# Weekly Papers on Quantum Foundations (10)

This is a list of this week’s papers on quantum foundations published in the various journals or uploaded to the preprint servers such as arxiv.org and PhilSci Archive.

Obtaining a contradiction between local realism and quantum mechanics using only one correlation function. (arXiv:1503.01679v1 [quant-ph])

quant-ph updates on arXiv.org

on 2015-3-07 7:20am GMT

Authors: Ramon LapiedraA. Pérez

An ensemble consisting on systems of two entangled spin 1/2 particles, all of them in the same global quantum state, are considered. The two spins are measured, each of them, on a fixed direction, at two randomly selected measurement times. Realism, plus locality and freedom of choice referred to these chosen times, are assumed. Then, from the sole correlation function related to the two measurements, without considering any Bell inequalities, a contradiction between these assumptions and quantum mechanics is found.

The meaning of “anomalous weak values” in quantum and classical theories

ScienceDirect Publication: Physics Letters A

on 2015-3-06 10:08am GMT

Publication date: 19 June 2015
Source:Physics Letters A, Volume 379, Issues 16–17
Author(s): D. Sokolovski
The readings of a highly inaccurate “weak” quantum meter, employed to determine the value of a dichotomous variable S without destroying the interference between the alternatives, may take arbitrary values. We show that the expected values of its readings may take any real value, depending on the choice of the states in which the system is pre- and post-selected. Some of these values must fall outside the range of eigenvalues of S, in which case they may be expressed as “anomalous” averages obtained with negative probability weights, constructed from available probability amplitudes. This behaviour is a natural consequence of the Uncertainty Principle. The phenomenon of “anomalous weak values” has no non-trivial analogue in classical statistics.

Extending dualities to trialities deepens the foundations of dynamics. (arXiv:1503.01424v1 [hep-th])

gr-qc updates on arXiv.org

on 2015-3-06 12:56am GMT

Authors: Lee Smolin

Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables.

To illustrate this, we study matrix models with a cubic action, and show how breaking its natural triality symmetry by imposing different compactifications yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born’s duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.

The hidden geometry of electromagnetism. (arXiv:1503.01150v1 [physics.class-ph])

gr-qc updates on arXiv.org

on 2015-3-06 12:56am GMT

Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field. Self-force is a pressing issue and an active research topic in gravitational phenomena, as well as a source of controversies in classical electromagnetism. In this work, we study a hidden geometrical structure manifested by the electromagnetic field-lines that has the potential of eliminating all singularities from classical electrodynamics. We explore preliminary results towards a consistent way of treating both self- and external fields.

Origin of structure: Statistical characterization of the primordial density fluctuations and the collapse of the wave function. (arXiv:1503.01417v1 [gr-qc])

gr-qc updates on arXiv.org

on 2015-3-06 12:56am GMT

Authors: Gabriel LeonDaniel Sudarsky

The statistical properties of the primordial density perturbations has been considered in the past decade as a powerful probe of the physical processes taking place in the early universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that serves to discriminate among competing scenarios concerning the details of the origin of cosmological perturbations. However, all of the scenarios, based on the conventional approach to the so-called “quantum-to-classical transition” during inflation, lack the ability to point out the precise physical mechanism responsible for generating the inhomogeneity and anisotropy of our universe starting from and exactly homogeneous and isotropic vacuum state associated with the early inflationary regime. In past works, we have shown that the proposals involving a spontaneous dynamical reduction of the quantum state provide plausible explanations for the birth of said primordial inhomogeneities and anisotropies. In the present manuscript we show that, when considering within the context of such proposals, the characterization of the spectrum and bispectrum turn out to be quite different from those found in the traditional approach, and in particular, some of the statistical features, must be treated in a different way leading to some rather different conclusions.

Hamilton–Jacobi meet M\”obius. (arXiv:1503.01286v1 [hep-th])

hep-th updates on arXiv.org

on 2015-3-06 12:56am GMT

Authors: Alon E. FaraggiMarco Matone

Adaptation of the Hamilton–Jacobi formalism to quantum mechanics leads to a cocycle condition, which is invariant under $D$–dimensional M\”obius transformations with Euclidean or Minkowski metrics. In this paper we aim to provide a pedagogical presentation of the proof of the M\”obius symmetry underlying the cocycle condition. The M\”obius symmetry implies energy quantization and undefinability of quantum trajectories, without assigning any prior interpretation to the wave function. As such, the Hamilton–Jacobi formalism, augmented with the global M\”obius symmetry, provides an alternative starting point, to the axiomatic probability interpretation of the wave function, for the formulation of quantum mechanics and the quantum spacetime. The M\”obius symmetry can only be implemented consistently if spatial space is compact, and correspondingly if there exist a finite ultraviolet length scale. Evidence for non–trivial space topology may exist in the cosmic microwave background radiation.

Laws of Nature and the Reality of the Wave Function. (arXiv:1503.01137v1 [quant-ph])

physics.hist-ph updates on arXiv.org

on 2015-3-06 12:56am GMT

Authors: Mauro Dorato

In this paper I review three different positions on the wave function, namely: nomological realism, dispositionalism, and configuration space realism by regarding as essential their capacity to account for the world of our experience. I conclude that the first two positions are committed to regard the wave function as an abstract entity. The third position will be shown to be a merely speculative attempt to derive a primitive ontology from a reified mathematical space. Without entering any discussion about nominalism, I conclude that an elimination of abstract entities from one’s ontology commits one to instrumentalism about the wave function, a position that therefore is not as unmotivated as it has seemed to be to many philosophers.

A bound on chaos. (arXiv:1503.01409v1 [hep-th])

quant-ph updates on arXiv.org

on 2015-3-06 12:56am GMT

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $\lambda_L \le 2 \pi k_B T/\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

Events and the Ontology of Quantum Mechanics. (arXiv:1503.01140v1 [quant-ph])

quant-ph updates on arXiv.org

on 2015-3-06 12:56am GMT

Authors: Mauro Dorato

In the first part of the paper I argue that an ontology of events is precise, flexible and general enough so as to cover the three main alternative formulations of quantum mechanics as well as theories advocating an antirealistic view of the wave function. Since these formulations advocate a primitive ontology of entities living in four-dimensional spacetime, they are good candidates to connect that quantum image with the manifest image of the world. However, to the extent that some form of realism about the wave function is also necessary, one needs to endorse also the idea that the wave function refers to some kind of power. In the second part, I discuss some difficulties raised by the recent proposal that in Bohmian mechanics this power is holistically possessed by all the particles in the universe.

Prediction and Retrodiction for a Continuously Monitored Superconducting Qubit

PRL Editors’ Suggestions

on 2015-3-05 3:00pm GMT

Author(s): D. Tan, S. J. Weber, I. Siddiqi, K. Mølmer, and K. W. Murch

Predictions for a quantum measurement are improved by probing the system after the measurement and evolving a model backward in time.

[Phys. Rev. Lett. 114, 090403] Published Thu Mar 05, 2015

Dynamical Correspondence in a Generalized Quantum Theory

Latest Results for Foundations of Physics

on 2015-3-04 12:00am GMT

Abstract

In order to figure out why quantum physics needs the complex Hilbert space, many attempts have been made to distinguish the C*-algebras and von Neumann algebras in more general classes of abstractly defined Jordan algebras (JB- and JBW-algebras). One particularly important distinguishing property was identified by Alfsen and Shultz and is the existence of a dynamical correspondence. It reproduces the dual role of the selfadjoint operators as observables and generators of dynamical groups in quantum mechanics. In the paper, this concept is extended to another class of nonassociative algebras, arising from recent studies of the quantum logics with a conditional probability calculus and particularly of those that rule out third-order interference. The conditional probability calculus is a mathematical model of the Lüders–von Neumann quantum measurement process, and third-order interference is a property of the conditional probabilities which was discovered by Sorkin (Mod Phys Lett A 9:3119–3127, 1994) and which is ruled out by quantum mechanics. It is shown then that the postulates that a dynamical correspondence exists and that the square of any algebra element is positive still characterize, in the class considered, those algebras that emerge from the selfadjoint parts of C*-algebras equipped with the Jordan product. Within this class, the two postulates thus result in ordinary quantum mechanics using the complex Hilbert space or, vice versa, a genuine generalization of quantum theory must omit at least one of them.

Higgs inflation and vacuum stability. (arXiv:1502.07952v1 [hep-ph])

gr-qc updates on arXiv.org

on 2015-3-03 12:44am GMT

Authors: Javier Rubio

Inflation is nowadays a well-established paradigm consistent with all the observations. The precise nature of the inflaton is however unknown and its role could be played by any candidate able to imitate a scalar condensate in the slow-roll regime. The discovery of a fundamental scalar in the LHC provides the less speculative candidate. Could the Higgs field itself be responsible for inflation? Do we really need to advocate new physics to explain the properties of the Universe at large scales? Which is the relation between the Standard Model parameters and the inflationary observables? What happens if our vacuum becomes unstable below the scale of inflation? We present an overview of Higgs inflation trying to provide answers to the previous questions with special emphasis on the vacuum stability issue.

Effect of quantum statistics on the gravitational weak equivalence principle. (arXiv:1502.07875v1 [quant-ph])

gr-qc updates on arXiv.org

on 2015-3-03 12:44am GMT

Authors: S. V. MousaviA. S. MajumdarD. Home

We study the effect of quantum statistics on the arrival time distribution of quantum particles computed through the probability current density. It is shown that symmetrization or asymmetrization of the wave function affects the arrival time distribution for even freely propagating particles. In order to investigate the effect of statistics on the weak equivalence principle in quantum mechanics (WEQ), we then compute the mean arrival time for wave packets in free fall. The violation of WEQ through the effect of statistics on the mass-dependence of the mean arrival time is clearly exhibited. We finally evaluate the effect of spin on the violation of WEQ using a different approach by including an explicit spin-dependence in the probability current distribution, and compare it with the approach using particle statistics. Our results show WEQ re-emerges smoothly in the limit of large mass.

Equivalence between Quantum Mechanics and PT Symmetric Quantum Mechanics. (arXiv:1502.07774v1 [quant-ph])

quant-ph updates on arXiv.org

on 2015-3-03 12:43am GMT

In this paper we develop a discussion about PT Symmetric Quantum Mechanics, working with basics elements of this theory. In a simple case of two body system, we developed the Quantum Brachistochrone problem. Comparing the results obtained through the PT Symmetric Quantum Mechanics with that ones obtained using the standard formalism, we conclude that this new approach is not able to reveal any new effect.

Particle Statistics Affects Quantum Decay and Fano Interference

PRL: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.

on 2015-3-02 3:00pm GMT

Author(s): Andrea Crespi, Linda Sansoni, Giuseppe Della Valle, Alessio Ciamei, Roberta Ramponi, Fabio Sciarrino, Paolo Mataloni, Stefano Longhi, and Roberto Osellame

Quantum mechanical decay, Fano interference, and bound states with energy in the continuum are ubiquitous phenomena in different areas of physics. Here we experimentally demonstrate that particle statistics strongly affects quantum mechanical decay in a multiparticle system. By considering propagati…

[Phys. Rev. Lett. 114, 090201] Published Mon Mar 02, 2015