Randomness in Classical Mechanics and?Quantum Mechanics

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in the classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations: Δq>0 and Δp>0, i.e. the uncertainty (errors of observation) in the determination of coordinate and momentum is always positive (non zero).     

Quantum Mechanics and Information Security

After a short review of the background and main theoretical results of quantum key distribution, I shall then introduce the existing problems for secure QKD in practice. Ishall then forus on the security problem of QKD with an imperfect source, in particular, the recently developed theory of the decoy-state method which can help to implement the secure QKD without a single-photon source. Basically, if the single-photon source is replaced by the weak coherent light, the protocol can betotally insecure due to the photon-number-splitting attack given a lossy channel. However, if werandomly change the intensity of each pulses among a few different values （ e. g. , 3 ） we can thenal- most exactly verify the fraction of bits generated by those single-photonpulses. This, together with the prior art theo- retical result, can raise the secure distance of QKD with currently existing technologies from less than 20 kms to more than 120 kms. Experimental implementation of decoy-state QKD have been done.     

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics—I

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.     

Fracture Criterion for Fracture Mechanics of Magnets

The applicability and limitation of some fracture criteria in the fracture mechanics of magnets are studied. It is shown that the magnetic field intensity factor can be used as a fracture criterion when the crack in a magnet is only affected by a magnetic field. For some magnetostrictive materials in which the components of magnetostriction strain do not satisfy the compatibility equation of deformation, the stress intensity factor can no longer be effectively applicable as a fracture criterion when the crack in a magnet is affected by a magnetic field and mechanical loads simultaneously.     

Is Indistinguishability in Quantum Mechanics Conventional?

Darrin Belousek has argued that the indistinguishability of quantum particles is conventional in the Duhemian–Einsteinian sense, in part by critially examining prior arguments given by Redhead and Teller. Belousek's discussion provides a useful occasion to clarify some of those arguments, acknowledge respects in which they were misleading, and comment on how they can be strengthened. We also comment briefly on the relevant sense of conventional.     

General Noncommuting Curvilinear Coordinates and Fluid Mechanics

We show that restricting the states of a charged particle to the lowest Landau level introduces noncommutativity between general curvilinear coordinate operators. The Cartesian, circular cylindrical and spherical polar coordinates are three special cases of our quite general method. The connection between U（1） gauge fields defined on a general noncommuting curvilinear coordinates and fluid mechanics is explained. We also recognize the Seiberg-Witten map from general noncommuting to commuting variables as the quantum correspondence of the Lagrange-to-Euler map in fluid mechanics.     

Path Integral Formulation for Chern-Simons Quantum Mechanics

Chern-Simons quantum mechanics is studied by using the path integral formulation. We find that the model can be decomposed into two independent oscillators when a set of new coordinate is chosen. The propagator is constructed in this new set of coordinate and the spectra is read off directly from it. The spectra will be divergent when the mass of the particle tends to zero. In order to get a physical result, one must regularize the spectra properly. We afford a new scheme of regularization. Interestingly, our scheme shows that the regularization we proposed amounts to erase one of the oscillators in the new set of coordinate. Physical interpretations for the regularization are given and some ambiguities in the literatures are clarified.     

Niels Bohr’s Generalization of Classical Mechanics

We clarify Bohrs interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible.     

Is Minkowski Space-Time Compatible with Quantum Mechanics?

In quantum relativistic Hamiltonian dynamics, the time evolution of interacting particles is described by the Hamiltonian with an interaction-dependent term (potential energy). Boost operators are responsible for (Lorentz) transformations of observables between different moving inertial frames of reference. Relativistic invariance requires that interaction-dependent terms (potential boosts) are present also in the boost operators and therefore Lorentz transformations depend on the interaction acting in the system. This fact is ignored in special relativity, which postulates the universality of Lorentz transformations and their independence of interactions. Taking into account potential boosts in Lorentz transformations allows us to resolve the no-interaction paradox formulated by Currie, Jordan, and Sudarshan [Rev. Mod. Phys. 35, 350 (1963)] and to predict a number of potentially observable effects contradicting special relativity. In particular, we demonstrate that the longitudinal electric field (Coulomb potential) of a moving charge propagates instantaneously. We show that this effect as well as superluminal spreading of localized particle states is in full agreement with causality in all inertial frames of reference. Formulas relating time and position of events in interacting systems reduce to the usual Lorentz transformations only in the classical limit (0) and for weak interactions. Therefore, the concept of Minkowski space-time is just an approximation which should be avoided in rigorous theoretical constructions.     

What is Quantum Mechanics? A Minimal Formulation

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called “microscopic theory”, applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen–Specker–Bell theorem and Gleason’s theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.     

On Schrödinger-Hermite Operators in Lattice Quantum Mechanics

Starting from the q-Heisenberg algebra, we derive from a few abstract principles a broad class of Schrödinger operators in lattice quantum mechanics for which one can determine explicit eigenvalues and spectral properties. This happens by algebras of creators and annihilators. Generalized inhomogeneous q-discrete Hermite polynomials occur via their recurrence relations. Within this framework we obtain the special case of an interesting result, proved by Christian Berg in a much larger ge-nerality: The orthogonality measure for q-discrete Hermite polynomials of type II is not uniquely determined on q-exponential lattices.     

Quantum Mechanics Helps in Learning for More Intelligent Robots

A learning algorithm based on the state superposition principle is presented. The theoretical analysis shows that the needed fundamental transformations to realize this algorithm are the same as those needed in the Grover algorithm and are within current state-of-the-art technology. The simulated experiment shows that the quantum learning algorithm can help robots to learn faster and to become more intelligent.     

Is the Epistemic View of Quantum Mechanics Incomplete?

One of the most tantalizing questions about the interpretation of Quantum Theory is the objective vs. subjective meaning of quantum states. Here, by focusing on a typical EPR experiment upon which a selection procedure is performed on one side, we will confront the fully epistemic view of quantum states with its results. Our statement is that such a view cannot be considered complete, although the opposite attitude would also pose well-known problems of interpretation.This paper is dedicated to Prof. Franco Selleri on the occasion of his 70th birthday     

Fundamental Equations of Quantum Mechanics in Time-Varying Domain

Fundamental equations of quantum mechanics in time-varying domain are presented. The used method consists in transforming the variable domain into a fixed domain. The transformation has to be covariant in relation to the wavefunction. The new fundamental equations turn out to be a generalization of the classical equations established in a Newtonian space-time. When the time-varying domain becomes stationary, we find again the fundamental equations of the classical quantum mechanics.     

Time Symmetric Quantum Mechanics and Causal Classical Physics ?

A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual “near future” macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.     

The Geometry of¶(Super) Conformal Quantum Mechanics

N-particle quantum mechanics described by a sigma model with an N-dimensional target space with torsion is considered. It is shown that an SL(2,ℝ) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector D ^a δ _a whose associated one-form D _a dX ^a is closed. Further, the SL(2,ℝ) can always be extended to Osp(1|2) superconformal symmetry, with a suitable choice of torsion, by the addition of N real fermions. Extension to SU(1,1|1) requires a complex structure I and a holomorphic U(1) isometry D ^a I _a ^b δ _b . Conditions for extension to the superconformal group D(2,1;α), which involve a triplet of complex structures and SU(2)×SU(2) isometries, are derived. Examples are given. Received: 3 September 1999 / Accepted: 30 January 2000     

Unreasonable and “Unreasonable” in Quantum Mechanics?

The particles of quantum mechanics (QM) are discrete undulatory entities which are described in terms of the complex state vectors of the theory in full agreement with experiment. The wave-particle paradox stems from the fact that undulation and discreteness are inconsistent within the classical theory which was historically the point of departure for the canonical foundation. The author describes his prolonged efforts of anchoring the state vector of QM in experiment rather in obsolete theory.     

Can Special Relativity Be Derived from Galilean Mechanics Alone?

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies’ motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws’ violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.