# Weekly Papers on Quantum Foundations (17)

Niestegge, Gerd (2022) A generic approach to the quantum mechanical transition probability. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478 (2260).

Williams, Porter (2022) Entanglement, Complexity, and Causal Asymmetry in Quantum Theories. Foundations of Physics.

Williams, Porter (2022) The fate of causal structure under time reversal. [Preprint]

Wallace, David (2022) On the reality of the global phase. [Preprint]

Ciepielewski, Gerardo Sanjuan and Okon, Elias (2022) From locality to factorizability: a novel escape from Bell’s theorem. [Preprint]

On the Interpretation of Quantum Indistinguishability : a No-Go Theorem. (arXiv:2204.09736v1 [quant-ph])

Despite being the most fundamental object in quantum theory, physicists are yet to reach a consensus on the interpretation of a quantum wavefunction. In the broad class of realist approaches, quantum states are viewed as Liouville-like probability distributions over some space of physical variables where indistinguishabity of non-orthogonal states is attributed to overlaps between these distributions. Here we argue that such an interpretation of quantum indistinguishability is wrong. In particular, we show that quantum mechanical prediction of maximal violation of Mermin inequality in certain thought experiment is incompatible with all ontological interpretations for quantum theory where indistinguishability of non-orthonal quantum states is explained, even partially, in terms of overlap of their Liouville distributions.

Decoherence: From Interpretation to Experiment. (arXiv:2204.09755v1 [quant-ph])

I offer a few selected reflections on the decoherence program, with an emphasis on Zeh’s role and views. First, I discuss Zeh’s commitment to a realistic interpretation of the quantum state, which he saw as necessary for a consistent understanding of the decoherence process. I suggest that this commitment has been more fundamental than, and prior to, his support of an Everett-style interpretation of quantum mechanics. Seen through this lens, both his defense of Everett and the genesis of his ideas on decoherence emerge as consequences of his realistic view of the quantum state. Second, I give an overview of experiments on decoherence and describe, using the study of collisional decoherence as an example, the close interplay between experimental advances and theoretical modeling in decoherence research.

Temperature uncertainty relation in non-equilibrium thermodynamics. (arXiv:2204.10044v1 [quant-ph])

Temperature uncertainty of a system in canonical ensemble is inversely determined by its energy fluctuation, which is known as the temperature-energy uncertainty relation. No such uncertainty relation was discovered for a non-equilibrium open quantum system. In this article, we derive a universal temperature uncertainty relation for general non-equilibrium processes. We find that it is the fluctuation of heat absorbed from the thermal bath, more specifically the sum of trajectory heat and correlation heat defined from sequential bath energy measurements, determines the temperature uncertainty. Detail analyses show that correlations between system and bath’s process function and state function are the resources for decreasing the temperature uncertainty. In addition to reveal a fundamental uncertainty relation, our results are conductive to design ultrahigh sensitive quantum thermometer.

Information flow in one-dimensional non-unitary quantum cellular automata. (arXiv:2204.09922v1 [quant-ph])

The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has been proposed for the quantification of the net flow of quantum information across a boundary. While the index is rigid in the sense of begin invariant under finite-depth local circuits, it is not defined when the system is coupled to an environment, i.e. for non-unitary time evolution of open quantum systems. We propose a new measure of information flow for non-unitary QCA denoted the information current which is not rigid, but can be computed locally based on the matrix-product operator representation of the map.

Life and death in the tails of the GRW wave function. (arXiv:1407.4746v2 [quant-ph] UPDATED)

It is often assumed that the only effect of the Ghirardi-Rimini-Weber (GRW’) dynamical collapse mechanism on the tails’ of the wavefunction (that is, the components of superpositions on which the collapse is \emph{not} centred) is to reduce their weight. In consequence the tails are often thought to behave exactly as do the various branches in the Everett interpretation except for their much lower weight.

These assumptions are demonstrably inaccurate: the collapse mechanism has substantial and detectable effects within the tails. The relevance of this misconception for the dynamical-collapse theories is debatable, though.

Does acceleration assist entanglement harvesting?. (arXiv:2111.04392v2 [quant-ph] UPDATED)

We explore whether acceleration assists entanglement harvesting for a pair of uniformly accelerated detectors in three different acceleration scenarios, i.e., parallel, anti-parallel and mutually perpendicular acceleration, both in the sense of the entanglement harvested and harvesting-achievable separation between the two detectors. Within the framework of entanglement harvesting protocols and the Unruh-DeWitt model of detectors locally interacting with massless scalar fields via a Gaussian switching function with an interaction duration parameter, we find that, in the sense of the entanglement harvested, acceleration is a mixed blessing insofar as it increases the harvested entanglement for a large detector energy gap relative to the interaction duration parameter, whilst inhibiting the entanglement harvested for a small energy gap. Regarding the harvesting-achievable separation range between the detectors, we further find that for very small acceleration and large energy gap, both relative to the duration parameter, acceleration-assisted enhancement can happen in all three acceleration scenarios. This is in sharp contrast to what was argued previously: that the harvesting-achievable range can be enhanced only for anti-parallel acceleration. However, for a not too small acceleration relative to the duration parameter and an energy gap larger than the acceleration, we find that only detectors in parallel acceleration possess a harvesting-achievable range larger than those at rest.

Ehrenfest theorem in relativistic quantum theory. (arXiv:2111.10798v2 [quant-ph] UPDATED)

Ehrenfest theorem is proven in relativistic quantum theory of charged particles, moving under the influence of an external electromagnetic field. In order to extend the classic Ehrenfest result to the relativistic domain we bypassed the problems with the relativistic position operator by deriving directly Newton’s second law. Our approach is characterized by its universality. The detailed form of the wave equation is not needed. All that is required is the existence of the conserved electric four-current built from the particle wave function. The derivation is based on the conservation laws for the energy and momentum.

Quantum Capacity and Vacuum Compressibility of Spacetime: Thermal Fields. (arXiv:2204.08634v1 [gr-qc] CROSS LISTED)

An important yet perplexing result from work in the 90s and 00s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was done by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields. In this paper we revisit this issue via a quantum thermodynamics approach, by calculating two quintessential thermodynamic quantities: the heat capacity and the quantum compressibility of some model geometries filled with a quantum field at high and low temperatures. This is because heat capacity at constant volume gives a measure of the fluctuations of the energy density to the mean. When this ratio approaches or exceeds unity, the validity of the canonical distribution is called into question. Likewise, a system’s compressibility at constant pressure is a criterion for the validity of grand canonical ensemble. We derive the free energy density and, from it, obtain the expressions for these two thermodynamic quantities for thermal and quantum fields in 2d Casimir space, 2d Einstein cylinder and 4d ($S^1 \times S^3$ ) Einstein universe. To examine the dependence on the dimensionality of space, for completeness, we have also derived these thermodynamic quantities for the Einstein universes with even-spatial dimensions: $S^1 \times S^2$ and $S^1 \times S^4$. With this array of spacetimes we can investigate the thermodynamic stability of quantum matter fields in them and make some qualitative observations on the compatibility condition for the co-existence between quantum fields and spacetimes, a fundamental issue in the quantum and gravitation conundrum.

On energy for accelerating observers in black hole spacetimes. (arXiv:2203.00085v2 [gr-qc] UPDATED)

Authors: Seth A. Major

Quasi-local energies for constantly accelerating observers in Ba\~nados, Teitelboim, and Zanelli (BTZ), Schwarzschild and Schwarzschild-de Sitter spacetimes are derived. The energies are expressed in terms of acceleration, cosmological constant, and area, quantities measurable by the observers. Based on results from quantum fields in curved spacetime for the redshifted Hawking temperature, entropy and thermodynamic-like laws are briefly explored in the three spacetimes.

Can the graviton have a large mass near black holes?. (arXiv:1709.07503v2 [gr-qc] UPDATED)

Authors: Jun ZhangShuang-Yong Zhou

The mass of the graviton, if nonzero, is usually considered to be very small, e.g. of the Hubble scale, from several observational constraints. In this paper, we propose a gravity model where the graviton mass is very small in the usual weak gravity environments, below all the current graviton mass bounds, but becomes much larger in the strong gravity regime such as a black hole’s vicinity. For black holes in this model, significant deviations from general relativity emerge very close to the black hole horizon and alter the black hole quasi-normal modes, which can be extracted from the ringdown waveform of black hole binary mergers. Also, the enhancement of the graviton mass near the horizon can result in echoes in the late time ringdown, which can be verified in the upcoming gravitational wave observations of higher sensitivity.

Entanglement and Superposition Are Equivalent Concepts in Any Physical Theory

Author(s): Guillaume Aubrun, Ludovico Lami, Carlos Palazuelos, and Martin Plávala

In general probabilistic theories, superposition, in the form of what the authors define as strong incompatibility, is equivalent to entanglement.

[Phys. Rev. Lett. 128, 160402] Published Fri Apr 22, 2022

The Introduction of Topology into Analytic Philosophy: Two Movements and a Coda

Fletcher, Samuel C. and Lackey, Nathan (2022) The Introduction of Topology into Analytic Philosophy: Two Movements and a Coda. [Preprint]

Justifying the use of purely formal analogies in physics

Fraser, Doreen (2022) Justifying the use of purely formal analogies in physics. In: UNSPECIFIED.

A Bayesian analysis of self-undermining arguments in physics

Wallace, David (2022) A Bayesian analysis of self-undermining arguments in physics. [Preprint]

Understanding Time Reversal in Quantum Mechanics: A Full Derivation

Gao, Shan (2022) Understanding Time Reversal in Quantum Mechanics: A Full Derivation. [Preprint]

Naturalism, Functionalism and Chance: Not a Best Fit for the Humean

Fernandes, Alison (2022) Naturalism, Functionalism and Chance: Not a Best Fit for the Humean. [Preprint]

Potters, Jan (2022) Conceptualizing paradigms: on reading Kuhn’s history of the quantum. Annals of Science.

Information is Physical: Cross-Perspective Links in Relational Quantum Mechanics

Adlam, Emily and ROVELLI, Carlo (2022) Information is Physical: Cross-Perspective Links in Relational Quantum Mechanics. [Preprint]

Econometric methods and Reichenbach’s principle

Abstract

Reichenbach’s ‘principle of the common cause’ is a foundational assumption of some important recent contributions to quantitative social science methodology but no similar principle appears in econometrics. Angrist et al. (Rubin J Am Stat Assoc 91:444–455, 1996) has argued that the principle is necessary for instrumental variables methods in econometrics, and Angrist Krueger (Quarterly Journal of Economics 106:976–1014, 1991) builds a framework using it that he proposes as a means of resolving an important methodological dispute among econometricians. Through analysis of instrumental variables methods and the issue of multicollinearity, we aim to show that the relationship of the principle to econometric methods is more nuanced than implied by previous work but nevertheless may make a valuable contribution to the coherence and validity of existing methods.

Discretised Hilbert Space and Superdeterminism [arXiv:2204.05763]

T.N. Palmer

In computational physics it is standard to approximate continuum systems with discretised representations. Here we consider a specific discretisation of the continuum complex Hilbert space of quantum mechanics – a discretisation where squared amplitudes and complex phases are rational numbers. The fineness of this discretisation is determined by a finite (prime-number) parameter p. As p→∞, unlike standard discretised representations in computational physics, this model does not tend smoothly to the continuum limit. Instead, the state space of quantum mechanics is a singular limit of the discretised model at p=∞. Using number theoretic properties of trigonometric functions, it is shown that for large enough values of p, discretised Hilbert space accurately describes ensemble representations of quantum systems within an inherently superdeterministic framework, one where the Statistical Independence assumption in Bell’s theorem is formally violated. In this sense, the discretised model can explain the violation of Bell inequalities without appealing to nonlocality or indefinite reality. It is shown that this discretised framework is not fine tuned (and hence not conspiratorial) with respect to its natural state-space p-adic metric. As described by Michael Berry, old theories of physics are typically the singular limits of new theories as a parameter of the new theory is set equal to zero or infinity. Using this, we can answer the challenge posed by Scott Aaronson, critic of superderminism: to explain when a great theory in physics (here quantum mechanics) has ever been grudgingly accommodated' rather than gloriously explained’ by its candidate successor theory (here a superdeterministic theory of quantum physics based on discretised Hilbert space).