The foundations of the poincaré group and the validity of general relativity

After discussions about accepted ideas concerning the nonlocalisability of the photon, the interpretation of the Minkowski space-time, the wave-corpuscle duality ideas of Niels Bohr and the concept of elementary particle by Eugene Wigner, the validity of the Poincaré group is brought into question and some other ideas are developed. Lukierski, Nowicki and Ruegg showed that the successes of the Poincaré group are preserved if we deform the group by introducing a constant κ. Such deformation replaces the Poincaré Hopf algebra by another one. We call such a deformation a mathematical deformation. The main inconvenience of this mathematical deformation is that the coproduct is not commutative. The consequence is that a two-particle state is defined in an ambiguous way because we must say which is the first particle and which is the second one. The only mathematical deformation of the Poincaré group which preserves the commutativity of the coproduct is the trivial one, that is the Poincaré Hopf algebra itself. That is why we reject the mathematical deformation of Lukierski, Nowicki and Ruegg. That is also why we propose what we call a physical deformation of the Poincaré group, which means that we reinterpret the Poincaré Hopf algebra, with the same constant κ. Our proposal has four advantages:

1.

1. The constant x has the dimensions of a mass. When this constant becomes infinite, we are left with the Poincaré group with its main successes.

2.

2. The two-particle states are unambiguously defined.

3.

3. The constant κ may be chosen in such a way that the search for a missing mass in the universe is useless.

4.

4. It consists in the disappearing of unphysical irreducible representations of the Poincaré group.

With the constant κ, we arrive at a reformulation of special relativity where the energy is no longer additive. This would imply a change in general relativity where the density of matter must be different from the density of energy. Unfortunately, we are not able to propose a substitute for the general relativity theory. Obviously, when the constant κ goes to infinity, the new general relativity would become the standard general relativity.     

Neutron Interference: Influence of the Mirror on the Spin

Advanced neutron interferometry includes the spinor properties of the neutrons. This makes it necessary to consider the influence of the mirrors on the spinor propagation. It is shown how the effect of an arbitrary mirror can be uniquely decomposed into a known kinematical part which is necessarily present, and a dynamical part which goes back to an interaction the neutron experiences in its rest-space. For any particular realization of a mirror this dynamical part can be determined experimentally. An argument is given as to why it vanishes for the usual perfect-crystal interferometer. The first relativistic approximations of the spinor reflection formula are discussed.     

Why Fundamental Physical Equations Are of Second Order

We use a deep mathematical result (namely, aminor modification of Kolmogorov's solution to Hilbert's13th problem) to explain why fundamental physicalequations are of second order. This same result explain why all these fundamental equations naturallylead to nonsmooth solutions likesingularities.     

New relaxation phenomena in the outer atomic layers of Fe{211}

A low-energy electron diffraction analysis of a {211} surface of body-centered cubic iron reveals relaxations in the directions perpendicular and parallel to the surface plane. Both relaxations alternate in successive layers. The perpendicular relaxation goes from contraction of 10.5% to expansion of 5% to contraction of 1%. The parallel relaxation goes from a shift of the first layer of 0.24Å (10% of the nearest neighbor distance) toward more symmetrical registration with the second layer, to an opposite shift of 0.035 Å of the second layer with respect to the third.     

Phase-integral calculation of quantal matrix elements between unbound states,without the use of wavefunctions

The paper deals with the calculation of diagonal as well as off-diagonal matrix elements between unbound states pertaining to a radial Schrödinger equation. For the case that the effective potential, i.e. the potential with the centrifugal barrier included, is real and that only a single generalized classical turning point exists, we derive, on the basis of a phase-integral method, a new, general formula for the calculation of such matrix elements without the use of wavefunctions. The formula applies to an arbitrary order of the phase-integral approximations used. While conventional methods may present difficulties when the radial wavefunctions oscillate rapidly in space, this formula, in which the wavefunctions do not appear, is expected to be more accurate the more rapidly the wavefunctions oscillate. The formula is tested numerically for a Lennard-Jones potential and is found to yield extremely accurate results.

When specialized to the first-order approximation, our formula goes over into a formula derived previously by other authors. They derived the formula by introducing the first-order JWKB approximation for the wave-functions in the integral defining the matrix element and simplifying the resulting expression by using simple qualitative arguments. The remarkably good accuracy of this first-order formula has puzzled previous authors. So has also the fact that attempts to improve it, by including quantities neglected on the basis of the simple qualitative arguments, and by using Airy functions or uniform approximations for the wavefunctions through the turning points, have failed. Our derivation throws light on the question of the accuracy to be expected, and it explains why already the first-order formula is remarkably accurate and why no improvement is gained in the attempts mentioned.     

Recent developments concerning generic spacelike singularities

This is a review of recent progress concerning generic spacelike singularities in general relativity. For brevity the main focus is on singularities in vacuum spacetimes, although the connection with, and the role of, matter for generic singularity formation is also commented on. The paper describes recent developments in two areas and show how these are connected within the context of the conformally Hubble-normalized state space approach. The first area is oscillatory singularities in spatially homogeneous cosmology and the connection between asymptotic behaviour and heteroclinic chains. The second area concerns oscillatory singularities in inhomogeneous models, especially spike chains and recurring spikes. The review also outlines some underlying reasons for why the structures that are the foundation for generic oscillatory behaviour exists at all, which entails discussing how underlying physical principles and applications of solution generating techniques yield hierarchical structures and connections between them. Finally, it is pointed out that recent progress concerning generic singularities motivates some speculations that suggest that a paradigm shift concerning their physical role, and what mathematical issues to address, might be in order.     

On the second law of thermodynamics I. General framework

In this paper a general framework for discussing the classical statements of the second law of thermodynamics is developed. The thermodynamic systems with which the theory deals need not obey the first law and can undergo general (not necessarily quasi-static) processes. By using the formalism of heat distribution measures introduced in previous papers of the author, the classical verbal statements are converted into meaningful mathematical conditions. These conditions can be put into a general form which is the same for all the classical statements. The main result of the paper is an abstract theorem which shows that the general condition leads to one or two inequalities for cyclic processes. In the subsequent part of the paper the abstract theorem is applied to the specific conditions corresponding to the classical statements of the second law. The number of the corresponding inequalities depends on the condition in question, but in each case these inequalities are generalization of the Clausius inequality to which they reduce if the first law holds. By comparing the inequalities corresponding to various statements of the second law also the relations among the statements are established in the second part of the paper.I wish to thank Dr. Jan Kratochvil, DrSc for a number of helpful suggestions concerning a previous draft of the paper.     

Three flavour neutrino oscillations in models with large extra dimensions

The key challenges for models with large extra dimensions, posed by neutrino physics are: first to understand why neutrino masses are small and second, whether one can have a simultaneous explanation of all observed oscillation phenomena. There exist models that answer the first challenge by using singlet bulk neutrinos coupled to the standard model in the brane. Our goal in this paper is to see to what extent the simplest versions of these models can answer the second challenge. Our conclusion is that the minimal framework that has no new physics beyond the above simple picture cannot simultaneously explain solar, atmospheric and LSND data, whereas there are several ways that it can accommodate the first two. This would suggest that confirmation of LSND data would indicate the existence of new physics either in the brane or in extra dimensions or both, if indeed it turns out that there are large extra dimensions.     

Equilibriumizing all food chain chaos through reproductive efficiency

The intraspecific interference of a top-predator is incorporated into a classical mathematical model for three-trophic food chains. All chaos types known to the classical model are shown to exist for this comprehensive model. It is further demonstrated that if the top-predator reproduces at high efficiency, then all chaotic dynamics will change to a stable coexisting equilibrium, a novel property not found in the classical model. This finding gives a mechanistic explanation to the question of why food chain chaos is rare in the field. It also suggests that high reproductive efficiency of top-predators tends to stabilize food chains.     

An extension of the plane-symmetric electrovac general solution to Einstein equations

We present the general solution to Einstein-Maxwell equations representing plane-symmetric metrics associated with electromagnetic fields that are not fully plane-symmetric. There are two classes in the general solution, the first approaches Taub's static metric or Kasner's spatially homogeneous one as the electromagnetic field goes to zero, while the second approaches the fiat metric.     

On “Decisions and Revisions Which a Minute Will Reverse”: Consciousness,The Unconscious and Mathematical Modeling of Thinking

This article considers a partly philosophical question: What are the ontological and epistemological reasons for using quantum-like models or theories (models and theories based on the mathematical formalism of quantum theory) vs. classical-like ones (based on the mathematics of classical physics), in considering human thinking and decision making? This question is only partly philosophical because it also concerns the scientific understanding of the phenomena considered by the theories that use mathematical models of either type, just as in physics itself, where this question also arises as a physical question. This is because this question is in effect: What are the physical reasons for using, even if not requiring, these types of theories in considering quantum phenomena, which these theories predict fully in accord with the experiment? This is clearly also a physical, rather than only philosophical, question and so is, accordingly, the question of whether one needs classical-like or quantum-like theories or both (just as in physics we use both classical and quantum theories) in considering human thinking in psychology and related fields, such as decision science. It comes as no surprise that many of these reasons are parallel to those that are responsible for the use of QM and QFT in the case of quantum phenomena. Still, the corresponding situations should be understood and justified in terms of the phenomena considered, phenomena defined by human thinking, because there are important differences between these phenomena and quantum phenomena, which this article aims to address. In order to do so, this article will first consider quantum phenomena and quantum theory, before turning to human thinking and decision making, in addressing which it will also discuss two recent quantum-like approaches to human thinking, that by M. G. D’Ariano and F. Faggin and that by A. Khrennikov. Both approaches are ontological in the sense of offering representations, different in character in each approach, of human thinking by the formalism of quantum theory. Whether such a representation, as opposed to only predicting the outcomes of relevant experiments, is possible either in quantum theory or in quantum-like theories of human thinking is one of the questions addressed in this article. The philosophical position adopted in it is that it may not be possible to make this assumption, which, however, is not the same as saying that it is impossible. I designate this view as the reality-without-realism, RWR, view and in considering strictly mental processes as the ideality-without-idealism, IWI, view, in the second case in part following, but also moving beyond, I. Kant’s philosophy.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: XVI. Depolarization and repolarization of polychromatic radiation in single-mode optical fibers with random inhomogeneities

The dependences of the degree of polarization of polychromatic radiation on the length of a single-mode optical fiber (SMF) with random inhomogeneities have been obtained by mathematical modeling. The case is considered where radiation having both polarization modes excited with equal weights of linear polarization is first introduced into a depolarizer of polychromatic radiation (a SMF segment with high linear birefringence) and arrives at an SMF with low linear birefringence. It is shown that the degree of polarization of radiation after transmission through the first segment becomes significantly suppressed and remains almost constant upon propagation through the second segment, after which it begins to sharply increase at some length; i.e., repolarization of radiation occurs. It is shown that repolarization of radiation depends weakly on the angle made by the axes of unperturbed linear birefringence of the first and second segments. The conditions for the length of the first segment (depolarizer) under which the degree of polarization remains minimum throughout the second segment are determined.     

Why optical data communications and why now?

Our focus here is on data communications within IT equipment and in IT data centers. Optical communications is not new. Thus the obvious question is likely; why a paper entitled, “Why optical data communications and why now?”. The reasons are twofold. First, optical data communications is more necessary now than it has ever been in the past. It is not excessive to even consider that it will be required in the not too distant future. Second, the advances in the broad field of photonics and optics have brought optical communications nearly to the point that it can finally cross over the threshold to be less expensive than electronic signaling. In this paper we make the case why we must aggressively pursue optics for data communications at all length scales within the data center. The summarization of this paper is that optical communications is inevitable, and we offer reasons why we believe this is true.     

Localized-Particles Approach for Classical and Quantum Crystals

This paper is the first review devoted to the localized-particles approach for strongly anharmonic crystals. We present mathematical basises of such an approach for classical and quantum cases and we discuss its different applications. In the framework of this method various technical tricks and detailes could, of course, be changed, but the main idea should be conserved: that of the localization of atoms, forming a solid, near their lattice sites. The localized-particles approach describes not only collective excitations as the phonons but the state of particles themselves too; that is why it is much more convenient for describing crystals with defects, crystal-gas intersurfaces, disordered solids and some phase transitions.     

Quantum probabilities,Kolmogorov probabilities,and informational probabilities

The relations between quantum probabilities, Kolmogorov probabilities, and informational probabilities are studied against the background offered by the concept of a quantum mechanical probability tree built in previous work. It is shown that the quantum mechanical transformation theory goes beyond the Kolmogorov concept of probabilities. It is furthermore shown that the quantum mechanical concept of probability is of the same essence as the informational one. The analyses that produce these conclusions bring forth the first lines of a general mathematical representation of the emergence and circulation of patterns of any kind.     

Is there a Problem with our Hamiltonians for Quantum Nonlinear Optical Processes?

The models we use, habitually, to describe quantum nonlinear optical processes have been remarkably successful, yet, with few exceptions, they each contain a mathematical flaw. We present this flaw, show how it can be fixed, and, in the process, suggest why we can continue to use our favored Hamiltonians.     

Quantum states and potentialities of quantum systems

In a previous article it was shown that in general quantum states represent perspectives on the potentialities of quantum systems, rather than the potentialities themselves. In the present paper the following questions are investigated in the context of this result: (1) How do quantum states which undergo collapse transform under pure translations? (2) Under what conditions do quantum states represent the potentialities themselves? Two alternatives are presented in response to the first question: (1) Quantum states are scalars under translations. (2) The collapse of a quantum state propagates between frames of reference at the speed of light. The advantages and disadvantages of the two alternatives are discussed. The response to the second question is shown to depend on the chosen alternative. In addition, the second alternative is shown to lead to a consistent view of quantum states as “potential perspectives on potentialities.”     

三腔介质壁质子加速器时序优化模拟及设计

采用自主研发的三维粒子模拟软件对三腔介质壁加速器进行系统仿真, 在此基础上, 计算三个腔质子的渡越时间并实现腔体间的时序优化设计。外加电压峰值100 kV, 顶宽1 ns, 半高宽10 ns, 绝缘微堆厚度2.0 cm, 质子初始束能40 keV, 加速电极添加钨网, 模拟结果显示:当电压持续6.5 ns时, 进入高梯度绝缘微堆的H+通过第一腔能得到最大加速效率90.84%, 相应的渡越时间为5.668 ns;当第二腔电压触发落后第一腔4.5 ns时, H+通过第二腔获得最大加速效率94.77%, 相应的渡越时间为3.545 ns;当第三腔电压触发落后第二腔3.0 ns时, H+通过第三腔获得最大加速效率97.30%, 相应的渡越时间为3.018 ns;最大能量H+渡越三个腔体的总时间为12.231 ns, H+总体加速效率94.31%;当质子束中心进入第一腔时刻落后脉冲电压触发6.5 ns, 且一二腔和二三腔电压触发延时分别为4.5 ns和3.0 ns情形下, 能将2.5 ns长度的质子束中的H+实现90%以上的加速, 4.0 ns长度的质子束中的H+实现80%以上的加速。     

Charged scalar fields in an external magnetic field: Renormalisation and universal diamagnetism

The physical and mathematical mechanism behind diamagnetism of N (finite) spinless bosons (relativistic or non-relativistic) is well known. The mathematical signature of this diamagnetism follows from Kato's inequality while its physical way of understanding goes back to Van Leeuwen. One can guess that it might be true in the field theoretic case also. While the work on systems with a finite number of degrees of freedom suggests that the same result is true in a field theory, it does not by any means prove it. In the field theoretic context one has to develop a suitable regularisation scheme to renormalise the free energy. We show that charged scalar fields in (2+1) and (3+1) dimensions are always diamagnetic, even in the presence of interactions and at finite temperatures. This generalises earlier work on the diamagnetism of charged spinless bosons to the case of infinite degrees of freedom. We also discuss possible applications of the theory.     

Kinetic theory of classical liquids. I. Basic theory

A somewhat new approach to a kinetic theory of classical liquids is presented, and it is used to calculate the dynamical structure factor S(qω). It gives correctly the zeroth, second, and fourth frequency moments of S(qω), and it goes correctly over to the free particle value for large q. For small q and ω it goes over to proper hydrodynamics, including the coupling to heat diffusion. Results of numerical calculations on liquid argon are presented and they show very good agreement with available neutron scattering and molecular dynamics data.