Showing papers in "Studies in History and Philosophy of Modern Physics in 1997"

The Equivalence Myth of Quantum Mechanics-Part I

Abstract: The author endeavours to show two things: first, that Schrodingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrodinger in 1926, is not foolproof; and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent. That they were is the Equivalence Myth. In order to make the theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrodingers equivalence paper. Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The paper is self-contained and presupposes only basic knowledge of quantum mechanics. For reasons of length, the paper is published in two parts; Part I appeared in the previous issue of this journal. Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims; so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments.

Superconductivity and structures: revisiting the London account

Abstract: Cartwright and her collaborators have elaborated a provocative view of science which emphasises the independence from theory ‘in methods and aims’ of phenomenological model building. This thesis has been supported in a recent paper by an analysis of the London and London model of superconductivity. In the present work we begin with a critique of Cartwright's account of the relationship between theoretical and phenomenological models before elaborating an alternative picture within the framework of the partial structures version of the semantic approach to theories. Drawing on the recent histories of superconductivity by Dahl and Gavroglu, together with the original works by London and London and by F. London separately, and taking due consideration of the heuristic aspects, we argue that the historical details fail to support Cartwright et al. 's claims but that they fit comfortably within the partial structures framework.

From physics to metaphysics

Abstract: First, let me begin by apologizing for the inevitable errors one brings into any discussion when the subjects are as deep and far-reaching as physics and metaphysics. I would be out of my league even if I were an expert in both (I am in neither). My great joy in life is theology and its practical implications to everyday people, yet even in this field I am no great scholar – just a preacher. This work is an attempt to deal, in an “everyday way,” with an issue that confronts all Christians at one time or another; science, of which physics is a part, and metaphysics, of which religion is a part. Thus, for those who know more than I in either, especially physics, I ask for longsuffering and a touch of sympathy. My request is to overlook any errors (which if there are errors, I believe they are inconsequence to the overall argument), to see ideas of consequence as one thinks of the truths of physics, and the possibility of a “Physik,” or physics-maker, God.

A Probabilistic Foundation of Elementary Particle Statistics. Part II

Abstract: The long history of ergodic and quasi-ergodic hypotheses provides the best example of the attempt to supply non-probabilistic justifications for the use of statistical mechanics in describing mechanical systems. In this paper we reverse the terms of the problem. We aim to show that accepting a probabilistic foundation of elementary particle statistics dispenses with the need to resort to ambiguous non-probabilistic notions like that of (in)distinguishability. In the quantum case, starting from suitable probability conditions, it is possible to deduce elementary particle statistics in a unified way. Following our approach Maxwell-Boltzmann statistics can also be deduced, and this deduction clarifies its status. Thus our primary aim in this paper is to give a mathematically rigorous deduction of the probability of a state with given energy for a perfect gas in statistical equilibrium; that is, a deduction of the equilibrium distribution for a perfect gas. A crucial step in this deduction is the statement of a unified statistical theory based on clearly formulated probability conditions from which the particle statistics follows. We believe that such a deduction represents an important improvement in elementary particle statistics, and a step towards a probabilistic foundation of statistical mechanics. In this Part I we first present some history: we recall some results of Boltzmann and Brillouin that go in the direction we will follow. Then we present a number of probability results we shall use in Part II. Finally, we state a notion of entropy referring to probability distributions, and give a natural solution to Gibbs' paradox.

A star in the Minkowskian sky: Anisotropic special relativity

Abstract: [I]f we want to learn about anything really deep, we have to study it not in its ‘normal’, regular, usual form, but in its critical state, in fever, in passion. If you want to know the normal healthy body, study it when it is abnormal, when it is ill. If you want to know functions, study their singularities. If you want to know ordinary polyhedra, study their lunatic fringe. This is how one can carry mathematical analysis into the very heart of the subject.

Conceptions of space-time: Problems and possible solutions

Abstract: In this paper, the implications of quantum mechanics and general relativity for the understanding of space-time are discussed. There are strong indications that Classical notions of space-time are inadequate as a basis for these theories. A number of proposals for non-Classical space-time structures are reviewed. Bohm's framework for the description of natural phenomena based on the notion of process is described. Here, space-time is no longer taken as basic; rather it is a derived feature of the underlying process. This approach opens up the possibility of investigating space-time problems from a new angle, where the nature of space-time is determined by the system under study.

Poincarés philosophy of geometry, or does geometric conventionalism deserve its name?

Abstract: Two main aims are pursued in this paper. The first is to show that, in mathematical geometry, Poincare was a conventionalist who rejected all forms of synthetic a priori geometric intuition. He moreover followed a unified heuristic based on the study of certain groups of Mobius transformations. This method was informed by his work on the theory of Fuchsian functions; it yielded two models of hyperbolic geometry: the disk model and the Poincare half-plane, which are connected by a Mobius transformation. From these group-theoretic considerations Poincare derived an expression for the Riemannian distance. I secondly defend the thesis that, in physical geometry, Poincare was a structural realist whose so-called conventionalism was epistemological, not ontological. Here he started directly from a Riemannian metric together with an associated universal field. He adopted a realist attitude towards both the field and that geometry which is most coherently integrated into some highly unified and empirically confirmed hypothesis. More generally, he looked upon the degree of unity of any system as an index of its verisimilitude. I finally show that, by Einsteins own admission, GTR is compatible with Poincares epistemological theses.

Gauge theory, anomalies and global geometry: The interplay of physics and mathematics

Abstract: Summary Figure 5 diagrams the evolution of the anomaly from its origins as the triangle diagram’s anomalous contribution to neutral pion decay to its realisation as a Chern character of a line bundle over an infinite-dimensional manifold. The elegance and completeness of the latter picture inspired physicists to tackle the formidable task of gaining control over the machinery of global differential geometry. 6 s The unintegrated Adler-Bell-Jackiw anomaly appears as the second Chern character of the vector bundle associated to Q. 6 Physicists were of course not unanimous in this. L. Alvarez-Gaume and P. Ginsparg (1984) extend Fujikawa’s fermionic integral approach to treat the Bardeen anomaly, which they interpret directly in terms of the cohomology of the space of gauge transformations, without referring to an underlying geometric picture, Though they are well-versed in the work of Atiyah and Singer, and adopt the language of differential forms, their explicit aim is to by-pass the families index

The conventionality of simultaneity in the light of the spinor representation of the lorentz group

Abstract: The assessment of the conventionality of simultaneity has commonly taken place so far within the traditional formulation of the special theory of relativity. The e-synchrony transformation is presented within this context in a sufficiently general manner that explores the connection of spatiotemporal measures to the choice of an e-simultaneity relation. Subsequently to the recent work of Zangari, the feasibility of the latter is then investigated in terms of the two-component spinor formulation of special relativity. This is motivated by the fact that the spinor formulation provides the most fundamental expression of a spacetime theory that is consistent with the principle of special relativity. It is shown within this context that the transformation elements of the spinor group (unlike its Lorentz counterparts) prevent the groups representations being extended to a representation of the e-class of non-standard synchrony transformations in four-dimensional space. The underlying reasons are traced down and discussed at length, whereas the compatibility of this finding with a general version of the principle of general relativity that is applicable to both tensor and spinor quantities is also demonstrated. It is finally established that the standard simultaneity relations far from constituting just a sensible choice in a range of conventional possibilities, is uniquely and objectively singled out by the properties of a spinor structure in Minkowski spacetime. The desirability of such a structure is anticipated by its fundamental status.

Dummett vs Bell on quantum mechanics

Abstract: The purpose of this paper is to cast doubt on the common allegation that quantum mechanics (QM) is incompatible with realism. I argue that the results usually considered inimical to realism, notably the violation of Bells inequality, in fact play the opposite role—they support realism. The argument is not intended, however, to demonstrate realism or refute its alternatives as general metaphysical positions. It is directed specifically at the view that QM differs from classical mechanics in that, unlike classical mechanics, it is not amenable to a realist interpretation.

Classical universes are perfectly predictable

Abstract: I argue that in a classical universe, all the events that ever happen are encoded in each of the universe's parts This conflicts with a statement which is widely believed to lie at the basis of relativity theory: that the events in a space-time region R determine only the events in R's domain of dependence but not those in other space-time regions I show how, from this understanding, a new prediction method (which I call the ‘Smoothness Method’) can be obtained which allows us to predict future events on the basis of local observational data Like traditional prediction methods, this method makes use of so-called ‘ceteris paribus clauses’, ie assumptions about the unobserved parts of the universe However, these assumptions are used in a way which enables us to predict the behaviour of open systems with arbitrary accuracy, regardless of the influence of their environment—which has not been achieved by traditional methods In a sequel to this paper (Schmidt, 1998), I will prove the Uniqueness and Predictability Theorems on which the Smoothness Method is based, and comment in more detail on its mathematical properties

A remark concerning prediction and spacetime singularities

Abstract: Intuitively, singularities may be thought to oppose prediction, but in this paper it will be shown that in a sense the opposite is true: if the universe admits at least one ‘predictable event’ (as precisely defined by Geroch), then a singularity is expected to exist. The method of proof for this theorem is to show that every spacetime that admits at least one predictable event must also admit a so-called ‘trapped set’. A version of the Hawking-Penrose singularity theorem is then employed to show that this set signals geodesic incompleteness, i.e. a singularity. A further result shows that the singularity cannot reside within a well-defined region ‘between’ the event of prediction and the event predicted.