R.I.G. Hughes presents a series of eight philosophical essays on the theoretical practices of physics. The first two essays examine these practices as they appear in physicists' treatises (e.g. Newton's Principia and Opticks ) and journal articles (by Einstein, Bohm and Pines, Aharonov and Bohm). By treating these publications as texts, Hughes casts the philosopher of science in the role of critic. This premise guides the following 6 essays which deal with various concerns of philosophy of physics such as laws, (...) disunities, models and representation, computer simulation, explanation, and the discourse of physics. (shrink)

The general Kantian claim that certain traits of the object of knowledge may be known a priori is reduced here to the scientific object. Scientific experience proceeds through certain operations, by which the life-world phenomena are transformed into scientific objects. These operations impose upon scientific objects certain formal structures. The latter cannot be empirical because data production is possible only on the basis of them. On the other side, they determine how and to what degree mathematics are applicable to the (...) data. (shrink)

Quite rightly, philosophers of physics examine the theories of physics, theories like Quantum Mechanics, Quantum Field Theory, the Special and General Theories of Relativity, and Statistical Mechanics. Far fewer, however, examine how these theories are put to use; that is to say, little attention is paid to the practices of theoretical physicists. In the early 1950s David Bohm and David Pines published a sequence of four papers, collectively entitled, ‘A Collective Description of Electron Interaction.’ This essay uses that quartet as (...) a case study in theoretical practice. In Part One of the essay, each of the Bohm-Pines papers is summarized, and within each summary an overview is given, framing a more detailed account. In Part Two theoretical practice is broken into six elements: (a) the use of models, (b) the use of theory, (c) modes of description and narrative, (d) the use of approximations, (e) experiment and theory, (f) the varied steps employed in a deduction. The last element is the largest, drawing as it does from the earlier ones. Part Three enlarges on the concept of ‘theoretical practice,’ and briefly outlines the subsequent theoretical advances which rendered the practices of Bohm and Pines obsolete, if still respected. (shrink)

Properties sometimes attributed to the “particle” aspect of a neutron, e.g., mass and magnetic moment, cannot straightforwardly be regarded in the Bohm interpretation of quantum mechanics as localized at the hypothetical position of the particle. This is shown by examining a series of effects in neutron interferometry. A related thought-experiment also provides a variation of a recent demonstration that which-way detectors can appear to behave anomolously in the Bohm theory.

A comparison is made between the Bohm trajectory and Feynman path approaches to the long-standing problem of determining the average lime taken for a particle described by the Schrödinger wave function ψ to tunnel through a potential barrier. The former approach follows simply and uniquely from the basic postulates of Bohm's causal interpretation of quantum mechanics; the latter is intimately related to the most frequently cited approaches based on conventional interpretations. Emphasis is given to the fact that fundamentally different transmission (...) (T)-reflection (R) decompositions, particlelike and wavelike respectively, are central to the two methods: ¦ψ¦2=[¦ψ¦2]T+[¦ψ¦2]R (Bohm trajectory approach); ψ=ψT+ψR (Feynman path approach). (shrink)

It is shown, in a large variety of manifestations, that the Aharonov—Bohm effect has classical counterparts in aspects concerning energy and momentum balance. No counterexamples are found in the cases considered, although whenever image charges shield the magnetic field region from the electric field of the passing electron the classical momentum effects, while present, would not be observable. Similarly, if the magnetic flux is maintained by superconductors, magnetic shielding will also render the classical energy effect unobservable. Partial shieldings of either (...) type will reduce but not totally eliminate the corresponding observable classical manifestations of these effects. (shrink)

I study in detail a proposal made by T. H. Boyer in an attempt to explain classically the Aharonov-Bohm (AB) effect. Boyer claims that in an AB experiment, the perturbation the external incident particle produces on the charge and current distributions within the solenoid will affect back the motion of the external particle. With a qualitative analysis based on energetic considerations, Boyer seemed to arrive at the conclusion that this perturbation could give account of the AB effect. In this paper (...) I make explicit calculations which show that Boyer's conjecture fails. Indeed I find that the perturbation produced on the solenoid, and then its effect on the external charge, is independent of the solenoid current and consequently cannot account for the AB effect, which is current dependent. (shrink)

In this paper we show how the dynamics of the Schrödinger, Pauli and Dirac particles can be described in a hierarchy of Clifford algebras, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{1,3}, {\mathcal{C}}_{3,0}$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathcal{C}}_{0,1}$\end{document}. Information normally carried by the wave function is encoded in elements of a minimal left ideal, so that all the physical information appears within the algebra itself. The state of the quantum process can be (...) completely characterised by algebraic invariants of the first and second kind. The latter enables us to show that the Bohm energy and momentum emerge from the energy-momentum tensor of standard quantum field theory. Our approach provides a new mathematical setting for quantum mechanics that enables us to obtain a complete relativistic version of the Bohm model for the Dirac particle, deriving expressions for the Bohm energy-momentum, the quantum potential and the relativistic time evolution of its spin for the first time. (shrink)

The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.

We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities, and its consequences. We describe the experiment of Aspect, Dalibard, and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory.

We propose a simple situation in which the magnetic Aharonov–Bohm potential influences the values of the deficiency indices of the initial Schrödinger operator, so determining whether the particle interacts with the solenoid or not. Even with the particle excluded from the magnetic field, the number of self-adjoint extensions of the initial Hamiltonian depends on the magnetic flux. This is a new point of view of the Aharonov–Bohm effect.

The first part of this long two-part work is a history of the development of the modern theory of the atom from Dalton to the present. The second part offers philosophical reflections on this history beginning with a discussion of epistemological implications and following that with an account of ontological implications. The author deals with familiar questions about the reality of micro-particles, complementarity, indeterminism, the role of the observer and other topics. But he also discusses topics like holism, atomic order, (...) the intelligibility of matter and others which are less commonly discussed by philosophers in connection with modern physical theories. The author, who is trained in physics as well as philosophy, has a flair for metaphysical speculation as well as wide knowledge of contemporary physical theory. He stresses the novelties of the quantum conception of matter, argues against its critics like Bohm, and sees it as presenting a radically new conception of atomic order despite its commitment to indeterminism. The views of Werner Heisenberg, who encouraged the author to write the book and who read it in manuscript, have clearly influenced the author, although they do not dominate his thinking.--R. H. K. (shrink)

We apply the distinction between parameter independence and outcome independence to the linear and nonlinear models of a recent nonrelativistic theory of continuous state vector reduction. We show that in the nonlinear model there is a set of realizations of the stochastic process that drives the state vector reduction for which parameter independence is violated for parallel spin components in the EPR-Bohm setup. Such a set has an appreciable probability of occurrence (≈ 1/2). On the other hand, the linear model (...) exhibits only extremely small parameter dependence effects. We investigate some specific features of the models and we recall that, as has been pointed out recently, if one wants to be able to speak of definite outcomes (or equivalently of possessed objective elements of reality) at finite times, one has to slightly change the criteria for their attribution to physical systems. The concluding section is devoted to a detailed discussion of the difficulties which one meets when one tries to take, as a starting point for the formulation of a relativistic theory, a nonrelativistic scheme which exhibits parameter dependence. Here we derive a theorem which identifies the precise sense in which the occurrence of parameter dependence forbids a genuinely relativistic generalization. Finally we show how the appreciable parameter dependence of the nonlinear model gives rise to problems with relativity, while the extremely weak parameter dependence of the linear model does not give rise to any difficulty, provided one takes into account the appropriate criteria for the attribution of definite outcomes. (shrink)

We discuss the application of the de Broglie-Bohm theory of relativistic spin-1/2 particles to the Klein paradox andzitterbewegung.

The action-reaction principle (AR) is examined in three contexts: (1) the inertial-gravitational interaction between a particle and space-time geometry, (2) protective observation of an extended wave function of a single particle, and (3) the causal-stochastic or Bohm interpretation of quantum mechanics. A new criterion of reality is formulated using the AR principle. This criterion implies that the wave function of a single particle is real and justifies in the Bohm interpretation the dual ontology of the particle and its associated wave (...) function. But it is concluded that the Bohm theory is not dynamically complete because the particle and its associated wave function do not satisfy the AR principle. (shrink)

In this paper, we re-examine a series of gedanken welcher Weg (WW) experiments introduced by Scully, Englert and Walther that contain the essential ideas underlying the quantum eraser. For this purpose we use the Bohm model which gives a sharp picture of the behaviour of the atoms involved in these experiments. This model supports the thesis that interference disappears in such WW experiments, even though the centre of mass wave function remains coherent throughout the experiment. It also shows exactly what (...) it means to say ‘that the interference can be restored by manipulating the WW detectors long after the atoms have passed’. It does not support Wheeler’s notion that ‘the past is undefined and undefinable without the observation (in the present)’. (shrink)

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting (...) with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential. (shrink)

The first part of this long two-part work is a history of the development of the modern theory of the atom from Dalton to the present. The second part offers philosophical reflections on this history beginning with a discussion of epistemological implications and following that with an account of ontological implications. The author deals with familiar questions about the reality of micro-particles, complementarity, indeterminism, the role of the observer and other topics. But he also discusses topics like holism, atomic order, (...) the intelligibility of matter and others which are less commonly discussed by philosophers in connection with modern physical theories. The author, who is trained in physics as well as philosophy, has a flair for metaphysical speculation as well as wide knowledge of contemporary physical theory. He stresses the novelties of the quantum conception of matter, argues against its critics like Bohm, and sees it as presenting a radically new conception of atomic order despite its commitment to indeterminism. The views of Werner Heisenberg, who encouraged the author to write the book and who read it in manuscript, have clearly influenced the author, although they do not dominate his thinking.--R. H. K. (shrink)

Recent experiments have renewed interest in nonlocal interpretations of quantum mechanics. The experimental observation of the violation of Bell's inequalities implies the existence of nonlocality. Bohm expressed the nonlocal connection between quantum particles through the wave function and the quantum potential. This paper shows that a similar connection exists in a relativistic dynamical theory known as parametrized relativistic quantum theory (PRQT). We present an introduction to PRQT, derive the quantum potential for a system of relativistic scalar particles, and discuss alternative (...) interpretations of nonlocality. (shrink)

It was shown by de Broglie and Bohm that the concept of a deterministic particle trajectory is compatible with quantum mechanics. It is demonstrated by explicit construction that there exists another more general deterministic trajectory interpretation. The method exploits an internal angular degree of freedom that is implicit in the Schrödinger equation, in addition to the particle position. The de Broglie-Bohm model is recovered when the new theory is averaged over the internal freedom. The model exhibits a strong form of (...) entanglement which implies a primary role for the wavefunction of the Universe. The conditions of autonomy are examined, and the viability of the theory is established by application to the measurement problem. (shrink)

Rumors of David Bohm's new ideas on cosmology, in the philosophical sense, have been circulating for some time. It was a pleasure to finally have the book in one's hands. The argument falls neatly into a number of stages.

In the Aharonov- Bohm effect, electromagnetic potentials alter the two-slit interference pattern formed by an electron beam. We discuss here a curious feature of this effect, namely that, even though the interference pattern changes, none of its moments are shifted.

We examine “de Broglie-Bohm” causal trajectories for the two electrons in a nonrelativistic helium atom, taking into account the spin-dependent momentum terms that arise from the Pauli current. Given that this many-body problem is not exactly solvable, we examine approximations to various helium eigenstates provided by a low-dimensional basis comprised of tensor products of one-particle hydrogenic eigenstates.First to be considered are the simplest approximations to the ground and first-excited electronic states found in every introductory quantum mechanics textbook. For example, the (...) trajectories associated with the simple 1s(1)1s(2) approximation to the ground state are, to say the least, nontrivial and nonclassical.We then examine higher-dimensional approximations, i.e., eigenstates Ψ α of the Hamiltonian in this truncated basis, and show that ∇ i S α =0 for both particles, implying that only the spin-dependent momentum term contributes to electronic motion. This result is independent of the size of the truncated basis set, implying that the qualitative features of the trajectories will be the same, regardless of the accuracy of the eigenfunction approximation.The electronic motion associated with these eigenstates is quite specialized due to the condition that the spins of the two electrons comprise a two-spin eigenfunction of the total spin operator. The electrons either (i) remain stationary or (ii) execute circular orbits around the z-axis with constant velocity. (shrink)

In this paper we study in details a system of two weakly coupled harmonic oscillators from the point of view of Bohm’s interpretation of quantum mechanics. This system may be viewed as a simple model for the interaction between a photon and a photodetector. We obtain exact solutions for the general case. We then compute approximate solutions for the case where one oscillator is initially in its first excited state (a single photon) reaching the other oscillator in its ground state (...) (the photodetector). The approximate solutions represent the state of both oscillators after the interaction, which is not an eigenstate of the individual hamiltonians for each oscillator, and therefore the energies for each oscillator do not exist in the Copenhagen interpretation of Quantum Mechanics. We use the approximate solutions that we obtained to compute Bohmian trajectories and to study the energy transfer between the oscillators. We conclude that, even using the Bohmian view, the energy of each individual oscillator is not well defined, as the nonlocal quantum potential is not negligible even after the coupling is turned off. (shrink)

In this paper we study in details a system of two weakly coupled harmonic oscillators from the point of view of Bohm's interpretation of quantum mechanics. This system may be viewed as a simple model for the interaction between a photon and a photodetector. We obtain exact solutions for the general case. We then compute approximate solutions for the case where one oscillator is initially in its first excited state (a single photon) reaching the other oscillator in its ground state (...) (the photodetector). The approximate solutions represent the state of both oscillators after the interaction, which is not an eigenstate of the individual hamiltonians for each oscillator, and therefore the energies for each oscillator do not exist in the Copenhagen interpretation of Quantum Mechanics. We use the approximate solutions that we obtained to compute Bohmian trajectories and to study the energy transfer between the oscillators. We conclude that, even using the Bohmian view, the energy of each individual oscillator is not well defined, as the nonlocal quantum potential is not negligible even after the coupling is turned off. (shrink)

Onc of thc problems of quantnun cosmology follows from thc fact that thc Hamiltonian H of classical general relativity equals zero. Quantizing canonically in thc Schrodinger picture, thc Schrodinger equation for thc wave function *1* of thc universe is thcreforc thc so-called Whcelc:r—DeWitt..