# Weekly Papers on Quantum Foundations (22)

Scientific Understanding in the Aharonov-Bohm Effect

Shech, Elay (2022) Scientific Understanding in the Aharonov-Bohm Effect. [Preprint]

Nature abhors redundancies: A no-go result for density matrix realism

Gao, Shan (2022) Nature abhors redundancies: A no-go result for density matrix realism. [Preprint]

Demonstrating quantum microscopic reversibility using coherent states of light. (arXiv:2205.13089v1 [quant-ph])

The principle of microscopic reversibility lies at the core of fluctuation theorems, which have extended our understanding of the second law of thermodynamics to the statistical level. In the quantum regime, however, this elementary principle should be amended as the system energy cannot be sharply determined at a given quantum phase space point. In this work, we propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath through energy-preserving unitary dynamics. Quantum effects can be identified by noting that the backward process is less likely to happen in the existence of quantum coherence between the system’s energy eigenstates. The experimental demonstration has been realized by mixing coherent and thermal states in a beam-splitter, followed by heterodyne detection in an optical setup. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit, while the quantum-to-classical transition is observed as the temperature of the thermal field gets higher.

Superposition of causal order in quantum walks: non-Markovianity and causal asymmetry. (arXiv:2205.13217v1 [quant-ph])

We set the criteria for a quantum walk to exhibit nontrivial dynamics when placed in an indefinite causal order and study two-period quantum walks when the evolution operators are arranged in a causally ordered sequence and in an indefinite causal order using quantum switch. When either forward or backward causal sequence is implemented, one observes a causal asymmetry in the dynamics, in the sense that the reduced dynamics of the coin state is more non-Markovian for one particular temporal order of operations than that of the other. When the dynamics is defined using evolution operators in a superposition of causal orders, the reduced dynamics of the coin space exhibit higher non-Markovian behavior than either of the definite causal orders. This effect can be interpreted as a Parrondo-like effect in non-Markovianity of the reduced state dynamics of the coin. We further generalize the qualitative description of our results pertaining to the dynamics when the walk has a higher number of periods.

Alternative interpretation of relativistic time-reversal and the time arrow. (arXiv:2205.13417v1 [physics.gen-ph])

It is well-known that the 4-rotation in the 4-dimensional space-time is equivalent to the CPT-transformation (C is the charge conjugation, P is the space inversion and T is the time-reversal). The standard definition of the T-reversal includes the change of the sign of time variable and replacement of the initial state of the particle (system of particles) by the final state and vice versa. Since the time-reversal operation changes the state of a particle, the particle’s wave function cannot be the eigenfunction of the corresponding operator with a certain eigenvalue, as in the case of space parity. Unlike the CPT-transformation, the separate P, T, or C transformations cannot be reduced to any 4-rotation. The extended Lorentz group incorporates all the separate C, P, or T transformations which do not bring the time axis out of the corresponding light cone. The latter restriction is included in the standard definition of the time-reversal. In the present communication, we ignore this restriction.

This allows to introduce the “time arrow” operator and characterize every particle by the new quantum number – “time arrow” value. The wave functions of all particles are eigenfunctions of this operator with eigenvalues equal to “time arrow” values. The particles with the “time arrow” values opposite to the “time arrow” value in our universe form another universe (anti-universe). The existence of anti-universe can be confirmed, in principle, by laboratory (atomic) experiments. The anti-universe may be also considered as a candidate to the role of dark matter.

Galileo and a forgotten poem on the 1604 supernova. (arXiv:2204.04001v3 [physics.hist-ph] UPDATED)

Authors: Alessandro De Angelis

A precision test of averaging in AdS/CFT. (arXiv:2205.12968v1 [hep-th])

Authors: Jordan CotlerKristan Jensen

We reconsider the role of wormholes in the AdS/CFT correspondence. We focus on Euclidean wormholes that connect two asymptotically AdS or hyperbolic regions with $\mathbb{S}^1\times \mathbb{S}^{d-1}$ boundary. There is no solution to Einstein’s equations of this sort, as the wormholes possess a modulus that runs to infinity. To find on-shell wormholes we must stabilize this modulus, which we can do by fixing the total energy on the two boundaries. Such a wormhole gives the saddle point approximation to a non-standard problem in quantum gravity, where we fix two asymptotic boundaries and constrain the common energy. Crucially the dual quantity does not factorize even when the bulk is dual to a single CFT, on account of the fixed energy constraint. From this quantity we extract the microcanonical spectral form factor. For a chaotic theory this quantity is self-averaging, i.e. well-approximated by averaging over energy windows, or over coupling constants.

We go on to give a precision test involving the microcanonical spectral form factor where the two replicas have slightly different coupling constants. In chaotic theories this form factor is known to smoothly decay at a rate universally predicted in terms of one replica physics, provided that there is an average either over a window or over couplings. We compute the expected decay rate for holographic theories, and the form factor from a wormhole, and the two exactly agree for a wide range of two-derivative effective field theories in AdS. This gives a precision test of averaging in AdS/CFT.

Our results interpret a number of confusing facts about wormholes and factorization in AdS and suggest that we should regard gravitational effective field theory as a mesoscopic description, analogous to semiclassical mesoscopic descriptions of quantum chaotic systems.

Black holes and cryptocurrencies. (arXiv:2205.12995v1 [hep-th])

Authors: Alexey Milekhin

It has been proposed in the literature that the volume of Einstein-Rosen bridge is equal to complexity of state preparation (“Complexity=Volume” conjecture). Taking this statement outside the horizon, one might be tempted to propose “Complexity=Time” correspondence. In this Essay we argue that in a blockchain protocol, which is the foundation of all modern cryptocurrencies, time is emergent and it is defined according to a version of “Complexity=Time”.

Probing the Information-Probabilistic Description. (arXiv:2105.05034v2 [gr-qc] UPDATED)

The information conservation principle is probed for classically isolated systems, like the Hubble sphere and black holes, for which the rise of entanglement entropy across their horizons is expected. We accept the analogy of Landauer’s principle that entanglement information should introduce some negative potential energy, which corresponds to the positive energy of measurements that destroy this quantum behavior. We estimated these dark-energy-like contributions and found that they can explain the dark energy of the Universe and also are able to resolve the observed superluminal motion and redshift controversies for black holes.

Non-universality of free fall in quantum theory. (arXiv:2204.03279v2 [gr-qc] UPDATED)

Authors: Viacheslav A. Emelyanov

We show by embodying the Einstein equivalence principle and general covariance in quantum theory that wave-function spreading rules out universality of free fall, and vice versa. Assuming the former is more fundamental than the latter, we gain a quantitative estimate of the free-fall non-universality, which turns out to be empirically testable in atom interferometry.

Entering the valley of formalism: trends and changes in mathematicians’ publication practice—1885 to 2015

Abstract

Over the last century, there have been considerable variations in the frequency of use and types of diagrams used in mathematical publications. In order to track these changes, we developed a method enabling large-scale quantitative analysis of mathematical publications to investigate the number and types of diagrams published in three leading mathematical journals in the period from 1885 to 2015. The results show that diagrams were relatively common at the beginning of the period under investigation. However, beginning in 1910, they were almost completely unused for about four decades before reappearing in the 1950s. The diagrams from the 1950s, however, were of a different type than those used earlier in the century. We see this change in publication practice as a clear indication that the formalist ideology has influenced mathematicians’ choice of representations. Although this could be seen as a minor stylistic aspect of mathematics, we argue that mathematicians’ representational practice is deeply connected to their cognitive practice and to the contentual development of the discipline. These changes in publication style therefore indicate more fundamental changes in the period under consideration.

Philosophical Issues raised by Quantum Theory and its Interpretations

Myrvold, Wayne C. (2022) Philosophical Issues raised by Quantum Theory and its Interpretations. The Oxford Handbook of the History of Quantum Interpretations. pp. 53-75.

Temporal Becoming in a Relativistic Universe: Causal Diamonds and Gödel’s Philosophy of Time

Aames, Jimmy (2022) Temporal Becoming in a Relativistic Universe: Causal Diamonds and Gödel’s Philosophy of Time. [Preprint]

Non-classical mechanical states guided in a phononic waveguide

Nature Physics, Published online: 23 May 2022; doi:10.1038/s41567-022-01612-0

Non-classical vibrations are generated and transmitted along a mechanical waveguide, providing a platform for distributing quantum information and realizing hybrid quantum devices using phonons in a solid-state system.

Grothendieck’s theory of schemes and the algebra–geometry duality

Abstract

We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry associated to Grothendieck’s theory of schemes. To do so, we shall revisit scheme theory from the standpoint provided by the problem of recovering a mathematical structure A from its representations $$A \rightarrow B$$ into other similar structures B. This vantage point will allow us to analyze the relationship between the algebra-geometry duality and (what we shall call) the structure-semiotics duality (of which the syntax-semantics duality for propositional and predicate logic are particular cases). Whereas in classical algebraic geometry a certain kind of  rings  can be recovered by considering their representations with respect to a unique codomain B, Grothendieck’s theory of schemes permits to reconstruct general (commutative) rings by considering representations with respect to a category of codomains. The strategy to reconstruct the object from its representations remains the same in both frameworks: the elements of the ring A can be realized—by means of what we shall generally call Gelfand transform—as quantities on a topological space that parameterizes the relevant representations of A.  As we shall argue, important dualities in different areas of mathematics (e.g. Stone duality, Gelfand duality, Pontryagin duality, Galois-Grothendieck duality, etc.) can be understood as particular cases of this general pattern. In the wake of Majid’s analysis of the Pontryagin duality, we shall propose a Kantian-oriented interpretation of this pattern. We shall use this conceptual framework to argue that Grothendieck’s notion of functor of points can be understood as a “relativization of the a priori” (Friedman) that generalizes the relativization already conveyed by the notion of domain extension to more general variations of the corresponding (co)domains.

A Discrete Analog of General Covariance — Part 2: Despite what you’ve heard, a perfectly Lorentzian lattice theory

Grimmer, Daniel (2022) A Discrete Analog of General Covariance — Part 2: Despite what you’ve heard, a perfectly Lorentzian lattice theory. [Preprint]

Spacetime Emergence: Collapsing the Distinction Between Content and Context?

Crowther, Karen (2022) Spacetime Emergence: Collapsing the Distinction Between Content and Context? [Preprint]

Quantum gravity in a laboratory?

Huggett, Nick and Linnemann, Niels and Schneider, Mike D. (2022) Quantum gravity in a laboratory? [Preprint]