# Weekly Papers on Quantum Foundations (2)

The hydrogen atom: consideration of the electron self-field. (arXiv:2101.02202v1 [quant-ph])

We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the spectrum of everywhere regular solutions to the self-consistent system of Dirac and Maxwell equations (with external Coulomb potential). We demonstrate that only particular classes of solutions, “nonlinear” analogues of s- and p-states, can be obtained through decomposition of a solution in a series, with respect to the fine structure constant parameter $\alpha$. In the zero approximation at $\alpha \rightarrow 0$ the reduction to the self-consistent non-relativistic system of Schr\”odinger-Poisson equations takes place. For the latter, using both numerical and variational methods, we obtain the solutions corresponding to the ground and set of excited states. Spectrum of the binding energies with remarkable precision reproduces the “Bohrian” dependence $W_n = W/ n^2$. For this, the ionization energy $W$ proves to be universal yet about two times smaller than its observed value. Possibility of the renormalization procedure and the problem of account for relativistic corrections to the binding energies of order $\alpha^2$ are considered

Quantum Indistinguishability by Path Identity: The awakening of a sleeping beauty. (arXiv:2101.02431v1 [quant-ph])

Two photon-pair creation processes can be arranged such that the paths of the emitted photons are identical. Thereby the path information is not erased but is never born in the first place. In addition to its implications for fundamental physics, this concept has recently led to a series of discoveries in the fields of imaging, spectroscopy, and quantum information science. Here we present the idea of path identity and provide a comprehensive review of the recent developments.

Classical Dynamics from Self-Consistency Equations in Quantum Mechanics — Extended Version. (arXiv:2009.04969v2 [math-ph] UPDATED)

During the last three decades, P. B\'{o}na has developed a non-linear generalization of quantum mechanics, based on symplectic structures for normal states and offering a general setting which is convenient to study the emergence of macroscopic classical dynamics from microscopic quantum processes. We propose here a new mathematical approach to Bona’s one, with much brother domain of applicability. It highlights the central role of self-consistency. This leads to a mathematical framework in which the classical and quantum worlds are naturally entangled. We build a Poisson bracket for the polynomial functions on the hermitian weak$^{\ast }$ continuous functionals on any $C^{\ast }$-algebra. This is reminiscent of a well-known construction for finite-dimensional Lie algebras. We then restrict this Poisson bracket to states of this $C^{\ast }$-algebra, by taking quotients with respect to Poisson ideals. This leads to densely defined symmetric derivations on the commutative $C^{\ast }$-algebras of real-valued functions on the set of states. Up to a closure, these are proven to generate $C_{0}$-groups of contractions. As a matter of fact, in general commutative $C^{\ast }$-algebras, even the closableness of unbounded symmetric derivations is a non-trivial issue. Some new mathematical concepts are introduced, which are possibly interesting by themselves: the convex weak $^{\ast }$ G\^{a}teaux derivative, state-dependent $C^{\ast }$-dynamical systems and the weak$^{\ast }$-Hausdorff hypertopology, a new hypertopology used to prove, among other things, that convex weak$^{\ast }$-compact sets generically have weak$^{\ast }$-dense extreme boundary in infinite dimension. Our recent results on macroscopic dynamical properties of lattice-fermion and quantum-spin systems with long-range, or mean-field, interactions corroborate the relevance of the general approach we present here.

Dual Aharanov-Bohm Berry Phase and the Electric Vector Potential due to the Generation of Electricity through Permanent Bound and Free Charge Polarization. (arXiv:2101.00945v2 [physics.class-ph] CROSS LISTED)

To understand the creation of electromagnetic energy (or a photonic degree of freedom) from an external energy source, an electromotive force must be generated, capable of separating positive and negative charges. The separation of charges (free or bound) may be modelled as a permanent polarization, which has a non-zero electric vector curl, created by an external force per unit charge, sometimes referred as an impressed electric field. The resulting system forms a physical dipole in the static case, or a Hertzian dipole in the time dependent case. This system is the electrical dual of the magnetic solenoid described by a magnetic vector potential and excited by an electrical current. Correspondingly, the creation of an electric dipole, from the forceful separation of positive and negative charge, may be described by an electric flux density, which exhibits an electric vector potential and a magnetic current boundary source, within the frame work of two-potential theory without the need for the existence of the magnetic monopole. From this result we derive the Dual electric Aharanov-Bohm (DAB) Berry phase and make the conjecture that it should be equivalent to the geometric phase that is described in modern electric polarization theory, which also describes the nature of the permanent polarization of a ferroelectric. This work gives a formal meaning to the electric vector potential that defines the DAB geometric phase, and determines that a permanent polarization has both a scalar and vector potential component, and we show that it must be considered to fully describe the nature of a physical electric dipole, which inevitably is a generator of electricity. Additionally, we show that Faraday’s and Ampere’s law may be derived from the time rate of change of the Aharanov-Bohm phase and the DAB phase respectively, independent of the electromagnetic gauge.

Discovery of the Relativistic Schr\”odinger Equation. (arXiv:2012.12467v2 [physics.hist-ph] UPDATED)

We discuss the discovery of the relativistic wave equation for a spin-zero charged particle in the Coulomb field by Erwin Schr\”odinger (and elaborate on why he didn’t publish it).

A simple characterization of doubly twisted spacetimes. (arXiv:2101.02208v1 [gr-qc])

In this note we characterize 1+n doubly twisted spacetimes in terms of `doubly torqued’ vector fields. They extend Bang-Yen Chen’s characterization of twisted and generalized Robertson-Walker spacetimes with torqued and concircular vector fields. The result is a simple classification of 1+n doubly-twisted, doubly-warped, twisted and generalized Robertson-Walker spacetimes.

Singularities, black holes, and cosmic censorship: A tribute to Roger Penrose. (arXiv:2101.02687v1 [gr-qc])

Authors: Klaas Landsman

In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile definition of a singular space-time does not match the generally accepted definition of a black hole (derived from his concept of null infinity). To overcome this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particular, we review both his own (mature) formulation and its later, inequivalent reformulation in the PDE literature. As a compromise, one might say that in “generic” or “physically reasonable” space-times, weak cosmic censorship postulates the appearance and stability of event horizons, whereas strong cosmic censorship asks for the instability and ensuing disappearance of Cauchy horizons. As an encore, an appendix by Erik Curiel reviews the early history of the definition of a black hole.

Nuclear decay oscillations, quantum-mechanical nonlinearity and emergent gravity. (arXiv:1812.01455v3 [quant-ph] CROSS LISTED)

Authors: S.N. Mayburov

Several experimental groups reported the evidence of multiple periodic modulations of nuclear decay constants which amplitudes are of the order 0.05% and have periods of one year, 24 hours or about one month. We argue that these deviations from radioactive decay law can be explained as the effect of small nonlinear corrections to standard quantum mechanics, in particular, to Hamiltonian of quantum system interaction with gravitational field. It’s shown that modified Doebner-Goldin nonlinear model predicts the similar decay parameter variations under influence of Sun gravity.

Einstein’s Equivalence principle for superpositions of gravitational fields. (arXiv:2012.13754v1 [quant-ph] CROSS LISTED)

Authors: Flaminia GiacominiČaslav Brukner

The Principle of Equivalence, stating that all laws of physics take their special-relativistic form in any local inertial frame, lies at the core of General Relativity. Because of its fundamental status, this principle could be a very powerful guide in formulating physical laws at regimes where both gravitational and quantum effects are relevant. However, its formulation implicitly presupposes that reference frames are abstracted from classical systems (rods and clocks) and that the spacetime background is well defined. It is unclear if it continues to hold when quantum systems, which can be in a quantum relationship with other physical systems, are taken as reference frames, and in a superposition of classical spacetime structures. Here, we tackle both questions by introducing a relational formalism to describe quantum systems in a superposition of curved spacetimes. We build a unitary transformation to the quantum reference frame (QRF) of a quantum system in curved spacetime, and in a superposition thereof. In both cases, a QRF can be found such that the metric looks locally flat. Hence, one cannot distinguish, with a local measurement, if the spacetime is flat or curved, or in a superposition of such spacetimes. This transformation identifies a Quantum Local Inertial Frame. We also find a spacetime path-integral encoding the dynamics of a quantum particle in spacetime and show that the state of a freely falling particle can be expressed as an infinite sum of all possible classical geodesics. We then build the QRF transformation to the Fermi normal coordinates of such freely falling quantum particle and show that the metric is locally flat. These results extend the Principle of Equivalence to QRFs in a superposition of gravitational fields. Verifying this principle may pave a fruitful path to establishing solid conceptual grounds for a future theory of quantum gravity.

Does General Relativity Highlight Necessary Connections in Nature?

Vassallo, Antonio (2021) Does General Relativity Highlight Necessary Connections in Nature? [Preprint]

Virtually a measurement

Nature Physics, Published online: 08 January 2021; doi:10.1038/s41567-020-01138-3

Simulations are as much a part of science as hypothesis and experiment. But can their outcomes be considered observations? Wendy S. Parker investigates.

Thermodynamic Uncertainty Relation for General Open Quantum Systems

Author(s): Yoshihiko Hasegawa

We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the system-environment interaction, we bound the counting observables in t…

[Phys. Rev. Lett. 126, 010602] Published Tue Jan 05, 2021

A challenge to the second law of thermodynamics from cognitive science and vice versa

Abstract

We show that the so-called MultipleComputations Theorem in cognitive science and philosophy of mind challenges Landauer’s Principle in physics. Since the orthodox wisdom in statistical physics is that Landauer’s Principle is implied by, or is the mechanical equivalent of, the Second Law of thermodynamics, our argument shows that the Multiple-Computations Theorem challenges the universal validity of the Second Law of thermodynamics itself. We construct two examples of computations carried out by one and the same dynamical process with respect to which Landauer’s principle implies contradictory predictions concerning the entropy increase. Our two examples are based on a weak version of the Multiple-Computations Theorem, which is quite uncontroversial, and therefore they amount to a clear refutation of the universal validity of Landauer’s Principle. We consider some responses to this argument that do not attempt to single out one computation over the others, and we show that they do not work. We further consider ways out of the argument by externalist approaches supporting the computational theory of the mind who propose that the interaction of a computing system with the environment is enough to select a single computation over the others. We show on physical grounds that this approach fails too. We then reverse the direction of our challenge and formulate a dilemma for supporters of the computational theory of the mind: (i) they must reject (or amend somehow) the causal closure of physic; or else (ii) they must accept on a priori grounds that Landauer’s Principle and the Second Law of thermodynamics are not universally valid. Finally, we present our version of a type–type mind-brain identity theory called Flat Physicalism, which is based on the paradigm case of statistical mechanics, and we show that it circumvents the challenge from Landauer’s Principle and the Multiple-Computations Theorem and does not fall prey to our dilemma.

The Relativistic Transactional Interpretation and The Quantum Direct-Action Theory

Kastner, Ruth (2021) The Relativistic Transactional Interpretation and The Quantum Direct-Action Theory. [Preprint]

The Empirical Under-determination Argument Against Scientific Realism for Dual Theories

De Haro, Sebastian (2021) The Empirical Under-determination Argument Against Scientific Realism for Dual Theories. [Preprint]

The Power of Inconsistency in Anti-Realist Realisms about Quantum Mechanics (Or: Lessons on How to Capture and Defeat Smoky Dragons)

de Ronde, Christian (2021) The Power of Inconsistency in Anti-Realist Realisms about Quantum Mechanics (Or: Lessons on How to Capture and Defeat Smoky Dragons). [Preprint]