Non-reflexive Logical Foundation for Quantum Mechanics

Latest Results for Foundations of Physics

on 2014-11-02 12:00am GMT

Abstract

On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity.

on 2014-11-01 1:42am GMT

Authors: J. W. Moffat

A variable speed of light (VSL) cosmology is developed with a spontaneous breaking of Lorentz invariance in the early universe. A non-minimal electromagnetic coupling to curvature and the resulting quantum electrodynamic vacuum polarization dispersive medium can produce $c\gg c_0$ in the early universe, where $c_0$ is the measured speed of light today. Higher derivative curvature contributions to the effective gravitational action and quantum gravity vacuum polarization can produce a dispersive medium and a large increase in the speed of gravitational waves $c_g\gg c_{g0}$ in the early universe, where $c_{g0}$ is the speed of gravitational waves today. The initial value problems of cosmology are solved: the horizon and flatness problems. The model predicts primordial scalar and tensor fluctuation spectral indices $n_s=0.96$ and $n_t=- 0.04$, respectively. The BICEP2 observation of $r=0.2$ yields $r/n_t=-5$ which is close to the single-field inflationary consistency condition $r/n_t=-8$.

Interferometric Probes of Planckian Quantum Geometry. (arXiv:1410.8197v1 [gr-qc])

on 2014-11-01 1:42am GMT

Authors: Ohkyung Kwon, Craig J. Hogan

The effect of Planck scale quantum geometrical effects on measurements with interferometers is estimated with standard physics, and with a variety of proposed extensions. It is shown that effects are negligible in standard field theory with canonically quantized gravity. Statistical noise levels are estimated in a variety of proposals for non-standard metric fluctuations, and these alternatives are constrained using upper bounds on stochastic metric fluctuations from LIGO. Idealized models of several interferometer system architectures are used to predict signal noise spectra in a quantum geometry that cannot be described by a fluctuating metric, in which position noise arises from holographic bounds on directional information. Predictions in this case are shown to be close to current and projected experimental bounds.

on 2014-11-01 12:00am GMT

Abstract

The ontology of Bohmian mechanics includes both the universal wave function (living in 3N-dimensional configuration space) and particles (living in ordinary 3-dimensional physical space). Proposals for understanding the physical significance of the wave function in this theory have included the idea of regarding it as a physically-real field in its 3N-dimensional space, as well as the idea of regarding it as a law of nature. Here we introduce and explore a third possibility in which the configuration space wave function is simply eliminated—replaced by a set of single-particle pilot-wave fields living in ordinary physical space. Such a re-formulation of the Bohmian pilot-wave theory can exactly reproduce the statistical predictions of ordinary quantum theory. But this comes at the rather high ontological price of introducing an infinite network of interacting potential fields (living in 3-dimensional space) which influence the particles’ motion through the pilot-wave fields. We thus introduce an alternative approach which aims at achieving empirical adequacy (like that enjoyed by GRW type theories) with a more modest ontological complexity, and provide some preliminary evidence for optimism regarding the (once popular but prematurely-abandoned) program of trying to replace the (philosophically puzzling) configuration space wave function with a (totally unproblematic) set of fields in ordinary physical space.

Primitive ontology and quantum state in the GRW matter density theory

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on 2014-10-31 6:28am GMT

Egg, Matthias and Esfeld, Michael (2014) Primitive ontology and quantum state in the GRW matter density theory. [Preprint]

Classical correlation alone supplies the anomaly to weak values. (arXiv:1410.8067v1 [quant-ph])

on 2014-10-30 8:42am GMT

Authors: Christopher Ferrie, Joshua Combes

The question of what is genuinely quantum about weak values is only ever going to elicit strongly subjective opinions—it is not a scientific question. Good questions, when comparing theories, are operational—they deal with the unquestionable outcomes of experiment. We give the anomalous shift of weak values an objective meaning through a generalization to an operational definition of anomalous post-selected averages. We show the presence of these averages necessitate correlations in every model giving rise to them—quantum or classical. Characterizing such correlations shows that they are ubiquitous. We present the simplest classical example without the need of disturbance realizing these generalized anomalous weak values.

Multipartite Bell-type Inequality by Generalizing Wigner’s Argument. (arXiv:1410.7936v1 [quant-ph])

on 2014-10-30 8:42am GMT

Authors: Dipankar Home, Debashis Saha, Siddhartha Das

Wigner’s argument inferring Bell-type inequality for the EPR-Bohm entangled state is generalized here for any N-partite state. This is based on assuming for the relevant dichotomic observables the existence of the overall joint probability distributions, satisfying the locality condition, that would yield the measurable marginal probabilities. For any N, such Generalized Wigner’s Inequality (GWI) is violated by quantum mechanics for all pure entangled states. The efficacy of GWI is probed, comparing with the Seevinck-Svetlichny multipartite inequality, by calculating threshold visibilities for the quadripartite GHZ, W and Cluster states that determine their respective robustness with respect to the quantum mechanical violation of GWI in the presence of white noise.

on 2014-10-30 8:42am GMT

Authors: Abdel Nasser Tawfik (Egyptian Ctr. Theor. Phys., Cairo, WLCAPP, Cairo), Abdel Magied Diab (WLCAPP, Cairo)

The recent background imaging of cosmic extragalactic polarization (BICEP2) observations are believed as an evidence for the cosmic inflation. BICEP2 provided a first direct evidence for the inflation, determined its energy scale and debriefed witnesses for the quantum gravitational processes. The ratio of scalar-to-tensor fluctuations $r$ which is the canonical measurement of the gravitational waves, was estimated as $r=0.2_{-0.05}^{+0.07}$. Apparently, this value agrees well with the upper bound value corresponding to PLANCK $r\leq 0.012$ and to WMAP9 experiment $r=0.2$. It is believed that the existence of a minimal length is one of the greatest predictions leading to modifications in the Heisenberg uncertainty principle or a GUP at the Planck scale. In the present work, we investigate the possibility of interpreting recent BICEP2 observations through quantum gravity or GUP. We estimate the slow-roll parameters, the tensorial and the scalar density fluctuations which are characterized by the scalar field $\phi$. Taking into account the background (matter and radiation) energy density, $\phi$ is assumed to interact with the gravity and with itself. We first review the Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe and then suggest modification in the Friedmann equation due to GUP. By using a single potential for a chaotic inflation model, various inflationary parameters are estimated and compared with the PLANCK and BICEP2 observations. While GUP is conjectured to break down the expansion of the early Universe (Hubble parameter and scale factor), two inflation potentials based on certain minimal supersymmetric extension of the standard model result in $r$ and spectral index matching well with the observations. Corresponding to BICEP2 observations, our estimation for $r$ depends on the inflation potential and the scalar field. A power-law inflation potential does not.

on 2014-10-29 5:24am GMT

Authors: Steven B. Giddings

Quantum information transfer necessary to reconcile black hole evaporation with quantum mechanics, while approximately preserving regular near-horizon geometry, can be simply parameterized in terms of couplings of the black hole internal state to quantum fields of the black hole atmosphere. The necessity of transferring sufficient information for unitarization sets the strengths of these couplings. Such couplings via the stress tensor offer apparently significant advantages, and behave like quantum fluctuations of the effective metric near the horizon. At the requisite strength, these fluctuations, while soft (low energy/momentum), have significant magnitude, and so can deflect near-horizon geodesics that span distances of order the black hole radius. Thus, the presence of such couplings can result in effects that could be detected or constrained by observation: disruption of near-horizon accretion flows, scintillation of light passing close to the black hole, and alteration of gravitational wave emission from inspirals. These effects could in particular distort features of Sgr A* expected to be observed, e.g., by the Event Horizon Telescope, such as the black hole shadow and photon ring.

Bending of Light in Quantum Gravity. (arXiv:1410.7590v1 [hep-th])

on 2014-10-29 5:24am GMT

Authors: N. E. J. Bjerrum-Bohr, John F. Donoghue, Barry R. Holstein, Ludovic Planté, Pierre Vanhove

We consider the scattering of light-like matter in the presence of a heavy scalar object (such as the sun or a black hole). By treating general relativity as an effective field theory we directly compute the non-analytic parts of the one-loop gravitational amplitude for the scattering of massless scalars or photons from an external massive scalar field. These results allow a semi-classical computation of the bending angle for light-rays grazing the sun, including long-range $\hbar$ contributions. We discuss implications of this computation, in particular the violation of some classical formulations of the equivalence principle.

Quantum tomography of an electron

on 2014-10-29 12:00am GMT

The complete knowledge of a quantum state allows the prediction of the probability of all possible measurement outcomes, a crucial step in quantum mechanics. It can be provided by tomographic methods which have been applied to atomic, molecular, spin and photonic states. For optical or microwave photons, standard tomography is obtained by mixing the unknown state with a large-amplitude coherent photon field. However, for fermions such as electrons in condensed matter, this approach is not applicable because fermionic fields are limited to small amplitudes (at most one particle per state), and so far no determination of an electron wavefunction has been made. Recent proposals involving quantum conductors suggest that the wavefunction can be obtained by measuring the time-dependent current of electronic wave interferometers or the current noise of electronic Hanbury-Brown/Twiss interferometers. Here we show that such measurements are possible despite the extreme noise sensitivity required, and present the reconstructed wavefunction quasi-probability, or Wigner distribution function, of single electrons injected into a ballistic conductor. Many identical electrons are prepared in well-controlled quantum states called levitons by repeatedly applying Lorentzian voltage pulses to a contact on the conductor. After passing through an electron beam splitter, the levitons are mixed with a weak-amplitude fermionic field formed by a coherent superposition of electron–hole pairs generated by a small alternating current with a frequency that is a multiple of the voltage pulse frequency. Antibunching of the electrons and holes with the levitons at the beam splitter changes the leviton partition statistics, and the noise variations provide the energy density matrix elements of the levitons. This demonstration of quantum tomography makes the developing field of electron quantum optics with ballistic conductors a new test-bed for quantum information with fermions. These results may find direct application in probing the entanglement of electron flying quantum bits, electron decoherence and electron interactions. They could also be applied to cold fermionic (or spin-1/2) atoms.

Nature 514 603 doi: 10.1038/nature13821

PhilSci-Archive: No conditions. Results ordered -Date Deposited.

on 2014-10-28 9:26pm GMT

Delhotel, Jean-Michel (2014) Quantum Mechanics Unscrambled. [Preprint]