Quantum Mechanics as a Principle Theory

I show how quantum mechanics, like the theory of relativity, can be understood as a ‘principle theory’ in Einstein's sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World.     

The physics and metaphysics of Tychistic Bohmian Mechanics

The paper takes up Bell's (1987) “Everett (?) theory” and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space – hence “Tychistic Bohmian Mechanics” (TBM). The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata for a Bohmian theory within the Primitive Ontology framework (for which we offer a metaphysically more perspicuous formulation than is customary). TBM's formalism is that of ordinary Bohmian Mechanics (BM), without the postulate of continuous particle trajectories and their deterministic dynamics. This “rump formalism” receives, however, a different interpretation. We defend TBM as an empirically adequate and coherent quantum theory. Objections voiced by Bell and Maudlin are rebutted. The “for all practical purposes”-classical, Everettian worlds (i.e. quasi-classical histories) exist sequentially in TBM (rather than simultaneously, as in the Everett interpretation). In a temporally coarse-grained sense, they quasi-persist. By contrast, the individual particles themselves cease to persist.     

在非线性系统中的微观粒子的特性和非线性量子力学理论(上)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用，微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此，必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化，说明了在线性作用和非线性场中微观粒子的性质是明显不同的，启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系，结合现代孤立子理论和超导与超流理论，我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系，并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性，它的运用范围以及它的重大意义。     

在非线性系统中的微观粒子的特性和非线性量子力学理论(下)

在非线性系统中由于存在着与粒子状态相关的非线性相互作用，微观粒子的状态和特征相对于线性系统而发生了很大变化。原有的线性型的量子力学理论不能很好地描述这些微观粒子的状态和特征。至此，必然要发展新的理论。本文研究了微观粒子在非线性作用下的运动特性和本性的变化，说明了在线性作用和非线性场中微观粒子的性质是明显不同的，启示我们必须建立微观粒子在非线性场中运动的新理论。接着我们研究了与微观量子效应迥然不同的宏观量子效应与非线性作用的孤立子运动的紧密关系，结合现代孤立子理论和超导与超流理论，我们首先提出了非线性量子力学的基本原理及在此基础上建立了系统、完整的非线性量子力学理论体系，并得到的一些新结论。最后我们还论证了这个理论的正确性和自洽性，它的运用范围以及它的重大意义。     

非线性量子力学的建立

笔者在长期研究工作的基础上,从提出非线性量子力学的基本原理出发,建立起了非线性量子力学理论,形成了完整的非线性量子力学的理论体系。从而把量子力学从线性领域推广和发展到非线性领域。在本文中笔者描述了建立这个非线性量子力学的物理背景,它的基本构思,研究的技术路线,产生的实际效果,与国际同类研究比较,本研究的创新和特点以及研究的重大意义。     

Two No-Go Theorems for Modal Interpretations of Quantum Mechanics

Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one system. The first theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems.     

Situated observation in Bohmian mechanics

Here we investigate what it might mean for a formulation of quantum mechanics to be empirically adequate. We begin by considering the measurement problem as an empirical problem and distinguishing between stronger and weaker varieties of empirical adequacy. A strongly adequate theory is one that explains the experiences of a physically situated observer. A formulation of quantum mechanics that provides such situated empirical adequacy also provides a particularly compelling response to the measurement problem. As a concrete example we consider how Bohmian mechanics explains the experience of a physically situated observer.     

The emergence and interpretation of probability in Bohmian mechanics

A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born's rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging the pros and cons of various positions, it defends particular answers to how the probabilities emerge from Bohmian mechanics and how they ought to be interpreted.     

Entanglement and Open Systems in Algebraic Quantum Field Theory

Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyse entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter's ability to perform operations on a field in one spacetime region that can disentangle its state from the state of the field in other spacelike-separated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum field theory, and yield a fresh perspective on the ways in which the theory differs conceptually from both standard non-relativistic quantum theory and classical relativistic field theory.     

Ergodic Theory, Interpretations of Probability and the Foundations of Statistical Mechanics

The traditional use of ergodic theory in the foundations of equilibrium statistical mechanics is that it provides a link between thermodynamic observables and microcanonical probabilities. First of all, the ergodic theorem demonstrates the equality of microcanonical phase averages and infinite time averages (albeit for a special class of systems, and up to a measure zero set of exceptions). Secondly, one argues that actual measurements of thermodynamic quantities yield time averaged quantities, since measurements take a long time. The combination of these two points is held to be an explanation why calculating microcanonical phase averages is a successful algorithm for predicting the values of thermodynamic observables. It is also well known that this account is problematic.This survey intends to show that ergodic theory nevertheless may have important roles to play, and it explores three other uses of ergodic theory. Particular attention is paid, firstly, to the relevance of specific interpretations of probability, and secondly, to the way in which the concern with systems in thermal equilibrium is translated into probabilistic language. With respect to the latter point, it is argued that equilibrium should not be represented as a stationary probability distribution as is standardly done; instead, a weaker definition is presented.     

Quantum sidelights on The Material Theory of Induction

John Norton's The Material Theory of Induction bristles with fresh insights and provocative ideas that provide a much needed stimulus to a stodgy if not moribund field. I use quantum mechanics (QM) as a medium for exploring some of these ideas. First, I note that QM offers more predictability than Newtonian mechanics for the Norton dome and other cases where classical determinism falters. But this ability of QM to partially cure the ills of classical determinism depends on facts about the quantum Hamiltonian operator that vary from case to case, providing an illustration of Norton's theme of the importance of contingent facts for inductive reasoning. Second, I agree with Norton that Bayesianism as developed for classical probability theory does not constitute a universal inference machine, and I use QM to explain the sense in which this is so. But at the same time I defend a brand of quantum Bayesianism as providing an illuminating account of how physicists' reasoning about quantum events. Third, I argue that if the probabilities induced by quantum states are regarded as objective chances then there are strong reasons to think that fair infinite lotteries are impossible in a quantum world.     

The Early Axiomatizations of Quantum Mechanics: Jordan, von Neumann and the Continuation of Hilbert's Program

Hilbert's axiomatization program of physical theories met an interesting challenge when it confronted the rise of quantum mechanics in the mid-twenties. The novelty of the mathematical apparatus of the then newly born theory was to be matched only by its substantial lack of any definite physical interpretation. The early attempts at axiomatization, which are described here, reflect all the difficulty of the task faced by Jordan, Hilbert, von Neumann and others. The role of von Neumann is examined in considerable detail as he can be viewed here as the most outstanding of Hilbert's heirs. Von Neumann, especially in his work devoted to the proof of the impossibility of hidden variables, not only continued Hilbert's program but pushed it to its very limits, blending axiomatic rigor and interpretative commitment. (Received September 9, 1999)     

Why were Matrix Mechanics and Wave Mechanics considered equivalent?

A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger's 1926 proof, a myth. Schrödinger supposedly failed to prove isomorphism, or even a weaker equivalence (“Schrödinger-equivalence”) of the mathematical structures of the two theories; developments in the early 1930s, especially the work of mathematician von Neumann provided sound proof of mathematical equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent on this equivalence, was deemed a myth as well.In response, I argue that Schrödinger's proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism or a weaker mathematical equivalence. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr's Model that was discovered and published by Schrödinger in his first and second communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics are satisfied by assigning the auxiliary role to eigenfunctions in the derivation of matrices (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of both isomorphism and Schrödinger-equivalence of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr's atom. And although the mathematical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr's complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics.I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it.     

Mechanics without mechanisms

At the time of Heinrich Hertz's premature death in 1894, he was regarded as one of the leading scientists of his generation. However, the posthumous publication of his treatise in the foundations of physics, Principles of Mechanics, presents a curious historical situation. Although Hertz's book was widely praised and admired, it was also met with a general sense of dissatisfaction. Almost all of Hertz's contemporaries criticized Principles for the lack of any plausible way to construct a mechanism from the “hidden masses” that are particularly characteristic of Hertz's framework. This issue seemed especially glaring given the expectation that Hertz's work might lead to a model of the underlying workings of the ether.In this paper I seek an explanation for why Hertz seemed so unperturbed by the difficulties of constructing such a mechanism. In arriving at this explanation, I explore how the development of Hertz's image-theory of representation framed the project of Principles. The image-theory brings with it an austere view of the “essential content” of mechanics, only requiring a kind of structural isomorphism between symbolic representations and target phenomena. I argue that bringing this into view makes clear why Hertz felt no need to work out the kinds of mechanisms that many of his readers looked for. Furthermore, I argue that a crucial role of Hertz's hypothesis of hidden masses has been widely overlooked. Far from acting as a proposal for the underlying structure of the ether, I show that Hertz's hypothesis ruled out knowledge of such underlying structure.     

基于散体动力学理论的掘进机星轮装载机构研究

为了解决掘进机星轮对物料推力过大,物料因惯性而不随轮齿同步运动的问题,运用散体动力学理论分析掘进机装载机构的星轮轮齿推移物料的运动过程.建立力学和数学模型,推导出掘进机星轮机构装载过程中保持物料稳定运行的推力计算公式和轮齿许用加速度范围;并用计算机模拟轮齿推力与轮齿参数的关系,提出了轮齿推移物料的动力学模型和方程,为星轮装载机构的设计和研究提供了参考依据.     

Quantum propensities

This paper reviews four attempts throughout the history of quantum mechanics to explicitly employ dispositional notions in order to solve the quantum paradoxes, namely: Margenau's latencies, Heisenberg's potentialities, Maxwell's propensitons, and the recent selective propensities interpretation of quantum mechanics. Difficulties and challenges are raised for all of them, and it is concluded that the selective propensities approach nicely encompasses the virtues of its predecessors. Finally, some strategies are discussed for reading similar dispositional notions into two other well-known interpretations of quantum mechanics, namely the GRW interpretation and Bohmian mechanics.     

微纳米尺度的力学行为

本文展述微纳米尺度力学行为的若干新进展：(1)微纳米尺度的断裂行为一侧重于从离散位错区到无位错区再到原子运动混沌区的纳观断裂力学描述；(2)微纳米尺度的塑性行为—探讨位错机制被抑制后的塑性变形机制；(3)纳米晶体中的扩散一以不均匀晶界和三晶交网络的扩散为主导：(4)微纳米尺度的接触与摩擦一讨论由于接触区域小而引起的反常行为；(5)微纳米尺度的碰撞一介绍新发现的超音速激波的机理；(6)跨层次算法一从原子／连续介质的可透越区模型到握手区连结的物质点／分子动力学方法。