Weekly Papers on Quantum Foundations (45)

Statistics on Lefschetz thimbles: Bell/Leggett-Garg inequalities and the classical-statistical approximation. (arXiv:2011.02657v1 [hep-th])

Inspired by Lefschetz thimble theory, we treat Quantum Field Theory as a statistical theory with a complex Probability Distribution Function (PDF). Such complex-valued PDFs permit the violation of Bell-type inequalities, which cannot be violated by a real-valued, non-negative PDF. In this paper, we consider the Classical-Statistical approximation in the context of Bell-type inequalities, viz. the familiar (spatial) Bell inequalities and the temporal Leggett-Garg inequalities. We show that the Classical-Statistical approximation does not violate temporal Bell-type inequalities, even though it is in some sense exact for a free theory, whereas the full quantum theory does. We explain the origin of this discrepancy, and point out the key difference between the spatial and temporal Bell-type inequalities. We comment on the import of this work for applications of the Classical-Statistical approximation.

The probabilistic world. (arXiv:2011.02867v1 [quant-ph])

This work attempts a fundamental formulation of physics based on probabilities. The basic assumptions are simple: One world exists. Humans can understand its properties by formulating laws based on probabilities. Our probabilistic setting only employs the notions of a probability distribution, observables and their expectation values, which are computed according to the classical statistical rule. Time is an ordering structure among observables. Understanding the probabilistic laws enables humans to make predictions for future events. Also space, spacetime and geometry emerge as structures among observables.

Within the classical statistical system the time structure induces the concepts of wave functions, density matrices, non-commuting operators and many other aspects of quantum physics. The classical density matrix encodes the probabilistic information of a time-local subsystem. Subsystems are typically correlated with their environment, offering a much richer structure than discussed commonly. We pay particular attention to subsystems with incomplete statistics and probabilistic observables.

Quantum systems are particular time-local subsystems that follow an unitary evolution law. All laws of quantum mechanics are derived from the basic law for expectation values in classical statistics. In particular, we discuss entangled quantum systems in terms of classical probability distributions. In our approach quantum field theories have to be described by an overall probability distribution for the whole Universe for all times. The fundamental functional integral for quantum field theories should define a probability distribution, underlying the functional integral with Minkowski signature.

While this work remains in the context of theoretical physics, the concepts developed here apply to a wide area of science.

Bekenstein bound from the Pauli principle. (arXiv:2005.13973v2 [hep-th] UPDATED)

Assuming that the degrees of freedom of a black hole are finite in number and of fermionic nature, we naturally obtain, within a second-quantized toy model of the evaporation, that the Bekenstein bound is a consequence of the Pauli exclusion principle for these fundamental degrees of freedom. We show that entanglement, Bekenstein and thermodynamic entropies of the black hole all stem from the same approach, based on the entropy operator whose structure is the one typical of Takahashi and Umezawa’s Thermofield Dynamics. We then evaluate the von Neumann black hole–environment entropy and noticeably obtain a Page-like evolution. We finally show that this is a consequence of a duality between our model and a quantum dissipative-like fermionic system.

The Heisenberg limit for laser coherence. (arXiv:2009.05296v2 [quant-ph] UPDATED)

To quantify quantum optical coherence requires both the particle- and wave-natures of light. For an ideal laser beam [1,2,3], it can be thought of roughly as the number of photons emitted consecutively into the beam with the same phase. This number, $\mathfrak{C}$, can be much larger than $\mu$, the number of photons in the laser itself. The limit on $\mathfrak{C}$ for an ideal laser was thought to be of order $\mu^2$ [4,5]. Here, assuming nothing about the laser operation, only that it produces a beam with certain properties close to those of an ideal laser beam, and that it does not have external sources of coherence, we derive an upper bound: $\mathfrak{C} = O(\mu^4)$. Moreover, using the matrix product states (MPSs) method [6,7,8,9], we find a model that achieves this scaling, and show that it could in principle be realised using circuit quantum electrodynamics (QED) [10]. Thus $\mathfrak{C} = O(\mu^2)$ is only a standard quantum limit (SQL); the ultimate quantum limit, or Heisenberg limit, is quadratically better.

Incompleteness for stably sound Turing machines. (arXiv:2001.07592v5 [cs.LO] UPDATED)

Authors: Yasha Savelyev

We first partly develop a mathematical notion of stable soundness intended to reflect the actual soundness property of human beings. Then we show that given an abstract query machine $M$ (a function) the following cannot hold simultaneously: $M$ is stably sound, $M$ is computable, $M$ can decide the truth of any arithmetic statement. This can be understood as an extension of the G\”odel incompleteness theorem to stably sound setting. This is a non-trivial extension as a stably sound Turing machine can decide the halting problem. In practice such an $M$ could be meant to represent a weakly idealized human being so that the above gives an obstruction to computability of intelligence, and this gives a formal extension of a famous disjunction of G\”odel.

Loop quantum gravity, signature change, and the no-boundary proposal. (arXiv:2011.02884v1 [gr-qc])

Authors: Martin BojowaldSuddhasattwa Brahma

Covariant models of loop quantum gravity generically imply dynamical signature change at high density. This article presents detailed derivations that show the fruitful interplay of this new kind of signature change with wave-function proposals of quantum cosmology, such as the no-boundary and tunneling proposals. In particular, instabilities of inhomogeneous perturbations found in a Lorentzian path-integral treatment are naturally cured. Importantly, dynamical signature change does not require Planckian densities when off-shell instantons are relevant.

Testing General Relativity with Gravitational Waves. (arXiv:2011.02938v1 [gr-qc])

Authors: Zack CarsonKent Yagi

Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity with gravitational waves. In particular, we focus on three theory-agnostic tests (parameterized tests, inspiral-merger-ringdown consistency tests, and gravitational-wave propagation tests) and explain how one can apply such tests to example modified theories of gravity. We conclude by giving some open questions that need to be resolved to carry out more accurate tests of gravity with gravitational waves.

Dark matter = modified gravity? Scrutinising the spacetime–matter distinction through the modified gravity/ dark matter lens

Publication date: Available online 3 November 2020

Source: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

Author(s): Niels C.M. Martens, Dennis Lehmkuhl

Completely real? A critical note on the claims by Colbeck and Renner

Publication date: Available online 2 November 2020

Source: Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

Author(s): R. Hermens

Angular momentum without rotation: turbocharging relationalism

Gomes, Henrique and Gryb, Sean (2020) Angular momentum without rotation: turbocharging relationalism. [Preprint]

Absolute Velocities Are Unmeasurable: Response to Middleton and Murgueitio Ramírez

Jacobs, Caspar (2020) Absolute Velocities Are Unmeasurable: Response to Middleton and Murgueitio Ramírez. [Preprint]

The force of perpetual problems

Nature Physics, Published online: 04 November 2020; doi:10.1038/s41567-020-01099-7

The force of perpetual problems

The Influence of Quantum Physics on Philosophy

Muller, F.A. (2020) The Influence of Quantum Physics on Philosophy. [Preprint]

Like Thermodynamics before Boltzmann. On the Emergence of Einstein’s Distinction between Constructive and Principle Theories

Giovanelli, Marco (2020) Like Thermodynamics before Boltzmann. On the Emergence of Einstein’s Distinction between Constructive and Principle Theories. [Preprint]

A Puzzle for the Field Ontologists

Gao, Shan (2020) A Puzzle for the Field Ontologists. Foundations of Physics.

Understanding and Equivalent Reformulations

Hunt, Josh (2020) Understanding and Equivalent Reformulations. In: UNSPECIFIED.

The Dissipative Approach to Quantum Field Theory: Conceptual Foundations and Ontological Implications

Oldofredi, Andrea and Öttinger, Hans Christian (2020) The Dissipative Approach to Quantum Field Theory: Conceptual Foundations and Ontological Implications. [Preprint]

The Montevideo Interpretation: How the inclusion of a Quantum Gravitational Notion of Time Solves the Measurement Problem

Rodolfo, Gambini and Jorge, Pullin (2020) The Montevideo Interpretation: How the inclusion of a Quantum Gravitational Notion of Time Solves the Measurement Problem. [Preprint]

A physical interpretation of Lewis’ discrepancy between personal and external time in time travels

Abstract

This paper deals with those time travels mostly considered by physics, namely those in the form of the so-called closed timelike curves. Some authoritative scholars have raised doubts about the status of these journeys as proper time travels. By using David Lewis’ famous definition of time travels proposed in 1976, we show that this proper status may actually be recovered, at least in some cosmological contexts containing spacetime regions, such as those concerning black holes described by the Kerr–Newman metric, that allow the formation of local closed curves. But, the mathematical incompatibility between ordinary black hole solutions to Einstein field equations and the cosmological solutions induces us to take into consideration the more general issue pertaining to the slippery interplay between models related to local and global aspects of the world, highlighting, in particular, the different notions of time that these domains inevitably imply. This leads us to think that time is not a univocal entity of the world, but is a scale-related characteristic which claims the adoption, when investigating its ontological status, of a sort of regional approach. We also briefly dwell upon the most appropriate form of realism that such a kind of dispute between local and global models may involve.