Feynman’s Relativistic Electrodynamics Paradox and the Aharonov-Bohm Effect

An analysis is done of a relativistic paradox posed in the Feynman Lectures of Physics involving two interacting charges. The physical system presented is compared with similar systems that also lead to relativistic paradoxes. The momentum conservation problem for these systems is presented. The relation between the presented analysis and the ongoing debates on momentum conservation in the Aharonov-Bohm problem is discussed.     

Von Neumann’s quantization of general relativity

Von Neumann’s procedure is applied to quantizing general relativity. Initial data for dynamical variables in the Planck epoch, where the Hubble parameter value coincided with the Planck mass are quantized. These initial data are defined in terms of the Fock orthogonal simplex in the tangent Minkowski spacetime and the Dirac conformal interval. The Einstein cosmological principle is used to average the logarithm of the determinant of the spatial metric over the spatial volume of the visible Universe. The splitting of general coordinate transformations into diffeomorphisms and transformations of the initial data is introduced. In accordance with von Neumann’s procedure, the vacuum state is treated is a quantum ensemble that is degenerate in quantum numbers of nonvacuum states. The distribution of the vacuum state leads to the Casimir effect in gravidynamics in just the same way as in electrodynamics. The generating functional for perturbation theory in gravidynamics is found by solving the quantum energy constraint. The applicability range of gravidynamics is discussed along with the possibility of employing this theory to interpret modern observational data.     

Cornelius Lanczos’s Derivation of the Usual Action Integral of Classical Electrodynamics

The usual action integral of classical electrodynamics is derived starting from Lanczos’s electrodynamics – a pure field theory in which charged particles are identified with singularities of the homogeneous Maxwell’s equations interpreted as a generalization of the Cauchy–Riemann regularity conditions from complex to biquaternion functions of four complex variables. It is shown that contrary to the usual theory based on the inhomogeneous Maxwell’s equations, in which charged particles are identified with the sources, there is no divergence in the self-interaction so that the mass is finite, and that the only approximations made in the derivation are the usual conditions required for the internal consistency of classical electrodynamics. Moreover, it is found that the radius of the boundary surface enclosing a singularity interpreted as an electron is on the same order as that of the hypothetical “bag” confining the quarks in a hadron, so that Lanczos’s electrodynamics is engaging the reconsideration of many fundamental concepts related to the nature of elementary particles.     

Quantum–Matter–Spacetime: Peter Mittelstaedt’s Contributions to Physics and Its Foundations

In a period of over 50 years, Peter Mittelstaedt has made substantial and lasting contributions to several fields in theoretical physics as well as the foundations and philosophy of physics. Here we present an overview of his achievements in physics and its foundations which may serve as a guide to the bibliography (printed in this Festschrift) of his publications. An appraisal of Peter Mittelstaedt’s work in the philosophy of physics is given in a separate contribution by B. Falkenburg.     

Can von Neumann’s Theory Meet the Deutsch-Jozsa Algorithm?

The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on von Neumann’s theory. We try to investigate whether von Neumann’s theory meet our physical world. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1≤N<+∞). This assumption intuitively depictures our physical world. However, the quantum predictions within the formalism of von Neumann’s projective measurement violate the proposition with a magnitude that grows exponentially with the number of particles. Therefore, von Neumann’s theory cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. Hence, von Neumann’s theory cannot meet the Deutsch-Jozsa algorithm. We propose the solution of the problem. Our solution is equivalent to changing Planck’s constant (?) to new constant (\(\hbar/\sqrt{2}\)). It may be that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does so.     

Von Neumann’s ‘No Hidden Variables’ Proof: A Re-Appraisal

Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann’s ‘no hidden variables’ proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense ‘like Bohm’s theory.’ His seminal result provides a positive answer to the question. I argue that Bell’s analysis misconstrues von Neumann’s argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the ‘beables’ of the theory, to use Bell’s term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm’s theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system.     

Bell’s inequality, Einstein, Podolsky, Rosen arguments and von Neumann’s projection postulate

This paper is devoted to analysis of the role of projection postulate in Einstein, Podolsky, and Rosen-EPR [1] argument against completeness of QM. It will be shown that the EPR considerations do not match with von Neumann’s quantum measurement theory (QMT). The root of EPR’s conclusion on incompleteness of QM is the misuse of von Neumann’s projection postulate. EPR applied this postulate to observables with degenerate spectra (which is totally forbidden by von Neumann’s axiomatics of QM). Consequences for Bell’s inequality and quantum information theory are analyzed. This paper might stimulate discussion on the role of projection postulate in quantum information theory, especially quantum cryptography and teleportation.     

Von Neumann’s growth model: Statistical mechanics and biological applications

We review recent work on the statistical mechanics of Von Neumann’s growth model and discuss its application to cellular metabolic networks. In this context, we present a detailed analysis of the physiological scenario underlying optimality à la Von Neumann in the metabolism of the bacterium E. coli, showing that optimal solutions are characterized by a considerable microscopic flexibility accompanied by a robust emergent picture for the key physiological functions. This suggests that the ideas behind optimal economic growth in Von Neumann’s model can be helpful in uncovering functional organization principles of cell energetics.     

Contributions to International and National Symposium

AIP International Conference Held in New York, America, in 2003 (1) X-ray Emissions from Highly Charges Heavy Ions Studied at Storage Rings, in X-ray and Inner Shell Processes. Ma Xinwen, et al.     

Entropic Corrections to Coulomb’s Law

Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde’s argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb’s law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb’s law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb’s law as well as the entropy corrected Poisson’s equation which governing the evolution of the scalar potential ϕ. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.     

Non-spectator Contributions to Lifetime of Λb

In this work, we study the contributions of non-spectator effects to the lifetimes of Λb and B-mesons comparatively. Based on the well-established theoretical framework about the effective weak Lagrangian, we derive the formulation of the non-spectator effects at the quark level. Especially, for Λb we have considered two pictures: the three-valence-quark picture and the quark-diquark picture. In the two pictures, the interference contributions to the total width are different, in this work, we investigate the interference effects in detail. As a preliminary estimate on the lifetimes, we evaluate the hadronic matrix elements appearing in the final formulas of the lifetimes by means of a simple phenomenological model for both pictures. Our results show that the contributions of the non-spectator effects can reduce the ratio of lifetime of Λb to that of B-mesons by 5 ～ 7%. It is noted that in the quark-diquark picture the ratio can be further reduced if excited states of the diquark system are taken into account. We conclude that the measured ratio τ(Λb)/τ(B0)(≈)0.79 [The Data Group, Phys. Rev. D66 (2002) 010001] can be partly understood by the non-spectator effects, although the problem on the discrepancy between theoretical prediction and experimental measurement is not fully solved.     

Non-spectator Contributions to Lifetime of ∧b

In this work, we study the contributions of non-spectator effects to the lifetimes of ∧b and B-mesons comparatively. Based on the well-established theoretical framework about the effective weak Lagrangian, we derive the formulation of the non-spectator effects at the quark level. Especially, for ∧b we have considered two pictures: the three-valence-quark picture and the quark-diquark picture. In the two pictures, the interference contributions to the total width are different, in this work, we investigate the interference effects in detail As a preliminary estimate on the lifetimes, we evaluate the hadronic matrix elements appearing in the final formulas of the lifetimes by means of a simple phenomenological model for both pictures. Our results show that the contributions of the non-spectator effects can reduce the ratio of lifetime of ∧b to that of B-mesons by 5-7％. It is noted that in the quark-diquark picture the ratio can be further reduced if excited states of the diquark system are taken into account. We conclude that the measured ratio τ(∧b)/τ(B^o)-0.79 [The Data Group, Phys. Rev. D66 (2002) 010001] can be partly understood by the non-spectator effects, although the problem on the discrepancy between theoretical prediction and experimental measurement is not fullv solved.     

Conformal transformation route to gravity’s rainbow

Conformal transformation as a mathematical tool has been used in many areas of gravitational physics. In this paper, we consider gravity’s rainbow, in which the metric can be treated as a conformal rescaling of the original metric. By using the conformal transformation technique, we get a specific form of a modified Newton’s constant and cosmological constant in gravity’s rainbow, which implies that the total vacuum energy is dependent on probe energy. Moreover, the result shows that Einstein gravity’s rainbow can be described by energy-dependent \(f(E,\tilde{R})\) gravity. At last, we study the f(R) gravity, when gravity’s rainbow is considered, which can also be described as energy-dependent \(\tilde{f}(E,\tilde{R})\) gravity.     

A Physical Approach to Tsirelson’s Problem

Tsirelson’s problem deals with how to model separate measurements in quantum mechanics. In addition to its theoretical importance, the resolution of Tsirelson’s problem could have great consequences for device independent quantum key distribution and certified randomness. Unfortunately, understanding present literature on the subject requires a heavy mathematical background. In this paper, we introduce quansality, a new theoretical concept that allows to reinterpret Tsirelson’s problem from a foundational point of view. Using quansality as a guide, we recover all known results on Tsirelson’s problem in a clear and intuitive way.     

Yet Another Approach to Loschmidt’s Paradox

Journal of Experimental and Theoretical Physics - The works by Lev Petrovich Pitaevskii are reference points for choosing an interesting research topic. An example is the article [1] which promotes...