# Weekly Papers on Quantum Foundations (17)

Revisiting the compatibility problem between the gauge principle and the observability of the canonical orbital angular momentum in the Landau problem. (arXiv:2104.10885v1 [quant-ph])

As is widely-known, the eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number $n$, whereas the second is the magnetic quantum number $m$, which is the eigen-value of the canonical orbital angular momentum (OAM) operator of the electron. The eigen-energies of the system depend only on the first quantum number $n$, and the second quantum number $m$ does not correspond to any direct observables. This seems natural since the canonical OAM is generally believed to be a {\it gauge-variant} quantity, and observation of a gauge-variant quantity would contradict a fundamental principle of physics called the {\it gauge principle}. In recent researches, however, Bliohk et al. analyzed the motion of helical electron beam along the direction of a uniform magnetic field, which was mostly neglected in past analyses of the Landau states. Their analyses revealed highly non-trivial $m$-dependent rotational dynamics of the Landau electron, but the problem is that their papers give an impression that the quantum number $m$ in the Landau eigen-states corresponds to a genuine observable. This compatibility problem between the gauge principle and the observability of the quantum number $m$ in the Landau eigen-states was attacked in our previous letter paper. In the present paper, we try to give more convincing answer to this delicate problem of physics, especially by paying attention not only to the {\it particle-like} aspect but also to the {\it wave-like} aspect of the Landau electron.

A note on “Algebraic approach to Casimir force between two $\delta$-like potentials” (K. Ziemian, Ann. Henri Poincar\’e, Online First, 2021). (arXiv:2104.11029v1 [quant-ph])

We comment on the recent work [1], and on its relations with our papers [2,3] cited therein. In particular we show that, contrarily to what stated in [1], the Casimir energy density determined therein in the case of a single delta-like singularity coincides with the energy density obtained previously in our paper [2] using a different approach.

Conflicts Between Science and Religion: Epistemology to the Rescue. (arXiv:2104.10776v1 [physics.hist-ph])

Both Albert Einstein and Erwin Schr\”{o}dinger have defined what science is. Einstein includes not only physics, but also all natural sciences dealing with both organic and inorganic processes in his definition of science. According to Schr\”{o}dinger, the present scientific worldview is based on the two basic attitudes of comprehensibility and objectivation. On the other hand, the notion of religion is quite equivocal and unless clearly defined will easily lead to all sorts of misunderstandings. Does science, as defined, encompass the whole of reality? More importantly, what is the whole of reality and how do we obtain data for it? The Christian worldview considers a human as body, mind, and spirit (soul), which is consistent with Cartesian ontology of only three elements: matter, mind, and God. Therefore, is it possible to give a precise definition of science showing that the conflicts are actually apparent and not real?

The Mereology of Thermodynamic Equilibrium. (arXiv:2104.11140v1 [physics.hist-ph])

Authors: Michael te Vrugt

The special composition question (SCQ), which asks under which conditions objects compose a further object, establishes a central debate in modern metaphysics. Recent successes of inductive metaphysics, which studies the implications of the natural sciences for metaphysical problems, suggest that insights into the SCQ can be gained by investigating the physics of composite systems. In this work, I show that the minus first law of thermodynamics, which is concerned with the approach to equilibrium, leads to a new approach to the SCQ, the thermodynamic composition principle (TCP): Multiple systems in (generalized) thermal contact compose a single system. This principle, which is justified based on a systematic classification of possible mereological models for thermodynamic systems, can form the basis of an inductive argument for universalism. A formal analysis of the TCP is provided on the basis of mereotopology, which is a combination of mereology and topology. Here, “thermal contact” can be analyzed using the mereotopological predicate “self-connectedness”. Self-connectedness has to be defined in terms of mereological sums to ensure that scattered objects cannot be self-connected.

Gravitational Footprints of Black Holes and Their Microstate Geometries. (arXiv:2104.10686v1 [hep-th])

We construct a family of non-supersymmetric extremal black holes and their horizonless microstate geometries in four dimensions. The black holes can have finite angular momentum and an arbitrary charge-to-mass ratio, unlike their supersymmetric cousins. These features make them and their microstate geometries astrophysically relevant. Thus, they provide interesting prototypes to study deviations from Kerr solutions caused by new horizon-scale physics. In this paper, we compute the gravitational multipole structure of these solutions and compare them to Kerr black holes. The multipoles of the black hole differ significantly from Kerr as they depend non-trivially on the charge-to-mass ratio. The horizonless microstate geometries have the same multipoles as their corresponding black hole, with small deviations set by the scale of their microstructure.

Beyond the Equivalence Principle: Gravitational Magnetic Monopoles. (arXiv:2104.11063v1 [gr-qc])

Authors: Mario NovelloAngelo E. S. Hartmann

We review the hypothesis of the existence of gravitational magnetic monopoles (H-pole for short) defined in analogy with the Dirac’s hypothesis of magnetic monopoles in electrodynamics. These hypothetical dual particles violate the equivalence principle and are accelerated by a gravitational field. We propose an expression for the gravitational force exerted upon an H-pole. According to GR ordinary matter (which we call E-poles) follows geodesics in a background metric. The dual H-poles follows geodesics in an effective metric.

New Results on Vacuum Fluctuations: Accelerated Detector versus Inertial Detector in a Quantum Field. (arXiv:2104.04142v2 [quant-ph] CROSS LISTED)

Authors: I-Chin Wang

We investigate the interaction between a moving detector and a quantum field, especially about how the trajectory of the detector would affect the vacuum fluctuations when the detector is moving in a quantum field (Unruh effect). We focus on two moving detectors system for the future application in quantum teleportation. We find that the trajectory of an uniformly accelerated detector in Rindler space can’t be extended to the trajectory that a detector moves at constant velocity. Based on the past work, we redo the calculations and find that a term is missing in the past calculations, also we find that there are some restrictions on the values for the parameters in the solutions. Besides, without including the missing term, the variance from the quantum field for the inertial detector will be zero and is unlikely for such system. Combining all these points, there is a difference on the two-point correlation function between the inertial detector and accelerated detector in early-time region. The influence from proper acceleration can be seen in the two-point correlation functions. This might play a role in the quantum teleportation process and worth to study thoroughly.

Observing a superposition

Abstract

The bare theory is a no-collapse version of quantum mechanics which predicts certain puzzling results for the introspective beliefs of human observers of superpositions. The bare theory can be interpreted to claim that an observer can form false beliefs about the outcome of an experiment which produces a superpositional result. It is argued that, when careful consideration is given to the observer’s belief states and their evolution, the observer does not end up with the beliefs claimed. This result leads to questions about whether there can be any allure for no-collapse theories as austere as the bare theory.

Simulating the Same Physics with Two Distinct Hamiltonians

Author(s): Karol Gietka, Ayaka Usui, Jianqiao Deng, and Thomas Busch

A new framework allows one to use a quantum simulation of one Hamiltonian to study another.

[Phys. Rev. Lett. 126, 160402] Published Thu Apr 22, 2021

Non-equilibrium Thermodynamics and the Free Energy Principle in Biology

Palacios, Patricia and Colombo, Matteo (2021) Non-equilibrium Thermodynamics and the Free Energy Principle in Biology. [Preprint]

Russell’s The Analysis of Matter as the First Book on Quantum Gravity

Mikki, Said (2021) Russell’s The Analysis of Matter as the First Book on Quantum Gravity. [Preprint]

The Democratization of Science

Kurtulmus, Faik (2021) The Democratization of Science. [Preprint]

Perspectival QM and Presentism: a New Paradigm

Merriam, Paul (2021) Perspectival QM and Presentism: a New Paradigm. [Preprint]

Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

Author(s): Katja Klobas, Bruno Bertini, and Lorenzo Piroli

New studies provide analytical descriptions and exact solutions for various aspects of thermodynamics in quantum many-body systems.

[Phys. Rev. Lett. 126, 160602] Published Mon Apr 19, 2021

Philosophy of Science in China: Politicized, De-politicized, and Re-politicized

Guo, Yuanlin and Ludwig, David (2021) Philosophy of Science in China: Politicized, De-politicized, and Re-politicized. [Preprint]

Norton, John D. and Parker, Matthew W. (2021) An Infinite Lottery Paradox. [Preprint]

A new paradox and the reconciliation of Lorentz and Galilean transformations

Abstract

One of the most debated problems in the foundations of the special relativity theory is the role of conventionality. A common belief is that the Lorentz transformation is correct but the Galilean transformation is wrong (only approximately correct in low speed limit). It is another common belief that the Galilean transformation is incompatible with Maxwell equations. However, the “principle of general covariance” in general relativity makes any spacetime coordinate transformation equally valid. This includes the Galilean transformation as well. This renders a new paradox. This new paradox is resolved with the argument that the Galilean transformation is equivalent to the Lorentz transformation. The resolution of this new paradox also provides the most straightforward resolution of an older paradox which is due to Selleri in (Found Phys Lett 10:73–83, 1997). I also present a consistent electrodynamics formulation including Maxwell equations and electromagnetic wave equations under the Galilean transformation, in the exact form for any high speed, rather than in low speed approximation. Electrodynamics in rotating reference frames is rarely addressed in textbooks. The presented formulation of electrodynamics under the Galilean transformation even works well in rotating frames if we replace the constant velocity $$\mathbf {v}$$ with $$\mathbf {v}=\varvec{\omega }\times \mathbf {r}$$ . This provides a practical tool for applications of electrodynamics in rotating frames. When electrodynamics is concerned, between two inertial reference frames, both Galilean and Lorentz transformations are equally valid, but the Lorentz transformation is more convenient. In rotating frames, although the Galilean electrodynamics does not seem convenient, it could be the most convenient formulation compared with other transformations, due to the intrinsic complex nature of the problem.

Fighting about frequency: an international journal for epistemology, methodology and philosophy of science

Abstract

Scientific disputes about how often different processes or patterns occur are relative frequency controversies. These controversies occur across the sciences. In some areas—especially biology—they are even the dominant mode of dispute. Yet they depart from the standard picture of what a scientific controversy is like. In fact, standard philosophical accounts of scientific controversies suggest that relative frequency controversies are irrational or lacking in epistemic value. This is because standard philosophical accounts of scientific controversies often assume that in order to be rational, a scientific controversy must (a) reach a resolution and (b) be about a scientifically interesting question. Relative frequency controversies rarely reach a resolution, however, and some scientists and philosophers are skeptical that these controversies center on scientifically interesting questions. In this paper, I provide a novel account of the epistemic contribution that relative frequency controversies make to science. I show that these controversies are rational in the sense of furthering the epistemic aims of the scientific communities in which they occur. They do this despite rarely reaching a resolution, and independent of whether the controversies are about scientifically interesting questions. This means that assumptions (a) and (b) about what is required for a controversy to be rational are wrong. Controversies do not need to reach a resolution in order to be rational. And they do not need to be about anything scientifically interesting in order to make valuable epistemic contributions to science.

Abstract

The last decade has seen an increasing number of references to quantum mechanics in the humanities and social sciences. This development has in particular been driven by Karen Barad’s agential realism: a theoretical framework that, based on Niels Bohr’s interpretation of quantum mechanics, aims to inform social theorizing. In dealing with notions such as agency, power, and embodiment as well as the relation between the material and the discursive level, the influence of agential realism in fields such as feminist science studies and posthumanism has been profound. However, no one has hitherto paused to assess agential realism’s proclaimed quantum mechanical origin including its relation to the writings of Niels Bohr. This is the task taken up here. We find that many of the implications that agential realism allegedly derives from a Bohrian interpretation of quantum mechanics dissent from Bohr’s own views and are in conflict with those of other interpretations of quantum mechanics. Agential realism is at best consistent with quantum mechanics and consequently, it does not capture what quantum mechanics in any strict sense implies for social science or any other domain of inquiry. Agential realism may be interesting and thought provoking from the perspective of social theorizing, but it is neither sanctioned by quantum mechanics nor by Bohr’s authority. This conclusion not only holds for agential realism in particular, it also serves as a general warning against the other attempts to use quantum mechanics in social theorizing.

The landscape and the multiverse: What’s the problem?

Abstract

As a candidate theory of quantum gravity, the popularity of string theory has waxed and waned over the past four decades. One current source of scepticism is that the theory can be used to derive, depending upon the input geometrical assumptions that one makes, a vast range of different quantum field theories, giving rise to the so-called landscape problem. One apparent way to address the landscape problem is to posit the existence of a multiverse; this, however, has in turn drawn heightened attention to questions regarding the empirical testability and predictivity of string theory. We argue first that the landscape problem relies on dubious assumptions and does not motivate a multiverse hypothesis. Nevertheless, we then show that the multiverse hypothesis is scientifically legitimate and could be coupled to string theory for other empirical reasons. Looking at various cosmological approaches, we offer an empirical criterion to assess the scientific status of multiverse hypotheses

The First Droplet in a Cloud Chamber Track

Jonathan F. Schonfeld

Foundations of Physics volume 51, Article number: 47 (2021)

Abstract

In a cloud chamber, the quantum measurement problem amounts to explaining the first droplet in a charged-particle track; subsequent droplets are explained by Mott’s 1929 wave-theoretic argument about collision-induced wavefunction collimation. I formulate a mechanism for how the first droplet in a cloud chamber track arises, making no reference to quantum measurement axioms. I look specifically at tracks of charged particles emitted in the simplest slow decays, because I can reason about rather than guess the form that wave packets take. The first visible droplet occurs when a randomly occurring, barely-subcritical vapor droplet is pushed past criticality by ionization triggered by the faint wavefunction of the emitted charged particle. This is possible because potential energy incurred when an ionized vapor molecule polarizes the other molecules in a droplet can balance the excitation energy needed for the emitted charged particle to create the ion in the first place. This degeneracy is a singular condition for Coulombic scattering, leading to infinite or near-infinite ionization cross sections, and from there to an emergent Born rule in position space, but not an operator projection as in the projection postulate. Analogous mechanisms may explain canonical quantum measurement behavior in detectors such as ionization chambers, proportional counters, photomultiplier tubes or bubble chambers. This work is important because attempts to understand canonical quantum measurement behavior and its limitations have become urgent in view of worldwide investment in quantum computing and in searches for super-rare processes (e.g., proton decay).