# Weekly Papers on Quantum Foundations (35)

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

Operational General Relativity: Possibilistic, Probabilistic, and Quantum. (arXiv:1608.06940v1 [gr-qc])

on 2016-8-27 4:36am GMT

Authors: Lucien Hardy

In this paper we develop an operational formulation of General Relativity similar in spirit to existing operational formulations of Quantum Theory. To do this we introduce an operational space (or op-space) built out of scalar fields. A point in op-space corresponds to some nominated set of scalar fields taking some given values in coincidence. We assert that op-space is the space in which we observe the world. We introduce also a notion of agency (this corresponds to the ability to set knob settings just like in Operational Quantum Theory). The effects of agents’ actions should only be felt to the future so we introduce also a time direction field. Agency and time direction can be understood as effective notions. We show how to formulate General Relativity as a possibilistic theory and as a probabilistic theory. In the possibilistic case we provide a compositional framework for calculating whether some operationally described situation is possible or not. In the probabilistic version we introduce probabilities and provide a compositional framework for calculating the probability of some operationally described situation. Finally we look at the quantum case. We review the operator tensor formulation of Quantum Theory and use it to set up an approach to Quantum Field Theory that is both operational and compositional. Then we consider strategies for solving the problem of Quantum Gravity. By referring only to operational quantities we are able to provide formulations for the possibilistic, probabilistic, and (the nascent) quantum cases that are manifestly invariant under diffeomorphisms.

Comment on “Non-representative Quantum Mechanical Weak Values”. (arXiv:1608.07185v1 [quant-ph])

on 2016-8-27 3:38am GMT

Authors: Alon Ben IsraelL. Vaidman

Svensson [Found. Phys. \textbf{45}, 1645 (2015)] argued that the concept of the weak value of an observable of a pre- and post-selected quantum system cannot be applied when the expectation value of the observable in the initial state vanishes. Svensson’s argument is analyzed and shown to be inconsistent using several examples.

Universal Decoherence under Gravity: A Perspective through the Equivalence Principle

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

on 2016-8-24 2:00pm GMT

Author(s): Belinda H. Pang, Yanbei Chen, and Farid Ya. Khalili

Pikovski et al. [Nat. Phys. 11, 668 (2015)] show that a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field undergoes a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein’s equivalence principle to …

[Phys. Rev. Lett. 117, 090401] Published Wed Aug 24, 2016

Quantum Mechanics of a Photon. (arXiv:1608.06479v1 [quant-ph])

on 2016-8-24 2:17am GMT

A first quantized free photon is a complex massless vector field $A=(A^\mu)$ whose field strength satisfies Maxwell’s equations in vacuum. We construct the Hilbert space $\mathscr{H}$ of the photon by endowing the vector space of the fields $A$ in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in $\mathscr{H}$, determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated helicity axis, and show that each choice of this axis determines a position basis and the corresponding position representation of the quantum mechanics of photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and determine the probability density for the spatial localization of the photon.

Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories

PRL Editors’ Suggestions

on 2016-8-23 2:00pm GMT

Author(s): Daniel A. Roberts and Brian Swingle

A universal regime describing charge transport in holographic theories with particle-hole symmetry is theoretically predicted, suggesting a link between strongly coupled quantum field theories and quantum chaos.

[Phys. Rev. Lett. 117, 091602] Published Tue Aug 23, 2016

Decoherent histories approach to the cosmological measure problem. (arXiv:1608.05672v1 [quant-ph])