# Weekly Papers on Quantum Foundations (16)

Entanglement, Complexity, and Causal Asymmetry in Quantum Theories. (arXiv:2204.06742v1 [physics.hist-ph])

It is often claimed that one cannot locate a notion of causation in fundamental physical theories. The reason most commonly given is that the dynamics of those theories do not support any distinction between the past and the future, and this vitiates any attempt to locate a notion of causal asymmetry — and thus of causation — in fundamental physical theories. I argue that this is incorrect: the ubiquitous generation of entanglement between quantum systems grounds a relevant asymmetry in the dynamical evolution of quantum systems. I show that by exploiting a connection between the amount of entanglement in a quantum state and the algorithmic complexity of that state, one can use recently developed tools for causal inference to identify a causal asymmetry — and a notion of causation — in the dynamical evolution of quantum systems. https://doi.org/10.1007/s10701-022-00562-0

Sign of the Feynman Propagator and Irreversibility. (arXiv:2204.06928v1 [quant-ph])

For the interacting Feynman propagator $\Delta_{F,int}(x,y)$ of scalar electrodynamics, we show that the sign property, $\operatorname{Re} i\Delta_{F,int} \geq 0$, hinges on the reversibility of time evolution. In contrast, $\operatorname{Im} i\Delta_{F,int}$ is indeterminate. When we switch to reduced dynamics under the weak coupling approximation, the positive semidefinite sign of $\operatorname{Re} i\Delta_{F,int}$ is generally lost, unless we impose severe restrictions on the Kraus operators that govern time evolution. With another approximation, the rotating wave approximation, we may recover the sign by restricting the test functions to exponentials under certain conditions.

Geometric model for the electron spin correlation. (arXiv:2108.07869v3 [quant-ph] UPDATED)

The quantum formula for the spin correlation of the bipartite singlet spin state, $C_{Q}(\boldsymbol{a},\boldsymbol{b})$, is derived on the basis of a probability distribution $\rho(\phi)$ that is generic, i. e., independent of $(\boldsymbol{a},\boldsymbol{b})$. In line with a previous result obtained within the framework of the quantum formalism, the probability space is partitioned according to the sign of the product $A=\alpha\beta$ of the individual spin projections $\alpha$ and $\beta$ onto $\boldsymbol{a}$ and $\boldsymbol{b}$; this precludes the transfer of $\alpha$ or $\beta$ from $C_{Q}(\boldsymbol{a},\boldsymbol{b})$ to $C_{Q}(\boldsymbol{a},\boldsymbol{b’})$, for $\boldsymbol{b’}\neq\boldsymbol{b}.$ A specific physical model that reproduces the quantum spin correlation serves to validate our approach.

Information is Physical: Cross-Perspective Links in Relational Quantum Mechanics. (arXiv:2203.13342v2 [quant-ph] UPDATED)

Relational quantum mechanics (RQM) is an interpretation of quantum mechanics based on the idea that quantum states describe not an absolute property of a system but rather a relationship between systems. In this article, we observe that there is a tension between RQM’s naturalistic emphasis on the physicality of information and the inaccessibility of certain sorts of information in current formulations of RQM. Therefore we propose a new postulate for RQM which requires that all of the information possessed by a certain observer is stored in physical variables of that observer and thus accessible by measurement to other observers, so observers can reach intersubjective agreement about quantum events which have occurred in the past. Based on this postulate, we suggest an ontology for RQM which upholds the principle that quantum states are always relational, but which also postulates a set of quantum events which are not strictly relational. We show that the new postulate helps address some existing objections to RQM and finally we address the Frauchiger-Renner experiment in the context of RQM.

The Fate of Causal Structure under Time Reversal. (arXiv:2204.06740v1 [physics.hist-ph])

Authors: Porter Williams

What happens to the causal structure of a world when time is reversed? At first glance it seems there are two possible answers: the causal relations are reversed, or they are not. I argue that neither of these answers is correct: we should either deny that time-reversed worlds have causal relations at all, or deny that causal concepts developed in the actual world are reliable guides to the causal structure of time-reversed worlds. The first option is motivated by the instability under intervention of time-reversed dynamical evolutions. The second option is motivated by a recognition of how contingent structural features of the actual world shape, and license the application of, our causal concepts and reasoning strategies.

Entanglement, Complexity, and Causal Asymmetry in Quantum Theories. (arXiv:2204.06742v1 [physics.hist-ph])

Authors: Porter Williams

It is often claimed that one cannot locate a notion of causation in fundamental physical theories. The reason most commonly given is that the dynamics of those theories do not support any distinction between the past and the future, and this vitiates any attempt to locate a notion of causal asymmetry — and thus of causation — in fundamental physical theories. I argue that this is incorrect: the ubiquitous generation of entanglement between quantum systems grounds a relevant asymmetry in the dynamical evolution of quantum systems. I show that by exploiting a connection between the amount of entanglement in a quantum state and the algorithmic complexity of that state, one can use recently developed tools for causal inference to identify a causal asymmetry — and a notion of causation — in the dynamical evolution of quantum systems. https://doi.org/10.1007/s10701-022-00562-0

Moir\’e Gravity and Cosmology. (arXiv:2204.06574v1 [hep-th])

Authors: Alireza ParhizkarVictor Galitski

The vacuum catastrophe is a fundamental puzzle, where the observed scales of the cosmological constant are many orders of magnitude smaller than the natural scales expected in the theory. This work proposes a new “bi-world” construction that may offer an insight into the cosmological constant problem. The model includes a (3+1)-dimensional manifold with two different geometries and matter fields residing on them. The diffeomorphism invariance and causality highly constrain the two metrics to be conformally related, $\eta_{\mu \nu} = \phi^2 g_{\mu \nu}$. This reduces the theory to a standard single-world description, but introduces a new inherently geometrical “moir\’e field,” $\phi$. Interestingly, the moir\’e field has the character of both a dilaton and Higgs field familiar in the conventional theory. Integrating out the moir\’e field naturally gives rise to the Starobinsky action and inflationary dynamics. In the framework of the Friedmann-Lemaitre-Robertson-Walker solution, we reduce an effective action for the moir\’e field to that of a particle moving in a Mexican hat potential. The equations of motion are then solved numerically and the moir\’e field is shown to approach a Mexican-hat minimum in an oscillatory fashion, which is accompanied by the decay of the Hubble parameter. Under additional reasonable assumptions, the vacuum energy asymptotically approaches zero in the end of inflationary evolution. The physics presented here shares similarities with the moir\’e phenomena in condensed matter and elsewhere, where two similar structures superimposed upon give rise to a superstructure with low emergent energy scales compared to the native theories.

A consistent approach to the path integral formalism of quantum mechanics based on the maximum length uncertainty. (arXiv:2204.06856v1 [hep-th])

Authors: Souvik Pramanik

We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics which contains a maximum observable length scale at the order of the Cosmological particle horizon, existing in cosmology. First, we have presented the modifications to the classical mechanics which shows non-minimal effects on the equation of motion of a particle. Next, we have provided representation of the deformed quantum mechanical algebra. With this algebra in hand, we have calculated the general form of the path integral propagator in this deformed background. Finally, as a most simple case, we have built up the explicit form of the free particle propagator. The modifications to the free particle propagator shows some non-trivial effects in this case, which can have some important significance.

Gravitational wave memory and its tail in cosmology. (arXiv:2204.06981v1 [gr-qc])

Authors: Niko JokelaK. KajantieMiika Sarkkinen

We study gravitational wave memory effect in the FRW cosmological model with matter and cosmological constant. Since the background is curved, gravitational radiation develops a tail part arriving after the main signal that travels along the past light cone of the observer. First we discuss first order gravitational wave sourced by a binary system, and find that the tail only gives a negligible memory, in accord with previous results. Then we study the nonlinear memory effect coming from induced gravitational radiation sourced by first order gravitational radiation propagating over cosmological distances. In the light cone part of the induced gravitational wave we find a novel term missed in previous studies of the cosmological memory effect. Furthermore, we show that the induced gravitational wave has a tail part that slowly accumulates after the light cone part has passed and grows to a sizeable magnitude over a cosmological timescale. This tail part of the memory effect will be a new component in the stochastic gravitational wave background.

Gauge Theories of Gravitation. (arXiv:1210.3775v4 [gr-qc] UPDATED)

Authors: Milutin BlagojevićFriedrich W. Hehl

During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent proponents of the theory. In the early 1960s, the gauge idea was successfully applied to the Poincar\’e group of spacetime symmetries and to the related conserved energy-momentum and angular momentum currents. The resulting theory, the Poincar\’e gauge theory, encompasses Einstein’s general relativity as well as the teleparallel theory of gravity as subcases. The spacetime structure is enriched by Cartan’s torsion, and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions \`a la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincar\’e gauge theory and its generalizations are explored and special topics, such as its Hamiltonian formulation and exact solutions, are studied. This guide to the literature on classical gauge theories of gravity is intended to be a stimulating introduction to the subject.

Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations

Author(s): Zhiyue Lu and Hong Qian

Thermodynamics as limiting behaviors of statistics is generalized to arbitrary systems with probability a priori where the thermodynamic infinite-size limit is replaced by a multiple-measurement limit. A duality symmetry between Massieu’s and Gibbs’s entropy arises in the limit of infinitely repeate…

[Phys. Rev. Lett. 128, 150603] Published Fri Apr 15, 2022

Thermal superconducting quantum interference proximity transistor

Nature Physics, Published online: 14 April 2022; doi:10.1038/s41567-022-01578-z

Heat transport in electronic systems is influenced by nearby superconductors due to the so-called proximity effect. Combining this with the manipulation of superconductivity using magnetic fields enables the control of nanoscale thermal transport.

Arithmetic logical Irreversibility and the Turing’s Halt Problem

Lapin, Yair (2021) Arithmetic logical Irreversibility and the Turing’s Halt Problem. [Preprint]

Maximal Speed for Macroscopic Particle Transport in the Bose-Hubbard Model

Author(s): Jérémy Faupin, Marius Lemm, and Israel Michael Sigal

The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due to their unbounded local interactions. Here we establish for the first time a general ballistic uppe…

[Phys. Rev. Lett. 128, 150602] Published Tue Apr 12, 2022

No free lunch for Schrödinger’s cat

Nature Physics, Published online: 12 April 2022; doi:10.1038/s41567-022-01593-0

No free lunch for Schrödinger’s cat

On the indispensability of theoretical terms and entities

Abstract

Some realists claim that theoretical entities like numbers and electrons are indispensable for describing the empirical world. Motivated by the meta-ontology of Quine, I take this claim to imply that, for some first-order theory T and formula $$\delta (x)$$ such that $$T \vdash \exists x \delta \wedge \exists x \lnot \delta$$ , where $$\delta (x)$$ is intended to apply to all and only empirical entities, there is no first-order theory $$T’$$ such that (a) T and $$T’$$ describe the $$\delta$$ :s in the same way, (b) $$T’ \vdash \forall x \delta$$ , and (c) $$T’$$ is at least as attractive as T in terms of other theoretical virtues. In an attempt to refute the realist claim, I try to solve the general problem of nominalizing T (with respect to $$\delta$$ ), namely to find a theory $$T’$$ satisfying conditions (a)–(c) under various precisifications thereof. In particular, I note that condition (a) can be understood either in terms of syntactic or semantic equivalence, where the latter is strictly stronger than the former. The results are somewhat mixed. On the positive side, even under the stronger precisification of (a), I establish that (1) if the vocabulary of T is finite, a nominalizing theory can always be found that is recursive if T is, and (2) if T postulates infinitely many $$\delta$$ :s, a nominalizing theory can always be found that is no more computationally complex than T. On the negative side, even under the weaker precisification of (a), I establish that (3) certain finite theories cannot be nominalized by a finite theory.

The a-theory of time, temporal passage, and comprehensiveness

Abstract

It has been argued recently that one major difficulty facing the A-theory of time consists in the view’s failure to provide a satisfactory account of the passage of time. Critics have objected that this particular charge is premised on an unduly strong conception of temporal passage, and that the argument does not go through on alternative, less demanding conceptions of passage. The resulting dialectical stalemate threatens to prove intractable, given the notorious elusiveness of the notion of temporal passage. Here I argue that there is progress to be made in this regard. The argument from passage takes issue with a certain feature of the standard versions of the A-theory that is in fact problematic independently of worries about temporal passage. To illustrate this, I present a new argument, the argument from comprehensiveness, which demonstrates that the standard A-theoretic account of temporal reality is inadequate, even if it is granted that it can accommodate passage.

Where Does General Relativity Break Down?

Weatherall, James Owen (2022) Where Does General Relativity Break Down? [Preprint]

A Conjecture on the Origin of Superselection Rules – with a Comment on “The Global Phase Is Real”

Gao, Shan (2022) A Conjecture on the Origin of Superselection Rules – with a Comment on “The Global Phase Is Real”. [Preprint]

Two Approaches to Reduction: A Case Study from Statistical Mechanics

Guo, Bixin (2020) Two Approaches to Reduction: A Case Study from Statistical Mechanics. [Preprint]

Quantum spatial superpositions and the possibility of superluminal signaling

Ávila, Partricio and Okon, Elias and Sudarsky, Daniel and Wiedemann, Martín (2022) Quantum spatial superpositions and the possibility of superluminal signaling. [Preprint]