This series consists of talks in the area of Foundations of Quantum Theory. http://pirsa.org/podcast/S002 Science 2009 http://blogs.law.harvard.edu/tech/rss en-ca Thu, 08 Jan 2009 07:56:56 -0500 sbradwell@perimeterinstitute.ca Thu, 08 Jan 2009 07:56:56 -0500 G 180 sbradwell@perimeterinstitute.ca Steve Bradwell's - Podcast Generator Howard Wiseman http://streamer.perimeterinstitute.ca/mp3/867319c6-5a88-4c07-8187-c6145f3529ff.mp3 Science http://streamer.perimeterinstitute.ca/mp3/867319c6-5a88-4c07-8187-c6145f3529ff.mp3 Thu, 14 Oct 2004 16:05:00 -0400 Alexei Grinbaum http://streamer.perimeterinstitute.ca/mp3/d161ce68-8607-4c91-957d-7d81f9f47285.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d161ce68-8607-4c91-957d-7d81f9f47285.mp3 Thu, 10 Feb 2005 11:30:00 -0500 Natural critical phenomena are characterized by laminar periods separated by events where bursts of activity take place, and by the interrelated self-similarity of space-time scales and of the event sizes. One example are earthquakes: for this case a new approach to quantify correlations between events reveals new phenomenology. By linking correlated earthquakes one creates a scale-free network of events, which can have applications in hazard assessment. Solar flares are another example of critical phenomenon, where event sizes and time scales are part of a single self-similar scenario: rescaling time by the rate of events with intensity greater than an intensity threshold, the waiting time distributions conform to scaling functions that are independent of the threshold. The concept of self-organized criticality (SOC) is suitable to describe critical phenomena, but we highlight problems with most of the classical models of SOC (usually called sandpiles) to fully capture the space-time complexity of real systems. In order to fix this shortcoming, we put forward a strategy giving good results when applied to the simplest sandpile models. Marco Blaiesi http://streamer.perimeterinstitute.ca/mp3/69ca696e-f5f8-4a21-8e0b-3567a6203131.mp3 Science http://streamer.perimeterinstitute.ca/mp3/69ca696e-f5f8-4a21-8e0b-3567a6203131.mp3 Thu, 14 Apr 2005 14:00:00 -0400 The problem of associating beables (hidden variables) to QFT, in the spirit of what Bohm did for nonrelativistic QM, is not trivial. In 1984, John Bell suggested a way of solving the problem, according to which the beables are the positions of fermions, in a discretized version of QFT, and obey a stochastic evolution that simulates all predictions of QFT. In the continuum limit, it will be shown that the Bell model becomes deterministic and that it is related to the choice of the charge density as a beable. Moreover, the charge superselection rule is a consequence of the Bell model. The non-relativistic limit and the derivation of Bohm's first quantized interpretation in this limit are also studied. I will also consider whether the Bell model can be applied to bosons. Samuel Colin http://streamer.perimeterinstitute.ca/mp3/37e98831-574d-43a8-a36b-72f2f194a0b2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/37e98831-574d-43a8-a36b-72f2f194a0b2.mp3 Tue, 31 Jan 2006 16:00:38 -0500 We will postulate a novel notion of probability; this will involve introducing an extra axiom of probability that seems natural from a Bayesian perspective. We will then provide an analogue of Gleason's theorem for these probabilities. We will also discuss why this approach may be useful for generalizations of quantum theory such as quantum gravity theories; this will involve discussing an analogy between Bayesian approaches and relational approaches. Thomas Marlow http://streamer.perimeterinstitute.ca/mp3/ffd9e2c7-50fc-47e0-953f-9afd2d7eb305.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ffd9e2c7-50fc-47e0-953f-9afd2d7eb305.mp3 Tue, 14 Feb 2006 16:00:50 -0500 Collapse models are one of the most promising attempts to overcome the measurement problem of quanum mechanics: they descibe, within one single framework, both the quantum properties of microscopic systems and the classical properties of macroscopic objects, and in particular they explain why measurements always have definite outcomes, distributed according to the Born probability rule. We will discuss some recent developments in this field: i) we will show how it is possible to formulate collapse models in such a way that the mean energy of physical system does non increse indefinitely, a typical feature of the models first proposed in the literature; ii) we will discuss recent experiments aiming at testing the validity of the superposition principle, thus of collapse models, at the mesoscopic level. Emiliano Ippoliti http://streamer.perimeterinstitute.ca/mp3/0bb3931c-9a45-49f8-be23-98c71fb5dca8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0bb3931c-9a45-49f8-be23-98c71fb5dca8.mp3 Mon, 20 Feb 2006 14:00:29 -0500 The mathematical formalism of quantum theory has many features whose physical origin remains obscure. In this paper, we attempt to systematically investigate the possibility that the concept of information may play a key role in understanding some of these features. We formulate a set of assumptions, based on generalizations of experimental facts that are representative of quantum phenomena and physically comprehensible theoretical ideas and principles, and show that it is possible to deduce the finite-dimensional quantum formalism from these assumptions. The concept of information, via an information-theoretic invariance principle, plays a central role in the derivation, and gives rise to some of the central structural features of the quantum formalism. Philip Goyal http://streamer.perimeterinstitute.ca/mp3/b2e89d35-a583-4ba1-8c6a-996ebd55bb26.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b2e89d35-a583-4ba1-8c6a-996ebd55bb26.mp3 Mon, 22 Jan 2007 14:00:00 -0500 Results in decoherence theory and entanglement theory will be considered as tools illuminating the foundation of quantum mechanics and the possible relationship of quantum information to it. Gregg Jaeger http://streamer.perimeterinstitute.ca/mp3/8499ba1d-e2c0-4f3d-acc7-a4bf385400d9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/8499ba1d-e2c0-4f3d-acc7-a4bf385400d9.mp3 Thu, 15 Mar 2007 16:00:00 -0400 Adrian Kent http://streamer.perimeterinstitute.ca/mp3/a9424df3-e9ce-4384-86bc-95d320c0579f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a9424df3-e9ce-4384-86bc-95d320c0579f.mp3 Thu, 27 Sep 2007 16:00:00 -0400 Harvey Brown http://streamer.perimeterinstitute.ca/mp3/f738f460-7062-4d34-ac59-618ecd112c70.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f738f460-7062-4d34-ac59-618ecd112c70.mp3 Tue, 16 Oct 2007 16:00:00 -0400 The solution of many problems in quantum information is critically dependent on the geometry of the space of density matrices. For a Hilbert space of dimension 2 this geometry is very simple: it is simply a sphere. However for Hilbert spaces of dimension greater than 2 the geometry is much more interesting as the bounding hypersurface is both highly symmetric (it has a d^2 real parameter symmetry group, where d is the dimension) and highly convoluted. The problem of getting a better understanding of this hypersurface is difficult (it is hard even in the case of a single qutrit). It is also, we believe, both physically important and mathematically deep. In this talk we relate the problem to MUBs (mutually unbiased bases) and SIC-POVMs (symmetric informationally complete positive operator valued measures). These structures were originally introduced in connection with tomography. However, that by no means exhausts their importance. In particular their existence (non-existence???) in a given dimension is a source of significant insight into the state space geometry in that dimension. SIC-POVMs are especially important in this regard as they provide a a natural set of coordinates for state space. In this talk we give an overview of the problem. We then go on to describe some recent results obtained in collaboration with Chris Fuchs and Hoan Dang (also see recent work by Wootters and Sussman). In particular we describe the connection with minimum uncertainty states. These states, besides being interesting in themselves (they are a kind of discrete analogue of coherent states with important cryptographic applications), suggest a potentially fruitful line of attack on the still outstanding SIC existence problem. Marcus Appleby http://streamer.perimeterinstitute.ca/mp3/81691831-fbf4-4111-ab3b-782dabeae12f.mp3 Science http://streamer.perimeterinstitute.ca/mp3/81691831-fbf4-4111-ab3b-782dabeae12f.mp3 Tue, 23 Oct 2007 16:00:00 -0400 The simplest algebraic curves of genus one are the nonsingular cubics in two-dimensional complex projective space. Interpreting CP^2 as the space of pure quantum states associated with a Hilbert space of dimension three, I will show how various properties of d=3 symmetric informationally complete positive operator valued measures can be understood in terms of the geometry of such curves. The resulting structure, although of considerable complexity, is very beautiful from a mathematical perspective. Lane Hughston http://streamer.perimeterinstitute.ca/mp3/de000ea9-d730-4972-9ad9-6f9bb630abd5.mp3 Science http://streamer.perimeterinstitute.ca/mp3/de000ea9-d730-4972-9ad9-6f9bb630abd5.mp3 Tue, 30 Oct 2007 16:00:00 -0400 What if the second law of thermodynamics, in the hierarchy of physical laws, were at the same level as the fundamental laws of mechanics, such as the great conservation principles? What if entropy were an intrinsic property of matter at the same level as energy is universally understood to be? What if irreversibility were an intrinsic feature of the microscopic dynamical law of all physical objects, including an individual qubit or qudit? This talk will show how positive answers to these questions need not contradict any of the known results of quantum mechanics. We construct a logically consistent, mathematically sound and definite, physically intriguing, non-relativistic and non-statistical quantum theory, in which the second law of thermodynamics is embedded as a fundamental microscopical law. The theory hinges upon a nonlinear extension of unitary Hamiltonian dynamics which for uncorrelated and noninteracting systems reduces to the usual Schroedinger equation for the zero entropy states, but in general generates a group (not a semi group) of irreversible time evolutions, where the non-Hamiltonian entropy generating term in the evolution equation attracts the state towards the direction of maximal entropy increase. Various examples and features of this highly non-conventional dynamical theory are discussed. References available at http://www.quantumthermodynamics.org/ Gian Paolo Beretta http://streamer.perimeterinstitute.ca/mp3/ab1be05e-5878-4494-b4e8-aa37086a137e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ab1be05e-5878-4494-b4e8-aa37086a137e.mp3 Thu, 08 Nov 2007 16:00:00 -0500 A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function. It is demonstrated that generic quantum systems therefore exhibit second-order phase transitions at finite temperatures. The talk is based on work carried out in collaboration with D.W. Hook and L.P. Hughston. Dorje Brody http://streamer.perimeterinstitute.ca/mp3/82207552-2da5-4ae9-9100-2daa2fb97797.mp3 Science http://streamer.perimeterinstitute.ca/mp3/82207552-2da5-4ae9-9100-2daa2fb97797.mp3 Tue, 13 Nov 2007 16:00:00 -0500 Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite dimensional quantum systems. Chris Ferrie http://streamer.perimeterinstitute.ca/mp3/e17ce84c-8c7e-47aa-a48e-565879150d49.mp3 Science http://streamer.perimeterinstitute.ca/mp3/e17ce84c-8c7e-47aa-a48e-565879150d49.mp3 Tue, 20 Nov 2007 16:00:00 -0500 We derive a set of Bell inequalities using correlated random variables. Our inequalities are necessary conditions for the existence of a local realistic description of projective measurements on qubits. We analyze our inequalities for the case of two qubits and find that they are equivalent to the well known CHSH inequalities. We also discuss the sufficiency of our inequalities as well as their applicability to more than two qubits. Matt Elliott http://streamer.perimeterinstitute.ca/mp3/177d7373-86de-40c8-9ffa-e06e22480986.mp3 Science http://streamer.perimeterinstitute.ca/mp3/177d7373-86de-40c8-9ffa-e06e22480986.mp3 Tue, 27 Nov 2007 16:00:00 -0500 In any attempt to construct a Quantum Theory of Gravity, one has to deal with the fact that Time in Quantum Mechanics appears to be very different from Time in General Relativity. This is the famous (or actually notorious!) "Problem of Time", and gives rise to both conceptual and technical problems. The decoherent histories approach to quantum theory, is an alternative formulation of quantum theory specially designed to deal with closed (no-external observer or environment) systems. This approach has been considered particularly promising, in dealing with the problem of time, since it puts space and time in equal footing (unlike standard QM) . This talk develops a particular implementation of the above expectations, i.e. we construct a general set of "Class Operators" corresponding to questions that appear to be "Timeless" (independent of the parameter time), but correspond to physically interesting questions. This is similar to finding a general enough set of timeless observables, in the evolving constants approach to the problem of time. Petros Wallden http://streamer.perimeterinstitute.ca/mp3/adf4942f-05d3-4ad4-bf0b-f9792389d52a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/adf4942f-05d3-4ad4-bf0b-f9792389d52a.mp3 Tue, 11 Dec 2007 16:00:00 -0500 Bell\'s theorem is commonly understood to show that EPR correlations are not explainable via a local hidden variable theory. But Bell\'s theorem assumes that the initial state of the particles is independent of the final detector settings. It has been proposed that this independence assumption might be undermined by a relativistically-allowed form of \"backward causation\", thereby allowing construction of a local hidden-variable model after all. In this talk, I will show that there is no backward causation model which yields the desired correlations. However, there are other physical scenarios yielding nontrivial nonlocal correlations which violated Bell\'s independence assumption. I will present two. Steve Weinstein http://streamer.perimeterinstitute.ca/mp3/4586fbbc-8249-4646-8eb1-1d62693ab30a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4586fbbc-8249-4646-8eb1-1d62693ab30a.mp3 Tue, 15 Jan 2008 16:00:00 -0500 Mutually unbiased bases (MUBs) have attracted a lot of attention the last years. These bases are interesting for their potential use within quantum information processing and when trying to understand quantum state space. A central question is if there exists complete sets of N+1 MUBs in N-dimensional Hilbert space, as these are desired for quantum state tomography. Despite a lot of effort they are only known in prime power dimensions. I will describe in geometrical terms how a complete set of MUBs would sit in the set of density matrices and present a distance between bases–a measure of unbiasedness. Then I will explain the relation between MUBs and Hadamard matrices, and report on a search for MUB-sets in dimension N=6. In this case no sets of more than three MUBs are found, but there are several inequivalent triplets. Åsa Ericsson http://streamer.perimeterinstitute.ca/mp3/129a237b-d52b-4f01-840d-580317f875d2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/129a237b-d52b-4f01-840d-580317f875d2.mp3 Tue, 12 Feb 2008 16:00:00 -0500 The purpose of this talk is to describe bosonic fields and their Lagrangians in the causal set context. Spin-0 fields are defined to be real-valued functions on a causal set. Gauge fields are viewed as SU(n)-valued functions on the set of pairs of elements of a causal set, and gravity is viewed as the causal relation itself. The purpose of this talk is to come up with expressions for the Lagrangian densities of these fields in such a way that they approximate the Lagrangian densities expected from regular Quantum Field Theory on a differentiable manifold in the special case where the causal set is a random sprinkling of points in the manifold. I will then conjecture that that same expression is appropriate for an arbitrary causal set. Roman Sverdlov http://streamer.perimeterinstitute.ca/mp3/a9485b59-130e-4c06-8a7d-b5bcd6c3b786.mp3 Science http://streamer.perimeterinstitute.ca/mp3/a9485b59-130e-4c06-8a7d-b5bcd6c3b786.mp3 Tue, 19 Feb 2008 16:00:00 -0500 We prove that all non-conspiratorial/retro-causal hidden variable theories has to be measurement ordering contextual, i.e. there exists *commuting* operator pair (A,B) and a hidden state \\lambda such that the outcome of A depends on whether we measure B before or after. Interestingly this rules out a recent proposal for a psi-epistemic due to Barrett, Hardy, and Spekkens. We also show that the model was in fact partly discovered already by vanFraassen 1973; the only thing missing was giving a probability distribution on the space of ontic states (the hidden variables). Hans Westman http://streamer.perimeterinstitute.ca/mp3/1e4f63a2-d0da-4484-84d5-1dd0e634bca2.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1e4f63a2-d0da-4484-84d5-1dd0e634bca2.mp3 Tue, 26 Feb 2008 16:00:00 -0500 A single classical system is characterized by its manifold of states; and to combine several systems, we take the product of manifolds. A single quantum system is characterized by its Hilbert space of states; and to combine several systems, we take the tensor product of Hilbert spaces. But what if we choose to combine an infinite number of systems? A naive attempt to describe such combinations fails, for there is apparently no natural notion of an infinite product of manifolds; nor of an infinite tensor product of Hilbert spaces. But, at least in the quantum case, the situation is not as hopeless as it might appear. We argue that there does indeed exist a natural mathematical framework for combinations of infinite numbers of quantum systems. Robert Geroch http://streamer.perimeterinstitute.ca/mp3/ed9ec9f4-d8c9-4d9e-aeb6-691bcc52ecc9.mp3 Science http://streamer.perimeterinstitute.ca/mp3/ed9ec9f4-d8c9-4d9e-aeb6-691bcc52ecc9.mp3 Thu, 13 Mar 2008 11:00:00 -0400 It is usually expected that nonrelativistic many-body Schroedinger equations emerge from some QFT models in the limit of infinite masses. For instance, from Yukawa's QFT, if the initial state contains 2 fermions, we expect to recover a 2-fermion nonrelativistic Schroedinger equation with 2-body Yukawa potential (in the limit of infinite fermion mass). I will give an easy (but still heuristic) derivation of this, based on the analysis of the corresponding Feynman diagrams and on the behaviour of the complete propagators for large spacetime distances. Then, I may outline another possible derivation based on the Schroedinger picture and dressed particles. Samuel Colin http://streamer.perimeterinstitute.ca/mp3/10a99636-77fa-430d-b802-7ec035112b78.mp3 Science http://streamer.perimeterinstitute.ca/mp3/10a99636-77fa-430d-b802-7ec035112b78.mp3 Tue, 18 Mar 2008 16:00:00 -0400 Quantum measure theory describes quantum theory as a generalization of a classical stochastic process, which may be fruitful for quantum gravity. I will describe the approach, and show that, in the context of an EPRB setup with two distant experimenters, two alternative experiments, and two outcomes per experiment, any set of no signaling probabilities can be realized, albeit by violating a `strong positivity' condition. David Rideout http://streamer.perimeterinstitute.ca/mp3/faf0a8ad-e988-4eba-ba2c-b6a62baa4125.mp3 Science http://streamer.perimeterinstitute.ca/mp3/faf0a8ad-e988-4eba-ba2c-b6a62baa4125.mp3 Tue, 01 Apr 2008 16:00:00 -0400 Chris Isham in pre-recorded video, with Andreas Doring fielding questions and clarifications. Like watching commentators Scott Hamilton and Katarina Witt analyze Kristi Yamaguchi's performance at the World Figure Skating Championships for CBS News, join us for something different in quantum foundations. Chris Isham parries the intricacies of topos theory; Andreas Doring shows us how to see the moves in slow motion. Bring your own popcorn and plenty of questions. Andreas Doering http://streamer.perimeterinstitute.ca/mp3/c437305e-e0e6-4364-8202-c4087d9b0aec.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c437305e-e0e6-4364-8202-c4087d9b0aec.mp3 Tue, 08 Apr 2008 16:00:00 -0400 The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a function of the proper time of the particles. The equations of motion for a single one-dimensional particle are obtained and numerically solved. A conservation law for the drift momentum of the particle during its random motion is shown. Moreover, the conservation of the mean value of the total linear momentum for two particles repelling each other according to the Coulomb interaction also follows. Therefore, the results indicate the realization of a kind of stochastic Noether theorem in the system under study. Alejandro Cabo http://streamer.perimeterinstitute.ca/mp3/10929e8a-b9d1-4f77-a1b8-533518c8b2c8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/10929e8a-b9d1-4f77-a1b8-533518c8b2c8.mp3 Tue, 22 Apr 2008 16:00:00 -0400 Consider the quantum predictions for EPR-type measurements on two systems with Hilbert space of dimension at least 3 in any maximally entangled state. I show that the only possible hidden variables model of these probabilities that satisfies both Shimony's and Jarrett's condition of parameter independence (or `locality') and Jones and Clifton's condition of conditional parameter independence (or `constrained locality') is trivial, i.e. given by the quantum probabilities themselves. I shall attempt to discuss also the meaning of the conditions and of this result. Guido Bacciagaluppi http://streamer.perimeterinstitute.ca/mp3/1b654c76-a4ed-4ff1-ba07-07013f3cd0cc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1b654c76-a4ed-4ff1-ba07-07013f3cd0cc.mp3 Tue, 29 Apr 2008 16:00:00 -0400 Shih-Yuin Lin http://streamer.perimeterinstitute.ca/mp3/1616ed7a-e037-490a-8e8e-ff0def89869c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1616ed7a-e037-490a-8e8e-ff0def89869c.mp3 Tue, 06 May 2008 16:00:00 -0400 Some theoretical physicists, Chris Fuchs among them, take quantum mechanics to go hand in hand with an anti-representationalist account of truth and reality such as that offered by the American pragmatists - William James, Charles Peirce, Richard Rorty, etc. On this view, scientific theories are instruments, rather than mirrors of the real world. In this talk, I’ll suggest that if the quantum physicist is to team up with the pragmatist, he’d do best to join not with James and Rorty, who see the world as radically plastic or malleable. He would do best to join with the founder of pragmatism, Peirce, who argued that a regulative assumption of inquiry is that there is a right or determinate answer to the question at hand. It may look as if the anti-representationalist quantum theorist will be unhappy with this suggestion, but I’ll argue that this would be a mistake. The trail of the human serpent, as James said, is over everything but, as Peirce saw, this does not toss us into the sea of post-modern arbitrariness, where there is nothing to say about what is true and what is real. Cheryl Misak http://streamer.perimeterinstitute.ca/mp3/61516ff6-a838-42d4-8a05-474d0839defa.mp3 Science http://streamer.perimeterinstitute.ca/mp3/61516ff6-a838-42d4-8a05-474d0839defa.mp3 Tue, 20 May 2008 16:00:00 -0400 The focus of this talk 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 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 traces of particleinteractions with objects and processes that are epistemically accessible to us. I hope to make it clear 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. William Demopoulos http://streamer.perimeterinstitute.ca/mp3/2ea7f711-9285-4fd1-a59a-8e7391e26d65.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2ea7f711-9285-4fd1-a59a-8e7391e26d65.mp3 Tue, 27 May 2008 16:00:00 -0400 TBA Daniel Parker http://streamer.perimeterinstitute.ca/mp3/2a4080f3-2a23-470f-a278-4988e6266339.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2a4080f3-2a23-470f-a278-4988e6266339.mp3 Thu, 29 May 2008 16:00:00 -0400 It is well known that the derivation of the Bell Inequality rests on two major assumptions, usually called outcome independence and parameter independence. Parameter independence seems to have a straightforward motivation: it expresses a non-signalling requirement between space-like separated sites and is thus motivated by locality. The status of outcome independence is much les clear. Many authors have argued that this assumption too expresses a locality requirement, in the form of a 'screening off' condition. I will argue that the assumption also admits of an entirely different interpretation, suggested by the concept of sufficiency in the general theory of statistical inference. In this view, the assumption of outcome independence can be explained as expressing the idea that the specification of the hidden variable is sufficient, i.e. it exhausts all the relevant statistical information about the measurement outcomes. In this view, the assumption has no roots in locality at all. Rather, I would claim, it stems from the assumption that there exists such an exhaustive state description in our putative hidden variable theories. Jos Uffink http://streamer.perimeterinstitute.ca/mp3/d732e94c-df62-41c8-aee8-76a9e155dc1d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d732e94c-df62-41c8-aee8-76a9e155dc1d.mp3 Tue, 10 Jun 2008 16:00:00 -0400 I will comment on the prevailing atmosphere and attitudes that provoked the CJS theorem, aspects of the theorem itself, some features of the aftermath following the theorem and, finally, a critique of the relevance of the theorem based on my own research on position operators in Lorentz covariant quantum theory. Gordon Fleming http://streamer.perimeterinstitute.ca/mp3/1a7787fa-5478-49ca-82c2-4b7a342117c8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1a7787fa-5478-49ca-82c2-4b7a342117c8.mp3 Tue, 17 Jun 2008 16:00:00 -0400 Set theory provides foundations of mathematics in the sense that all the mathematical notions like numbers, functions, relations, structures are defined in the axiomatic set theory called ZFC. Quantum set theory naturally extends ZFC to quantum logic. Hence, we can expect that quantum set theory provides mathematics based on quantum logic. In this talk, I will show a useful application of quantum set theory to quantum mechanics based on the fact that the real numbers constructed in quantum set theory exactly corresponds to the quantum observables. The standard formulation of quantum mechanics answers the question as to in what state an observable A has the value in an interval I. However, the question is not answered as to in what state two observables A and B have the same value. The notion of equality between the values of observables will play many important roles in foundations of quantum mechanics. The notion of measurement of an observable relies on the condition that the observable to be measured and the meter after the measurement should have the same value. We can define the notion of quantum disturbance through the condition whether the values of the given observable before and after the process is the same. It is shown that all the observational propositions on a quantum system corresponds to some propositions in quantum set theory and the equality relation naturally provides the proposition that two observables have the same value. It has been broadly accepted that we cannot speak of the values of quantum observables without assuming a hidden variable theory. However, quantum set theory enables us to do so without assuming hidden variables but alternatively under the consist use of quantum logic, which is more or less considered as logic of the superposition principle. [1] M. Ozawa, Transfer principle in quantum set theory, J. Symbolic Logic 72, 625-648 (2007), online preprint: http://arxiv.org/abs/math.LO/0604349. [2] M. Ozawa, Quantum perfect correlations, Ann. Phys. (N.Y.) 321, 744--769 (2006), online preprint: LANL quant-ph/0501081. Masanao Ozawa http://streamer.perimeterinstitute.ca/mp3/5f52bfe9-d841-45b0-b89d-bf7ab2b6dc9d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/5f52bfe9-d841-45b0-b89d-bf7ab2b6dc9d.mp3 Tue, 24 Jun 2008 16:00:00 -0400 We investigate the strengths and weaknesses of the Spekkens toy model for quantum states. We axiomatize the Spekkens toy model into a set of five axioms, regarding valid states, transformations, measurements and composition of systems. We present two relaxations of the Spekkens toy model, giving rise to two variant toy theories. By relaxing the axiom regarding valid transformations a group of toy operations is obtained that is equivalent to the projective extended Clifford Group for one and two qubits. However, the physical state of affairs resulting from this relaxation is undesirable, violating the desideratum that single toy bit operations must compose under the tensor product. The second variant toy theory is obtained by relaxing the axioms regarding valid states and measurements, resulting in a toy model that exhibits the Kochen-Specker property. Like the previous toy model, the relaxation renders the toy model physically undesirable. Therefore, we claim that the Spekkens toy model is optimal; altering its axioms does not yield a better epistemic description of quantum theory. This work is a collaboration with Gilad Gour, Aidan Roy and Barry C. Sanders. Michael Skotiniotis http://streamer.perimeterinstitute.ca/mp3/00506931-3440-4b3b-9c6b-be46e70618e7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/00506931-3440-4b3b-9c6b-be46e70618e7.mp3 Tue, 08 Jul 2008 16:00:00 -0400 In deBroglie-Bohm theory the quantum state plays the role of a guiding agent. In this seminar we will explore if this is a universal feature shared by all hidden variable theories or merely a peculiar feature of deBroglie-Bohm theory. We present the bare bones of a model in which the quantum state represents a probability distribution and does not act as a guiding agent. The theory is also psi-epistemic according to Spekken's and Harrigan's definition. For simplicity we develop the model for a 1D discrete lattice but the generalization to higher dimensions is straightforward. The ontic state consists of a definite particle position and in addition possible non-local links between spatially separated lattice points. These non-local links comes in two types: directed links and non-directed links. Entanglement manifests itself through these links. Interestingly, this ontology seems to be the simplest possible and immediately suggested by the structure of quantum theory itself. For N lattice points there are N*3^(N(N-1)) ontic states growing exponentially with the Hilbert space dimension N as expected. We further require that the evolution of the probability distribution on the ontic state space is dictated by a master equation with non-negative transition rates. It is then easy to show that one can reproduce the Schroedinger equation if an only if there are positive solutions to a gigantic system of linear equations. This is a highly non-trivial problem and whether there exists such positive solutions or not is still not clear to me. Alternatively one can view this set of linear equations as constraints on the possible types of Hamiltonians. We end by speculating how one might incorporate gravity into this theory by requiring permutation invariance of the dynamical evolution law. Hans Westman http://streamer.perimeterinstitute.ca/mp3/0718a5a5-8336-4e33-b0c8-93db608d66f7.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0718a5a5-8336-4e33-b0c8-93db608d66f7.mp3 Tue, 22 Jul 2008 04:00:00 -0400 Domains were introduced in computer science in the late 1960's by Dana Scott to provide a semantics for the lambda calculus (the lambda calculus is the basic prototype for a functional programming language i.e. ML). The study of domains with measurements was initiated in the speaker's thesis: a domain provides a qualitative view of information expressed in part by an 'information order' and a measurement on a domain expresses a quantitative view of information with respect to the underlying qualitative aspect. The theory of domains and measurements was initially introduced to provide a first order model of computation, one in which a computation is viewed as a process that evolves in a space of informatic objects, where processes have informatic rates of change determined by the manner in which they manipulate information. There is a domain of binary channels with capacity as a measurement. There is a domain of finite probability distributions with entropy as a measurement. There is a domain of quantum mixed states with entropy as a measurement. There is a domain of spacetime intervals with global time as a measurement. In this setting, similarities between QM and GR emerge, but also some important differences. In a domain, if we write x <= y, then it means that x carries information about y, while x << y is a stronger relation that means x carries *essential* information about y. In GR, the domain theoretic relation << can be proven to be timelike causality. It possesses stronger mathematical properties than << does in QM. However, by an application of the maximum entropy principle, we can restrict the mixed states in consideration and this difference is removed: the domains of events and mixed states are both globally hyperbolic -- where globally hyperbolic is a purely order theoretic idea that just happens to coincide with the usual notion in the case of GR. Along the way, we will see domain theoretic ways of distinguishing between the Newtonian and relativistic notions of time, how to reconstruct the topology and geometry of spacetime in a purely order theoretic manner beginning from only a countable set, see that the Holevo capacity of a unital qubit channel is determined by the largest value of its informatic derivative and have reason to wonder if distance can be defined as the amount of information (capacity) that can be transmitted between two points. Keye Martin http://streamer.perimeterinstitute.ca/mp3/79f2d303-4699-426c-b318-30fecff75cc4.mp3 Science http://streamer.perimeterinstitute.ca/mp3/79f2d303-4699-426c-b318-30fecff75cc4.mp3 Tue, 12 Aug 2008 16:00:00 -0400 Theoretical and experimental results on the Quantum Injected Optical Parametric Amplification (QI-OPA) of optical qubits in the high gain regime (g > 6) are reported. The entanglement of the related Schroedinger Cat-State (SCS) is demonstrated as well as the establishment of Phase-Covariant quantum cloning for a Macrostate consisting of about 106 particles. In addition, the violation of the CHSH inequality is has been realized experimentally. According to the original 1935 definition of the SCS, the overall apparatus establishes for the first time the nonlocal correlations between a microcopic spin (qubit) and a high J angular momentum i.e. a macroscopic multiparticle system close to the classical limit. Applications to Quantum Information will be discussed. Francesco De Martini http://streamer.perimeterinstitute.ca/mp3/3fd65f19-b8d5-4d0a-af9b-1cb2d8d5bd8e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3fd65f19-b8d5-4d0a-af9b-1cb2d8d5bd8e.mp3 Tue, 26 Aug 2008 16:00:00 -0400 After using the complex Hilbert space formalism for quantum theory for so long, it is very easy to begin to take for granted features like projection operators and the projection postulate, the algebra of observables, symmetric transition probabilities, linear evolution, etc.... Over the past 50 years there have been many attempts to gain a better understanding of this formalism by reconstructing it from different kinds of (sometimes) physically motivated assumptions. By looking at how the above features are motivated and used in different reconstructions, it becomes clear just how special and restrictive many of them are. The question is then what a theory which does not have some of these features looks like. Another interesting question is whether there are any reasons to be suspicious of postulating them in reconstructions or when trying to generalize or apply the quantum formalism to untested situations. Cozmin Ududec http://streamer.perimeterinstitute.ca/mp3/2bdfe5ad-006e-40aa-aaca-1a29c0b2c64e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2bdfe5ad-006e-40aa-aaca-1a29c0b2c64e.mp3 Tue, 23 Sep 2008 16:00:00 -0400 A simple theorem of Dirac identifies primary first-class constraints as generators of transformations, 'that do not affect the physical state'. This result has profound implications for the definition of physical states and observables in the quantization of constrained systems, and leads to one aspect of the infamous 'problem of time' in quantum gravity. As I will discuss, a close look at the theorem reveals that it depends crucially on the assumption of an absolute time. This assumption does not hold for reparametrization invariant theories, such as parametrized particle mechanics, and in these theories, the primary Hamiltonian constraint does generate physical change. I will also look at just what Dirac did and did not say about this case, and what has been said by reviewers since. Brendan Foster http://streamer.perimeterinstitute.ca/mp3/27de5f96-211d-4753-a8f5-21deb22746fc.mp3 Science http://streamer.perimeterinstitute.ca/mp3/27de5f96-211d-4753-a8f5-21deb22746fc.mp3 Tue, 07 Oct 2008 16:00:00 -0400 We start by studying the non-computational geometry of fractionally-dimensioned measure-zero dynamically-invariant subsets of phase space, associated with certain deterministic nonlinear dissipative dynamical systems. Then, by studying the asymptotic states of the Hawking Box, the existence of such invariant subsets is conjectured for gravitationally-bound systems. The argument hinges around the phase-space properties of black holes. Like Penrose, it is assumed that phase-space volumes shrink when the contents of the Hawking Box contain black holes. However, unlike Penrose, we do not argue for any corresponding phase-space divergence when the Box does not contain black holes. We now make the hypothesis that these invariant phase-space subsets play a primitive role in fundamental physics; specifically that the state of the universe (“reality”) lies on such an invariant subset (now and hence forever). Attention is focussed on the implications of this hypothesis for the foundations of quantum theory. For example, what are referred to as “measurements” of the quantum state, are defined in terms of symbolic dynamics on the invariant set, relative to some partition of the invariant set. This immediately leads to the notion that any theory which treats these invariant sets as primitive, must be contextual (since counterfactual perturbations almost certainly take states off the measure-zero invariant set and hence to “unreal” regions of phase space where the symbolic partition is undefined). This in turn leads to a new perspective, both on the foundations of quantum theory and on the role of gravity in formulating these foundations. In particular, a measurement-free Neo-Copenhagen Interpretation of quantum theory, based on the Invariant Set Hypothesis will be presented. Tim Palmer http://streamer.perimeterinstitute.ca/mp3/3ec5cb07-90a1-43a0-9c68-bb15084679fa.mp3 Science http://streamer.perimeterinstitute.ca/mp3/3ec5cb07-90a1-43a0-9c68-bb15084679fa.mp3 Tue, 21 Oct 2008 16:00:00 -0400 TBA Stuart Kauffman http://streamer.perimeterinstitute.ca/mp3/204d8729-6cfa-43b6-b0a5-048254e72e03.mp3 Science http://streamer.perimeterinstitute.ca/mp3/204d8729-6cfa-43b6-b0a5-048254e72e03.mp3 Tue, 28 Oct 2008 16:00:00 -0400 The unparalleled empirical success of quantum theory strongly suggests that it accurately captures fundamental aspects of the workings of the physical world. The clear articulation of these aspects is of inestimable value --- not only for the deeper understanding of quantum theory in itself, but for its further development, particularly for the development of a theory of quantum gravity. Recently, there has been growing interest in elucidating these aspects by expressing, in a less abstract mathematical language, what we think quantum theory might be telling us about how nature works, and trying to derive, or reconstruct, quantum theory from these postulates. In this talk, I describe a simple reconstruction of the finite- dimensional quantum formalism. The derivation takes places with a classical probabilistic framework equipped with the information (or Fisher-Rao) metric, and rests upon a small number of elementary ideas (such as complementarity and global gauge invariance). The complex structure of quantum formalism arises very naturally. The derivation provides a number of non-trivial insights into the quantum formalism, such as the extensive nature of the role of information geometry in determining the quantum formalism, the importance of global gauge invariance, and the importance (or lack thereof) of assumptions concerning separated systems. Philip Goyal http://streamer.perimeterinstitute.ca/mp3/1eb8c532-8496-4983-8f29-8ee270498bad.mp3 Science http://streamer.perimeterinstitute.ca/mp3/1eb8c532-8496-4983-8f29-8ee270498bad.mp3 Tue, 04 Nov 2008 16:00:00 -0500 I show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. I call devices with that structure ``inference devices''. I present a set of existence and impossibility results concerning inference devices. These results hold independent of the precise physical laws governing our universe. In a limited sense, the impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, these impossibility results can be viewed as a non-quantum mechanical ``uncertainty principle''. Next I explore the close connections between the mathematics of inference devices and of Turing Machines. I end by informally discussing the philosophical implications of these results, e.g., for whether the universe ``is'' a computer. David Wolpert http://streamer.perimeterinstitute.ca/mp3/c8c2fcda-0a83-47a7-8544-3f52dc9fca5d.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c8c2fcda-0a83-47a7-8544-3f52dc9fca5d.mp3 Tue, 11 Nov 2008 16:00:00 -0500 Many statistics problems involve predicting the joint strategy that will be chosen by the players in a noncooperative game. Conventional game theory predicts that the joint strategy will satisfy an ``equilibrium concept''. The relative probabilities of the joint strategies satisfying the equilibrium concept are not given, and all joint strategies that do not satisfy it are given probability zero. As an alternative, I view the prediction problem as one of statistical inference, where the ``data'' includes the details of the noncooperative game. This replaces conventional game theory's focus on how to specify a set of equilibrium joint strategies with a focus on how to specify a density function over joint strategies. I explore a Bayesian version of such a Predictive Game Theory (PGT) that provides a posterior density over joint strategies. It is based on the the entropic prior and on a likelihood that quantifies the rationalities of the players. The Quantal Response Equilibrium (QRE) is a popular game theory equilibrium concept parameterized by player rationalities. I show that for some games the local peaks of the posterior density over joint strategies approximate the associated QRE's, and derive the associated correction terms. I also discuss how to estimate parameters of the likelihood from observational data, and how to sample from the posterior. I end by showing how PGT can be used to specify a {it{unique}} equilibrium for any noncooperative game, thereby providing a solution to a long-standing problem of conventional game theory. David Wolpert http://streamer.perimeterinstitute.ca/mp3/379333f8-54d8-4351-8bb6-34c5b114d10c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/379333f8-54d8-4351-8bb6-34c5b114d10c.mp3 Thu, 13 Nov 2008 16:00:00 -0500 Conventional quantum mechanics answers this question by specifying the required mathematical properties of wavefunctions and invoking the Born postulate. The ontological question remains unanswered. There is one exception to this. A variation of the Feynman chessboard model allows a classical stochastic process to assemble a wavefunction, based solely on the geometry of spacetime paths. A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ from the perspective of an underlying kinetic theory. If the fine-scale motion of a particle through spacetime is continuous and position is a single valued function of time, then we are able to describe ensembles of paths directly by PDFs. However, should paths have time reversed portions so that position is not a single-valued function of time, a simple Bernoulli counting of paths fails, breaking the link to PDF's! Under certain circumstances, correcting the path-counting to accommodate time-reversed sections results in wavefunctions not PDFs. The result is that a single `switch' simultaneously turns on both special relativity and quantum propagation. Physically, fine-scale random motion in space alone yields a diffusive process with PDFs governed by the Telegraph equations. If the fine-scale motion includes both directions in time, the result is a wavefunction satisfying the Dirac equation that also provides a detailed answer to the title question. Garnet Ord http://streamer.perimeterinstitute.ca/mp3/4978c233-5a5e-49db-8270-f39dc83a3a7b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/4978c233-5a5e-49db-8270-f39dc83a3a7b.mp3 Tue, 18 Nov 2008 16:00:00 -0500 Bob Batterman http://streamer.perimeterinstitute.ca/mp3/2fbc2233-2c08-4cc8-9bf0-ee697034857c.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2fbc2233-2c08-4cc8-9bf0-ee697034857c.mp3 Fri, 21 Nov 2008 11:00:00 -0500 This paper critically examines the view of quantum mechanics that emerged shortly after the introduction of quantum mechanics and that has been widespread ever since. Although N. Bohr, P. A. M. Dirac, and W. Heisenberg advanced this view earlier, it is best exemplified by J. von Neumann’s argument in Mathematical Foundations of Quantum Mechanics (1932) that the transformation of 'a [quantum] state ... under the action of an energy operator . . . is purely causal,' while, 'on the other hand, the state ... which may measure a [given] quantity ... undergoes in a measurement a non-casual change.' Accordingly, while the paper discusses all four of these arguments, it will especially focus on that of von Neumann. The paper also offers an alternative, radically noncausal, view of the quantum-mechanical situation and considers the differences between the ensemble and the Bayesian understanding quantum mechanics. It will also discuss the Bayesian approach to quantum information theory in this set of contexts. Arkady Plotnitsky http://streamer.perimeterinstitute.ca/mp3/b6b3515b-ccbe-484a-876d-29703872e0dd.mp3 Science http://streamer.perimeterinstitute.ca/mp3/b6b3515b-ccbe-484a-876d-29703872e0dd.mp3 Tue, 25 Nov 2008 16:00:00 -0500 We all know that the EPR argument fails, and we can all provide proofs of one sort or another that it can't work. But in spite of this, there's something curiously tempting about the reasoning, and the temptation sometimes leads to needless perplexity about other issues. This paper will do two things. It will offer a diagnosis of where the EPR argument goes wrong that shows why we should be suspicious long before we get to Bell-type results, and then use the thought behind this diagnosis to suggest an orientation toward thinking about quantum states. The proposal for understanding states will have some things in common with Bayesian approaches, but will part company with them on some crucial points. Allen Stairs http://streamer.perimeterinstitute.ca/mp3/93c868e7-51f9-4e39-a841-30a39d36e554.mp3 Science http://streamer.perimeterinstitute.ca/mp3/93c868e7-51f9-4e39-a841-30a39d36e554.mp3 Tue, 02 Dec 2008 16:00:00 -0500 Quantum entanglement has two remarkable properties. First, according to Bell's theorem, the statistical correlations between entangled quantum systems are inconsistent with any theory of local hidden variables. Second, entanglement is monogamous -- that is, to the degree that A and B are entangled with each other, they cannot be entangled with any other systems. It turns out that these properties are intimately related. Ben Schumacher http://streamer.perimeterinstitute.ca/mp3/2a53cc39-30cb-4e06-aec3-cd9ec718afad.mp3 Science http://streamer.perimeterinstitute.ca/mp3/2a53cc39-30cb-4e06-aec3-cd9ec718afad.mp3 Wed, 03 Dec 2008 11:00:00 -0500 Lee Smolin has argued that one of the barriers to understanding time in a quantum world is our tendency to spatialize time. The question is whether there is anything in physics that could lead us to mathematically characterize time so that it is not just another funny spatial dimension. I will explore the possibility(already considered by Smolin and others) that time may be distinguished from space by what I will call a measure of Booleanity. The Bell-Kochen-Specker Theorem shows that the statistics of quantum systems (unlike that of classical systems) do not in general permit of a Boolean substructure. I will outline reasons for thinking that time is the dimension in which the Booleanity of spacetime (considered as a quantum system) varies, while space is characterized by constant Booleanity. I will not be able to give a mathematically complete characterization of the Booleanity of a region of spacetime, since that would require nothing less than knowing how to quantize spacetime; however, I will argue that something like this is needed if one is to make any sense of an ontological distinction between past, present, and future in terms of modern physics. I will also briefly consider possible objections to this view arising from the relativity of simultaneity, which (on its usual interpretation) apparently places all events on an equal ontological footing. In order to get around this we need a generalized conception of simultaneity that treats Einstein&#39;s notion of simultaneity as a special case, and which allows for equivalence classes of spacelike separate events distinguished by covariant quantities such as action, phase, and (as I will argue) any reasonable measure of Booleanity. Kent Peacock http://streamer.perimeterinstitute.ca/mp3/f1dd9e8f-7f22-4b04-a0ee-85874452cfd8.mp3 Science http://streamer.perimeterinstitute.ca/mp3/f1dd9e8f-7f22-4b04-a0ee-85874452cfd8.mp3 Tue, 16 Dec 2008 16:00:00 -0500