The physical meaning of quantization

After analyzing the difficulties for a local realistic interpretation of quantum theory, it is argued that such an interpretation might be possible if some new postulates are added to the standard ones. We propose a stochastic interpretation of quantum theory, which involves the need of joint probability distributions for all relevant observables. The well known problems for the existence of joint distributions are solved by assuming that neither all Hermitian operators correspond to observables nor all density matrices represent physical states. A research program along these lines is presented studying in particular the Maxwell quantum field and the Dirac field.     

The topological meaning of non-abelian anomalies

We show how the non-abelian anomaly for gauge fields coupled to Weyl fermions in 2n dimensions is related to the non-trivial topology of gauge orbit space. The form of the anomaly and its normalization are shown to follow from a familiar index theorem for a certain (2n + 2)-dimensional Dirac operator. We are thus able to recover and give topological meaning to a variety of results concerning anomalies in 4- and higher-dimensional theories.     

The physical meaning of Fermi coordinates

Fermi coordinates (FC) are supposed to be the natural extension of Cartesian coordinates for an arbitrary moving observer in curved space-time. Since their construction cannot be done on the whole space or even in the whole past of the observer we examine which construction principles are responsible for this effect and how they may be modified. A proposal for a modification is made and applied to the observer with constant acceleration in the two- and four-dimensional Minkowski space. The two-dimensional case shows some surprising similarities to Kruskal space which generalize those found by Rindler for the outer region of Kruskal space and the Rindler wedge. In perturbational approaches the modification also leads to different predictions for certain physical systems. As an example we consider atomic interferometry and derive the deviation of the acceleration-induced phase shift from the standard result in Fermi coordinates.     

The meaning and significance of quantum states

Recent investigations have conclusively proved that, because of their collapse, quantum states transform noncovariantly under Lorentz transformations. This result is shown to imply that quantum states do not represent probability distributions for the results of measurements. They represent, rather, perspectives of such probability distributions from the point of view of the frame of reference in which they are given. The ontological status of these perspectives of potentialities is discussed. It is conjectured that they propagate from the location of a measurement to the origins of all frames of reference at the speed of light.This work was supported in part by the Colgate Research Council.     

The meaning of the Kelly-Lochbaum acoustic-tube model

The scattering equations of the Kelly-Lochbaum segmented tube, including the time-varying extension by Strube, are originally based on the assumption of uniform spatial segments and stepwise time update of the acoustic impedances. Here, it is shown that the same equations can be derived without these assumptions for a nonuniform time-varying tube from the discretization of space and time derivatives by the bilinear z transform or by centered differences along the rotated coordinates ct+/-x. Moreover, the same equations also hold for a chain of lattice circuits (or equivalents) with appropriate parameters, if time derivatives are discretized by the bilinear z transform. These circuits can also be extended to simulate uniform segments of varying length.     

The physical meaning of the de Sitter invariants

We study the Lie algebras of the covariant representations transforming the matter fields under the de Sitter isometries. We point out that the Casimir operators of these representations can be written in closed forms and we deduce how their eigenvalues depend on the field’s rest energy and spin. For the scalar, vector and Dirac fields, which have well-defined field equations, we express these eigenvalues in terms of mass and spin obtaining thus the principal invariants of the theory of free fields on the de Sitter spacetime. We show that in the flat limit we recover the corresponding invariants of the Wigner irreducible representations of the Poincaré group.     

量子论中狄拉克符号积分的意义

量子的引入最先是普朗克在1900年为理论“凑合”黑体辐射实验曲线的无奈之举(曲线拟合),然此举如招幡令旗,呼风唤雨,聚溪成流,乘奔御风,浩浩汤汤,终成今日量子流行的漫山遍野之势,是几个能人的集灵思积广益而相辅相成,还是时势造英雄,还是两者兼而有之！普朗克以能量分离的观点看待微观世界,是他在理论推导拟合实验结果逐渐形成的信仰。物理学家狄拉克指出,伟大的物理学家如牛顿和爱因斯坦是靠基本信仰“从上到下”推导出一些大自然的定律的。狄拉克自己的信仰是相信方程的美有时比实验结果更重要,因为实验会有误差。量子的时髦,自然引来众说纷纭,惟在量子园地里“种过树”的人才可能有较深刻的体会。
作者历经50多年的理论探索,首创了有序算符内的积分理论,对发展量子力学数理基础——狄拉克的符号法略有建树,既能抑制爱因斯坦认为量子力学数学不够完美的抱怨,为爱因斯坦的量子纠缠思想提供纠缠态表象,也从数学上将量子力学几率假说落实到有序算符的正态分布,从而推陈出新、别开生面地丰富量子力学、量子统计力学和量子光学的内容。     

The global topological meaning of cocycles in a Gauge group

This Letter shows explicitly that the descent sequence of cocycles in a gauge group realizes the ech-de Rham double complex. Meanwhile the ech complex corresponds to finite gauge transformations. This Letter also shows how the indices of each order of cocycles characterizes the obstructions on overlapping spheres in different dimensions and how these indices are equal to a common one.     

The physical meaning of canonical quantization in terms of reference systems

The canonical approach to general relativity in terms of reference systems is discussed to show that Einstein's principles of equivalence and general relativity imply the physical insignificance of quantized general relativity. In particular it is demonstrated that even the (anholonomic) flat-space canonical formalism leads to physically uninterpretable results. This lack of quantum content of general relativity is reflected by Rosenfeld's uncertainty relations and can especially be removed by modifying general relativity in the spirit of classical Einstein-Cartan theory with teleparallelism.     

The physical meaning of scattering matrix singularities in coupled-channel formalisms⋆

The physical meaning of bare and dressed scattering matrix singularities has been investigated. Special attention has been attributed to the role of the well-known invariance of the scattering matrix with respect to the field transformation of the effective Lagrangian. Examples of evaluating bare and dressed quantities in various models are given.     

非厄米哈密顿量的物理意义

分析了一个脉冲激光与原子相互作用的四能级系统，并考虑最上层能级的自电离过程，从而引入非厄米哈密顿量.在缀饰原子模型下，通过直接求解此哈密顿量的本征值与本征函数，得到系统布居的演化函数.与数值方法所得演化函数的对比表明二者相当符合，从而肯定了非厄米哈密顿量在量子力学框架中的地位，并得到其本征值虚部的物理意义.这将使传统量子力学中力学量的定义得以拓展. 关键词： 非厄米哈密顿量 缀饰原子模型     

The computer-based model of quantum measurements

Physics of Atomic Nuclei - Quantum theory of measurements is an extremely important part of quantum mechanics. Currently perturbations by quantum measurements of observable quantities of atomic...     

On the meaning of extensivity

It is shown that the various definitions of an extensive quantity appearing in the standard thermodynamics texts are not equivalent. Furthermore, none of these is found to be equivalent to the usual statistical-mechanical meaning. It is proposed that the statistical-mechanical meaning of an extensive quantity be adopted as the universal definition.     

The meaning of general covariance of einstein’s theory of gravity

The fundamental symmetry of Einstein’s theory of gravity is Lorentz-invariance which leads to a well defined energy-momentum tensor. This is also true for Maxwell’s theory of electromagnetism which has an additional symmetry due to its spin one, restmass zero character. Similarly, the spin two, restmass zero character of the gravitational field leads to an additional gauge symmetry that happens to be isomorphic to the concept of general covariance. The gauge-covariant energy-momentum tensor for gravitational interactions vanishes identically.     

The method of volumetric measurements under high pressure. II. Quantitative measurements

Abstract

Method of measurements of the jumps of volume during phase transitions at high pressures and temperatures is suggested. Theoretical ground of the method is given. Values of the jumps of volume during melting of Pb and In up to 8 GPa, transition in the melt of Sn (these are first quantitative measurements of the jump of volume in the melt under high pressure), are presented.     

The effective use of precision electroweak measurements

Bound state population dynamics in a diatom modelled by an appropriate Morse oscillator with a time-dependent well-depth is investigated perturbatively both in the absence and presence of high intensity radiation. For sinusoidally oscillating well-depth, the population of themth bound vibrational level,P _mm(t), is predicted to be a parabolic function of the amplitude of the oscillation of the well-depth (ΔD ₀) at a fixed laser intensity. For a fixed value of ΔD ₀,P _mm(t) is also predicted to be quadratic function of the field intensity (ɛ ₀). Accurate numerical calculations using a time-dependent Fourier grid Hamiltonian (TDFGH) method proposed earlier corroborate the predictions of perturbation theory. As to the dissociation dynamics, the numerical results indicate that the intensity threshold is slightly lowered if the well-depth oscillates. Possibility of the existence of pulse-shape effect on the dissociation dynamics has also been investigated.