Can the Past Be Changed?

The paper shows that the past, history in a non-technical sense, can be changed in quantum mechanics. The first part of the paper reviews Deutsch's analysis in his paper of 1991. It is demonstrated that Deutsch assumes the existence of a multiplicity of essentially classical worlds. Such a multiplicity of worlds would allow the past to be changed in classical mechanics. It is argued that the existence of multiple classical worlds is not required by quantum mechanics. It is then shown that it is possible to change the past in conventional quantum mechanics even without the assumption of a multiplicity of worlds.     

Geometric structures approximated by Maxwell's equations

We show that classical electrodynamics can be obtained as a limit of a system of geodesic equations on 2-vector fields in an Artinian manifold. The limit method is geometrically analogous to the method used to obtain Newtonian mechanics as the limit of the geodesic equations on a Lorentzian manifold. It is also shown that the current and energy-momentum conservation law of electrodynamics can be obtained directly from the geodesic formulation. The geometric structures introduced are related to semi-Kählerian and balanced structures in complex geometry.     

Analyticity of effective coupling and propagators in massless models of quantum field theory

For massless models of quantum field theory, some general theorems are proved concerning the analytic continuation of the renormalization group functions as well as the effective coupling and the propagators. Starting points are analytic properties of the effective coupling and the propagators in the momentum variablek ², which can be converted into analyticity of - and -functions in the coupling parameter . It is shown that the -function can have branch point singularities related to stationary points of the effective coupling as a function ofk ². The type of these singularities of () can be determined explicitly. Examples of possible physical interest are extremal values of the effective coupling at space-like points in the momentum variable, as well as complex conjugate stationary points close to the realk ²-axis. The latter may be related to the sudden transition between weak and strong coupling regimes in quantum chromodynamics. Finally, for the effective coupling and for the propagators, the analytic continuation in both variablesk ² and is discussed.On leave from the Max-Planck-Institut für Physik und Astrophysik, D-8000 München, Federal Republic of Germany     

On the equivalence of the relativistic theories of gravitation

Einstein's equations are rewritten in terms of a certain torsionless linear connection which differs, in general, from the Levi-Civita metric connection . The torsionless connection appears in a natural way as the canonical momentum of the gravitational field g . Einstein's equations have a simple interpretation in terms of the connection . The equivalence of the so-calledpurely metric, purely affine, andmetricaffine theories of gravitation is proved.This work has been written under the financial support of Gruppo Nazionale per la Fisica Matematica of the Italian National Research Council.     

The dependence of susceptibility on the high-frequency field at ferromagnetic resonance

The dependence of the uniform precession amplitude and susceptibility at ferromagnetic resonance on the high-frequency fieldh is discussed on the basis of an equation for the energy balance and classical equations for the spin wave amplitudes. The dependence (h) is first determined in the lowest non-linear approximation. According to these calculations, the initial decline of the susceptibility differs from Schlömann's quadratic law. The influence of other nonlinear interactions between spin wavesk0 is then discussed on a certain special assumption of the type of two-magnon scattering. It is shown that such interactions can lead to the appearance of a maximum in the h.f. field dependence of the uniform precession amplitude.     

On the universal linear in-layer resistivity ϱ∝T 1of high-T c superconductors

Based on the Boltzmann equation an inversion formula for the resistivity is deduced which for a general coupling between two carrier bands yields, in dimensionD, T ^D–1. While being well known inD=3, this is a new result inD=2. It is then shown that in a 2-band model of strongly anisotropic masses as are found in the cuprate layer structures, the in-layer resistivity follows the law forD=2, T ¹, in agreement with the majority of experiments. Exceptions to the linear law and to the 2-band assumption are also discussed. Assuming the spin-flip term of the interaction to be dominant, the spin-flip relaxation time _sf is estimated by using the data on · _sf is found to be orders of magnitude shorter than the EPR period thus explaining the complete absence of intrinsic EPR signals in the cuprates. It is also shown that the spin-flip interaction gives rise to pairing, preferentially of the heavier carriers.     

On Poisson brackets and symplectic structures for the classical and quantum zitterbewegung

The symplectic structures (brackets, Hamilton's equations, and Lagrange's equations) for the Dirac electron and its classical model have exactly the same form. We give explicitly the Poisson brackets in the dynamical variables (x ,p ,v ,S ^v). The only difference is in the normalization of the Dirac velocities =4 which has significant consequences.Dedicated to David Hestenes, whose work profoundly connects geometry (spacetime), algebra (Clifford), and physics (electron).     

On the electromagnetic structure of elementary particles

Using modern similarity and dimensionality methods, criteria of similarity are derived and used as transformations, which effect the conversion from one natural system of units to another. The exclusion principles thus defined are used to determine the powers of the similarity criteria in quantitative relations.Systems of units of the fermion and boson types are used in the simplest identification of the parameters corresponding to elementary particles.A set of electric and magnetic physical constants with dimensionality length, area, and volume, is obtained and successfully unified within the limits of a vortex ring, the maximum dimensions of which are defined by the Compton wavelength, and the minimum by the classical radius of the particle. The vortex ring model is in accordance with the latest experimental data, and it enables the behavior of the incident and target particles in the scattering process to be predicted.In modern theoretical physics the elementary particles are still considered as essentially structureless point formations, and hence it is impossible to give a purely theoretical treatment of the structure of the particles. Thus the various attempts in this direction (Hofstadter, Blokhintsev) have a polyphenomenological character and are internally inconsistent. (The search for the structure of an elementary particle is carried out on the assumption that it is not elementary, since truly elementary particles are defined as point size.) The author recognizes the need for an original approach to the structure of elementary particles, based on a method of study adequate for the problem. Such a method is the theory of dimensionality and similarity (Sedov, Gukhman, and Kirpichev), which serves as a scientific basis of a physical experiment (Kirpichev), or as the scientific basis for a model of the phenomena, insofar as the criteria of similarity are a reflection of the physical model of the process (Gukhman).It is a pleasure to thank Academician L. I. Sedov and Professor K. A. Putilov for valuable criticism and advice, and Professor A. S. Irisov and V. V. Lokhin for useful discussions.     

THE ORIGIN OF ENTROPY IN THE UNIVERSE

We discuss the entropy generation in quantum tunneling of a relativistic particle under the influence of a time-varying force with the help of squeezing formalism. It is shown that if one associates classical coarse grained entropy to the phase space volume, there is an inevitable entropy growth due to the changes in position and momentum variances. The entropy change can be quantified by a simple expression S=ln cosh 2r, where r, is the squeeze parameter measuring the height and width of the potential barrier. We suggest that the universe could have acquired its initial entropy in a quantum squeeze from nothing and briefly discuss the implications of our proposal.     

Properties of theL p -solutions of linear impulsive equations in a banach space

Conditions for the existence ofL _p-solutions (1p) of linear impulsive equations in a Banach space are found.     

The physical properties of linear and action-angle coordinates in classical and quantum mechanics

The quantum harmonic oscillator is described in terms of two basic sets of coordinates: linear coordinates x, p_x and angular coordinates eⁱ, P (action-angle variables). The angular coordinate eⁱ is assumed unitary, the conjugate momentum p is assumed Hermitian, and eⁱ and p are assumed to be a canonical pair. Two transformations are defined connecting the angular coordinates to the linear coordinates. It is found that x, p_x can be physical, i.e., Hermitian and canonical, only under constraints on the p eigenvalue spectrum. The conclusion is that eⁱ can be a unitary operator. A parallel analysis of the classical harmonic oscillator is done with equivalent results.     

The nonsymmetric Kaluza-Klein (Jordan-Thiry) theory in the electromagnetic case

We present the nonsymmetric Kaluza-Klein and Jordan-Thiry theories as interesting propositions of physics in higher dimensions. We consider the five-dimensional (electromagnetic) case. The work is devoted to a five-dimensional unification of the NGT (nonsymmetric theory of gravitation), electromagnetism, and scalar forces in a Jordan-Thiry manner. We find interference effects between gravitational and electromagnetic fields which appear to be due to the skew-symmetric part of the metric. Our unification, called the nonsymmetric Jordan-Thiry theory, becomes the classical Jordan-Thiry theory if the skew-symmetric part of the metric is zero. It becomes the classical Kaluza-Klein theory if the scalar field=1 (Kaluza's Ansatz). We also deal with material sources in the nonsymmetric Kaluza-Klein theory for the electromagnetic case. We consider phenomenological sources with a nonzero fermion current, a nonzero electric current, and a nonzero spin density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodetic equations in the theory and the equation of motion for charged test particles. We consider some numerical predictions of the nonsymmetric Kaluza-Klein theory with nonzero (and with zero) material sources. We prove that they do not contradict any experimental data for the solar system and on the surface of a neutron star. We deal also with spin sources in the nonsymmetric Kaluza-Klein theory. We find an exact, static, spherically symmetric solution in the nonsymmetric Kaluza-Klein theory in the electromagnetic case. This solution has the remarkable property of describing mass without mass and charge without charge. We examine its properties and a physical interpretation. We consider a linear version of the theory, finding the electromagnetic Lagrangian up to the second order of approximation with respect toh _v =g _v –n _v . We prove that in the zeroth and first orders of approximation there is no skewonoton interaction. We deal also with the Lagrangian for the scalar field (connected to the gravitational constant). We prove that in the zeroth and first orders of approximation the Lagrangian vanishes.     

Hamilton and the Law of Varying Action Revisited

According to history texts, philosophers searched for a unifying natural law whereby natural phenomena and numbers are related. More than 2300 years ago, Aristotle postulated that nature requires minimum energy. More than 220 years ago, Euler applied the minimum energy postulate. More than 200 years ago, Lagrange provided a mathematical proof of the postulate for conservative systems. The resulting Principle of Least Action served only to derive the differential equations of motion of a conservative system. Then, 170 years ago, Hamilton presented what he claimed to be a general method in dynamics. Hamilton's resulting Law of Varying Action was supposed to apply to both conservative and non-conservative systems and was supposed to yield either the differential equations of motion or the integrals of those differential equations. However, no direct evaluation of the integrals of motion ever resulted from Hamilton's law of varying action. In 1975, a scant 29 years ago, following five years of controversy with engineer mechanicians, Dr. Wolfgang Yourgrau, Editor, Foundations of Physics, published my first paper based on Aristotle's postulate, without mathematical proof. That and subsequent papers present, through applications, a true general method in dynamics. In this essay, I present the mathematical proof that is missing from my 1975 and subsequent papers. Six fundamental integrals of analytical mechanics are derived from Aristotle's postulate. First, however, Hamilton must be revisited to show why his H function and his force function prevents the law of varying action from being the general method in dynamics that he claimed it to be. I have found that Hamiltons Law of Varying Action (HLVA), as Hamilton presented it, cannot be applied to systems for which the force function is non-integrable. In 1972, Dr. B.E. Gatewood and Dr. D.P. Beres (then a graduate student) discovered that the end-point term associated with the principle of least action does not vanish. I named the new equation, the general energy equation. In 1973, because I was doing with it what Hamilton claimed could be done with HLVA, I simply assumed that this new equation was HLVA. I gave the new equation the misnomer HLVA. In 2001, I learned that I had made a grave mistake. I found that HLVA is at most a special case of the general energy equation. My interpretation of Aristotle's postulate permits one to by-pass the differential equations of motion completely for both conservative and non-conservative systems (no calculus of variations).     

On the existence of rotating stars in general relativity

The Newtonian equations of motion, and Newton's law of gravitation can be obtained by a limit of Einstein's equations. For a sufficiently small constant the existence of a set of solutions (0) of Einstein's equations of a stationary, axisymmetric star is proven. This existence is proven in weighted Sobolev spaces with the implicit function theorem. Since the value of the causality constant depends only on the units used to measure the velocity, the existence of a solution for any small is physically interesting.     

On the spherical symmetry of static stellar models

This paper completes the proof of the necessity of spherical symmetry in the static general-relativistic stellar models that have equations of state satisfying certain inequalities. The technical assumption — that there exists a reference spherical stellar model — that was essential in the previous discussions of this problem is removed. This paper also extends beyond previous discussions the class of equations of state included in the proof. The analysis of the equations for spherical stellar models, used here to demonstrate the existence of a reference spherical model, may also be of independent interest.     

The variation of Zipf’s law in human language

Words in humans follow the so-called Zipfs law. More precisely, the word frequency spectrum follows a power function, whose typical exponent is 2, but significant variations are found. We hypothesize that the full range of variation reflects our ability to balance the goal of communication, i.e. maximizing the information transfer and the cost of communication, imposed by the limitations of the human brain. We show that the higher the importance of satisfying the goal of communication, the higher the exponent. Here, assuming that words are used according to their meaning we explain why variation in should be limited to a particular domain. From the one hand, we explain a non-trivial lower bound at about =1.6 for communication systems neglecting the goal of the communication. From the other hand, we find a sudden divergence of if a certain critical balance is crossed. At the same time a sharp transition to maximum information transfer and unfortunately, maximum communication cost, is found. Consistently with the upper bound of real exponents, the maximum finite value predicted is about =2.4. It is convenient for human language not to cross the transition and remain in a domain where maximum information transfer is high but at a reasonable cost. Therefore, only a particular range of exponents should be found in human speakers. The exponent contains information about the balance between cost and communicative efficiency.     

Generalized two-level quantum dynamics. II. Non-Hamiltonian state evolution

A theorem is derived that enables a systematic enumeration of all the linear superoperators (associated with a two-level quantum system) that generate, via the law of motion = , mappings (0) (t) restricted to the domain of statistical operators. Such dynamical evolutions include the usual Hamiltonian motion as a special case, but they also encompass more general motions, which are noncyclic and feature a destination state (t ) that is in some cases independent of (0).     

Cosmological Coriolis fields in the Newton-Cartan theory

If the Newton-Cartan theory of gravitation is not restricted by a law of existence of absolute rotation, its statements for infinite systems may differ from those of Newton's classical theory through the existence of intrinsic (gravitational) Coriolis fields. Explicit examples are given.     

Traffic Jams in a Lattice-Gas Model

We propose a simple lattice-gas model characterized by two states of atoms, the thermalized state, which is the same as in the standard lattice-gas model, and the running state, where the atoms jump in one direction only. The model exhibits the existence of traffice jams (bunching of thermalized atoms in compact groups), the nonlinear dependence of mobility on the jump probability, and the hysteresis.     

The temperature vibrations of urea molecules

The structural and dynamic parameters of urea at 112°K and 295°K were determined by the least squares method. The characteristic temperature of the torsional optical vibrations of a molecule about a C-O bond was determined and is in good agreement with the value determined by Raman scattering. The fractional X-coordinate of the nitrogen atom corrected for torsional vibrations was determined and it was found that the magnitude of the projection of the C-N bond in the given temperature range changes only within the limits of observational errors. A new method, called temperature difference synthesis, is described and it is shown that it is suitable for rapid qualitative determination of the thermal anisotropy of the vibrations of atoms in a crystal lattice.

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112°K 295°K. C-O , , . X- , C-N . , , , .