Facts,Values and Quanta

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.     

Classical Mechanics and Quantum Mechanics

The Newton equation of motion is derived from quantum mechanics.     

量子理论的诞生和发展——从量子论到量子力学

简要叙述 ,从普朗克 190 0年首次对电磁波提出量子假设到狄拉克 192 8年对电子提出相对论性方程这段时间内 ,量子理论特别是量子力学诞生和发展的演化过程 .内容分黑体辐射和量子假设 ;老量子论的兴与衰 ;第一条通向量子力学的路———对应原理 ,包括矩阵力学 ,狄拉克的q -数 ;第二条通向量子力学的路———波粒二象性 ,波动力学 ;以及量子力学初步成长 (指 192 7年的表象理论、不确定关系、氦原子及氢分子和 192 8年的狄拉克相对性电子理论 )五个部分 .     

纪念普郎克发现量子论100周年

简要地回顾了普郎克发现量子论和由量子论发展为量子力学的简明历程,以及量子力学对科学和人类社会的贡献,讨论了科学创新的评价标准问题,指出量子力学应得到最高的评价,亦即是美学评价标准、学术评价标准和实践评价标准的统一,还讨论了江泽民主席所提出的“三个代表”的理论,指出这一理论应成为评价一切科学工作的根本标准,也是评价我国各方面工作的根本标准,指出我国科学工作除了要集中力量于解决足以影响国民经济或国防建设的全局的8－10个重大科学技术问题外,还要集中一定的力量于看起来是“无用”的基础研究,当前正在发展中的物理学的第四次大突破,就是值得关注的问题之一。     

A Continuous Transition Between Quantum and Classical Mechanics. I

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of mechanics which provides a continuous transition between quantum and classical mechanics via environment-induced decoherence.     

Maximally causal quantum mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics     

q-Deformation of algebraic structures of quantum and classical mechanics

There exists a coassociative and cocommutative coproduct in the linear space spanned by the two algebraic products of a classical Hamilton algebra (the algebraic structure underlying classical mechanics [1]). The transition from classical to quantum Hamilton algebra (the algebraic structure underlying quantum mechanics) is anħ-deformation which preserves not only the Lie property of the classical Hamilton algebra but also the coassociativity and cocommutativity of the above coproduct. By explicit construction we obtain the algebraic structures of theq-deformed Hamilton algebras which preserve the said properties of the coproduct. Some algorithms of these structures are obtained and their implications discussed. The problem of consistency of time evolution with theq-deformed kinematical structure is discussed. A characteristic distinction between the parametersħ andq is brought out to stress the fact thatq cannot be regarded as a fundamental constant.     

Quantum Machine and Semantic Realism Approach: a Unified Model

The Geneva–Brussels approach to quantum mechanics (QM) and the semantic realism (SR) nonstandard interpretation of QM exhibit some common features and some deep conceptual differences. We discuss in this paper two elementary models provided in the two approaches as intuitive supports to general reasonings and as a proof of consistency of general assumptions, and show that Aerts’ quantum machine can be embodied into a macroscopic version of the microscopic SR model, overcoming the seeming incompatibility between the two models. This result provides some hints for the construction of a unified perspective in which the two approaches can be properly placed.     

Foundations of Quantum Mechanics: The Connection Between QM and the Central Limit Theorem

In this paper we unravel the connection between the quantum mechanical formalism and the Central limit theorem (CLT). We proceed to connect the results coming from this theorem with the derivations of the Schrödinger equation from the Liouville equation, presented by ourselves in other papers. In those papers we had used the concept of an infinitesimal parameter x that raised some controversy. The status of this infinitesimal parameter is then elucidated in the framework of the CLT. Finally, we use the formal apparatus developed in our previous papers and the results of the present one to advance an alternative objective interpretation of quantum mechanics in which its relations with the classical framework are made explicit. The relations between our approach and those using the Wigner–Moyal transformation are also addressed.     

A Continuous Transition Between Quantum and Classical Mechanics. II

Examples are worked out using a new equation proposed in the previous paper to show that it has new physical predictions for mesoscopic systems.     

Has Quantum Field Theory the Standard Transition from Poisson Brackets?

This paper is devoted to the problem of the validity of claims that commutation rules of quantum field theories have its origin in Poisson brackets of classical mechanics.     

Mobility and non-separability

A mobility phenomenon is typical for a large class of non-linear evolutions. It is shown that the mobility can be responsible for a malignant form of quantum mechanical non separability of two correlated systems. An explicit example based on Weinberg's non linear quantum mechanics is considered. We show that in such a theory a transfer of information without a transfer of energy is possible and discuss physical roots of this phenomenon. In Polchinski's approach this effect is not present.1 Permanent address: Laboratory of Dielectrics and Organic Semiconductors, Technical University of Gdask, Gdask, Poland.     

Dephasing in an atom

When an atom in vacuum is near the surface of a dielectric the energy of a fluctuating electromagnetic field depends on a distance between them resulting, as known, in a force called van der Waals. Besides this fluctuation phenomenon there is one associated with formation of a mean electric field, which is equivalent to an order parameter. In this case atomic electrons are localized within atomic distances close to the atom and the total ground state energy is larger, compared to the bare atom, due to the polarization of the dielectric and the creation of a mean electric field locally distributed in the dielectric. The phenomenon differs from the usual ferroelectricity and has a pure quantum origin. This results in (i) an unusual atom-dielectric force different from the van der Waals one and (ii) an anomalous Lamb shift in the atom.     

曲面上的动量和动能算符

对约束在曲面上粒子运动的描述可以在内部坐标即曲面局部坐标下进行,也可以在外部坐标即在笛卡尔坐标下进行.在量子力学中,动量和动能算符的表示在这两种描述中各有不同,前者的动量算符仅包含内禀几何量,后者的动量算符包含了曲面的平均曲率.考虑到算符次序问题,动能算符对动量算符的依赖关系也不同,前者的依赖关系仅发现存在一种,后者的依赖关系已经发现有两种. 关键词： 量子力学 微分几何     

力学综合课程建设的研究和实践

简述了我校物理系进行力学综合课程建设的基本思想和措施，以及建立将普通物理力学、理论力学和量子力学基础综合成一门课程的新的教学内容结构体系的具体做法．这样做，不但大大减少了重复内容和课时。而且有助于学生从整体上把握力学理论的基本框架，有助于培养学生的综合研究能力和创新能力。     

Entanglement of Formation of an Arbitrary State of Two Rebits

We consider entanglement for quantum states defined in vector spaces over the real numbers. Such real entanglement is different from entanglement in standard quantum mechanics over the complex numbers. The differences provide insight into the nature of entanglement in standard quantum theory. Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. We give a contrasting formula for the entanglement of formation of an arbitrary state of two rebits, a rebit being a system whose Hilbert space is a 2-dimensional real vector space.     

曲面上的动量和动能算符

对约束在曲面上粒子运动的描述可以在内部坐标即曲面局部坐标下进行，也可以在外部坐标即在笛卡尔坐标下进行.在量子力学中，动量和动能算符的表示在这两种描述中各有不同，前者的动量算符仅包含内禀几何量，后者的动量算符包含了曲面的平均曲率.考虑到算符次序问题，动能算符对动量算符的依赖关系也不同，前者的依赖关系仅发现存在一种，后者的依赖关系已经发现有两种.