# Weekly Papers on Quantum Foundations (5)

Aharonov-Bohm effect with an effective complex-valued vector potential. (arXiv:2101.11914v1 [quant-ph])

The interaction between a quantum charge and a quantized source of a magnetic field is considered in the Aharonov-Bohm scenario. It is shown that, if the source has a relatively small uncertainty while the particle encircles it, an effective magnetic vector potential arises and the final state of the joint system is approximately a tensor product. Furthermore, if a post-selection of the source is considered, the effective vector potential is, in general, complex-valued. This leads to a new prediction in the Aharonov-Bohm scenario before the magnetic field is fully enclosed that has a parallel with Berry phases in open quantum systems. Also, new insights into the correspondence principle, which makes complex vector potentials relevant in the study of classical systems, are discussed.

Inertial Theorem: Overcoming the quantum adiabatic limit. (arXiv:1810.12094v3 [quant-ph] UPDATED)

We present a new theorem describing stable solutions for a driven quantum system. The theorem, coined `inertial theorem’, is applicable for fast driving, provided the acceleration rate is small. The theorem states that in the inertial limit eigenoperators of the propagator remain invariant throughout the dynamics, accumulating dynamical and geometric phases. The proof of the theorem utilizes the structure of Liouville space and a closed Lie algebra of operators. We demonstrate applications of the theorem by studying three explicit solutions of a harmonic oscillator, a two-level and three-level system models. These examples demonstrate that the inertial solution is superior to that obtained with the adiabatic approximation. Inertial protocols can be combined to generate a new family of solutions. The inertial theorem is then employed to extend the validity of the Markovian Master equation to strongly driven open quantum systems. In addition, we explore the consequence of new geometric phases associated with the driving parameters.

Collapse and Measures of Consciousness. (arXiv:2009.13224v3 [quant-ph] UPDATED)

There has been an upsurge of interest lately in developing Wigner’s hypothesis that conscious observation causes collapse by exploring dynamical collapse models in which some purportedly quantifiable aspect(s) of consciousness resist superposition. Kremnizer-Ranchin, Chalmers-McQueen and Okon-Sebasti\’an have explored the idea that collapse may be associated with a numerical measure of consciousness. More recently, Chalmers-McQueen have argued that any single measure is inadequate because it will allow superpositions of distinct states of equal consciousness measure to persist. They suggest a satisfactory model needs to associate collapse with a set of measures quantifying aspects of consciousness, such as the “Q-shapes” defined by Tononi et al. in their “integrated information theory” (IIT) of consciousness. I argue here that Chalmers-McQueen’s argument against associating a single measure with collapse requires a precise symmetry between brain states associated with different experiences and thus does not apply to the only case where we have strong intuitions, namely human (or other terrestrial biological) observers. In defence of Chalmers-McQueen’s stance, it might be argued that idealized artificial information processing networks could display such symmetries. However, I argue that any theory (such as IIT) that postulates a map from network states to mind states should assign identical mind states to isomorphic network states (as IIT does). This suggests that, if such a map exists, no familiar components of mind states, such as viewing different colours, or experiencing pleasure or pain, are likely to be related by symmetries.

Hard Problem and Free Will: an information-theoretical approach. (arXiv:2012.06580v2 [quant-ph] UPDATED)

We explore definite theoretical assertions about consciousness, starting from a non-reductive psycho-informational solution of David Chalmers’s ‘hard problem’, based on the hypothesis that a fundamental property of ‘information’ is its experience by the supporting ‘system’. The kind of information involved in consciousness needs to be quantum for multiple reasons, including its intrinsic privacy and its power of building up thoughts by entangling qualia states. As a result we reach a quantum-information-based panpsychism, with classical physics supervening on quantum physics, quantum physics supervening on quantum information, and quantum information supervening on consciousness. We then argue that the internally experienced quantum state, since it corresponds to a definite experience-not to a random choice-must be pure, and we call it ontic, in contrast with the state predictable from the outside (i.e. the state describing the knowledge of the experience from the point of view of an external observer) which we call epistemic and is generally mixed. Purity of the ontic state requires an evolution that is purity preserving, namely a so-called ‘atomic’ quantum operation. The latter is generally probabilistic, and its particular outcome is interpreted as the free will, which is unpredictable even in principle since quantum probability cannot be interpreted as lack of knowledge. The same purity of state and evolution allows solving the ‘combination problem’ of panpsychism. Quantum state evolution accounts for a short-term buffer of experience and contains itself quantum-to-classical and classical-to-quantum information transfers. Long term memory, on the other hand, is classical, and needs memorization and recall processes that are quantum-to-classical and classical-to-quantum, respectively…

A technical analog of the cosmological constant problem and a solution thereof. (arXiv:2101.11620v1 [hep-th])

The near vanishing of the cosmological constant is one of the most puzzling open problems in theoretical physics. We consider a system, the so-called framid, that features a technically similar problem. Its stress-energy tensor has a Lorentz-invariant expectation value on the ground state, yet there are no standard, symmetry-based selection rules enforcing this, since the ground state spontaneously breaks boosts. We verify the Lorentz invariance of the expectation value in question with explicit one-loop computations. These, however, yield the expected result only thanks to highly nontrivial cancellations, which are quite mysterious from the low-energy effective theory viewpoint.

Causality in gravitational theories with second order equations of motion. (arXiv:2101.11623v1 [gr-qc])

Authors: Harvey S. Reall

This paper considers diffeomorphism invariant theories of gravity coupled to matter, with second order equations of motion. This includes Einstein-Maxwell and Einstein-scalar field theory with (after field redefinitions) the most general parity-symmetric four-derivative effective field theory corrections. A gauge-invariant approach is used to study the characteristics associated to the physical degrees of freedom in an arbitrary background solution. The symmetries of the principal symbol arising from diffeomorphism invariance and the action principle are determined. For gravity coupled to a single scalar field (i.e. a Horndeski theory) it is shown that causality is governed by a characteristic polynomial of degree $6$ which factorises into a product of quadratic and quartic polynomials. The former is defined in terms of an “effective metric” and is associated with a “purely gravitational” polarisation, whereas the latter generically involves a mixture of gravitational and scalar field polarisations. The “fastest” degrees of freedom are associated with the quartic polynomial, which defines a surface analogous to the Fresnel surface in crystal optics. In contrast with optics, this surface is generically non-singular except on certain surfaces in spacetime. It is shown that a Killing horizon is an example of such a surface. It is also shown that a Killing horizon satisfies the zeroth law of black hole mechanics. The characteristic polynomial defines a cone in the cotangent space and a dual cone in the tangent space. The latter is used to define basic notions of causality and to provide a definition of a dynamical black hole in these theories.

Spacetime Quantum Reference Frames and superpositions of proper times. (arXiv:2101.11628v1 [quant-ph])

Authors: Flaminia Giacomini

In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames, through which spacetime can be given an operational meaning.

Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime, and we give a manifestly covariant formulation of physical laws from the perspective of such a quantum reference frame. In particular, we consider a system of $N$ relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the $N$ particles appears “frozen”, but the dynamical evolution is recovered in terms of relational quantities. We describe both the external and the internal degrees of freedom of the particles. The external degrees of freedom are used to fix the quantum reference frame via a transformation to the local frame of the particle such that the metric is locally flat at the origin of the quantum reference frame. The internal degrees of freedom are used as clocks keeping the proper time in the local frame of the particle. We then show how the remaining particles evolve dynamically in the relational variables from the perspective of the quantum reference frame. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the quantum reference frame.

Testing quantum gravity with interactive information sensing. (arXiv:2101.11629v1 [quant-ph])

We suggest a test of a central prediction of perturbatively quantized general relativity: the coherent communication of quantum information between massive objects through gravity. To do this, we introduce the concept of interactive quantum information sensing, a protocol tailored to the verification of dynamical entanglement generation between a pair of systems. Concretely, we propose to monitor the periodic wavefunction collapse and revival in an atomic interferometer which is gravitationally coupled to a mechanical oscillator. We prove a theorem which shows that, under the assumption of time-translation invariance, this collapse and revival is possible if and only if the gravitational interaction forms an entangling channel. Remarkably, as this approach improves at moderate temperatures and relies primarily upon atomic coherence, our numerical estimates indicate feasibility with current devices.

Quantum information probes of charge fractionalization. (arXiv:2101.11636v1 [hep-th])

We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of gauge theories. For concreteness, we focus on a simple holographic $(2+1)$-dimensional strongly coupled electron fluid whose charged states organize themselves into a fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To overcome this challenge, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a $U(1)$ gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic $c$-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

Energy-mass equivalence from Maxwell equations. (arXiv:2101.11923v1 [gr-qc])

Authors: Alejandro PerezSalvatore Ribisi

Since the appearance of Einstein’s paper {\em”On the Electrodynamics of Moving Bodies”} and the birth of special relativity, it is understood that the theory was basically coded within Maxwell’s equations. The celebrated mass-energy equivalence relation, $E=mc^2$, is derived by Einstein using thought experiments involving the kinematics of the emission of light (electromagnetic energy) and the relativity principle. Text book derivations often follow paths similar to Einstein’s, or the analysis of the kinematics of particle collisions interpreted from the perspective of different inertial frames. All the same, in such derivations the direct dynamical link with hypothetical fundamental fields describing matter (e.g. Maxwell theory or other) is overshadowed by the use of powerful symmetry arguments, kinematics, and the relativity principle.

Here we show that the formula can be derived directly form the dynamical equations of a massless matter model confined in a box (which can be thought of as a toy model of a composite particle). The only assumptions in the derivation are that the field equations hold and the energy-momentum tensor admits a universal interpretation in arbitrary coordinate systems. The mass-energy equivalence relation follows from the inertia or (taking the equivalence principle for granted) weight of confined field radiation. The present derivation offers an interesting pedagogical perspective on the formula providing a simple toy model on the origin of mass and a natural bridge to the foundations of general relativity.

Emergent gauge symmetries: Yang-Mills theory. (arXiv:2101.12188v1 [hep-th])

Gauge symmetries are typically interpreted as redundancies in our description of a physical system, needed in order to make Lorentz invariance explicit when working with fields of spin 1 or higher. However, another perspective on gauge symmetries is that they represent an effective decoupling of some degrees of freedom of the theory. In this work we discuss the extension of a mechanism for the emergence of gauge symmetries proposed in a previous article \cite{barcelo2016} in order to account for non-Abelian gauge symmetries. We begin by examining the linearized theory and then move on to discuss the possible non-linear extensions via a perturbative bootstrapping process. In particular, we show that the bootstrapping procedure is essential in order to determine the physical principles under which the decoupling observed at the linear level (and therefore, the emergence of gauge symmetries) extends to the non-linear scenario. These principles are the following: low-energy Lorentz invariance, emergence of massless vector fields describable by an action quadratic in those fields and their derivatives, and self-coupling to a conserved current. This serves as a step-forward in the emergent gravity program.

The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe. (arXiv:2006.16182v2 [astro-ph.CO] UPDATED)

It is commonly assumed that the energy density of the Universe was dominated by radiation between reheating after inflation and the onset of matter domination 54,000 years later. While the abundance of light elements indicates that the Universe was radiation dominated during Big Bang Nucleosynthesis (BBN), there is scant evidence that the Universe was radiation dominated prior to BBN. It is therefore possible that the cosmological history was more complicated, with deviations from the standard radiation domination during the earliest epochs. Indeed, several interesting proposals regarding various topics such as the generation of dark matter, matter-antimatter asymmetry, gravitational waves, primordial black holes, or microhalos during a nonstandard expansion phase have been recently made. In this paper, we review various possible causes and consequences of deviations from radiation domination in the early Universe – taking place either before or after BBN – and the constraints on them, as they have been discussed in the literature during the recent years.

Entanglement View of Dynamical Quantum Phase Transitions

Author(s): Stefano De Nicola, Alexios A. Michailidis, and Maksym Serbyn

The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude and are present in many models. In some cases, DQPTs can b…

[Phys. Rev. Lett. 126, 040602] Published Fri Jan 29, 2021

Reviving frequentism

Abstract

Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the thermodynamic arrow of time can be grounded on typicality within statistical mechanics. This account, which I will call typicality frequentism, will evade the major criticisms raised against previous forms of frequentism. In this theory, probabilities arise within a physical theory from statistical behavior of almost all initial conditions. The main advantage of typicality frequentism is that it shows which kinds of probabilities (that also have empirical relevance) can be derived from physics. Although one cannot recover all probability talk in this account, this is rather a virtue than a vice, because it shows which types of probabilities can in fact arise from physics and which types need to be explained in different ways, thereby opening the path for a pluralistic account of probabilities.

The life of an analogue black hole

Nature Physics, Published online: 28 January 2021; doi:10.1038/s41567-020-01160-5

Table-top superfluid experiments offer a way of bringing the physics of astrophysical black holes into the lab. But the presence of two event horizons in these superfluid black holes complicates matters — and makes them more interesting.

Muon colliders to expand frontiers of particle physics

Nature Physics, Published online: 28 January 2021; doi:10.1038/s41567-020-01130-x

Muon colliders offer enormous potential for the exploration of the particle physics frontier but are challenging to realize. A new international collaboration is forming to make such a muon collider a reality.

A hydrodynamic instability drives protein droplet formation on microtubules to nucleate branches

Nature Physics, Published online: 28 January 2021; doi:10.1038/s41567-020-01141-8

Branching microtubule nucleation plays a major part in cellular processes driving eukaryotic cell division. A combination of microscopy approaches and hydrodynamic theory is used to show how the condensed protein TPX2 on a microtubule reorganizes according to the Rayleigh–Plateau instability.

In Praise of Clausius Entropy: Reassessing the Foundations of Boltzmannian Statistical Mechanics

Weaver, Christopher (2020) In Praise of Clausius Entropy: Reassessing the Foundations of Boltzmannian Statistical Mechanics. [Preprint]

Phenomenology and the unity of consciousness

Abstract

The phenomenology of the unity of consciousness can be analyzed in terms of perceptual spatial and object unity. Subject unity—what we commonly understand by “the unity of consciousness”—has no attendant phenomenology. The further, non-phenomenological, effects of unity can be analyzed in terms of the functional notion of access unity. The unity of consciousness in general can therefore be analyzed in terms of access unity. As a consequence, we can avoid the theoretical introduction of problematic notions such as subsumptive or phenomenal unity.

On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics

Ellerman, David (2021) On Abstraction in Mathematics and Indefiniteness in Quantum Mechanics. [Preprint]

The relativity of indetermininacy

Del Santo, Flavio and Gisin, Nicolas (2021) The relativity of indetermininacy. [Preprint]

Beyond Causal Explanation: Einstein’s Principle Not Reichenbach’s

Abstract

Our account provides a local, realist and fully non-causal principle explanation for EPR correlations, contextuality, no-signalling, and the Tsirelson bound. Indeed, the account herein is fully consistent with the causal structure of Minkowski spacetime. We argue that retrocausal accounts of quantum mechanics are problematic precisely because they do not fully transcend the assumption that causal or constructive explanation must always be fundamental. Unlike retrocausal accounts, our principle explanation is a complete rejection of Reichenbach’s Principle. Furthermore, we will argue that the basis for our principle account of quantum mechanics is the physical principle sought by quantum information theorists for their reconstructions of quantum mechanics. Finally, we explain why our account is both fully realist and psi-epistemic. View Full-Text