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Philosophy Today

Methodological Solipsism and the Multiverse

Daniel King

Published Jan 1, 2004• 1 citation
Publisher

Abstract

It is well known that quantum physics deals with phenomena characterized by uncertainty. A typical expression of this uncertainty is the uncertainty principle, where, the more precisely we know the position of a particle, the more imprecisely we know its momentum (and vice versa).Opinions are divided as to whether this epistemological uncertainty is also an ontological uncertainty. Of some relevance here is the following observation by Quentin Smith: Heisenberg originally interpreted [the uncertainty] epistemically, but Bohr convinced him in private communications to accept a verificationist metaphysics, with its attendant ontological interpretation of the uncertainty relations (Smith 2002, 137) There are many competing interpretations of the quantum mechanical mathematical formalism. Of these interpretations, particularly well-known are the so-called Copenhagen interpretation of Bohr (where it is asserted that the position-view and the momentum-view of reality are complementary, and cannot be considered in the same context), and the many-universes interpretation of Hugh Everett. Roughly speaking, the latter asserts that whenever a measurement is made of a particle, the universe splits into copies, each one of which corresponds to the different possible outcomes of the measurement. Many scientists are happy to work with the many-universes interpretation-provided that their working with the theory has no ontological commitment. That is, they are not prepared to believe that the many universes actually exist. David Deutsch, who is one of the leading researchers in the field of quantum computation, is an exception. Indeed, he is the main advocate of the reality of the many universes; and he provides a number of important reasons why he is such an advocate. In the present essay, I intend to look at the arguments for and the arguments against the existence of the many universes, clarifying along the way what the meaning of exist in this regard should be considered to be. A first conclusion will be that while Deutsch's arguments are highly persuasive, there is one telling objection to the existence of the many universes-or multiverse, as the collection of them is becoming known-that must be addressed. My procedure then will be to show that the objection can in fact be met, using the so-called methodological solipsism approach introduced by Hans Driesch and employed subsequently by such theorists as Fodor and Putnam. The Many-Universes Interpretation of Quantum Physics It is not my intention in this essay to become bogged down in the minutiae of quantum physics, where the complexities of the mathematics are exacerbated by the lack of any single way of interpreting it. However, in order to provide a background for my subsequent arguments, I shall discuss briefly a typical and familiar quantum-mechanical scenario: the so-called experiment. My account is based on that of Penrose (1985). The results that may be expected in a performance of the two-slit experiment depend on the fact that sub-microscopic particles, such as electrons or photons, behave sometimes like particles and sometimes like waves. The experiment is simple to describe: typically, a beam of light is directed through a pair of closely-separated and parallel narrow slits to a screen located behind it. Penrose describes the scenario as follows (it is worth quoting him at length): The most evident manifestation of the light as particles . . occurs at the screen. The light arrives there in discrete localized units of energy.. .. Never is the energy of just half a photon... received. Light reception is an all-or-nothing phenomenon in photon units. Only whole numbers of photons are ever seen. However, a wavelike behaviour seems to arise as the photons pass through the slits. Suppose, first, that only one slit is open (the other being blocked off). After passing through, the light will spread out-by. …

DOI
10.5840/philtoday200448326

Related papers

Many Worlds?: Everett, Quantum Theory, and Reality

Robert M. Wald

Few, if any, issues in physics have engendered as much discussion as the measurement problem in quantum mechanics. It is generally agreed that the `normal' dynamical evolution of the state vector in quantum mechanics is given by a unitary map. The linearity of this map implies that the state vector will, in general, be found in a superposition of eigenstates of a given observable (or, similarly, that the density matrix describing a subsystem will not correspond to a definite value of this observable). However, when we make a measurement of an observable, we always obtain a define value—although it is impossible to predict with certainty which value will be obtained. The traditional response to this issue is to postulate that when a measurement is made, the wavefunction `collapses' to an eigenstate of the observable being measured, perhaps due to the inherent classicality of the measuring apparatus (Bohr), or to the consciousness of the observer (Wigner), or possibly to some modification of quantum dynamics that occurs even when observations are not being made. The main motivation for the Everett (`many worlds') interpretation is to avoid introducing any such collapse postulate. This volume commemorates the 50th anniversary of the publication of Everett's paper in 1957 and contains 20 original articles as well as the transcripts of several discussions that took place at meetings devoted to the Everett interpretation at Oxford University and the Perimeter Institute. The attractiveness of the Everett interpretation is very succinctly summarized by a sentence from Vaidman's contribution (p 582): `The collapse, with its randomness, non-locality and the lack of a well-defined moment of occurrence, is such an ugly scar on quantum theory, that I, along with many others, am ready to follow Everett and deny its existence.' But the main drawback of the interpretation is then equally succinctly stated in the next sentence: `The price is the many worlds interpretation, i.e., the existence of numerous parallel worlds.' In other words, if the state vector evolves to have a non-zero amplitude for two different values of an observable that I `measure' (i.e., interact with in an appropriate way), each of these alternatives remains equally `real', i.e., there is a `branch' of the wavefunction in which the observable takes the first value and I believe that it has this first value and a branch of the wavefunction where it takes the second value and I believe that it has this second value. Each of these `me's' sees a definite value for the observable, thus nicely accounting for what I believe I experience without invoking collapse. But then, it seems that I have to believe that there are many other `me's' around—even if they are very difficult for this particular me to access—and no way I can predict which `me' I will be in the future. Indeed, Saunders writes on p 192, `If Alice is a person (of course she is) then we must say, even prior to branching at tj that there are many Alices present, atom for atom duplicates...Alice should be uncertain after all— each Alice should be uncertain—for each as of tj does not (and as a matter of principle, cannot) know which of these branching persons she is.' Thus, if taken seriously, the Everett viewpoint leads directly to questions like `What determines which ``me'' I am now and/or will feel that I am in the future?' The response `You are all of them' somehow doesn't seem satisfying, and further pursuit of these issues would seem to lead to questions as fruitless as questions like `Why am I ``me'' and not ``you''?' I believe that this accounts for why the Everett interpretation does not have universal appeal. But enough of `me' for now (more later); let's discuss the book. Unlike many edited volumes and conference proceedings in physics—which often consist of hastily slapped-together re-hashes of previous papers—this volume meets very high standards in the choice of topics and authors and in the quality of the writing. Although each of the articles is closely tied in with the Everett interpretation, there are many articles of considerable value and interest in their own right, such as the discussion of quasiclassical realms by Hartle and and the discussion of the de Broglie–Bohm interpretation by Valentini. There is also an excellent introduction by Saunders to the quantum measurement problem and the main issues that arise in the Everett interpretation. A central issue in the Everett interpretation is the status of the `Born rule', which asserts that, for state ψ, the probability of obtaining a particular outcome of a measurement is ||Pψ||2, where P is the projection operator onto the eigensubspace associated with the measurement outcome. In traditional interpretations, the Born rule is simply postulated as part of the collapse hypothesis. In the Everett interpretation, it is far from obvious that the Born rule even has any meaning—if all outcomes occur, how can one talk about the probability of a particular outcome? Given the importance of this issue, it is highly appropriate that four chapters of the book (by Saunders, Papineau, Wallace, and Greaves and Myrvold) are devoted to addressing probability and the Born rule from the Everett viewpoint, and three chapters (by Kent, Albert, and Price) are devoted to criticising these views. As indicated by the above quote from Saunders' article, uncertainty and probability can enter the Everett interpretation via each Alice being uncertain as to which Alice she is or will be. However, in view of the difficulties to which this kind of argumentation will lead, it is perhaps not surprising that in the 123 pages of combined discussion by Saunders, Papineau, Wallace, and Greaves and Myrvold, there are only fleeting references to the use of probability along these lines. Rather, the approach taken is reminiscent of that of adept politicians: if you can't answer a question, then answer a different question, and answer it with conviction and detail. Instead of considering probabilities of outcomes—a highly problematical notion when all of the possible outcomes actually occur—consider only decision theory issues. In particular, Wallace gives a precise and detailed mathematical proof that, under certain hypotheses, the only rational strategy that a quantum observer can follow in making decisions is to weight the possible outcomes by Born rule probabilities. To illustrate this more graphically, suppose tomorrow's weather were determined by some quantum mechanical, Stern–Gerlach-like process. I would like to know whether it is likely to rain tomorrow. However, when I ask an Everett follower (who knows the state vector and has done the Born rule calculation), all she will tell me in direct response to my question is that `it will rain and it won't rain.' Nevertheless, she is willing tell me whether or not it is rational for me to take an umbrella. I suppose that if she tells me that it would be highly irrational for me to take an umbrella, I can take the hint and deduce that it is very unlikely to rain. However, there does seem something wrong with the fact that she is not allowed to say this directly. In any case, if the conclusion of a mathematically correct argument is that rational decision strategies require the Born rule, then there must be quite a bit lying in the assumptions. The articles by Kent, Albert, and Price do a good job of fleshing out these assumptions and pointing out the weaknesses and flaws in the probability and decision theory discussions within the Everett framework. I hope it is clear from what I have written above that this is an outstanding volume, which should be of great interest to anyone interested in the foundations of quantum theory. Indeed, I feel quite fortunate to be the particular `me' that happens to exist in the same branch of the wavefunction of the universe in which this book was published.

Classical and Quantum Gravity•Apr 21, 2011•24 citations

Cosmology and the many worlds interpretation of quantum mechanics

Viatcheslav Mukhanov

Introduction Although the mathematical structure of quantum mechanics was understood within a few years after it was invented, numerous quantum paradoxes still disturb ‘simple-minded’ physicists. Most of them, as ‘naïve realists’, would probably never take Bohr's own over-philosophical and over-complicated treatment of these paradoxes seriously if they realized the philosophical consequences of the Copenhagen interpretation. To make my meaning clearer, let me quote Bohr's answer to Professor Hoffding's question regarding the double-slit experiment [1]. Bohr was asked: ‘What can the electron be said to be in its travel from the point of entry to the point of detection?’ And he replied: ‘ To be ? To be ? What does it mean to be ?’ However, if one questions the existence of microscopic constituents of macroscopic bodies, then the next logical step would be to question the existence of the macroscopic bodies and even ourselves. Needless to say, very few (if any) of us, when making experiments or analyzing their results, address the question of what it means ‘to be’ every time. Even in the context of elementary particles, probably nobody doubts that the particles exist and somehow travel from the point of entry to the point of detection. Moreover, within the accuracy allowed by the uncertainty relation, these particles can be localized and described just as well as macroscopic ‘classical’ objects.

Cambridge University Press eBooks•Jun 21, 2007•3 citations

Evidence and Uncertainty in Everett’s Multiverse

Paul Tappenden

How does it come about then, that great scientists such as Einstein, Schrödinger and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. […] The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road. (Born [1954], pp. 8, 11) It is truly surprising how little difference all this makes. Most physicists use quantum mechanics every day in their working lives without needing to worry about the fundamental problem of its interpretation. (Weinberg [1992], p. 66) I endorse the view that it may be of no relevance to the acceptability of the Everett interpretation of quantum mechanics as a physical theory whether or not an informed observer can be uncertain about the outcome of a quantum measurement prior to its having occurred. However, I suggest that the very possibility of post-measurement, pre-observation uncertainty has an essential role to play in both confirmation theory and decision theory in a branching universe. This is supported by arguments which do not appeal to van Fraassen’s Reflection Principle. 1. Dendritic Unitary Evolution 2. The Born–Vaidman Rule 3. Greaves on Uncertainty 4. Retroactive Counterfactual Uncertainty 5. Odds and Ends

The British Journal for the Philosophy of Science•Jun 11, 2010•64 citations

Multipartite Nonlocality in Ontological Models of Quantum Theory

Fumiaki Morikoshi

Quantum nonlocality has been a long-standing and fascinating problem in the foundations of quantum theory since its proof by the Bell inequality. It seems to contradict our intuitive picture of space-time and thus urges us to reconsider its foundation. With the advent of quantum information science, it has attracted renewed interest from a fundamental point of view as well as from a quantum information-theoretic one. Another fundamental question on the nature of quantum theory is how we understand what quantum states represent. (Quantum states hereafter refer to pure states.) This is also a long-standing problem since the early days of quantum theory. Roughly speaking, there are two conflicting views on this matter: one is ontology and the other is epistemology. Ontological models of quantum theory are models in which we assume some underlying reality for physical systems and require that all the predictions of quantum theory should be reproduced. The ontological models are divided into two categories, depending on which views the models are based on, ontology or epistemology. In the models based on ontology, quantum states represent the underlying reality in some sense, and different quantum states correspond to different realities. In the models based on epistemology, quantum states do not necessarily correspond to the underlying realities, and even different quantum states can be consistent with a common underlying reality. The former type of ontological models of quantum theory is called 1⁄4-ontic. The latter is called 1⁄4-epistemic. Thus, it might be rather confusing that ontological models are classified further into 1⁄4-ontic models and 1⁄4-epistemic ones. We use these terms here in accordance with the recent literature on quantum foundations. (For details of these notions in the ontological models of quantum theory, see the paper by Harrigan and Spekkens.) Quite recently, the question just mentioned has been answered by Pusey et al., and one of the above models has been refuted. It was shown that 1⁄4-epistemic models are inconsistent with the predictions of quantum theory. In other words, epistemological views on quantum states turned out to be false as long as we assume some underlying reality for physical systems. Therefore, only 1⁄4-ontic models of quantum theory are valid for describing quantum systems. This significantly advances our understanding on the nature of quantum states. It is expected that various conclusions will be drawn from this fact. In this paper, we will discuss a connection with nonlocality. The above two fundamental questions, nonlocality and the nature of quantum states, are intimately connected, and the connection was first implicitly recognised by Einstein in the early days of quantum theory. In a private correspondence with Schrodinger, Einstein constructed a fascinating argument that relates the above two. (That argument is distinctly different from the well-known EPR argument.) Recently, it was revisited and reconstructed in accordance with more rigorous notions in quantum foundations. Nonlocality is usually shown by violations of Bell inequalities. (Bell inequalities hereafter include all the subsequent developments such as the CHSH inequality.) Even if it is not clear whether the models of quantum theory are 1⁄4-ontic or 1⁄4-epistemic, we can prove nonlocality just by showing the violation of Bell inequalities. However, the above argument originated by Einstein implies that if we know the models are 1⁄4-ontic in advance (as we do now), we can prove nonlocality in a simpler way without Bell inequalities. (This argument had been known in quantum foundations before the refutation of 1⁄4-epistemic models.) Nonlocality is rigorously defined as a violation of the notion of local causality defined by Bell. Showing the violation of Bell inequalities is one way of demonstrating the violation of local causality. Since the simpler proof initiated by Einstein directly demonstrates the violation of local causality, it is a more straightforward proof of nonlocality from a conceptual point of view. In the following, we will see that this simple argument of nonlocality without Bell inequalities can be used to show multipartite nonlocality as well. Before moving onto multipartite cases, first let us define the necessary notions for presenting our result. First of all, we assume that there exists a complete specification of the properties of a physical system, which we refer to as the ontic state of that system. The ontic states represent the underlying realities and are not necessarily equal to ordinary quantum states. (In other words, the ontic states correspond to hidden variables.) Ontological models of quantum theory are models that assume ontic states and reproduce all the predictions of quantum theory. An important question is how ontic states correspond to quantum states in quantum theory. In order to frame the question accurately, we need the notion of an epistemic state, which represents the relation between them. Suppose we prepare a physical system in a quantum state 1⁄4. Although the system is uniquely specified as 1⁄4 in quantum theory, there still remains a possibility that it allows a more detailed specification in the ontic state space, in which case many different ontic states turn out to be consistent with 1⁄4. The relation between ontic states and the preparation procedure, P1⁄4, is described by a conditional probability distribution over the ontic state space, pð jP1⁄4Þ, which we refer to as an epistemic state. In general, the preparation P can be a preparation of a physical system in a mixed sate. Unless there exists a one-to-one correspondence between ontic states and quantum states, the probability distribution spreads over . (See Fig. 1.) The question of whether an ontological model is 1⁄4-ontic or 1⁄4-epistemic is concerned with the behaviour of the epistemic states for two distinct preparations of quantum states. Consider two distinct preparations of quantum states, Journal of the Physical Society of Japan 82 (2013) 055003

Journal of the Physical Society of Japan•Apr 23, 2013•0 citations

On philosophy of mind, quantum physics and metaphysics of the uni-multiverse

Paolo Di Sia

Metaphysics, as discipline dealing with the most fundamental aspects of reality, studies the essence of entities, leaving to particular sciences the study of empirical, specific, changeable and unstable aspects. In this sense metaphysics is close to ontology, tackling problems as the existence of God, the being in himself, the immortality of consciousness, the origin and meaning of the universe. Speculative physics pushes its interest to metaphysical questions too, both at atechnical (mathematical) level, and at the level of thought (in relation to philosophy). In recentyears interesting concepts and ideas have been considered and developed, involving the latest unified quantum-relativistic theories and the consequences on reality deriving from them.The search for a meaning of life, one of Anscombe’s themes, finds ferment in the search for meaning about the existence of our universe in itself and as a possible part of a multiverse containing it.The problem of measurement in quantum mechanics appears from the application of themathematical formalism to macroscopic situations and the central position of the observer in this process has produced a deviation towards a metaphysical subjectivism. There are controversial aspects about the role of consciousness in the process of reducing the wave function of quantum mechanics. This narrows the field of validity of some fundamental principles during the interaction between microsystems and macrosystems, with consequent diversification of thedefinition of the ontological state of consciousness and reality. (Local) holism has often been linked to Wittgenstein. From Wittgenstein’s answers to the paradoxes of communication and conceptual relativism, a tension emerges in his vision of linguistic games and in his mental experiments, traditionally interpreted in contrasting ways. This tension can be better understoodthrough some reflections by Wittgenstein on Einstein and his theory of relativity.

•Oct 20, 2019•11 citations

Locating Oneself in a Quantum World.

Charles T. Sebens

There appear to be multiple mathematically and physically distinct theories that successfully reproduce the empirical predictions of quantum mechanics, so-called "interpretations" of quantum mechanics. This dissertation uses the tools of formal epistemology (prominently, the concept of self-locating uncertainty) to investigate which of the theories that have been put forward really are empirically adequate and what alternatives can be devised. The first chapter introduces a novel theory that incorporates aspects of two well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. The quantum wave function can be represented as a field on configuration space, the space of possible ways particles can be arranged. According to Bohmian mechanics a single point in this space is special; it represents the way all of the particles actually are arranged. The newly introduced theory holds that many of the points in configuration space are special; for each, there is a world in which particles are arranged that way. In general, there will be multiple worlds that are so similar that an agent cannot tell directly from experience which they are in; self-locating uncertainty is unavoidable. The next chapter argues for the empirical adequacy of the many-worlds interpretation. In this version of quantum mechanics, processes like quantum measurements cause agents to split into multiple copies and enter periods of self-locating uncertainty. An epistemic principle demarcating which facts about the world one's credences might reasonably depend on (only facts about what's happening around here) is used to derive probabilistic predictions from the many-worlds interpretation. In the third chapter self-locating uncertainty is employed in evaluating another version of quantum mechanics, Ghirardi-Rimini-Weber theory. In this theory, random collapse events prevent our world from splitting into many. If the collapse events are rare, this prevention fails. Other worlds have time to form but most are short-lived. Our survival provides evidence against that kind of theory. The final chapter is an original introduction to relativistic quantum field theory which lays groundwork for evaluating the prospects of extending various interpretations of quantum mechanics to this more sophisticated theory.

•Jan 1, 2015•0 citations
It is well known that quantum physics deals with phenomena characterized by uncertainty. A typical expression of this uncertainty is the uncertainty principle, where, the more precisely we know the position of a particle, the more imprecisely we know its momentum (and vice versa).Opinions are divided as to whether this epistemological uncertainty is also an ontological uncertainty. Of some relevance here is the following observation by Quentin Smith: Heisenberg originally interpreted [the uncertainty] epistemically, but Bohr convinced him in private communications to accept a verificationist metaphysics, with its attendant ontological interpretation of the uncertainty relations (Smith 2002, 137) There are many competing interpretations of the quantum mechanical mathematical formalism. Of these interpretations, particularly well-known are the so-called Copenhagen interpretation of Bohr (where it is asserted that the position-view and the momentum-view of reality are complementary, and cannot be considered in the same context), and the many-universes interpretation of Hugh Everett. Roughly speaking, the latter asserts that whenever a measurement is made of a particle, the universe splits into copies, each one of which corresponds to the different possible outcomes of the measurement. Many scientists are happy to work with the many-universes interpretation-provided that their working with the theory has no ontological commitment. That is, they are not prepared to believe that the many universes actually exist. David Deutsch, who is one of the leading researchers in the field of quantum computation, is an exception. Indeed, he is the main advocate of the reality of the many universes; and he provides a number of important reasons why he is such an advocate. In the present essay, I intend to look at the arguments for and the arguments against the existence of the many universes, clarifying along the way what the meaning of exist in this regard should be considered to be. A first conclusion will be that while Deutsch's arguments are highly persuasive, there is one telling objection to the existence of the many universes-or multiverse, as the collection of them is becoming known-that must be addressed. My procedure then will be to show that the objection can in fact be met, using the so-called methodological solipsism approach introduced by Hans Driesch and employed subsequently by such theorists as Fodor and Putnam. The Many-Universes Interpretation of Quantum Physics It is not my intention in this essay to become bogged down in the minutiae of quantum physics, where the complexities of the mathematics are exacerbated by the lack of any single way of interpreting it. However, in order to provide a background for my subsequent arguments, I shall discuss briefly a typical and familiar quantum-mechanical scenario: the so-called experiment. My account is based on that of Penrose (1985). The results that may be expected in a performance of the two-slit experiment depend on the fact that sub-microscopic particles, such as electrons or photons, behave sometimes like particles and sometimes like waves. The experiment is simple to describe: typically, a beam of light is directed through a pair of closely-separated and parallel narrow slits to a screen located behind it. Penrose describes the scenario as follows (it is worth quoting him at length): The most evident manifestation of the light as particles . . occurs at the screen. The light arrives there in discrete localized units of energy.. .. Never is the energy of just half a photon... received. Light reception is an all-or-nothing phenomenon in photon units. Only whole numbers of photons are ever seen. However, a wavelike behaviour seems to arise as the photons pass through the slits. Suppose, first, that only one slit is open (the other being blocked off). After passing through, the light will spread out-by. …
Few, if any, issues in physics have engendered as much discussion as the measurement problem in quantum mechanics. It is generally agreed that the `normal' dynamical evolution of the state vector in quantum mechanics is given by a unitary map. The linearity of this map implies that the state vector will, in general, be found in a superposition of eigenstates of a given observable (or, similarly, that the density matrix describing a subsystem will not correspond to a definite value of this observable). However, when we make a measurement of an observable, we always obtain a define value—although it is impossible to predict with certainty which value will be obtained. The traditional response to this issue is to postulate that when a measurement is made, the wavefunction `collapses' to an eigenstate of the observable being measured, perhaps due to the inherent classicality of the measuring apparatus (Bohr), or to the consciousness of the observer (Wigner), or possibly to some modification of quantum dynamics that occurs even when observations are not being made. The main motivation for the Everett (`many worlds') interpretation is to avoid introducing any such collapse postulate. This volume commemorates the 50th anniversary of the publication of Everett's paper in 1957 and contains 20 original articles as well as the transcripts of several discussions that took place at meetings devoted to the Everett interpretation at Oxford University and the Perimeter Institute. The attractiveness of the Everett interpretation is very succinctly summarized by a sentence from Vaidman's contribution (p 582): `The collapse, with its randomness, non-locality and the lack of a well-defined moment of occurrence, is such an ugly scar on quantum theory, that I, along with many others, am ready to follow Everett and deny its existence.' But the main drawback of the interpretation is then equally succinctly stated in the next sentence: `The price is the many worlds interpretation, i.e., the existence of numerous parallel worlds.' In other words, if the state vector evolves to have a non-zero amplitude for two different values of an observable that I `measure' (i.e., interact with in an appropriate way), each of these alternatives remains equally `real', i.e., there is a `branch' of the wavefunction in which the observable takes the first value and I believe that it has this first value and a branch of the wavefunction where it takes the second value and I believe that it has this second value. Each of these `me's' sees a definite value for the observable, thus nicely accounting for what I believe I experience without invoking collapse. But then, it seems that I have to believe that there are many other `me's' around—even if they are very difficult for this particular me to access—and no way I can predict which `me' I will be in the future. Indeed, Saunders writes on p 192, `If Alice is a person (of course she is) then we must say, even prior to branching at tj that there are many Alices present, atom for atom duplicates...Alice should be uncertain after all— each Alice should be uncertain—for each as of tj does not (and as a matter of principle, cannot) know which of these branching persons she is.' Thus, if taken seriously, the Everett viewpoint leads directly to questions like `What determines which ``me'' I am now and/or will feel that I am in the future?' The response `You are all of them' somehow doesn't seem satisfying, and further pursuit of these issues would seem to lead to questions as fruitless as questions like `Why am I ``me'' and not ``you''?' I believe that this accounts for why the Everett interpretation does not have universal appeal. But enough of `me' for now (more later); let's discuss the book. Unlike many edited volumes and conference proceedings in physics—which often consist of hastily slapped-together re-hashes of previous papers—this volume meets very high standards in the choice of topics and authors and in the quality of the writing. Although each of the articles is closely tied in with the Everett interpretation, there are many articles of considerable value and interest in their own right, such as the discussion of quasiclassical realms by Hartle and and the discussion of the de Broglie–Bohm interpretation by Valentini. There is also an excellent introduction by Saunders to the quantum measurement problem and the main issues that arise in the Everett interpretation. A central issue in the Everett interpretation is the status of the `Born rule', which asserts that, for state ψ, the probability of obtaining a particular outcome of a measurement is ||Pψ||2, where P is the projection operator onto the eigensubspace associated with the measurement outcome. In traditional interpretations, the Born rule is simply postulated as part of the collapse hypothesis. In the Everett interpretation, it is far from obvious that the Born rule even has any meaning—if all outcomes occur, how can one talk about the probability of a particular outcome? Given the importance of this issue, it is highly appropriate that four chapters of the book (by Saunders, Papineau, Wallace, and Greaves and Myrvold) are devoted to addressing probability and the Born rule from the Everett viewpoint, and three chapters (by Kent, Albert, and Price) are devoted to criticising these views. As indicated by the above quote from Saunders' article, uncertainty and probability can enter the Everett interpretation via each Alice being uncertain as to which Alice she is or will be. However, in view of the difficulties to which this kind of argumentation will lead, it is perhaps not surprising that in the 123 pages of combined discussion by Saunders, Papineau, Wallace, and Greaves and Myrvold, there are only fleeting references to the use of probability along these lines. Rather, the approach taken is reminiscent of that of adept politicians: if you can't answer a question, then answer a different question, and answer it with conviction and detail. Instead of considering probabilities of outcomes—a highly problematical notion when all of the possible outcomes actually occur—consider only decision theory issues. In particular, Wallace gives a precise and detailed mathematical proof that, under certain hypotheses, the only rational strategy that a quantum observer can follow in making decisions is to weight the possible outcomes by Born rule probabilities. To illustrate this more graphically, suppose tomorrow's weather were determined by some quantum mechanical, Stern–Gerlach-like process. I would like to know whether it is likely to rain tomorrow. However, when I ask an Everett follower (who knows the state vector and has done the Born rule calculation), all she will tell me in direct response to my question is that `it will rain and it won't rain.' Nevertheless, she is willing tell me whether or not it is rational for me to take an umbrella. I suppose that if she tells me that it would be highly irrational for me to take an umbrella, I can take the hint and deduce that it is very unlikely to rain. However, there does seem something wrong with the fact that she is not allowed to say this directly. In any case, if the conclusion of a mathematically correct argument is that rational decision strategies require the Born rule, then there must be quite a bit lying in the assumptions. The articles by Kent, Albert, and Price do a good job of fleshing out these assumptions and pointing out the weaknesses and flaws in the probability and decision theory discussions within the Everett framework. I hope it is clear from what I have written above that this is an outstanding volume, which should be of great interest to anyone interested in the foundations of quantum theory. Indeed, I feel quite fortunate to be the particular `me' that happens to exist in the same branch of the wavefunction of the universe in which this book was published.
Introduction Although the mathematical structure of quantum mechanics was understood within a few years after it was invented, numerous quantum paradoxes still disturb ‘simple-minded’ physicists. Most of them, as ‘naïve realists’, would probably never take Bohr's own over-philosophical and over-complicated treatment of these paradoxes seriously if they realized the philosophical consequences of the Copenhagen interpretation. To make my meaning clearer, let me quote Bohr's answer to Professor Hoffding's question regarding the double-slit experiment [1]. Bohr was asked: ‘What can the electron be said to be in its travel from the point of entry to the point of detection?’ And he replied: ‘ To be ? To be ? What does it mean to be ?’ However, if one questions the existence of microscopic constituents of macroscopic bodies, then the next logical step would be to question the existence of the macroscopic bodies and even ourselves. Needless to say, very few (if any) of us, when making experiments or analyzing their results, address the question of what it means ‘to be’ every time. Even in the context of elementary particles, probably nobody doubts that the particles exist and somehow travel from the point of entry to the point of detection. Moreover, within the accuracy allowed by the uncertainty relation, these particles can be localized and described just as well as macroscopic ‘classical’ objects.
How does it come about then, that great scientists such as Einstein, Schrödinger and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. […] The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road. (Born [1954], pp. 8, 11) It is truly surprising how little difference all this makes. Most physicists use quantum mechanics every day in their working lives without needing to worry about the fundamental problem of its interpretation. (Weinberg [1992], p. 66) I endorse the view that it may be of no relevance to the acceptability of the Everett interpretation of quantum mechanics as a physical theory whether or not an informed observer can be uncertain about the outcome of a quantum measurement prior to its having occurred. However, I suggest that the very possibility of post-measurement, pre-observation uncertainty has an essential role to play in both confirmation theory and decision theory in a branching universe. This is supported by arguments which do not appeal to van Fraassen’s Reflection Principle. 1. Dendritic Unitary Evolution 2. The Born–Vaidman Rule 3. Greaves on Uncertainty 4. Retroactive Counterfactual Uncertainty 5. Odds and Ends
Quantum nonlocality has been a long-standing and fascinating problem in the foundations of quantum theory since its proof by the Bell inequality. It seems to contradict our intuitive picture of space-time and thus urges us to reconsider its foundation. With the advent of quantum information science, it has attracted renewed interest from a fundamental point of view as well as from a quantum information-theoretic one. Another fundamental question on the nature of quantum theory is how we understand what quantum states represent. (Quantum states hereafter refer to pure states.) This is also a long-standing problem since the early days of quantum theory. Roughly speaking, there are two conflicting views on this matter: one is ontology and the other is epistemology. Ontological models of quantum theory are models in which we assume some underlying reality for physical systems and require that all the predictions of quantum theory should be reproduced. The ontological models are divided into two categories, depending on which views the models are based on, ontology or epistemology. In the models based on ontology, quantum states represent the underlying reality in some sense, and different quantum states correspond to different realities. In the models based on epistemology, quantum states do not necessarily correspond to the underlying realities, and even different quantum states can be consistent with a common underlying reality. The former type of ontological models of quantum theory is called 1⁄4-ontic. The latter is called 1⁄4-epistemic. Thus, it might be rather confusing that ontological models are classified further into 1⁄4-ontic models and 1⁄4-epistemic ones. We use these terms here in accordance with the recent literature on quantum foundations. (For details of these notions in the ontological models of quantum theory, see the paper by Harrigan and Spekkens.) Quite recently, the question just mentioned has been answered by Pusey et al., and one of the above models has been refuted. It was shown that 1⁄4-epistemic models are inconsistent with the predictions of quantum theory. In other words, epistemological views on quantum states turned out to be false as long as we assume some underlying reality for physical systems. Therefore, only 1⁄4-ontic models of quantum theory are valid for describing quantum systems. This significantly advances our understanding on the nature of quantum states. It is expected that various conclusions will be drawn from this fact. In this paper, we will discuss a connection with nonlocality. The above two fundamental questions, nonlocality and the nature of quantum states, are intimately connected, and the connection was first implicitly recognised by Einstein in the early days of quantum theory. In a private correspondence with Schrodinger, Einstein constructed a fascinating argument that relates the above two. (That argument is distinctly different from the well-known EPR argument.) Recently, it was revisited and reconstructed in accordance with more rigorous notions in quantum foundations. Nonlocality is usually shown by violations of Bell inequalities. (Bell inequalities hereafter include all the subsequent developments such as the CHSH inequality.) Even if it is not clear whether the models of quantum theory are 1⁄4-ontic or 1⁄4-epistemic, we can prove nonlocality just by showing the violation of Bell inequalities. However, the above argument originated by Einstein implies that if we know the models are 1⁄4-ontic in advance (as we do now), we can prove nonlocality in a simpler way without Bell inequalities. (This argument had been known in quantum foundations before the refutation of 1⁄4-epistemic models.) Nonlocality is rigorously defined as a violation of the notion of local causality defined by Bell. Showing the violation of Bell inequalities is one way of demonstrating the violation of local causality. Since the simpler proof initiated by Einstein directly demonstrates the violation of local causality, it is a more straightforward proof of nonlocality from a conceptual point of view. In the following, we will see that this simple argument of nonlocality without Bell inequalities can be used to show multipartite nonlocality as well. Before moving onto multipartite cases, first let us define the necessary notions for presenting our result. First of all, we assume that there exists a complete specification of the properties of a physical system, which we refer to as the ontic state of that system. The ontic states represent the underlying realities and are not necessarily equal to ordinary quantum states. (In other words, the ontic states correspond to hidden variables.) Ontological models of quantum theory are models that assume ontic states and reproduce all the predictions of quantum theory. An important question is how ontic states correspond to quantum states in quantum theory. In order to frame the question accurately, we need the notion of an epistemic state, which represents the relation between them. Suppose we prepare a physical system in a quantum state 1⁄4. Although the system is uniquely specified as 1⁄4 in quantum theory, there still remains a possibility that it allows a more detailed specification in the ontic state space, in which case many different ontic states turn out to be consistent with 1⁄4. The relation between ontic states and the preparation procedure, P1⁄4, is described by a conditional probability distribution over the ontic state space, pð jP1⁄4Þ, which we refer to as an epistemic state. In general, the preparation P can be a preparation of a physical system in a mixed sate. Unless there exists a one-to-one correspondence between ontic states and quantum states, the probability distribution spreads over . (See Fig. 1.) The question of whether an ontological model is 1⁄4-ontic or 1⁄4-epistemic is concerned with the behaviour of the epistemic states for two distinct preparations of quantum states. Consider two distinct preparations of quantum states, Journal of the Physical Society of Japan 82 (2013) 055003
Metaphysics, as discipline dealing with the most fundamental aspects of reality, studies the essence of entities, leaving to particular sciences the study of empirical, specific, changeable and unstable aspects. In this sense metaphysics is close to ontology, tackling problems as the existence of God, the being in himself, the immortality of consciousness, the origin and meaning of the universe. Speculative physics pushes its interest to metaphysical questions too, both at atechnical (mathematical) level, and at the level of thought (in relation to philosophy). In recentyears interesting concepts and ideas have been considered and developed, involving the latest unified quantum-relativistic theories and the consequences on reality deriving from them.The search for a meaning of life, one of Anscombe’s themes, finds ferment in the search for meaning about the existence of our universe in itself and as a possible part of a multiverse containing it.The problem of measurement in quantum mechanics appears from the application of themathematical formalism to macroscopic situations and the central position of the observer in this process has produced a deviation towards a metaphysical subjectivism. There are controversial aspects about the role of consciousness in the process of reducing the wave function of quantum mechanics. This narrows the field of validity of some fundamental principles during the interaction between microsystems and macrosystems, with consequent diversification of thedefinition of the ontological state of consciousness and reality. (Local) holism has often been linked to Wittgenstein. From Wittgenstein’s answers to the paradoxes of communication and conceptual relativism, a tension emerges in his vision of linguistic games and in his mental experiments, traditionally interpreted in contrasting ways. This tension can be better understoodthrough some reflections by Wittgenstein on Einstein and his theory of relativity.
There appear to be multiple mathematically and physically distinct theories that successfully reproduce the empirical predictions of quantum mechanics, so-called "interpretations" of quantum mechanics. This dissertation uses the tools of formal epistemology (prominently, the concept of self-locating uncertainty) to investigate which of the theories that have been put forward really are empirically adequate and what alternatives can be devised. The first chapter introduces a novel theory that incorporates aspects of two well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. The quantum wave function can be represented as a field on configuration space, the space of possible ways particles can be arranged. According to Bohmian mechanics a single point in this space is special; it represents the way all of the particles actually are arranged. The newly introduced theory holds that many of the points in configuration space are special; for each, there is a world in which particles are arranged that way. In general, there will be multiple worlds that are so similar that an agent cannot tell directly from experience which they are in; self-locating uncertainty is unavoidable. The next chapter argues for the empirical adequacy of the many-worlds interpretation. In this version of quantum mechanics, processes like quantum measurements cause agents to split into multiple copies and enter periods of self-locating uncertainty. An epistemic principle demarcating which facts about the world one's credences might reasonably depend on (only facts about what's happening around here) is used to derive probabilistic predictions from the many-worlds interpretation. In the third chapter self-locating uncertainty is employed in evaluating another version of quantum mechanics, Ghirardi-Rimini-Weber theory. In this theory, random collapse events prevent our world from splitting into many. If the collapse events are rare, this prevention fails. Other worlds have time to form but most are short-lived. Our survival provides evidence against that kind of theory. The final chapter is an original introduction to relativistic quantum field theory which lays groundwork for evaluating the prospects of extending various interpretations of quantum mechanics to this more sophisticated theory.