories, and widely discussed in their interpretation. Copenhagen theory deviates from this prescription, which is modeled on experience. A complete quantum experiment is "bimodal". An experimenter creates the system-under-study in initial mode of experiment, and annihilates it in the final. The (...) experimental intervention lies beyond the theory. I theorize most rudimentary bimodal quantum experiments studied by Finkelstein [2], and deduce "bimodal probability density" P=|In><Fin| to represent complete quantum experiments. It resembles core insights of the Copenhagen theory. (shrink)

The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...) subsets so there is a dual concept of logical entropy which is the normalized counting measure on distinctions of partitions. Thus the logical notion of information is a measure of distinctions. Classical logical entropy naturally extends to the notion of quantum logical entropy which provides a more natural and informative alternative to the usual Von Neumann entropy in quantum information theory. The quantum logical entropy of a post-measurement density matrix has the simple interpretation as the probability that two independent measurements of the same state using the same observable will have different results. The main result of the paper is that the increase in quantum logical entropy due to a projective measurement of a pure state is the sum of the absolute squares of the off-diagonal entries ("coherences") of the pure state density matrix that are zeroed ("decohered") by the measurement, i.e., the measure of the distinctions ("decoherences") created by the measurement. (shrink)

We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of arbitrary (...) spin. The class of correlations allowed by quantum mechanics is still represented by the elliptope; the subclass of those allowed by local hidden-variable theories by polyhedra with increasing numbers of vertices and facets that get closer and closer to the elliptope. We use these results to advocate for an interpretation of quantum mechanics like Bub's. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the equation for the elliptope derived in this paper is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation. (shrink)

The universality assumption (“U”) that quantum wave states only evolve by linear or unitary dynamics has led to a variety of paradoxes in the foundations of physics. U is not directly supported by empirical evidence but is rather an inference from data obtained from microscopic systems. The inference of U conflicts with empirical observations of macroscopic systems, giving rise to the century-old measurement problem and subjecting the inference of U to a higher standard of proof, the burden of which lies (...) with its proponents. This burden remains unmet because the intentional choice by scientists to perform interference experiments that only probe the microscopic realm disqualifies the resulting data from supporting an inference that wave states always evolve linearly in the macroscopic realm. Further, the nature of the physical world creates an asymptotic size limit above which interference experiments, and verification of U in the realm in which it causes the measurement problem, seem impossible for all practical purposes if nevertheless possible in principle. This apparent natural limit serves as evidence against an inference of U, providing a further hurdle to the proponent’s currently unmet burden of proof. The measurement problem should never have arisen because the inference of U is entirely unfounded, logically and empirically. (shrink)

This is the second of two reports concerning the issue of time directionality in fundamental theoretical physics. Here a fresh perspective is offered on several aspects of the problem of the interpretation of quantum theory which centers around a reconsideration of the significance of the requirement of time reversal symmetry. Following a critical review of early time-symmetric formulations of quantum mechanics, it is argued that a more consistent approach must overcome the contradictions of the orthodox interpretation that follow from its (...) rejection of scientific realism. It is also shown that the condition of time-reversal invariance provides strong enough a constraint to allow a realist interpretation of quantum theory to satisfy the principle of local causality in the face of quantum entanglement. It is then explained that the existence of a maximum quasiclassical domain can only be predicted to arise and to persist, following measurement, once we consider the problem of the emergence of time in quantum cosmology from the perspective of the solution provided in the preceding report to the problem of the origin of thermodynamic time asymmetry. It is also suggested that in the context of a semi-classical theory of the gravitational field the proposed realist, time-symmetric interpretation of quantum theory would allow the formulation of a satisfactory solution to the problem of objectification. (shrink)

In this paper I present and critically discuss the main strategies that Bohr used and could have used to fend off the charge that his interpretation does not provide a clear-cut distinction between the classical and the quantum domain. In particular, in the first part of the paper I reassess the main arguments used by Bohr to advocate the indispensability of a classical framework to refer to quantum phenomena. In this respect, by using a distinction coming from an apparently unrelated (...) philosophical corner, we could say that Bohr is not a revisionist philosopher of physics but rather a descriptivist one in the sense of Strawson. I will then go on discussing the nature of the holistic link between classical measurement apparatuses and observed system that he also advocated. The oft-repeated conclusion that Bohr’s interpretation of the quantum formalism is untenable can only be established by giving his arguments as much force as possible, which is what I will try to do in the following by remaining as faithful as possible to his published work. (shrink)

One of the most serious challenges (if not the most serious challenge) for interactive psycho-physical dualism (henceforth interactive dualism or ID) is the so-called ‘interaction problem’. It has two facets, one of which this article focuses on, namely the apparent tension between interactions of non-physical minds in the physical world and physical laws of nature. One family of approaches to alleviate or even dissolve this tension is based on a collapse solution (‘consciousness collapse/CC) of the measurement problem in quantum mechanics (...) (QM). The idea is that the mind brings about the collapse of a superposed wave function onto one of its eigenstates. Thus, it is claimed, can the mind change the course of things without violating any law figuring in physical theory. I will first show that this hope is premature because energy and momentum are probably not conserved in collapse processes, and that even if this can be dealt with, the violations are either severe or produce further ontological problems. Second, I point out several conceptual difficulties for interactionist CC. I will also present solutions for those problems, but it will become clear that those solutions come at a high cost. Third, I shall briefly list some empirical problems which make life even harder for interactionist CC. I conclude with remarks about why no- collapse interpretations of QM don’t help either and what the present study has shown is the real issue for ID: namely to find a plausible integrative view of dualistic mental causation and laws of nature. (shrink)

It is shown that the Born Rule probabilities, i.e. the squares of the moduli of the coefficients in a pure state superposition, refer to mutually exclusive events consequent on measurement. It is also shown that the eigenstates in a pure state superposition are not mutually exclusive events. If the Born Rule is to be retained as the fundamental interpretative postulate of quantum mechanics then it follows, firstly, that the probabilities necessarily refer not to the eigenstates but to the eigenvalues to (...) which the eigenstates belong and, secondly, that the eigenvalues are necessarily mutually exclusive events. This means that to ask why a measurement of an observable on a system in a pure state superposition of eigenstates yields a single state rather than all the states in the superposition is to ill-pose the quantum measurement problem. The events the Born Rule probabilities properly refer to are not states but values. And it also means that the correctly-posed measurement problem, why does a measurement of an observable in a pure state superposition of the eigenstates of the observable yield a single eigenvalue rather than all the eigenvalues implicit in the superposition, admits of the answer: the values, being mutually exclusive events, constitute a statistical mixture of values, and as such, a measurement will yield just one of them. (shrink)

Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the fact that you can't stop a (...) measurement part-way through and uncover the underlying 'ontic' dynamics of the system in question. Having discussed the hidden dynamics of a system's ontic state during measurement, we turn to more general forms of open-system dynamics and explore the extent to which the details of the underlying ontic behavior of a system can be described. We construct a space of ontic trajectories and describe obstructions to defining a probability measure on this space. (shrink)

In his recent book Bananaworld. Quantum mechanics for primates, Jeff Bub revives and provides a mature version of his influential information-theoretic interpretation of Quantum Theory (QT). In this paper, I test Bub’s conjecture that QT should be interpreted as a theory about information, by examining whether his information-theoretic interpretation has the resources to explain (or explain away) quantum conundrums. The discussion of Bub’s theses will also serve to investigate, more in general, whether other approaches succeed in defending the claim that (...) QT is about quantum information. First of all, I argue that Bub’s interpretation of QT as a principle theory fails to fully explain quantum non-locality. Secondly, I argue that a constructive interpretation, where the quantum state is interpreted ontically as information, also fails at providing a full explanation of quantum correlations. Finally, while epistemic interpretations might succeed in this respect, I argue that such a success comes at the price of rejecting some in between the most basic scientific standards of physical theories. (shrink)

The apparent nonlocality of quantum theory has been a persistent concern. Einstein et al. and Bell emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's "no-go" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the (...) experimentally confirmed entanglement correlations, we make clear that it is the conjunction of the three axioms that is ruled out by these correlations. We then show that by assuming local causality and no superdeterminism, we can give a direct proof of many worlds. The remainder of the paper searches for a consistent, local, formulation of many worlds. We show that prominent formulations whose ontology is given by the wave function violate local causality, and we critically evaluate claims in the literature to the contrary. We ultimately identify a local many worlds interpretation that replaces the wave function with a separable Lorentz-invariant wave-field. We conclude with discussions of the Born rule, and other interpretations of quantum mechanics. (shrink)

We defend the many-worlds interpretation of quantum mechanics against the objection that it cannot explain why measurement outcomes are predicted by the Born probability rule. We understand quantum probabilities in terms of an observer's self-location probabilities. We formulate a probability postulate for the MWI: the probability of self-location in a world with a given set of outcomes is the absolute square of that world's amplitude. We provide a proof of this postulate, which assumes the quantum formalism and two principles concerning (...) symmetry and locality. We also show how a structurally similar proof of the Born rule is available for collapse theories. We conclude by comparing our account to the recent account offered by Sebens and Carroll. (shrink)

The connection between quantum physics and the mind has been debated for almost a hundred years. There are several proposals as to how quantum effects might be relevant to understanding consciousness, including von Neumann’s Consciousness Causes Collapse interpretation (CCC), Penrose’s Orchestrated objective reduction (Orch OR), Atmanspacher quantum emergence theory, or Vitiello’s field theory. In this paper, we examine the CCC, in particular Stapp’s theory of interaction of mind and matter, and discuss how this imposes constraints to possible brain structures. We (...) then argue that those constraints may allow us to identify a possible locus of the interaction between mind and matter, if CCC is true. (shrink)

Effects associated in quantum mechanics with a divisible probability wave are explained as physically real consequences of the equal but opposite reaction of the apparatus as a particle is measured. Taking as illustration a Mach-Zehnder interferometer operating by refraction, it is shown that this reaction must comprise a fluctuation in the reradiation field of complementary effect to the changes occurring in the photon as it is projected into one or other path. The evolution of this fluctuation through the experiment will (...) explain the alternative states of the particle discerned in self interference, while the maintenance of equilibrium in the face of such fluctuations becomes the source of the Born probabilities. In this scheme, the probability wave is a mathematical artifact, epistemic rather than ontic, and akin in this respect to the simplifying constructions of geometrical optics. (shrink)

This book explores the prospects of rivaling ontological and epistemic interpretations of quantum mechanics (QM). It concludes with a suggestion for how to interpret QM from an epistemological point of view and with a Kantian touch. It thus refines, extends, and combines existing approaches in a similar direction. -/- The author first looks at current, hotly debated ontological interpretations. These include hidden variables-approaches, Bohmian mechanics, collapse interpretations, and the many worlds interpretation. He demonstrates why none of these ontological interpretations can (...) claim to be the clear winner amongst its rivals. Next, coverage explores the possibility of interpreting QM in terms of knowledge but without the assumption of hidden variables. It examines QBism as well as Healey’s pragmatist view. The author finds both interpretations or programs wanting in certain respects. As a result, he then goes on to advance a genuine proposal as to how to interpret QM from the perspective of an internal realism in the sense of Putnam and Kant. -/- The book also includes two philosophical interludes. One details the notions of probability and realism. The other highlights the connections between the notions of locality, causality, and reality in the context of violations of Bell-type inequalities. (shrink)

Simon Friederich’s Therapeutic Approach to quantum theory (QT) sheds new light on the status of the quantum state. In particular, Friederich presents revisionary ideas on how to exactly differentiate objective from subjective elements of the theory and thereby improves upon previous stabs at an epistemic interpretation of quantum states. The book not only provides interesting perspectives for the cognoscenti but is also written with sufficient care and free of unnecessary technicalities so as to be accessible and worth reading for the (...) physical layman interested in the foundations of QT. The main achievement of the book is an innovative outline for interpreting quantum states epistemically while avoiding many problems of previous attempts. (shrink)

We expound an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. The ψ function is no longer interpreted as a probability amplitude of the observed behaviour of elementary particles but as an objective physical field representing the particles themselves. The particles are thus extended objects whose extension varies in time according to (...) the variation of ψ. They are considered as fundamental regions of space with some kind of nonlocality. Special consideration is given to the Heisenberg relations, the Einstein-Podolsky- Rosen correlations, the reduction process, the problem of measurement, and the quantum-statistical distributions. (shrink)

Karl Popper is famous for having proposed that science advances by a process of conjecture and refutation. He is also famous for defending the open society against what he saw as its arch enemies – Plato and Marx. Popper’s contributions to thought are of profound importance, but they are not the last word on the subject. They need to be improved. My concern in this book is to spell out what is of greatest importance in Popper’s work, what its failings (...) are, how it needs to be improved to overcome these failings, and what implications emerge as a result. The book consists of a collection of essays which dramatically develop Karl Popper’s views about natural and social science, and how we should go about trying to solve social problems. Criticism of Popper’s falsificationist philosophy of natural science leads to a conception of science that I call aim-oriented empiricism. This makes explicit metaphysical theses concerning the comprehensibility and knowability of the universe that are an implicit part of scientific knowledge – implicit in the way science excludes all theories that are not explanatory, even those that are more successful empirically than accepted theories. Aim-oriented empiricism has major implications, not just for the academic discipline of philosophy of science, but for science itself. Popper generalized his philosophy of science of falsificationism to arrive at a new conception of rationality – critical rationalism – the key methodological idea of Popper’s profound critical exploration of political and social issues in his The Open Society and Its Enemies, and The Poverty of Historicism. This path of Popper, from scientific method to rationality and social and political issues is followed here, but the starting point is aim-oriented empiricism rather than falsificationism. Aim-oriented empiricism is generalized to form a conception of rationality I call aim-oriented rationalism. This has far-reaching implications for political and social issues, for the nature of social inquiry and the humanities, and indeed for academic inquiry as a whole. The strategies for tackling social problems that arise from aim-oriented rationalism improve on Popper’s recommended strategies of piecemeal social engineering and critical rationalism, associated with Popper’s conception of the open society. This book thus sets out to develop Popper’s philosophy in new and fruitful directions. The theme of the book, in short, is to discover what can be learned from scientific progress about how to achieve social progress towards a better world. (shrink)

The purpose of this book is to explain Quantum Bayesianism (‘QBism’) to “people without easy access to mathematical formulas and equations” (4-5). Qbism is an interpretation of quantum mechanics that “doesn’t meddle with the technical aspects of the theory [but instead] reinterprets the fundamental terms of the theory and gives them new meaning” (3). The most important motivation for QBism, enthusiastically stated on the book’s cover, is that QBism provides “a way past quantum theory’s paradoxes and puzzles” such that much (...) of the weirdness associated with quantum theory “dissolves under the lens of QBism”. (shrink)

Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata, and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the manifested world (...) and its manifestation. A single, intrinsically undifferentiated Being manifests the macroworld by entering into reflexive spatial relations. This atemporal process implies a new kind of causality and sheds new light on the mysterious nonlocality of quantum mechanics. Unlike other realist interpretations, which proceed from an evolving-states formulation, the present interpretation proceeds from Feynman’s formulation of the theory, and it introduces a new interpretive principle, replacing the collapse postulate and the eigenvalue–eigenstate link of evolving-states formulations. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete. Applied to alternatives involving distinctions between things, it warrants the claim that, intrinsically, all fundamental particles are identical in the strong sense of numerical identical. They are the aforementioned intrinsically undifferentiated Being, which manifests the macroworld by entering into reflexive spatial relations. (shrink)

This paper provides a prospectus for a new way of thinking about the wavefunction of the universe: a Ψ-epistemic quantum cosmology. We present a proposal that, if successfully implemented, would resolve the cosmological measurement problem and simultaneously allow us to think sensibly about probability and evolution in quantum cosmology. Our analysis draws upon recent work on the problem of time in quantum gravity and causally symmet- ric local hidden variable theories. Our conclusion weighs the strengths and weaknesses of the approach (...) and points towards paths for future development. (shrink)

How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is answered without invoking knowledge or observers, by interpreting the necessary distinction between two kinds of physical quantities - unconditionally definite quantities and quantities that have values only if they are measured - as a distinction between the manifested world and its manifestation.(The arXived version contains (...) an Appendix which the version published at Cosmology.com lacks. While the latter touches on various ways in which quantum mechanics does not have to do with consciousness, the Appendix concerns what quantum mechanics has to do with consciousness.). (shrink)

I show explicitly how concerns about wave function collapse and ontology can be decoupled from the bulk of technical analysis necessary to recover localized, approximately Newtonian trajectories from quantum theory. In doing so, I demonstrate that the account of classical behavior provided by decoherence theory can be straightforwardly tailored to give accounts of classical behavior on multiple interpretations of quantum theory, including the Everett, de Broglie-Bohm and GRW interpretations. I further show that this interpretation-neutral, decoherence-based account conforms to a general (...) view of inter-theoretic reduction in physics that I have elaborated elsewhere, which differs from the oversimplified and often ambiguous picture that treats reduction simply as a matter of taking limits. This interpretation-neutral account rests on a general three-pronged strategy for reduction between quantum and classical theories that combines decoherence, an appropriate form of Ehrenfest's Theorem, and a decoherence-compatible mechanism for collapse. It also incorporates a novel argument as to why branch-relative trajectories should be approximately Newtonian, which is based on a little-discussed extension of Ehrenfest's Theorem to open systems, rather than on the more commonly cited but less germane closed-systems version. In the Conclusion, I briefly suggest how the strategy for quantum-classical reduction described here might be extended to reduction between other classical and quantum theories, including classical and quantum field theory and classical and quantum gravity. (shrink)

Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuously. In this article, written in dialogue form, we suggest that quantum mechanics can be taken even more seriously, if the many-worlds view is replaced by a many-measurements view. This allows not only to derive the (...) Born rule, thus solving the measurement problem, but also to deduce a one-world non-spatial reality, providing an even more fantastic scenario than that of the multiverse. (shrink)

The aim of this paper is to summarize a particular approach of doing metaphysics through physics - the primitive ontology approach. The idea is that any fundamental physical theory has a well-defined architecture, to the foundation of which there is the primitive ontology, which represents matter. According to the framework provided by this approach when applied to quantum mechanics, the wave function is not suitable to represent matter. Rather, the wave function has a nomological character, given that its role in (...) the theory is to implement the law of evolution for the primitive ontology. (shrink)

Quantum mechanics is an area of Physics that deals with subatomic phenomena. It can be extracted from a vision of the physical world which contradicts many aspects of our everyday perception, prompting many philosophical debates and admitting different interpretations. Among the wide range of problems within the interpretation of quantum theory, there is the measurement problem. Some philosophical aspects of the problems concerning the notion of “measurement” in quantum mechanics are analyzed in order to identify how the problem arises in (...) discussions about the foundations of the interpretation of quantum theory and how it holds up even in the most recent interpretations, conflicting in various ways (including ontological) with a worldview that can be drawn from classical physics – assuming that it provides a worldview. Although Bohr has, on several occasions, addressed the measurement problem, he did not get to properly formulate a measurement theory. This was done by von Neumann, who presented an axiomatic formulation of a measurement theory along with a critique of the Bohrian model and, at the same time, an alternative grounded in the introduction of a dualistic notion of consciousness (nonphysical) with causal power in quantum measurement. It is precisely the introduction of the dualistic concept of consciousness within the scope of the concept of measurement that inserts into the philosophical discussion as an ontological problem insofar as it comes to the introduction of a new entity in the universe. The first subjetivistic interpretations, proposed by London and Bauer, are analysed, passing through the solipsistic difficulty to this subjectivist interpretations placed through Wigner’s work, up to the interpretations inspired by the late work of the physicist Erwin Schrödinger, which proposes a monistic interpretation of the notion of “consciousness”. Some distinct attitudes towards measuring the philosophical problems are outlined very briefly in the form of sampling, to illustrate the plural character of the proposals for interpretation of the term “measurement” in quantum mechanics. Although strictly speaking there is no “best” interpretation of quantum mechanics, it is suggested that the formulation of an ontology that takes into account quantum mechanics could help in understanding certain concepts, such as “measurement” or “consciousness” without that philosophical difficulties – as dualism – or paradoxical situations – such as solipsism – necessarily accompany them. (shrink)

It is an experimental fact that \ -decays produce in a cloud chamber at most one track and that this track points in a random direction. This seems to contradict the description of decay in Quantum Mechanics: according to Gamow a spherical wave is produced and moves radially according to Schrödinger’s equation. It is as if the interaction with the supersaturated vapor turned the wave into a particle. The aim of this note is to place this effect in the context (...) of Schrödinger’s Quantum Mechanics. We shall see that the properties of the initial wave function suggest the introduction of a semiclassical formalism in which the \ -wave can be described as a collection of semiclassical wavelets; each of them interacts with an atom and forms an entangled state. The interaction can be regarded as a semiclassical inelastic scattering event. The measurement selects the wave function of one of the ions, with a probability given by Born’s rule. This ion interacts with the atoms nearby leading to the formation of a droplet. One can reasonably assume that also the wavelet entangled with the selected ion has probability one to remain as part of the description of the system. The measurement process is therefore represented by a unitary operator. The wavelet remains sharply localized on a classical path \ It is still a probability wave: it determines the probability that another atom be ionized. This probability is essentially zero unless the atom lies on \ . This gives the visible track. (shrink)

The primary quantum mechanical equation of motion entails that measurements typically do not have determinate outcomes, but result in superpositions of all possible outcomes. Dynamical collapse theories (e.g. GRW) supplement this equation with a stochastic Gaussian collapse function, intended to collapse the superposition of outcomes into one outcome. But the Gaussian collapses are imperfect in a way that leaves the superpositions intact. This is the tails problem. There are several ways of making this problem more precise. But many authors dismiss (...) the problem without considering the more severe formulations. Here I distinguish four distinct tails problems. The first (bare tails problem) and second (structured tails problem) exist in the literature. I argue that while the first is a pseudo-problem, the second has not been adequately addressed. The third (multiverse tails problem) reformulates the second to account for recently discovered dynamical consequences of collapse. Finally the fourth (tails problem dilemma) shows that solving the third by replacing the Gaussian with a non-Gaussian collapse function introduces new conflict with relativity theory. (shrink)

I distinguish two types of reduction within the context of quantum-classical relations, which I designate “formal” and “empirical”. Formal reduction holds or fails to hold solely by virtue of the mathematical relationship between two theories; it is therefore a two-place, a priori relation between theories. Empirical reduction requires one theory to encompass the range of physical behaviors that are well-modeled in another theory; in a certain sense, it is a three-place, a posteriori relation connecting the theories and the domain of (...) physical reality that both serve to describe. Focusing on the relationship between classical and quantum mechanics, I argue that while certain formal results concerning singular \ limits have been taken to preclude the possibility of reduction between these theories, such results at most provide support for the claim that singular limits block reduction in the formal sense; little if any reason has been given for thinking that they block reduction in the empirical sense. I then briefly outline a strategy for empirical reduction that is suggested by work on decoherence theory, arguing that this sort of account remains a fully viable route to the empirical reduction of classical to quantum mechanics and is unaffected by such singular limits. (shrink)

Taking Arthur Fine’s The Shaky Game as my inspiration, and the recent 25th anniversary of the publication of that work as the occasion to exercise that inspiration, I sketch an alternative to the “Naturalism” prevalent among philosophers of physics. Naturalism is a methodology eventuating in a metaphysics. The methodology is to seek the deep framework assumptions that make the best sense of science; the metaphysics is furnished by those assumptions and supported by their own support of science. The alternative presented (...) here, which I call “Locavoracity,” shares Naturalism’s commitment to making sense of science, but alters Naturalism’s methodology. The Locavore’s sense-making projects are piecemeal, rather than sweeping. The Locavore’s hypothesis is that the collection of local sense-making projects fails to issue a single overarching unifying framework deserving of the title “the metaphysics that makes the best sense of science.” I muster some examples supporting the Locavore hypothesis from the interpretation of quantum field theories. (shrink)

A major disagreement between different views about the foundations of quantum mechanics concerns whether for a theory to be intelligible as a fundamental physical theory it must involve a ‘primitive ontology’ (PO), i.e. variables describing the distribution of matter in four-dimensional space–time. In this article, we illustrate the value of having a PO. We do so by focusing on the role that the PO plays for extracting predictions from a given theory and discuss valid and invalid derivations of predictions. To (...) this end, we investigate a number of examples based on toy models built from the elements of familiar interpretations of quantum theory. (shrink)

Quantum theory’s irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be consistent with it. It must make it possible to identify a system of observables that have measurement-independent values.What makes this possible is the incompleteness of the spatiotemporal differentiation of the physical world. This is shown by applying a novel interpretive principle to interfering (...) alternatives involving distinctions between regions of space. Applying the same interpretive principle to alternatives involving distinctions between things makes it safe to claim that the macroworld comes into being through a progressive differentiation of a single, intrinsically undifferentiated entity. By entering into reflexive spatial relations, this entity gives rise to (1) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (2) what looks like a substantial expanse if the spatial quality of the relations is reified. The necessary distinction between two domains (classical and quantum, or macro and micro) and their mutual dependence is best understood as a distinction between the manifested world and its manifestation. [Paper presented at BergeFest, a conference celebrating the 60th birthday of Berge Englert, held at the Centre for Quantum Technologies, National University of Singapore, 22–25 April 2014]. (shrink)

We define a complete measurement of a quantum observable (POVM) as a measurement of the maximally refined (rank-1) version of the POVM. Complete measurements give information on the multiplicities of the measurement outcomes and can be viewed as state preparation procedures. We show that any POVM can be measured completely by using sequential measurements or maximally refinable instruments. Moreover, the ancillary space of a complete measurement can be chosen to be minimal.

In order to claim that one has experimentally tested whether a noncontextual ontological model could underlie certain measurement statistics in quantum theory, it is necessary to have a notion of noncontextuality that applies to unsharp measurements, i.e., those that can only be represented by positive operator-valued measures rather than projection-valued measures. This is because any realistic measurement necessarily has some nonvanishing amount of noise and therefore never achieves the ideal of sharpness. Assuming a generalized notion of noncontextuality that applies to (...) arbitrary experimental procedures, it is shown that the outcome of a measurement depends deterministically on the ontic state of the system being measured if and only if the measurement is sharp. Hence for every unsharp measurement, its outcome necessarily has an indeterministic dependence on the ontic state. We defend this proposal against alternatives. In particular, we demonstrate why considerations parallel to Fine’s theorem do not challenge this conclusion. (shrink)

What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wave function ontology: the view according to which the wave function mathematically represents in a complete way fundamentally all there is in the world. Erwin Schroedinger was one of the first proponents of such a view, but he dismissed it after he realized it led to macroscopic superpositions (if the wave function evolves in (...) time according to the equations that has his name). The Many-Worlds interpretation1 accepts the existence of such macroscopic superpositions but takes it that they can never be observed. Superposed objects and superposed observers split together in different worlds of the type of the one we appear to live in. For these who, like Schroedinger, think that macroscopic superpositions are a problem, the common wisdom is that there are two alternative views: "Either the wave function, as given by the Schroedinger equation, is not everything, or is not right" [Bell 1987]. The deBroglie-Bohm theory, now commonly known as Bohmian Mechanics, takes the first option: the description provided by a Schroedinger-evolving wave function is supplemented by the information provided by the configuration of the particles. The second possibility consists in assuming that, while the wave function provides the complete description of the system, its temporal evolution is not given by the Schroedinger equation. Rather, the usual Schroedinger evolution is interrupted by random and sudden "collapses". The most promising theory of this kind is the GRW theory, named after the scientists that developed it: Gian Carlo Ghirardi, Alberto Rimini and Tullio Weber.. It seems tempting to think that in GRW we can take the wave function ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper we will argue that such "bare" wave function ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wave function simpliciter. That is, we need more structure than the one provided by the wave function. As a response, quantum theories about the wave function can be supplemented with structure, without taking it as an additional ontology. We argue in reply that such "dressed-up" versions of wave function ontology are not sensible, since they compromise the acceptability of the theory as a satisfactory fundamental physical theory. Therefore we maintain that: 1- Strictly speaking, it is not possible to interpret quantum theories as theories about the wave function; 2- Even if the wave function is supplemented by additional non-ontological structures, there are reasons not to take the resulting theory seriously. Moreover, we will argue that any of the traditional responses to the measurement problem of quantum mechanics (Bohmian mechanics, GRW and Many-Worlds), contrarily to what commonly believed, share a common structure. That is, we maintain that: 3- All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time. (shrink)

For a long time it was believed that it was impossible to be realist about quantum mechanics. It took quite a while for the researchers in the foundations of physics, beginning with John Stuart Bell [Bell 1987], to convince others that such an alleged impossibility had no foundation. Nowadays there are several quantum theories that can be interpreted realistically, among which Bohmian mechanics, the GRW theory, and the many-worlds theory. The debate, though, is far from being over: in what respect (...) should we be realist regarding these theories? Two diff erent proposals have been made: on the one hand, there are those who insist on a direct ontological interpretation of the wave function as representing physical bodies, and on the other hand there are those who claim that quantum mechanics is not really about the wave function. In this paper we will present and discuss one proposal of the latter kind that focuses on the notion of primitive ontology. (shrink)

I present a very general and simple argument—based on the no-signalling theorem—showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility (...) of reproducing the macroscopic measurement results). Although I believe this form of the argument is new, I argue it is essentially a variant of Einstein’s reasoning in the context of the EPR paradox—which is thereby illuminated from a new angle. (shrink)

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to (...) zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process. (shrink)

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting ‘not completely positive’ evolution, but as linear extensions, to a system’s entire state space, of CP maps that are only partially (...) defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted. (shrink)

Stochastic dynamical reduction for the case of spin-z measurement of a spin-1/2 particle describes a random walk on the spin-z axis. The measurement’s result depends on which of the two points: spin-z=±ħ/2 is reached first. Born’s rule is recovered as long as the expected step size in spin-z is independent of proximity to endpoints. Here, we address the questions raised by this description: (1) When is collapse triggered, and what triggers it? (2) Why is the expected step size in spin-z (...) (as opposed to polar angle) independent of proximity to endpoints? (3) Why does spin “lock” in the vertical directions? The difficulties associated with (1) are rooted, as is Bell’s theorem, in the time-asymmetric assumption that the present distribution over hidden variables is independent of future settings. We believe, a priori of any of the experiments of modern physics, that such a time-asymmetric assumption is dubious when probing the microscopic scale. As for (2) and (3), they are simultaneously resolved by abandoning the fundamental distinction drawn between spin and spatial angular momentum, and by appealing to very tiny (in both magnitude and spatial extent) but numerous patches of magnetic noise in the Stern-Gerlach’s field. (shrink)

This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies (...) of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)

In our previous work, a new approach to the notorious problem of quantum measurement was proposed. Existing treatments of the problem were incorrect because they ignored the disturbance of measurement by identical particles and standard quantum mechanics had to be modified to obey the cluster separability principle. The key tool was the notion of separation status. Changes of separation status occur during preparations, registrations and scattering on macroscopic targets. Standard quantum mechanics does not provide any correct rules that would govern (...) these changes. This gives us the possibility to add new rules to quantum mechanics that would satisfy the objectification requirement. The method of the present paper is to start from the standard unitary evolution and then introduce minimal corrections. Several representative examples of registration and particle scattering on macroscopic targets are analysed case by case in order to see their common features. The resulting general Rule of Separation Status Changes is stated in the Conclusion. (shrink)

When a single beam-splitter receives two beams of bosons described by Fock states (Bose-Einstein condensates at very low temperatures), interesting generalizations of the two-photon Hong-Ou-Mandel effect take place for larger number of particles. The distributions of particles at two detectors behind the beam splitter can be understood as resulting from the combination of two effects, the spontaneous phase appearing during quantum measurement, and the quantum angle. The latter introduces quantum “population oscillations”, which can be seen as a generalized Hong-Ou-Mandel effect, (...) although they do not always correspond to even-odd oscillations. (shrink)

Machine generated contents note: Introduction; 1. Historical perspective; 2. Present situation, remaining conceptual difficulties; 3. The theorem of Einstein, Podolsky and Rosen; 4. Bell theorem; 5. More theorems; 6. Quantum entanglement; 7. Applications of quantum entanglement; 8. Quantum measurement; 9. Experiments, quantum reduction seen in real time; 10. Various interpretations; Conclusion; Appendices; Index.