Nonstandard analysis in classical physics and quantum formal scattering

After a rigorous introduction to hyperreal numbers, we give in terms of non standard analysis, (1) a Lagrangian statement of classical physics, and (2) a statement of formal quantum scattering.     

The concept of indistinguishable particles in classical and quantum physics

The consequences of the following definition of indistinguishability are analyzed. Indistinguishable classical or quantum particles are identical classical or quantum particles in a state characterized by a probability measure, a statistical operator respectively, which is invariant under any permutation of the particles. According to this definition the particles of classical Maxwell-Boltzmann statistics are indistinguishable.     

Magnetic monopoles: From classical to quantum physics

A modified Metropolis algorithm is developed and used to construct axial-symmetric and multimonopole classical solutions in the (lattice-regularized) SO(3) Georgi-Glashow model outside the BPS limit. As an example one of those solutions is then used as an ansatz to study the quantum stability of the configuration.     

Outline of a classical theory of quantum physics and gravitation

It is argued that in the manner in which the Galilean-Newtonian physics may be said to have explained the Ptolemaic-Copernican theories in terms which have since been called classical, so also Milner's theories of the structure of matter may be said to explain present day quantum and relativistic theory. In both cases the former employ the concept of force and the latter, by contrast, are geometrical theories. Milner envisaged space as being stressed, whereas Einstein thought of it as strained. Development of Milner's theory from criticisms and suggestions made by Kilmister has taken it further into the realms of quantum and gravitational physics, where it is found to give a more physically comprehensible explanation of the phenomena. Further, it shows why present day quantum theory is cast in a statistical form. The theory is supported by many predictions such as the ratio of Planck's constant to the mass of the electron, the value of the fine structure constant and reason for apparent variations in past measurements, the magnetic moment of the electron and proton of the stable particles such as the neutron Λ and Σ together with the kaon, and a relation between the universal gravitational constant and Hubble's constant—all within published experimental accuracy. The latest results to be accounted for by the theory are the masses of the newly discovered ψ particles and confirmation of the value of the decay of Newton's gravitational constant obtained from lunar measurements. While this paper is being typed, new particles are rapidly being discovered—the latest being a neutral ψ particle. A short Appendix discusses the significance of these.     

An application of information theory: Longitudinal measurability bounds in classical and quantum physics

We examine the problem of the existence (in classical and/or quantum physics) of longitudinal limitations of measurability, defined as limitations preventing the measurement of a given quantity with arbitrarily high accuracy. We consider a measuring device as a generalized communication system, which enables us to use methods of information theory. As a direct consequence of the Shannon theorem on channel capacity, we obtain an inequality which limits the accuracy of a measurement in terms of the average power necessary to transmit the information content of the measurement itself. This inequality holds in a classical as well as in a quantum framework.     

谐振子系统的量子-经典轨道、Berry相及Hannay角

从量子-经典轨道和几何相两方面, 研究了二维旋转平移谐振子系统的量子-经典对应. 通过广义规范变换得到了Lissajous经典周期轨道和Hannay角. 另外, 使用含时规范变换解析推导了旋转平移谐振子系统Schrödinger方程的本征波函数和Berry相, 得出结论: 原规范中的非绝热Berry相是经典Hannay角的-n倍. 最后, 使用SU(2)自旋相干态叠加, 构造一稳态波函数, 其波函数的概率云很好地局域于经典轨道上, 满足几何相位和经典轨道同时对应.     

Minimum signals in classical physics

The bandwidth theorem for Fourier analysis on any time-dependent classical signal is shown using the operator approeoch to quantum mechanics. Following discussions about squeezed states in quantum optics, the problem of minimum signals presented by a single quantity and its squeezing is proposed. It is generally proved that all such minimum signals, squeezed or not, must be real Gaussian functions of time.     

Nonstationary quantum mechanics. III. Quantum mechanics does not incorporate classical physics

It is shown that disagreement between the prediction of classical and conventional quantum mechanics about momentum probabilities exists in the case of a quasiclassical motion. The discussion is based on the detailed consideration of two specific potentials:U(x)=x and the oscillatory potentialU(x)=m ² x ²/2. The results of the present Part III represent a further development of the idea in Todorov (1980) about the possible inefficiency of conventional theory in the case of potentials swiftly varying with time.     

The theoretical apparatus of semantic realism: A new language for classical and quantum physics

The standard interpretation of quantum physics (QP) and some recent generalizations of this theory rest on the adoption of a rerificationist theory of truth and meaning, while most proposals for modifying and interpreting QP in a realistic way attribute an ontological status to theoretical physical entities (ontological realism). Both terms of this dichotomy are criticizable, and many quantum paradoxes can be attributed to it. We discuss a new viewpoint in this paper (semantic realism, or briefly SR), which applies both to classical physics (CP) and to QP. and is characterized by the attempt of giving up verificationism without adopting ontological realism. As a first step, we construct a formalized observative language L endowed with a correspondence truth theory. Then, we state a set of axioms by means of L which hold both in CP and in QP. and construct a further language L_v which can express bothtestable andtheoretical properties of a given physical system. The concepts ofmeaning andtestability do not collapse in L and L_e hence we can distinguish between semantic and pragmatic compatibility of physical properties and define the concepts of testability and conjoint testability of statements of L and L_e. In this context a new metatheoretical principle (MGP) is stated, which limits the validity of empirical physical laws. By applying SR (in particular. MGP) to QP, one can interpret quantum logic as a theory of testability in QP, show that QP is semantically incomplete, and invalidate the widespread claim that contextuality is unavoidable in QP. Furthermore. SR introduces some changes in the conventional interpretation of ideal measurements and Heisenbergs uncertainty principle.     

Inference in quantum physics

In quantum physics all experimental information is discrete and stochastic. But the values of physical quantities are considered to depict definite properties of the physical world. Thus physical quantities should be identified with mathematical variables which are derived from the experimental data, but which exhibit as little randomness as possible. We look for such variables in two examples by investigating how it is possible to arrive at a value of a physical quantity from intrinsically stochastic data. With the aid of standard probability calculus and elementary information theory, we are necessarily led to the quantum theoretical phases and state vectors as the first candidates for physical quantities.     

几何量子计算

实现可集成的量子计算的关键步骤是实现保真度足够高的一组普适量子逻辑门，最近几年发展的几何量子计算使用几何位相来实现量子逻辑门，其特点是利用几何位相的整体几何性质来避免某些局域的无规噪声的影响，从而实现较高保真度的量子门，文章先简要介绍常规几何量子逻辑门的概念，然后重点介绍最近提出的非常规几何量子计算：量子计算中使用的逻辑门的总位相既包含有几何位相，又包含有动力学位相，但它仅依赖于一些几何特征，而且，对于任意的量子位输入态，在量子门操作过程中积累的位相要么是零，要么是仅依赖几何特征的位相。     

Time asymmetries in classical and in nonclassical physics

A comparative study is made of the eigenvalue problems of electromagnetics and quantum mechanics, with special reference to the operations of spatial inversionP and time inversionT. Electromagnetics, which permits closer agreement with the dictates of relativity (when the latter is extended toP andT), exhibits characteristic differences with respect to quantum mechanics. An evaluation of these distinctions is presented against the backdrop of a choice between absolute scalar action and charge versus pseudoscalar action and charge.     

Novel quantum phases and mesoscopic physics in quantum gases

Among many notable jubilees brought by the year 2012, the one of a special importance for the community of statistical physicists was the 140th birth anniversary of Marian Smoluchowski (Maryan Ritter von Smolan Smoluchowski, 28.05.1872 - 5.09.1917), who was one of the pioneers of statistical physics and, on a larger scale, one of those who shaped modern physical science as a whole. The present issue of EPJ ST entitled From Brownian motion to self-avoiding walks and Lévy flights aims to reflect the evolution of Smoluchowski’s ideas in the field of statistics of interacting random and self-avoiding walks, stochastic equations for many-particle systems, physics of glass-forming and noise driven systems. Majority of papers in this issue were presented at the international conference in statistical physics that took place in Lviv (Ukraine) on July 3-6, 2012.     

Preparation and measurement in quantum physics

To honor Henry Margenau on the occasion of his 90th birthday, we attempt in this essay to integrate certain aspects of the physics, philosophy, and pedagogy of quantum mechanics in a manner very much inspired by Margenau's idealist scientific epistemology. Over half a century ago, Margenau was perhaps the first philosopher of science to recognize and elaborate upon the essential distinction between thepreparation of a quantum state and themeasurement of an observable associated with a system in that state; yet in contemporary quantum texts that distinction rarely receives adequate emphasis even though, as we demonstrate, it may be explicated through a series of simple illustrations.     

The borderline between classical physics and quantum theory: Towards a theory of the Planck's constant

A dynamical mechanism is discussed to account for the numerical value of the Planck's constant .Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.     

Superposition in quantum and classical mechanics

Using the mathematical notion of an entity to represent states in quantum and classical mechanics, we show that, in a strict sense, proper superpositions are possible in classical mechanics.Dedicated to the Memory of Charles H. Randall.     

Local quantum physics and models

The problem of characterizing a specific model within the frame of local quantum physics is addressed.Dedicated to Huzihiro Araki