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  1. Itamar Pitowsky, Correlation Polytopes and the Geometry of Limit Laws in Probability.
    Let be n events in a probability space, and suppose that we have only partial information about the distribution: The probabilites of the events themselves, and their pair intersections. With this partial information we cannot, usually, deternine the probability of an event B in the algebra generated by the 's, but we can obtain lower and upper bounds. This is done by a linear program related to the correlation polytope c(n), a structure introduced in [3], [4]. In the first part (...)
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  2. Itamar Pitowsky, Macroscopic Objects in Quantum Mechanics: A Combinatorial Approach.
    Why do we not see large macroscopic objects in entangled states? There are two ways to approach this question. The first is dynamic. The coupling of a large object to its environment cause any entanglement to decrease considerably. The second approach, which is discussed in this paper, puts the stress on the difficulty of observeing a large-scale entanglement. As the number of particles n grows we need an ever more precise knowledge of the state and an ever more carefully designed (...)
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  3. Itamar Pitowsky, Optimal Tests of Quantum Nonlocality.
    We present a general method for obtaining all Bell inequalities for a given experimental setup. Although the algorithm runs slowly, we apply it to two cases. First, the Greenberger-Horne-Zeilinger setup with three observers each performing one of two possible measurements. Second, the case of two observers each performing one of three possible experiments. In both cases we obtain hundreds of inequalities. Since this is the set of all inequalities, the one that is maximally violated in a given quantum state must (...)
     
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  4. Itamar Pitowsky, The Einstein Podolsky Rosen Argument- From an Embarrassment to an Asset.
    More specifically, one notices that X1  X2, P1  P2  0 where X1, X2 are the position operators for the first and second particles respectively, and P1, P2 their momenta operators. This means that, in principle, one can prepare the pair of particles with simultaneously known values of X1  X2 and P1  P2. Then the knowledge of the value of P2 allows to infer the value of P1.(However, performing the experiment with these continuous variables is technically (...)
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  5. Itamar Pitowsky, The Number of Elements in a Subset: A Grover-Kronecker Quantum Algorithm.
    In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can …nd a single marked object in a database of size N by using only O(pN ) queries of the oracle that identi…es the object. His result was generalized to the case of …nding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M (...)
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  6. Itamar Pitowsky, Deterministic Model of Spin and Statistics.
    A deterministic model that accounts for the statistical behavior of random samples of identical particles is presented. The model is based on some nonmeasurable distribution of spin values in all directions. The mathematical existence of such distributions is proved by set-theoretical techniques, and the relation between these distributions and observed frequencies is explored within an appropriate extension of probability theory. The relation between quantum mechanics and the model is specified. The model is shown to be consistent with known polarization phenomena (...)
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  7. Itamar Pitowsky, From Logic to Physics: How the Meaning of Computation Changed Over Time.
    The intuition guiding the de…nition of computation has shifted over time, a process that is re‡ected in the changing formulations of the Church-Turing thesis. The theory of computation began with logic and gradually moved to the capacity of …nite automata. Consequently, modern computer models rely on general physical principles, with quantum computers representing the extreme case. The paper discusses this development, and the challenges to the Church-Turing thesis in its physical form, in particular, Kieu’s quantum computer and relativistic hyper-computation. Finally, (...)
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  8. Itamar Pitowsky, New Bell Inequalities for the Singlet State: Going Beyond the Grothendieck Bound.
    Contemporary versions of Bell’s argument against local hidden variable (LHV) theories are based on the Clauser Horne Shimony and Holt (CHSH) inequality, and various attempts to generalize it. The amount of violation of these inequalities cannot exceed the bound set by the Grothendieck constants. However, if we go back to the original derivation by Bell, and use the perfect anticorrelation embodied in the singlet spin state, we can go beyond these bounds. In this paper we derive two-particle Bell inequalities for (...)
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  9. Itamar Pitowsky (2012). Typicality and the Role of the Lebesgue Measure in Statistical Mechanics. In. In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. 41--58.
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  10. Jeffrey Bub & Itamar Pitowsky (2010). Two Dogmas About Quantum Mechanics. In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory, & Reality. Oup Oxford.
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  11. Itamar Pitowsky (2007). On Kuhn's The Structure of Scientific Revolutions. Iyyun 56:119.
    Kuhnʼs influential book, The Structure of Scientific Revolutions,1 is often viewed as a revolt against empiricist philosophy of science. However, Friedman has reminded us lately2 that the book was commissioned by logical positivists, who were delighted with the result. In fact, the book was part of the International Encyclopedia of United Science initiated by members of the Vienna Circle, whose first volumes were published in 1938.3 The project aimed at providing a systematic positivist perspective on all the sciences, from logic (...)
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  12. Itamar Pitowsky (2006). On the Definition of Equilibrium. Studies in History and Philosophy of Science Part B 37 (3):431-438.
    Boltzmann’s approach to statistical mechanics is widely believed to be conceptually superior to Gibbs’ formulation. However, the microcanonical distribution often fails to behave as expected: The ergodicity of the motion relative to it can rarely be established for realistic systems; worse, it can often be proved to fail. Also, the approach involves idealizations that have little physical basis. Here we take Khinchin’s advice and propose a de…nition of equilibrium that is more realistic: The de…nition re‡ects the fact that the system (...)
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  13. Ehud Hrushovski & Itamar Pitowsky (2004). Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem. Studies in History and Philosophy of Science Part B 35 (2):177-194.
    Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.
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  14. Itamar Pitowsky (2004). Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem. Studies in History and Philosophy of Science Part B 35 (2):177-194.
    Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated. r 2003 Elsevier Ltd. All rights reserved.
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  15. Itamar Pitowsky, Random Witnesses and the Classical Character of Macroscopic Objects.
    Why don't we see large macroscopic objects in entangled states? Even if the particles composing the object were all entangled and insulated from the environment, we shall still find it almost always impossible to observe the superposition. The reason is that as the number of particles n grows, we need an ever more careful preparation, and an ever more carefully designed experiment, in order to recognize the entangled character of the state of the object. An observable W that distinguishes all (...)
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  16. Meir Hemmo & Itamar Pitowsky (2003). Probability and Nonlocality in Many Minds Interpretations of Quantum Mechanics. British Journal for the Philosophy of Science 54 (2):225-243.
    We argue that certain types of many minds (and many worlds) interpretations of quantum mechanics, e.g. Lockwood ([1996a]), Deutsch ([1985]) do not provide a coherent interpretation of the quantum mechanical probabilistic algorithm. By contrast, in Albert and Loewer's ([1988]) version of the many minds interpretation, there is a coherent interpretation of the quantum mechanical probabilities. We consider Albert and Loewer's probability interpretation in the context of Bell-type and GHZ-type states and argue that it implies a certain (weak) form of nonlocality. (...)
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  17. Itamar Pitowsky (2003). Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability. Studies in History and Philosophy of Science Part B 34 (3):395-414.
    We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance, the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These (...)
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  18. Itamar Pitowsky (2003). Probability and Nonlocality in Many Minds Interpretations of Quantum Mechanics. British Journal for the Philosophy of Science 54 (2):225 - 243.
    We argue that certain types of many minds (and many worlds) interpretations of quantum mechanics, e.g. Lockwood ([1996a]), Deutsch ([1985]) do not provide a coherent interpretation of the quantum mechanical probabilistic algorithm. By contrast, in Albert and Loewer's ([1988]) version of the many minds interpretation, there is a coherent interpretation of the quantum mechanical probabilities. We consider Albert and Loewer's probability interpretation in the context of Bell-type and GHZ-type states and argue that it implies a certain (weak) form of nonlocality.
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  19. Itamar Pitowsky (2003). Physical Hypercomputation and the Church–Turing Thesis. Minds and Machines 13 (1):87-101.
    We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy’s thesis.
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  20. Oron Shagrir & Itamar Pitowsky (2003). Physical Hypercomputation and the Church–Turing Thesis. Minds and Machines 13 (1):87-101.
    We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.
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  21. Itamar Pitowsky (2002). Quantum Speed-Up of Computations. Proceedings of the Philosophy of Science Association 2002 (3):S168-S177.
    1. The Physical Church-Turing Thesis. Physicists often interpret the Church-Turing Thesis as saying something about the scope and limitations of physical computing machines. Although this was not the intention of Church or Turing, the Physical Church Turing thesis is interesting in its own right. Consider, for example, Wolfram’s formulation: One can expect in fact that universal computers are as powerful in their computational capabilities as any physically realizable system can be, that they can simulate any physical system . . . (...)
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  22. S. L. Zabell, Brian Skyrms, Elliott Sober, Malcolm R. Forster, Wayne C. Myrvold, William L. Harper, Rob Clifton, Itamar Pitowsky, Robyn M. Dawes & David Faust (2002). 10. It All Adds Up: The Dynamic Coherence of Radical Probabilism It All Adds Up: The Dynamic Coherence of Radical Probabilism (Pp. S98-S103). [REVIEW] Philosophy of Science 69 (S3).
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  23. Yemima Ben-Menahem & Itamar Pitowsky (2001). Introduction. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):503-510.
  24. Itamar Pitowsky (2001). Local Fluctuations and Local Observers in Equilibrium Statistical Mechanics. Studies in History and Philosophy of Science Part B 32 (4):595-607.
    The distribution function associated with a classical gas at equilibrium is considered. We prove that apart from a factorisable multiplier, the distribution function is fully determined by the correlations among local momenta fluctuations. Using this result we discuss the conditions which enable idealised local observers, who are immersed in the gas and form a part of it, to determine the distribution 'from within'. This analysis sheds light on two views on thermodynamic equilibrium, the 'ergodic' and the 'thermodynamic limit' schools, and (...)
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  25. Itamar Pitowsky & Noam Shoresh (1996). Locality, Factorizability, and the Maxwell Boltzmann Distribution. Foundations of Physics 26 (9):1231-1242.
    A classical gas at equilibrium satisfies the locality conditionif the correlations between local fluctuations at a pair of remote small regions diminish in the thermodynamic limit. The gas satisfies a strong locality conditionif the local fluctuations at any number of remote locations have no (pair, triple, quadruple....) correlations among them in the thermodynamic limit. We prove that locality is equivalent to a certain factorizability condition on the distribution function. The analogous quantum condition fails in the case of a freeBose gas. (...)
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  26. Itamar Pitowsky (1994). George Boole's 'Conditions of Possible Experience' and the Quantum Puzzle. British Journal for the Philosophy of Science 45 (1):95-125.
    In the mid-nineteenth century George Boole formulated his ‘conditions of possible experience’. These are equations and ineqaulities that the relative frequencies of (logically connected) events must satisfy. Some of Boole's conditions have been rediscovered in more recent years by physicists, including Bell inequalities, Clauser Horne inequalities, and many others. In this paper, the nature of Boole's conditions and their relation to propositional logic is explained, and the puzzle associated with their violation by quantum frequencies is investigated in relation to a (...)
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  27. Robert Clifton, Constantine Pagonis & Itamar Pitowsky (1992). Relativity, Quantum Mechanics and EPR. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:114 - 128.
    The Einstein-Podolsky-Rosen argument for the incompleteness of quantum mechanics involves two assumptions: one about locality and the other about when it is legitimate to infer the existence of an element-of-reality. Using one simple thought experiment, we argue that quantum predictions and the relativity of simultaneity require that both these assumptions fail, whether or not quantum mechanics is complete.
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  28. Itamar Pitowsky (1992). Why Does Physics Need Mathematics? A Comment. In. In Edna Ullmann-Margalit (ed.), The Scientific Enterprise. Kluwer. 163--167.
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  29. Itamar Pitowsky (1991). Bohm's Quantum Potentials and Quantum Gravity. Foundations of Physics 21 (3):343-352.
    A generally covariant theory, written in the spirit of Bohm's theory of quantum potentials, which applies to spinless, non interacting, gravitating systems, is formulated. In this theory the quantum state ψ is coupled to the metric tensor g, and the effect of the “quantum potential” is absorbed in the geometry. At the same time, ψ satisfies a covariant wave equation with respect to the very same g. This provides sufficient constraints to derive 11 coupled equations in the 11 unknowns: ψ (...)
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  30. Jeffrey Bub & Itamar Pitowsky (1985). Postscript to the Logic of Scientific Discovery. Canadian Journal of Philosophy 15 (3):539-552.
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  31. Itamar Pitowsky (1985). On the Status of Statistical Inferences. Synthese 63 (2):233 - 247.
    Can the axioms of probability theory and the classical patterns of statistical inference ever be falsified by observation? Various possible answers to this question are examined in a set theoretical context and in relation to the findings of microphysics.
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  32. Itamar Pitowsky (1985). Quantum Mechanics and Value Definiteness. Philosophy of Science 52 (1):154-156.
  33. Itamar Pitowsky (1984). Unified Field Theory and the Conventionality of Geometry. Philosophy of Science 51 (4):685-689.
    The existence of fields besides gravitation may provide us with a way to decide empirically whether spacetime is really a nonflat Riemannian manifold or a flat Minkowskian manifold that appears curved as a result of gravitational distortions. This idea is explained using a modification of Poincaré's famous 'diskworld'.
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  34. Itamar Pitowsky (1982). Substitution and Truth in Quantum Logic. Philosophy of Science 49 (3):380-401.
    If p(x 1 ,...,x n ) and q(x 1 ,...,x n ) are two logically equivalent propositions then p(π (x 1 ),...,π (x n )) and q(π (x 1 ),...,π (x n )) are also logically equivalent where π is an arbitrary permutation of the elementary constituents x 1 ,...,x n . In Quantum Logic the invariance of logical equivalences breaks down. It is proved that the distribution rules of classical logic are in fact equivalent to the meta-linguistic rule of (...)
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  35. Itamar Pitowsky (1982). Where the Theory of Probability Fails. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982:616 - 623.
    A local "resolution" of the Einstein-Podolsky-Rosen Paradox by way of a mechanical analogue (roul ette) is presented together with some notes regarding the consequences of such models for the foundations of mathematics and the theory of probability.
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  36. Itamar Pitowsky, On the Geometry of Quantum Correlations.
    Consider the set Q of quantum correlation vectors for two observers, each with two possible binary measurements. Quadric (hyperbolic) inequalities which are satis…ed by every q 2 Q are proved, and equality holds on a two dimensional manifold consisting of the local boxes, and all..
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  37. Itamar Pitowsky, Quantum Mechanics as a Theory of Probability.
    We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it. The construction proceeds in the following steps: (a) Axioms for the algebra of events are introduced following Birkhoff and von Neumann. All axioms, except the one that expresses the uncertainty principle, are shared with the classical event space. The only models for (...)
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  38. Itamar Pitowsky, Range Theorems for Quantum Probability and Entanglement.
    We consider the set of all matrices of the form pij = tr[W (Ei ⊗ Fj)] where Ei, Fj are projections on a Hilbert space H, and W is some state on H ⊗ H. We derive the basic properties of this set, compare it with the classical range of probability, and note how its properties may be related to a geometric measures of entanglement.
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