The implicate order and Prigogine's notions of irreversibility

In this paper, a very close relationship between Prigogine's notions of irreversibility and the implicate order is brought out. Certain of Prigogine's basic assumptions with regard to irreversible processes are also shown to be the equivalent of the introduction of nilpotent operators in the algebra underlying the implicate order.     

The implicate order,algebras, and the spinor

We review some of the essential novel ideas introduced by Bohm through the implicate order and indicate how they can be given mathematical expression in terms of an algebra. We also show how some of the features that are needed in the implicate order were anticipated in the work of Grassmann, Hamilton, and Clifford. By developing these ideas further we are able to show how the spinor itself, when viewed as a geometric object within a geometric algebra, can be given a meaning which transcends the notion of the usual metric geometry in the sense that it must be regarded as an element of a broader and more general pregeometry.     

The transitions among classical mechanics,quantum mechanics,and stochastic quantum mechanics

Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given.     

Semiclassical quantum mechanics. III. The large order asymptotics and more general states

We solve the time dependent Schrödinger Equation $\text{i?(}\text{?ψ}\text{?t}\text{) = ?(?}{}^2\text{/2m) Δψ + Vψ}$ modulo errors which have L² norms on the order of $\text{?}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for arbitrarily large l. The initial conditions we consider are fairly general states whose position and momentum uncertainties are proportional to $\text{?}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$.     

N = 4 supersymmetric quantum mechanics and its large order behaviour

A model of N = 4 supersymmetric quantum mechanics is shown to have a perturbative expansion for which the large order behaviour is - (3/2)ⁿn!(9/π + 5/n + …). In the space of the coupling constants the supersymmetric case is found to be the dividing point between two different types of large order behaviour. In this way the large order behaviour of supersymmetric theories is special.     

邮票上的物理学史45——量子力学的建立

量子力学的兴起和发展 ,是 2 0世纪物理学史上最大的事件 .量子力学是研究原子、分子、凝聚态以至原子核和粒子的基础理论 ,是从 1 9世纪末以来对微观世界进行的越来越深入的探索的总结 .量子力学的兴起是由不同的物理学家、在不同的地方、从不同的角度、按不同的思路开始的 .其发展过程有两条主要线索 :德国物理学家海森伯 1 92 5年建立的矩阵力学是玻尔的对应原理的嫡传后裔 ;而奥地利物理学家薛定谔 1 92 6年建立的波动力学则是为了回答“德布罗意波遵循什么样的波动方程”这个问题 .薛定谔随即论证了矩阵力学和波动力学的等价性 .英国物…     

中国物理学会2002年学术活动计划

序号会议名称内容日期人数地点联系单位 (人 )邮编1静电专业委员会第十届学术报告会 学术交流 2月 70海口 海口市海南大学理工学院熊建平Ｔｅｌ:0 898- 6 6 2 5 8112 - 2 412 5 70 2 2 82 第五届中美大 (中 )学生科学素质现状与培养对策研究研讨会 教学研讨 3月 5 0 江苏太仓南京东南大学物理系恽　瑛Ｔｅｌ:0 2 5 - 3792 870 - 80 0 82 10 0 963全国青年同步辐射应用研讨会学术交流 3月 40上海 复旦大学应用表面实验室蒋最敏Ｔｅｌ:0 2 1- 6 5 6 435 2 2 2 0 0 4334“全国大学物理教学优秀论文奖”评选颁奖大会暨《大学物理》创刊2 0周年学…     

The foundations of quantum mechanics

Starting from a set of assumptions mainly of an operational or experimentally based nature, a derivation of quantum mechanics is presented, with the aim of clarifying the essential features of the theory and their interpretation. Various properties of quantum mechanics such as the addition of amplitudes, the calculation of probabilities, de Broglie's equations, and energy-momentum conservation are derived from first principles. It is investigated whether quantum amplitudes may be constructed from quantities of higher order than complex numbers. Measurable physical quantitics, as traditionally understood, are seen to play a role distinct from and supplementary to the behavior of the quantum amplitudes themselves. This is related to two distinct aspects of the nature of time in the context of quantum mechanics.     

The conceptual and the anecdotal history of quantum mechanics

The aim of this paper is to combine the intellectual and the psychosocial aspects. blurring the distinction between the conceptual and the anecdotal history of quantum mechanics. The full realization of the importance of such anecdotal factors leads to the revision of our understanding of the conceptual development itself. The paper concludes with the suggestion that a major part of numerous inconsistencies in the Copenhagen interpretation of quantum physics are of a psychosocial origin.     

The Ithaca interpretation of quantum mechanics

I list several strong requirements for what I would consider a sensible interpretation of quantum mechanics and discuss two simple recent theorems which have important implications for such an interpretation. My talk will not clear everything up; indeed, you may conclude that it has not cleared anything up. But I hope it will provide a different perspective from which to view some old and vexing puzzles (or, if you believe nothing needs to be cleared up, some ancient verities.)     

The quantum mechanics of affine variables

We study the wrapping of N-type IIB Dp-branes on a compact Riemann surface Σ in genus g>1 by means of the Sen–Witten construction, as a superposition of N′-type IIB Dp′-brane/antibrane pairs, with p′>p. A background Neveu–Schwarz field B deforms the commutative C-algebra of functions on Σ to a non-commutative C-algebra. Our construction provides an explicit example of the N′→∞ limit advocated by Bouwknegt-Mathai and Witten in order to deal with twisted K-theory. We provide the necessary elements to formulate M(atrix) theory on this new C-algebra, by explicitly constructing a family of projective C-modules admitting constant-curvature connections. This allows us to define the g>1 analogue of the BPS spectrum of states in g=1, by means of Donaldson’s formulation of the Narasimhan–Seshadri theorem.     

The zitterbewegung interpretation of quantum mechanics

Thezitterbewegung is a local circulatory motion of the electron presumed to be the basis of the electron spin and magnetic moment. A reformulation of the Dirac theory shows that thezitterbewegung need not be attributed to interference between positive and negative energy states as originally proposed by Schroedinger. Rather, it provides a physical interpretation for the complex phase factor in the Dirac wave function generally. Moreover, it extends to a coherent physical interpretation of the entire Dirac theory, and it implies azitterbewegung interpretation for the Schroedinger theory as well.     

The QCD Hamiltonian and nonlinear quantum mechanics

We study the canonical quantization of SU(N) gauge theory in linear, noncovariant gauges. The canonical formalism is first discussed for the classical theory, with special attention to the features involving nonlinearity and the gauge degrees of freedom. The transition to the quantum theory is then performed for an arbitrary linear gauge, using the covariant quantization rules of nonlinear quantum mechanics. When the quantum Hamiltonian is written in the Weyl-ordered form appropriate for the application of the usual Dyson-Wick perturbative techniques, additional ordering terms appear with respects to the classical Hamiltonian. We discuss the relation of our results to those of previous authors, and the relevance of the ordering terms in field theory.     

The stochastic quantum mechanics approach to the unification of relativity and quantum theory

The stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed. It leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents. The resulting particle propagators are used in the formulation of stochastic geometries underlying a concept of quantum spacetime that is operationally based on stochastically extended quantum test particles. The epistemological implications of the intrinsic stochasticity of such quantum spacetime frameworks for microcausality, the EPR paradox, etc., are discussed.Supported in part by NSERC Grant A5208.     

The large numbers hypothesis and quantum mechanics

In this paper, the suggested similarity between micro and macrocosmos is extended to quantum behavior, postulating that quantum mechanics, like general relativity and classical electrodynamics, is invariant under discrete scale transformations. This hypothesis leads to a large scale quantization of angular momenta. Using the scale factor Λ ~ 10³⁸, the corresponding quantum of action, obtained by scaling the Planck constant, is close to the Kerr limit for the spin of the universe - when this is considered as a huge rotating black hole - and to the spin of Gödel’s universe, solution of Einstein equations of gravitation. Besides, we suggest the existence of another, intermediate, scale invariance, with scale factor λ ~ 10¹⁹. With this factor we obtain, from Fermi’s scale, the values for the gravitational radius and for the collapse proper time of a typical black hole, besides the Kerr limit value for its spin. It is shown that the mass-spin relations implied by the two referred scale transformations are in accordance with Muradian’s Regge-like relations for galaxy clusters and stars. Impressive results are derived when we use a λ-scaled quantum approach to calculate the mean radii of planetary orbits in solar system. Finally, a possible explanation for the observed quantization of galactic redshifts is suggested, based on the large scale quantization conjecture.     

Quaternionic quantum mechanics is consistent with complex quantum mechanics

Quaternionic quantum mechanics is investigated in the light of the great success of complex quantum mechanics. It is shown that to reproduce the results of complex quantum mechanics, quaternionic quantum mechanics must contain complex quantum mechanics.     

Modalities and quantum mechanics

Three approaches concerning the usage of modalities in the language of quantum mechanics were considered; Mittelstaedt and I built up a dialog semantics for modalities on a metalinguistic level, and a calculus of quantum modal logic is known that is complete and sound with respect to this dialogic semantics. Van Fraassen replaced the usual interpretation of quantum mechanics (with the projection postulate) by his modal interpretation based on a modal object language. Dalla Chiara translated a nonmodal object language for quantum mechanics and the appropriate quantum logic into a modal language. Specifically we are interested in the similarities and the differences of these three approaches.