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)

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)

Is the quantum state part of the furniture of the world? Einstein found such a position indigestible, but here I present a different understanding of the wavefunction that is easy to stomach. First, I develop the idea that the wavefunction is nomological in nature, showing how the quantum It or Bit debate gets subsumed by the corresponding It or Bit debate about laws of nature. Second, I motivate the nomological view by casting quantum mechanics in a “classical” formalism (Hamilton–Jacobi theory) (...) and classical mechanics in a “quantum” formalism (Koopman–von Neumann theory) and then comparing and contrasting classical and quantum wave functions. I argue that Humeans about laws can treat classical and quantum wave functions on a par and that doing so yields many benefits. (shrink)

Delineating the framework for a fundamental model of long-range coherence in biological systems is said to rely on principles beyond parameters addressed by current physical science. Just as phenomena of quantum mechanics lay beyond tools of classical Newtonian mechanics we must now enter a 3rd regime of unified field, UF mechanics. In this paper we present a battery of nine empirical protocols for manipulating long-range coherence in complex self-organized living systems (SOLS) in a manner surmounting the Copenhagen Interpretation of quantum (...) uncertainty (space-quantization) thereby allowing empirical access to underlying coherent biophysical principles driving self-organization. Interestingly, while the UF is not indicative of a 5th fundamental force in the usual phenomenal sense of quantal transfer during field interactions; it does however provide an inherent ‘force of coherence’ in an energyless ontological sense by a process called ‘topological switching’ of higher dimensional (HD) brane dynamics. It is this putative inherent property that produces long-range coherence and leads to the possibility of its direct experimental mediation. (shrink)

A model for measurement in collapse-free nonrelativistic fermionic quantum field theory is presented. In addition to local propagation and effectively-local interactions, the model incorporates explicit representations of localized observers, thus extending an earlier model of entanglement generation in Everett quantum field theory (Rubin in Found. Phys. 32:1495–1523, 2002). Transformations of the field operators from the Heisenberg picture to the Deutsch-Hayden picture, involving fictitious auxiliary fields, establish the locality of the model. The model is applied to manifestly-local calculations of the results (...) of measurements, using a type of sudden approximation and in the limit of massive systems in narrow-wavepacket states. Detection of the presence of a spin-1/2 system in a given spin state by a freely-moving two-state observer illustrates the features of the model and the nonperturbative computational methodology. With the help of perturbation theory the model is applied to a calculation of the quintessential “nonlocal” quantum phenomenon, spin correlations in the Einstein-Podolsky-Rosen-Bohm experiment. (shrink)

The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best (...) available interpretation defended. The main objections to the interpretation, including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all. (shrink)

The purpose of this paper is to review and clarify the quantum “measurement problem.” The latter originates in the ambivalent nature of the “observer”: Although the observer is not described by the Schrödinger equation, it should nevertheless be possible to “quantize” him and include him in the wave function if quantum theory is universally valid. The problem is to prove that no contradiction may arise in these two conflicting descriptions. The proof invokes the notion of irreversibility. The validity of the (...) latter is questionable, because the standard rationale for classical irreversibility, namely mixing and coarse graining, does not apply to quantum theory. There is no chaos in a closed, finite quantum system. However, when a system is large enough, it cannot be perfectly isolated from its “environment,” namely from external (or even internal) degrees of freedom which are not fully accounted for in the Hamiltonian of that system. As a consequence, the long-range evolution of such a quantum system is essentially unpredictable. It follows that the notion of irreversibility is a valid one in quantum theory and the “measurement problem” can be brought to a satisfactory solution. (shrink)

James Ladyman has argued that constructive empiricism entails modal realism, and that this renders constructive empiricism untenable. We maintain that constructive empiricism is compatible with modal nominalism. Although the central term 'observable' has been analyzed in terms of counterfactuals, and in general counterfactuals do not have objective truth conditions, the property of being observable is not a modal property, and hence there are objective, non-modal facts about what is observable. Both modal nominalism and constructive empiricism require clarification in the face (...) of Ladyman's argument. But we also argue that, even if Ladyman were right that constructive empiricism entails modal realism, this would not be a problem for constructive empiricism. (shrink)

This paper argues that ontic structural realism (OSR) faces a dilemma: either it remains on the general level of realism with respect to the structure of a given theory, but then it is, like epistemic structural realism, only a partial realism; or it is a complete realism, but then it has to answer the question how the structure of a given theory is implemented, instantiated or realized and thus has to argue for a particular interpretation of the theory in question. (...) This claim is illustrated by examining how OSR fares with respect to the three main candidates for an ontology of quantum mechanics, namely many worlds-type interpretations, collapse-type interpretations and hidden variable-type interpretations. The result is that OSR as such is not sufficient to answer the question of what the world is like if quantum mechanics is correct. (shrink)

At a first glance, and even at a second one, it seems that if time is linear the threat of determinism is more severe than if time is branching, since in the latter case the future is open in a way it is not in the former one where, so to speak, there exists only one branch – one future. In this paper, I want to give a 'third glance' at this claim. I acknowledge that such a claim is intuitive (...) (this is the first glance) and that it is also meaningfully and interestingly defended in recent literature where branching time is either said to imply indeterminism or at least to be compatible with it. To try to make my third glance as precise and as fleshed out as possible, I shall first concentrate on what 'branching' is or could be, and I shall discuss various versions and interpretations of this view. I shall then (more quickly) turn my attention to what determinism is or could be, and I will distinguish three (well-known) kinds of it – focusing mainly on 'metaphysical determinism'. Having these tools in hand, I will then ask (and answer) the question whether branching time helps with avoiding determinism or not. As we shall see, it is incorrect to think that under the branching hypothesis the threat of determinism is any smaller – rather, I will argue that if one has reasons to think that determinism is true, branching will not help, and that the issue of branching versus linear time is then actually neutral with respect to the question whether determinism or indeterminism is true. (shrink)

David Wallace has given a decision-theoretic argument for the Born Rule in the context of Everettian quantum mechanics. This approach promises to resolve some long-standing problems with probability in EQM, but it has faced plenty of resistance. One kind of objection charges that the requisite notion of decision-theoretic uncertainty is unavailable in the Everettian picture, so that the argument cannot gain any traction; another kind of objection grants the proof’s applicability and targets the premises. In this article I propose some (...) novel principles connecting the physics of EQM with the metaphysics of modality, and argue that in the resulting framework the incoherence problem does not arise. These principles also help to justify one of the most controversial premises of Wallace’s argument, ‘branching indifference’. Absent any a priori reason to align the metaphysics with the physics in some other way, the proposed principles can be adopted on grounds of theoretical utility. The upshot is that Everettians can, after all, make clear sense of objective probability. 1 Introduction2 Setup3 Individualism versus Collectivism4 The Ingredients of Indexicalism5 Indexicalism and Incoherence5.1 The trivialization problem5.2 The uncertainty problem6 Indexicalism and Branching Indifference6.1 Introducing branching indifference6.2 The pragmatic defence of branching indifference6.3 The non-existence defence of branching indifference6.4 The indexicalist defence of branching indifference7 Conclusion. (shrink)

In the age of ubiquitous technology, humans are reshaped through each transaction they are involved in. AI-driven networks, online games, and multisensory interactive environments make up alternate realities. Within such alternate worlds, users are reshaped as deterministic agents. Technology’s focus on reducing complexity leads to a human being dependent on prediction-driven machines and behaving like them. Meaning and information are disconnected. Existence is reduced to energy processes. The immense gain in efficiency translates as prosperity. Citizens of advanced economies, hurrying in (...) the rhythm of machine-driven interactions, feel entitled to it. Successful at the price of self-awareness, they no longer know what this means. Happiness and prosperity are not consubstantial. Lack of happiness leads to aggression. This is the image of the world as we see it, no longer looking at each other, eye to eye, but screen to screen. The questions eliminated in the process of transferring responsibility from the individual to machines will inevitably become society’s new focus. When the goal is to get everyone to behave like a machine, the Singularity hypothesis becomes self-fulfilling prophecy. If, in addition to having exhausted natural resources, society does not want to end up making the human mind superfluous, it has to seek a better understanding of what makes anticipation possible. As a definitory characteristic of the living, corresponding to its complexity, anticipation can no longer be taken for granted, while every effort is made to reduce complexity for efficiency’s sake. Awareness of the processes conducive to its expression in successful human action will position human beings as masters of their destiny, not slaves of their own making. Antecapere ergo sum might be the counterclaim to Descartes’ Dubito ergo sum . To resist being perfected into oblivion, that is, unsustainable prosperity, means to reclaim the knowledge corresponding to higher levels of complexity. (shrink)

We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and (...) relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

This article analyzes the implications of protective measurement for the meaning of the wave function. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wave function. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion is not continuous but (...) discontinuous and random. This result suggests a new interpretation of the wave function, according to which the wave function is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wave function disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wave function. (shrink)

Neuropsychological research on the neural basis of behaviour generally posits that brain mechanisms will ultimately suffice to explain all psychologically described phenomena. This assumption stems from the idea that the brain is made up entirely of material particles and fields, and that all causal mechanisms relevant to neuroscience can therefore be formulated solely in terms of properties of these elements. Thus, terms having intrinsic mentalistic and/or experiential content (e.g. ‘feeling’, ‘knowing’ and ‘effort’) are not included as primary causal factors. This (...) theoretical restriction is motivated primarily by ideas about the natural world that have been known to be fundamentally incorrect for more than three-quarters of a century. Contemporary basic physical theory differs profoundly from classic physics on the important matter of how the consciousness of human agents enters into the structure of empirical phenomena. The new principles contradict the older idea that local mechanical processes alone can account for the structure of all observed empirical data. Contemporary physical theory brings directly and irreducibly into the overall causal structure certain psychologically described choices made by human agents about how they will act. This key development in basic physical theory is applicable to neuroscience, and it provides neuroscientists and psychologists with an alternative conceptual framework for describing neural processes. Indeed, owing to certain structural features of ion channels critical to synaptic function, contemporary physical theory must in principle be used when analysing human brain dynamics. The new framework, unlike its classic-physics-based predecessor, is erected directly upon, and is compatible with, the prevailing principles of physics. It is able to represent more adequately than classic concepts the neuroplastic mechanisms relevant to the growing number of empirical studies of the capacity of directed attention and mental effort to systematically alter brain function.. (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)

An account is given of a recent proposal to complete modern quantum theory by adding a characterisation of consciousness. The resulting theory is applied to give mechanisms for typical parapsychological phenomena, and ways of testing it are discussed.

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

This is a philosophical paper in favor of the many-worlds interpretation of quantum theory. The necessity of introducing many worlds is explained by analyzing a neutron interference experiment. The concept of the “measure of existence of a world” is introduced and some difficulties with the issue of probability in the framework of the MWI are resolved.

The central part of Everett's formulation of quantum mechanics is a quantum mechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. ;The fundamental aim of this dissertation is to find a set of simpler assumptions (...) which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantum mechanical systems; an assumption of supervenience of mental states over quantum mechanical properties; and an assumption about the interpretation of quantum mechanical states in general: quantum mechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantum mechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. ;Using the three assumptions, I argue that introspection cannot determine the objective quantum mechanical state of an observer. Rather, the introspective qualities of a quantum mechanical state can be represented by a statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantum mechanical state is impossible in principle. Empirical reality for a conscious observer is not described by the objective state, but by a Everettian relative state conditional on the subjective state, and no theoretical 'mark of reality' is necessary for this concept of reality. I compare the resulting concept of reality to Kant's distinction between empirical and transcendental reality. (shrink)

The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

Deutsch and Hayden claim to have provided an account of quantum mechanics which is particularly local, and which clarifies the nature of information transmission in entangled quantum systems. In this paper, a perspicuous description of their formalism is offered and their claim assessed. It proves essential to distinguish, as Deutsch and Hayden do not, between two ways of interpreting the formalism. On the first, conservative, interpretation, no benefits with respect to locality accrue that are not already available on either an (...) Everettian or a statistical interpretation; and the conclusions regarding information flow are equivocal. The second, ontological, interpretation, offers a framework with the novel feature that global properties of quantum systems are reduced to local ones; but no conclusions follow concerning information flow in more standard quantum mechanics. (shrink)

A Philosopher Looks at Quantum Mechanics’ (Putnam [1965]) explained why the interpretation of quantum mechanics is a philosophical problem in detail, but with only the necessary minimum of technicalities, in the hope of making the difficulties intelligible to as wide an audience as possible. When I wrote it, I had not seen Bell ([1964]), nor (of course) had I seen Ghirardi et al. ([1986]). And I did not discuss the ‘Many Worlds’ interpretation. For all these reasons, I have decided to (...) make a similar attempt forty years later, taking account of additional interpretations and of our knowledge concerning non-locality. (The Quantum Logical interpretation proposed in Putnam [1968] is not considered in the present paper, however, because Putnam [1994b] concluded that it was unworkable.) Rather than advocate a particular interpretation, this paper classifies the possible kinds of interpretation, subject only to the constraints of a very broadly construed scientific realism. Section 7 does, however, argue that two sorts of interpretation—ones according to which a ‘collapse’ is brought about by the measurement (e.g. the traditional ‘Copenhagen’ interpretation), and the Many Worlds interpretation or interpretations—should be ruled out. The concluding section suggests some possible morals of a cosmological character. Background Scientific realism is the premise of my discussion What ‘quantum mechanics’ says—and some problems Other interpretations of quantum mechanics The problem of Einstein's bed Classification of the possible kinds of interpretation Which interpretations I think we can rule out The ‘moral’ of this discussion. (shrink)

The aim of this essay is to distinguish and analyze several difficulties confronting attempts to reconcile the fundamental quantum mechanical dynamics with Born''s rule. It is shown that many of the proposed accounts of measurement fail at least one of the problems. In particular, only collapse theories and hidden variables theories have a chance of succeeding, and, of the latter, the modal interpretations fail. Any real solution demands new physics.

This article provides an overview of the philosophical literature on the GRW theory of quantum mechanics, and argues for a particular position regarding that literature. Much of the literature is ontological; it attempts to defend a conception of what the world is like according to the GRW theory against perceived competitors. I argue that there is no real debate here, since these supposedly conflicting positions are better regarded as alternative and compatible ways of describing the world of the GRW theory.

Recent developments in cosmology indicate that every history having a non-zero probability is realized in infinitely many distinct regions of spacetime. Thus, it appears that the universe contains infinitely many civilizations exactly like our own, as well as infinitely many civilizations that differ from our own in any way permitted by physical laws. We explore the implications of this conclusion for ethical theory and for the doomsday argument. In the infinite universe, we find that the doomsday argument applies only to (...) effects which change the average lifetime of all civilizations, and not those which affect our civilization alone. (shrink)

A source of much difficulty and confusion in the interpretation of quantum mechanics is a naive realism about operators. By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about measuring operators that occurs when the subject is quantum mechanics. Without a specification of what should be meant by measuring a quantum observable, such an expression can have no clear meaning. A definite specification is provided by (...) Bohmian mechanics, a theory that emerges from Schrödinger's equation for a system of particles when we merely insist that particles means particles. Bohmian mechanics clarifies the status and the role of operators as observables in quantum mechanics by providing the operational details absent from standard quantum mechanics. It thereby allows us to readily dismiss all the radical claims traditionally enveloping the transition from the classical to the quantum realm — for example, that we must abandon classical logic or classical probability. The moral is rather simple: Beware naive realism, especially about operators! (shrink)

In a recent paper, Howard Stein makes a number of criticisms of an earlier paper of mine ('Are Probabilism and Special Relativity Incompatible?', Phil. Sci., 1985), which explored the question of whether the idea that the future is genuinely 'open' in a probabilistic universe is compatible with special relativity. I disagree with almost all of Stein's criticisms.

There is a recurring line of argument in the literature to the effect that Bohm's theory fails to solve the measurement problem. I show that this argument fails in all its variants. Hence Bohm's theory, whatever its drawbacks, at least succeeds in solving the measurement problem. I briefly discuss a similar argument that has been raised against the GRW theory.

The Everett interpretation of quantum theory requires either the existence of an infinite number of conscious minds associated with each brain or the existence of one universal consciousness. Reasons are given, and the two ideas are compared.

Christopher G. Timpson provides the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. He argues for an ontologically deflationary account of the nature of quantum information, which is grounded in a revisionary analysis of the concepts of information.

In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two separate noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements on a d-state particle, we recast the standard von Neumann measurement formalism by replacing the familiar pointer variable with an array of such detectors, one for each of the d possible outcomes. We show that the unitary dynamics of the pre-measurement process restricts the detector outputs to the (...) subspace of single outcomes, so that the pointer emerges from the apparatus. We propose a physical extension of this apparatus which replaces each detector with an ancilla qubit coupled to a readout device. This explicitly separates the pointer into distinct quantum and (effectively) classical parts, and delays the quantum to classical transition. As a result, one not only recovers the collapse scenario of an ordinary apparatus, but one can also observe a superposition of the quantum pointer states. (shrink)

We give an analysis over a variation of causal sets where the light cone of an event is represented by finitely branching trees with respect to any given arbitrary dynamics. We argue through basic topological properties of Cantor space that under certain assumptions about the universe, spacetime structure and causation, given any event x, the number of all possible future worldlines of x within the many-worlds interpretation is uncountable. However, if all worldlines extending the event x are ‘eventually deterministic’, then (...) the cardinality of the set of future worldlines with respect to x is exactly ℵ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\aleph _0$$\end{document}, i.e., countably infinite. We also observe that if there are countably many future worldlines with respect to x, then at least one of them must be necessarily ‘decidable’ in the sense that there is an algorithm which determines whether or not any given event belongs to that worldline. We then show that if there are only finitely many worldlines in the future of an event x, then they are all decidable. We finally point out the fact that there can be only countably many terminating worldlines. (shrink)

Hájek (Erkenntnis 70(2):211–235, 2009) argues that probabilities cannot be the limits of relative frequencies in counterfactual infinite sequences. I argue for a different understanding of these limits, drawing on Norton’s (Philos Sci 79(2):207–232, 2012) distinction between approximations (inexact descriptions of a target) and idealizations (separate models that bear analogies to the target). Then, I adapt Hájek’s arguments to this new context. These arguments provide excellent reasons not to use hypothetical frequencies as idealizations, but no reason not to use them as (...) approximations. (shrink)

We start by very briefly describing the measurement problem in quantum mechanics and its solution by the Many Worlds Interpretation. We then describe the preferred basis problem, and the role of decoherence in the MWI. We discuss a number of approaches to the preferred basis problem and argue that contrary to the received wisdom, decoherence by itself does not solve the problem. We address Wallace’s emergentist approach based on what he calls Dennett’s criterion, and we compare the logical structure of (...) Wallace’s argument that the Hilbert space structure and the unitary dynamics should be considered a complete description of the physics of the universe with the logical structure of the EPR argument against the completeness of quantum mechanics. Then, we consider the nature of so-called “high level emergent facts” and Dennett’s criterion in Wallace’s approach and we discuss the implications of its non-reductive nature. Finally, we conclude that the MWI is not a straightforward interpretation of pure quantum mechanics that doesn't add anything to it. Whether or not it is more parsimonious than other quantum mechanical theories depends on the details of the additions. (shrink)

The problem of multiple-computations discovered by Hilary Putnam presents a deep difficulty for functionalism (of all sorts, computational and causal). We describe in out- line why Putnam’s result, and likewise the more restricted result we call the Multiple- Computations Theorem, are in fact theorems of statistical mechanics. We show why the mere interaction of a computing system with its environment cannot single out a computation as the preferred one amongst the many computations implemented by the system. We explain why nonreductive (...) approaches to solving the multiple- computations problem, and in particular why computational externalism, are dualistic in the sense that they imply that nonphysical facts in the environment of a computing system single out the computation. We discuss certain attempts to dissolve Putnam’s unrestricted result by appealing to systems with certain kinds of input and output states as a special case of computational externalism, and show why this approach is not workable without collapsing to behaviorism. We conclude with some remarks about the nonphysical nature of mainstream approaches to both statistical mechanics and the quantum theory of measurement with respect to the singling out of partitions and observables. (shrink)

The second law of thermodynamics is traditionally interpreted as a coarse-grained result of classical mechanics. Recently its relation with quantum mechanical processes such as decoherence and measurement has been revealed in literature. In this paper we will formulate the second law and the associated time irreversibility following Everett’s idea: systems entangled with an object getting to know the branch in which they live. Accounting for this self-locating knowledge, we get two forms of entropy: objective entropy measuring the uncertainty of the (...) state of the object alone, and subjective entropy measuring the information carried by the self-locating knowledge. By showing that the summation of the two forms of entropy is a conserved and perspective-free quantity, we interpret the second law as a statement of irreversibility in knowledge acquisition. This essentially derives the thermodynamic arrow of time from the subjective arrow of time, and provides a unified explanation for varieties of the second law, as well as the past hypothesis. (shrink)

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

The question “what is an interpretation?” is often intertwined with the perhaps even harder question “what is a scientific theory?”. Given this proximity, we try to clarify the first question to acquire some ground for the latter. The quarrel between the syntactic and semantic conceptions of scientific theories occupied a large part of the scenario of the philosophy of science in the 20th century. For many authors, one of the two currents needed to be victorious. We endorse that such debate, (...) at least in the terms commonly expressed, can be misleading. We argue that the traditional notion of “interpretation” within the syntax/semantic debate is not the same as that of the debate concerning the interpretation of quantum mechanics. As much as the term is the same, the term “interpretation” as employed in quantum mechanics has its meaning beyond (pure) logic. Our main focus here lies on the formal aspects of the solutions to the measurement problem. There are many versions of quantum theory, many of them incompatible with each other. In order to encompass a wider variety of approaches to quantum theory, we propose a different one with an emphasis on pure formalism. This perspective has the intent of elucidating the role of each so-called “interpretation” of quantum mechanics, as well as the precise origin of the need to interpret it. (shrink)

An Aristotelian philosophy of nature rejects the modern prejudice in favor of the microscopic, a rejection that is crucial if we are to penetrate the mysteries of the quantum world. I defend an Aristotelian model by drawing on both quantum chemistry and recent work on the measurement problem. By building on the work of Hans Primas, using the distinction between quantum and classical properties that emerges in quantum chemistry at the thermodynamic or continuum limit, I develop a new version of (...) the Copenhagen interpretation, a version that is realist, holistic, and hylomorphic in character, allowing for the attribution of fundamental causal powers to human observers and their instruments. I conclude with a critique of non-hylomorphic theories of primitive ontology, including Bohmian mechanics, Everettianism, and GRW mass-density. (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)

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain (...) localized around approximately-classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. This formalism could be relevant to the emergence of spacetime from quantum entanglement. (shrink)

This thesis inquires what it means to interpret non-relativistic quantum mechanics (QM), and the philosophical limits of this interpretation. In pursuit of a scientific-realist stance, a metametaphysical method is expanded and applied to evaluate rival interpretations of QM, based on the conceptual distinction between ontology and metaphysics, for objective theory choice in metaphysical discussions relating to QM. Three cases are examined, in which this metametaphysical method succeeds in indicating what are the wrong alternatives to interpret QM in metaphysical terms. The (...) first two cases failed in doing so due to different kinds of underdetermination. In the third case, unlike underdetermination, where there are many choices to be made, a “null-determination” is proposed where there may be no metaphysical choices in the available metaphysical literature. Considering what has been discussed, an agnostic philosophic position is adopted concerning the possibility of interpreting QM from a scientific-realistic point of view. (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)