Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session R26: Foundations of Quantum Theory |
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Sponsoring Units: GQI Chair: Caslav Brukner, University of Austria Room: 328 |
Wednesday, March 20, 2013 2:30PM - 2:42PM |
R26.00001: Distinct Quantum States Can Be Compatible with a Single State of Reality Peter Lewis, David Jennings, Jonathan Barrett, Terry Rudolph Perhaps the quantum state represents information available to some agent or experimenter about reality, and not reality directly. This view is attractive because if quantum states represent only information, then wave function collapse is possibly no more mysterious than a Bayesian update of a probability distribution given new data. Several other ``puzzling'' features of quantum theory also follow naturally given this view. In order to explore this idea rigorously, we consider models for quantum systems with probabilities for measurement outcomes determined by some underlying physical state of the system, where the underlying state is not necessarily described by quantum theory. In our model, quantum states correspond to probability distributions over the underlying states so that the Born rule is recovered. More specifically, we consider models for quantum systems where several quantum states are consistent with a single underlying state--i.e., probability distributions for distinct quantum states overlap. Recent work shows that such a model is impossible (e.g. the PBR theorem (Nat. Phys. 8, p.474)). Significantly, our example demonstrates that non-trivial assumptions (beyond those required for a well-defined realistic model) are necessary for the PBR theorem and those like it. [Preview Abstract] |
Wednesday, March 20, 2013 2:42PM - 2:54PM |
R26.00002: ABSTRACT WITHDRAWN |
Wednesday, March 20, 2013 2:54PM - 3:06PM |
R26.00003: Our Current Concept of Locality May be Incomplete Armin Nikkhah Shirazi The predictions of Bell's inequalities, and their subsequent experimental verification in the form of correlations between spacelike separated events have led to the prevailing current view that `nature is non-local'. Here we examine the possibility that our current concept of locality may at present not be sufficiently differentiated, and that by using 'nature' synonymously with `spacetime' we may have missed an implication of special relativity which by rendering a more complete conception of locality permits such quantum correlations without either hidden variables or violations of locality. [Preview Abstract] |
Wednesday, March 20, 2013 3:06PM - 3:18PM |
R26.00004: No Drama Quantum Theory? Andrey Akhmeteli Is it possible to offer a ``no drama'' quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations (PDE) in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the Fock space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field (EMF). 2. After introduction of a complex 4-potential (producing the same EMF as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of EMF. 3. The resulting theories for EMF can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order PDE for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed. A. Akhmeteli, Int'l Journal of Quantum Information, Vol. 9, Suppl., 17-26 (2011) A. Akhmeteli, Journal of Mathematical Physics, Vol. 52, 082303 (2011) A. Akhmeteli, quant-ph/1111.4630 A. Akhmeteli, J. Phys.: Conf. Ser., Vol. 361, 012037 (2012) [Preview Abstract] |
Wednesday, March 20, 2013 3:18PM - 3:30PM |
R26.00005: A realist, ``local,'' ``hidden variable'' model of quantum mechanics without observers William Sulis The violation of Bell type inequalities hinges upon the non-Kolmogorov nature of quantum probability structures. I show that a Process theory based, game theoretic formulation of quantum mechanics admits non-Kolmogorov probability structures. This formulation is realist, discrete and local at the level of space-time events while having nonlocal properties at the process level. These nonlocal effects respect relativistic constraints. Solutions to the Schrodinger equation arise through sinc interpolation of local samples generated by local path integral calculations based upon local information. Nonrelativistic quantum mechanics emerges in the continuum limit with perfect information transfer. This model avoids Kochen-Specker type restrictions and violates Bell and Leggett-Garg type inequalities. This formulation will be illustrated with a model of the classical two slit experiment. [Preview Abstract] |
Wednesday, March 20, 2013 3:30PM - 3:42PM |
R26.00006: Quantized Energy Spectrum of a Linear Classical Harmonic Oscillator in Classical Electromagnetic Zero-Point Radiation Wayne Huang, Herman Batelaan Since the early development of Quantum Mechanics, the discrete atomic spectra have been considered as the defining feature of Quantum Mechanics. However, when the classical electromagnetic zero-point radiation is introduced as a modification to Classical Mechanics, our simulation shows that a linear classical harmonic oscillator, when excited by a laser pulse, can exhibit an integer spaced energy spectrum just as its quantum counterpart. This finding may be surprising given the use of a fully classical theory, and it may help us identify the true quantum features in physical systems such as harmonic oscillator and ultimately atoms. [Preview Abstract] |
Wednesday, March 20, 2013 3:42PM - 3:54PM |
R26.00007: Normalized spacings between zeros of Riemann zeta function follow normalized Maxwell-Boltzmann distribution Siavash Sohrab Through \textit{Planck} relation $\varepsilon =$ h$\nu $ normalized spacings between energy levels of oscillators are related to those between frequencies expressed as \textit{Gauss} clock calculator or \textit{Hensel} p$_{\mathrm{j}}$-adic numbers. Energy-level spacings are related to spacings between ``stationary states'' and through \textit{Euler} golden key to zeros of \textit{Riemann} zeta function. The latter are shown to follow normalized \textit{Maxwell-Boltzmann} (NMB) distribution function, \begin{equation} \rho_{\beta} = (8/\pi_{\beta}) [(2/\sqrt{\pi_{\beta}} )x_{\beta} ]^{2} e^{-[(2/\sqrt{\pi_{\beta}} )x_{\beta}]^{2}} \end{equation} , hence providing physical explanations of \textit{Montgomery-Odlyzko} law and \textit{Hilbert-Polya} conjecture. Position of the critical line is found to coincide with that of stationary states. Normalized spacing between eigenvalues of GUE of an \textit{Adele} space constructed by superposition of infinite NMB distribution functions will coincide with spacing of zeros of \textit{Riemann} zeta function according to the theory of noncommutative geometry of \textit{Connes}. [Preview Abstract] |
Wednesday, March 20, 2013 3:54PM - 4:06PM |
R26.00008: Shape Invariance in Deformation Quantization Constantin Rasinariu Shape invariance is a powerful solvability condition, that allows for complete knowledge of the energy spectrum, and eigenfunctions of a system. After a short introduction into the deformation quantization formalism, this work explores the implications of the supersymmetric quantum mechanics and shape invariance techniques to the phase space formalism. We show that shape invariance induces a new set of relations between the Wigner functions of the system, that allows for their direct calculation, once we know one of them. The simple harmonic oscillator and the Morse potential are presented as examples. [Preview Abstract] |
Wednesday, March 20, 2013 4:06PM - 4:18PM |
R26.00009: Entangled states associated with N-qubit GHZ paradoxes Mordecai Waegell, P.K. Aravind Many workers have generalized the original GHZ paradox by replacing the qubits in it by qudits and the three observers by an arbitrary number of observers. We point out that if one stays with qubits but allows an arbitrary number of observers, a large number of paradoxes are possible. Some of the paradoxes come in families that extend upwards to all numbers of qubits. The entangled states connected within these paradoxes come in a wide variety. We survey the different types of entangled states that occur and also discuss some of their applications. [Preview Abstract] |
Wednesday, March 20, 2013 4:18PM - 4:30PM |
R26.00010: Logical difficulty from combining counterfactuals in the GHZ-Bell theorems Louis Sica Since it depends on predictions of single sets of measurements on three particles, the Greenberger, Horne, Zeilinger (GHZ) theorem eliminates the sampling loophole encountered by the Bell theorem that requires a large number of observations to obtain a relatively small number of useful joint measurements. In evading this problem, the GHZ theorem is believed to have confirmed Bell's historic conclusion that local hidden variables are inconsistent with the results of quantum mechanics. The GHZ theorem depends on predicting the results of sets of measurements of which only one may be performed, i.e., counterfactuals. In the present paper, the non-commutative aspects of these unperformed measurement sequences are critically examined. Three classical examples and the logic of the GHZ construction are analyzed to demonstrate that combined counterfactual results of non-commuting operations may be logically absurd, and in general are logically inconsistent with performed measurement sequences that take non-commutation into account. The Bell theorem is also revisited in the light of this result. It is concluded that negative conclusions regarding local hidden variables do not follow from the GHZ and Bell theorems as historically reasoned. [Preview Abstract] |
Wednesday, March 20, 2013 4:30PM - 4:42PM |
R26.00011: Observation of a Fast Evolution in a Parity-time-symmetric System Chao Zheng, Liang Hao, Gui Lu Long In the parity-time-symmetric (PT-symmetric) Hamiltonian theory, the optimal evolution time can be reduced drastically and can even be zero. In this letter, we report our experimental simulation of the fast evolution of a PT-symmetric Hamiltonian in a nuclear magnetic resonance quantum system. The experimental results demonstrate that the PT-symmetric Hamiltonian system can indeed evolve much faster than the quantum system, and the evolution time can be arbitrarily close to zero. [Preview Abstract] |
Wednesday, March 20, 2013 4:42PM - 4:54PM |
R26.00012: Second law of thermodynamics for random walk of quantum particle in a presence of detectors Ivan Sadovskyy, Gordey Lesovik We test H-theorem for a several models of particle random walk. We study interaction with a reservoir/detectors and its influence on entropy and found entropy growing in the time for some models and behaving non-monotonically for the others. We discuss the details of the system-reservoir interaction (such as presence of the interference in the system and number of interactions with detector parts) and their impact on the monotonicity of entropy. [Preview Abstract] |
Wednesday, March 20, 2013 4:54PM - 5:06PM |
R26.00013: Analogy between optical interferometry and integer factorization inspires novel mathematical results Gabriel Seiden Prime factorization of integers is an outstanding problem in arithmetic with important consequences in a variety of fields, most notably cryptography. We explore the intriguing relationship between prime factorization and optical interferometry with the aim of obtaining novel analytic expressions for number-theoretic functions directly related to prime factorization [1]. [1] G. Seiden, Phys. Rev. A 85, 043842 (2012) [Preview Abstract] |
Wednesday, March 20, 2013 5:06PM - 5:18PM |
R26.00014: Glimpses of the quantal algebra in early papers on quantum mechanics Samir Lipovaca A closer reading of early papers on quantum mechanics reveals that the quantal algebra lies hidden beneath the surface. We will show from the standpoint of the quantal algebra that, in essence, Heisenberg came across the symmetric product of the quantal algebra in his remarkable 1925 paper, Born and Jordan limited a general Hamiltonian function to a linear form of the terms containing the symmetric product of the quantal algebra, and Dirac found that the most general operation d/dv is the Leibnitz identity of the quantal algebra. [Preview Abstract] |
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