Probability Workshop

Abstracts

Sunday 14 December, 9:30 – 13:00

John Earman
Understanding the Unruh Effect

The importance of the Unruh effect lies in the fact that, together with the related (but distinct) Hawking effect, it serves to link the three main branches of modern physics: thermal/statistical physics, relativity theory/gravitation, and quantum physics. However, different researchers can have in mind different phenomena when they speak of "the Unruh effect" in flat spacetime and its generalization to curved spacetimes. Three different approaches are reviewed. They are shown to yield results that are sometimes concordant and sometimes discordant. The discordance is disconcerting only if one insists on taking literally the definite article in "the Unruh effect." It is argued that the role of linking different branches of physics is better served by taking "the Unruh effect" to designate of family of related phenomena. The relation between the Hawking effect and the generalized Unruh effect for curved spacetimes is briefly discussed.

Laura Ruetsche
Why Be Normal? Probabilities in Ordinary QM, Relativistic QFT, and QSM

Many philosophical accounts of quantum theory suppose that the observables pertaining to a quantum system are the self-adjoint elements of B(H), the algebra of bounded operators acting on a separable Hilbert space H. Operating within the scope of this assumption, the first part of this paper reviews (i) Gleason’s theorem, (ii) justifications for Luder’s Rule, and (iii) the conditions under which a Kolmogorovian probability space can be associated with the restriction of a countably additive state on B(H) to a subalgebra of B(H). (We contend that Bell’s theorem is properly understood as indicating that there must be such conditions.) B(H) is a Type I von Neumann algebra. Relativistic QFT and the thermodynamic limit of QSM make extensive use of von Neumann algebras of more general types. Thus the second part of this paper asks whether aspects of the quantum probability formalism reviewed in the first part persist in the more general setting. We catalog features of non-type I von Neumann algebras that may not be familiar to philosophers accustomed to working with B(H), and argue that while these novel features do not cause the familiar formalism of quantum probability to falter, they do render the problem of the interpretation of quantum probability more intricate.

David Albert
Physics and Chance

I will attempt a panoramic overview of the role of chance in the architecture of fundamental physical theories, with particular attention to the question of the unity of science.

Sunday 14 December, 14:30 – 17:30

Shelly Goldstein
Typicality and Notions of Probability in Physics

A variety of different notions of probability, playing different roles, are relevant in physics. One crucial notion, typicality, while not genuinely probabilistic at all, is arguably the mother of all these notions.

Meir Hemmo
The Significance of Laws of Large Numbers in Statistical Mechanics

We argue that attempts to derive the probability measure in statistical mechanics by proving a sort of weak law of large numbers from certain features of the dynamics (e.g. the uniform probability distribution relative to the Lebesgue measure from the pointwise ergodic theorem) are circular.

Orly Shenker
Probabilities over Initial Conditions in Statistical Mechanics

We propose a way to understand the meaning of the probabilities over initial conditions in statistical mechanics. This leads the way to define transition probabilities between macrostates, given some assumptions about the dynamics. We then characterize what needs to be proved in order to account for the approach to thermodynamic equilibrium.

Monday 15 December, 9:30 – 13:00

Jos Uffink
Will Someone Say Exactly What the H-theorem Proves?

The above question was famously raised in a letter to Nature by E. Culverwell (1894) after Boltzmann’s visit to a meeting in Oxford where his H-theorem was much discussed. Culverwell’s letter triggered a number of responses trying to pinpoint the exact ingredient in the derivation that is responsible for the time-asymmetry of the theorem, culminating in Boltzmann’s own formulation of the Hypotheses of Molecular Disorder. We will look at the contributions of the key figures in this debate (Burbury, Boltzmann Bryan and Jeans) and argue that some of the confusion in their views is to some extent still present in modern presentations of the H-theorem.

Roman Frigg
Why Typicality does Not Explain the Approach to Equilibrium

Why do systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question by an appeal to the notion of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such, much less clearly distinguished, and we often find different arguments pursued side by side. The aim of this paper is to disentangle different versions of typicality-based explanations of thermodynamic behaviour and evaluate their respective success. My conclusion will be that the boldest version fails for technical reasons, while more prudent versions leave unanswered essential questions.

Wayne Myrvold
Physical Chances in a Deterministic Setting

As has often been remarked, "probability" has at least two distinct senses (in Ian Hacking's phrase, probability is "Janus-faced"). There is a subjective sense, having to do with degrees of belief, or credences, and an objective sense, on which physical probabilities, or chances, are associated with certain physical processes, or "chance set-ups.". The question I wish to address is: Can we make sense of the latter in the context of a deterministic physics, or does determinism entail that all probabilities are subjective? I will take up the thread of what Jan von Plato has called "a neglected chapter in the foundations of probability"---namely, the (somewhat misnamed) "method of arbitrary functions" pioneered by von Kries and Poincare, and will attempt to argue that, with the appropriate interplay of subjective and objective considerations, one can make sense of a notion of objective chances appropriate to games of chance and classical statistical mechanics.

Monday 15 December, 14:30 – 18:00

Simon Saunders
Chance in the Everett Interpretation of Quantum Mechanics

In the Everett interpretation of quantum mechanics, the wave function of the universe has the macroscopic structure of innumerable branches, in each of which quasiclassical equations hold to high accuracy. I argue that ratios in the squared norms of branch amplitudes fulfill the three key roles of objective chance: (i) the statistical inference role (chance is manifested in statistics); (ii) the decision theory role (chance as a guide to credence); and (iii) the link with uncertainty (chance events are uncertain). (i) is easily demonstrated, whilst (ii), granted the structure to the wave-function, is established by the Born-rule theorem due to Deutsch and Wallace. This talk is concerned with (iii), considered by many the 'Achilles heel' of the Everett interpretation. It can be relegated to a semantic problem, but it can also be given a more substantive basis given the atemporal representation of the wave-function in terms of quantum histories. Vaidman's recent proposal, that uncertainty in the Everett interpretation be anchored to Aharonov's 2-vector formalism, is also considered. On either count, Everettian worlds have a natural representation as divergent worlds, rather than overlapping worlds (in Lewis' sense), whereupon quantum mechanical uncertainty reflects self-locating ignorance.

Lev Vaidman
Probability in the Many Worlds Interpretation of Quantum Mechanics

Tuesday 16 December 16:00 – 19:00

Joseph Berkovitz
The World According to De Finetti

Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the axioms and theorems of the probability calculus and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that an agent’s degrees of belief be coherent. A common view has it that degrees of belief are coherent just in case they are represented by a probability function. I propose that de Finetti had a somewhat different view: an agent’s degrees of belief are coherent if they could be represented by a set of probability functions, each of which corresponds to a subset of the agent’s degrees of belief in propositions that can in principle be jointly verified. On this view, coherence imposes weaker constraints on degrees of belief. I then consider the implications of this interpretation of de Finetti for probabilities in quantum mechanics, focusing on the EPR/Bohm experiment and Bell’s theorem.

Ruediger Schack
From Dutch Book Coherence to Quantum Coherence

In the Bayesian approach to quantum mechanics developed by Caves, Fuchs and the speaker, all quantum states---mixed or pure---are always, in any particular instance, interpreted as a specific agent's decision-theoretic degrees of belief. Whereas in classical decision theory, the probability formalism can be derived from Dutch book coherence alone, quantum mechanics requires extra, empirical ingredients. For quantum mechanics is in the end about physics, rather than pure law of thought. This talk gives an overview of the Bayesian approach and shows how one may hope to derive the quantum formalism from a simple addition to the classical rules.

Alexander Wilce
Entanglement and Measurement in General Probabilistic Theories

Quantum mechanics is a non-classical probability theory, but hardly the most general one imaginable: any compact convex set can serve as the state space for an abstract probabilistic model. From this altitude, one sees that many characteristically quantum phenomena are in fact characteristic of virtually all non-classical probabilistic theories, quantum or otherwise. In particular, the existence of entangled pure states is a generically non-classical, rather than a specifically quantum, phenomenon. A consequence of this is that almost any non-classical probabilistic theory shares with QM a version of the so-called measurement problem. This raises the question of whether familiar strategies for solving the measurement problem, that is, interpretations of QM, are equally generic. In this talk, I'll show that the viability of one such strategy, a somewhat attenuated Everettian interpretation, imposes some non-trivial structural constraints on a probabilistic theory.

Wednesday 17 December, 9:30 – 13:00

Daniel Rohrlich
Quantum Fun with Classical Energy Distributions

Jeffrey Bub
Pseudo-Telepathic Games, Nonlocal Boxes, and All That

A pseudo-telepathic game is an n-party game that the players have a finite probability of losing with any strategy involving only shared randomness as a resource, but that can always be won by players sharing an entangled quantum state. The term is intended to suggest that the behaviour of consistently successful players, who are not allowed to communicate with each other via classical information channels after the start of the game, would appear to require some hidden 'telepathic' form of communication in a classical world. A nonlocal box is a non-signaling device shared by two players, with an input and output for each player, where the box, considered as an information-theoretic resource, produces statistical correlations between inputs and outputs that cannot be simulated by noncommunicating players with only shared randomness as a resource. (Shared quantum entanglement constitutes a nonlocal box, but it is useful to also consider hypothetical nonlocal boxes like the Popescu-Rohrlich (PR) box that produce superquantum correlations.) I discuss some recent results involving pseudo-telepathic games and nonlocal boxes, and the significance of these results for the difference between classical and quantum probabilities.

Yemima Ben-Menahem
Locality and Determinism as Members of the Causal Family

I suggest that rather than a single concept of causality we have a spectrum of causal notions. On this view, the philosophically interesting questions pertain first and foremost to the relations between these concepts. Here I will focus on the relation between determinism and locality.

Wednesday 17 December 14:30 – 17:30

Avshalom Elitzur and Eric Fanchon
What does Maxwell's Demon Select, and How?

Alon Drory
Revising Boltzmann's Program

Boltzmann’s program in statistical mechanics is plagued by a conflict between the time-symmetry of the micro-dynamics and the time-asymmetry of the unidirectional increase of entropy it seeks to explain. One expression of this conflict is the reversibility paradox, which claims that the retrodictions of Boltzmann's theory are usually incorrect. I will argue that this view needs refining, and that our actual retrodictions are in fact conditional on the entire history of the system, specifically on whether the system has always been close or whether it was open at some time in the relatively recent past. Once this distinction is clearly made, Boltzmann's program becomes paradox-free when applied to always-closed systems. Furthermore, I argue that Boltzmann's notion of probability actually precludes the consistent application of the program to systems that are not always closed. For such systems, the relative phase space volume occupied by a macrostate cannot be identified in principle with the probability of corresponding microstates, either in the past or in the future. As a result, Boltzmann's program in its usual form is inapplicable to these systems. It can be revised, however, by introducing an explicitly time-asymmetric assumption, which asserts that during the (possibly short) period in which a system is closed, its macroscopic future behavior is uniquely determined, in some sense. Its past behavior, however, is not. The addition of this assumption makes Boltzmann's program consistent, but it is not suggested as a new fundamental principle. On the contrary, I suggest that the continuing debate about the thermodynamic time asymmetry would benefit by focusing on the origin and domain of validity of this assumption.

Itamar Pitowsky
On Certainty (Probability One and Probability Zero) in Quantum Mechanics

The view that observables in quantum mechanics can be defined only in terms of measurements is shared, ironically, by Bohrians and the modern Bohmians. On the other hand, conservation laws, and other laws of nature are expressed in quantum theory as functional relations among observables, often non-commuting observables that cannot be measured together. How can valid laws be expressed as relations among the ghosts of ill defined quantities? This discrepancy lies at the heart of von Neumann's effort to turn quantum observables into random variables on a different kind of probability space. In this approach one can keep the laws valid while holding to uncertainty.

William Demopoulos
The Framework of Effects

The focus of this paper is a particular feature of the statistical behavior of elementary particles, simple composite systems of them and the quantum probability theory to which this behavior gives rise. The standard interpretation of a generalized probability theory of the sort found in elementary, non-relativistic quantum mechanics is that its probabilities are probabilities of propositions belonging to particles, where a proposition belongs to a particle if its constituent dynamical property is a possible property of the particle. The feature of interest is the fact that there exist simple systems and finite combinations of propositions belonging to them for which no two-valued measures are possible. I will argue that quantum probabilities are not satisfactorily interpretable as probabilities of propositions belonging to particles, and that such an interpretation is possible only when the propositions to which probabilities are assigned form an algebraic structure, which is homomorphic to a Boolean algebra. The idea I will develop is that the probabilities of quantum mechanics are probabilities of “effects,” probabilities of the observable and measurable result of particle-interactions with objects and processes that are epistemically accessible to us. I hope to show that such a view is not committed to any kind of anti-realism about the micro-world, that its mildly instrumentalist flavor is not a defect but a strength, and that it illuminates at least one otherwise paradoxical feature of quantum mechanics.

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