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Summary Bohmian mechanics is an alternative to quantum mechanics that is popular amongst philosophers of physics. In the non-relativistic n-particle domain, it is empirically equivalent to quantum mechanics despite being fully deterministic. The ontology of the theory includes a specification of 'local beables' - for example, corpuscles with precise positions - along with a guidance equation, with the structure of the quantum state, which determines the evolution of the beables. Recent work has extended the Bohmian treatment to quantum field theories.
Key works The approach is often called 'de Broglie-Bohm theory' after the early contribution of Louis deBroglie to the 1927 Solvay conference. It was rediscovered and set out in detail by David Bohm (Bohm 1952). It was again rediscovered, and ably championed within the foundations of physics community, by Bell 2004
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  1. David Albert & Barry Loewer (1989). Symposiums Papers: Two No-Collapse Interpretations of Quantum Theory. Noûs 23 (2):169-186.
  2. Valia Allori, Sheldon Goldstein, Roderich Tumulka & and Nino Zanghì (2008). On the Common Structure of Bohmian Mechanics and the Ghirardi–Rimini–Weber Theory: Dedicated to Giancarlo Ghirardi on the Occasion of His 70th Birthday. British Journal for the Philosophy of Science 59 (3):353-389.
    Bohmian mechanics and the Ghirardi–Rimini–Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about ‘matter’ moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...)
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  3. Valia Allori (2013). On the Metaphysics of Quantum Mechanics. In Soazig Lebihan (ed.), Precis de la Philosophie de la Physique. Vuibert.
    What is quantum mechanics about? The most natural way to interpret quantum mechanics realistically as a theory about the world might seem to be what is called wave function ontology: the view according to which the wave function mathematically represents in a complete way fundamentally all there is in the world. Erwin Schroedinger was one of the first proponents of such a view, but he dismissed it after he realized it led to macroscopic superpositions (if the wave function evolves in (...)
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  4. Valia Allori (2013). Primitive Ontology and the Structure of Fundamental Physical Theories. In Alyssa Ney & David Z. Albert (eds.), The Wave Function: Essays in the Metaphysics of Quantum Mechanics. Oxford University Press.
    For a long time it was believed that it was impossible to be realist about quantum mechanics. It took quite a while for the researchers in the foundations of physics, beginning with John Stuart Bell [Bell 1987], to convince others that such an alleged impossibility had no foundation. Nowadays there are several quantum theories that can be interpreted realistically, among which Bohmian mechanics, the GRW theory, and the many-worlds theory. The debate, though, is far from being over: in what respect (...)
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  5. Valia Allori, Detlef Duerr, Nino Zanghi & Sheldon Goldstein (2002). Seven Steps Toward the Classical World. Journal of Optics B 4:482–488.
    Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard quantum mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical (...)
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  6. Valia Allori, Sheldon Goldstein, Roderich Tumulka & Nino Zanghi (2008). On the Common Structure of Bohmian Mechanics and the Ghirardi-Rimini-Weber Theory. British Journal for the Philosophy of Science 59 (3):353 - 389.
    Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter implements spontaneous collapses of the wave function by a nonlinear and stochastic modification of Schrödinger's equation. Still, both theories, when understood appropriately, share the following structure: They are ultimately not about wave functions but about 'matter' moving in space, represented by either particle trajectories, fields on space-time, or a discrete set of (...)
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  7. Valia Allori & Nino Zanghi (2008). On the Classical Limit of Quantum Mechanics. Foundations of Physics 10.1007/S10701-008-9259-4 39 (1):20-32.
    Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing (...)
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  8. Valia Allori & Nino Zanghi (2004). What is Bohmian Mechanics. International Journal of Theoretical Physics 43:1743-1755.
    Bohmian mechanics is a quantum theory with a clear ontology. To make clear what we mean by this, we shall proceed by recalling first what are the problems of quantum mechanics. We shall then briefly sketch the basics of Bohmian mechanics and indicate how Bohmian mechanics solves these problems and clarifies the status and the role of of the quantum formalism.
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  9. D. M. Appleby (1999). Bohmian Trajectories Post-Decoherence. Foundations of Physics 29 (12):1885-1916.
    The role of the environment in producing the correct classical limit in the Bohm interpretation of quantum mechanics is investigated, in the context of a model of quantum Brownian motion. One of the effects of the interaction is to produce a rapid approximate diagonalisation of the reduced density matrix in the position representation. This effect is, by itself, insufficient to produce generically quasi-classical behaviour of the Bohmian trajectory. However, it is shown that, if the system particle is initially in an (...)
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  10. D. M. Appleby (1999). Generic Bohmian Trajectories of an Isolated Particle. Foundations of Physics 29 (12):1863-1883.
    The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown that the necessary and sufficient condition for there to be a negligible probability of the trajectory deviating significantly from the classical trajectory at any stage in the motion is that the state be a narrowly localised wave packet. The properties of the Bohmian trajectories are compared with those in the interpretation recently proposed by García de Polavieja. (...)
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  11. Mahdi Atiq, Mozafar Karamian & Mahdi Golshani (2009). A New Way for the Extension of Quantum Theory: Non-Bohmian Quantum Potentials. [REVIEW] Foundations of Physics 39 (1):33-44.
    Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics. Of course, at the nuclear level, because of some complications, it is not clear that we can claim the same confidence. One way of taking these complications and corrections into account seems to be a modification of the standard quantum theory. In this (...)
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  12. Guido Bacciagaluppi (2009). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press.
    This book will be of interest to graduate students and researchers in physics and in the history and philosophy of quantum theory.
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  13. C. Baladrón (2011). Study on a Possible Darwinian Origin of Quantum Mechanics. Foundations of Physics 41 (3):389-395.
    A sketchy subquantum theory deeply influenced by Wheeler’s ideas (Am. J. Phys. 51:398–404, 1983) and by the de Broglie-Bohm interpretation (Goldstein in Stanford Encyclopedia of Philosophy, 2006) of quantum mechanics is further analyzed. In this theory a fundamental system is defined as a dual entity formed by bare matter and a methodological probabilistic classical Turing machine. The evolution of the system would be determined by three Darwinian informational regulating principles. Some progress in the derivation of the postulates of quantum mechanics (...)
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  14. Jeffrey A. Barrett (1996). Empirical Adequacy and the Availability of Reliable Records in Quantum Mechanics. Philosophy of Science 63 (1):49-64.
    In order to judge whether a theory is empirically adequate one must have epistemic access to reliable records of past measurement results that can be compared against the predictions of the theory. Some formulations of quantum mechanics fail to satisfy this condition. The standard theory without the collapse postulate is an example. Bell's reading of Everett's relative-state formulation is another. Furthermore, there are formulations of quantum mechanics that only satisfy this condition for a special class of observers, formulations whose empirical (...)
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  15. Jeffrey A. Barrett (1995). The Distribution Postulate in Bohm's Theory. Topoi 14 (1):45-54.
    On Bohm''s formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm''s theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make the right statistical (...)
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  16. David Bohm (2003). The Essential David Bohm. Routledge.
    There are few scientists of the twentieth century whose life's work has created more excitement and controversy than that of physicist David Bohm (1917-1992). Exploring the philosophical implication of both physics and consciousness, Bohm's penchant for questioning scientific and social orthodoxy was the expression of a rare and maverick intelligence. For Bohm, the world of matter and the experience of consciousness were two aspects of a more fundamental process he called the implicate order. Without a working sensibility of what this (...)
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  17. David Bohm (1985). Unfolding Meaning: A Weekend of Dialogue with David Bohm. Foundation House.
    David Bohm argues that our fragmented, mechanistic notion of order permeates not only modern science and technology today, but also has profound implications ...
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  18. David Bohm (1962). Classical and Non-Classical Concepts in the Quantum Theory. An Answer to Heisenberg's Physics and Philosophy. British Journal for the Philosophy of Science 12 (48):265-280.
  19. David Bohm (1952). A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables, I and II. Physical Review (85):166-193.
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  20. Harvey Brown & David Wallace (2005). Solving the Measurement Problem: De Broglie-Bohm Loses Out to Everett. [REVIEW] Foundations of Physics 35 (4):517-540.
    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.
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  21. Jeremy Butterfield, On Hamilton-Jacobi Theory as a Classical Root of Quantum Theory.
    This paper gives a technically elementary treatment of some aspects of <span class='Hi'>Hamilton</span>-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the optico-mechanical analogy and the transition to quantum mechanics. Finally, I report recent work of Holland providing a Hamiltonian formulation of the pilot-wave theory.
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  22. Craig Callender, Discussion: The Redundancy Argument Against Bohm's Theory.
    Advocates of the Everett interpretation of quantum mechanics have long claimed that other interpretations needlessly invoke "new physics" to solve the measurement problem. Call the argument fashioned that gives voice to this claim the Redundancy Argument, or ’Redundancy’ for short. Originating right in Everett’s doctoral thesis, Redundancy has recently enjoyed much attention, having been advanced and developed by a number of commentators, as well as criticized by a few others.[1] Although versions of this argument can target collapse theories of quantum (...)
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  23. Craig Callender (2007). The Emergence and Interpretation of Probability in Bohmian Mechanics. Studies in History and Philosophy of Science Part B 38 (2):351-370.
    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 (...)
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  24. James T. Cushing (1995). Quantum Tunneling Times: A Crucial Test for the Causal Program? [REVIEW] Foundations of Physics 25 (2):269-280.
    It is generally believed that Bohm's version of quantum mechanics is observationally equivalent to standard quantum mechanics. A more careful statement is that the two theories will always make the same predictions for any question or problem that is well posed in both interpretations. The transit time of a “particle” between two points in space is not necessarily well defined in standard quantum mechanics, whereas it is in Bohm's theory since there is always a particle following a definite trajectory. For (...)
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  25. James T. Cushing, Arthur Fine & Sheldon Goldstein (1996). Bohmian Mechanics and Quantum Theory: An Appraisal. Springer.
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  26. M. Daumer & S. Goldstein, On the Flux-Across-Surfaces Theorem.
    The quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that surface at some time. We prove the free fluxacross-surfaces theorem, which was conjectured by Combes, Newton and Shtokhamer [1], and which relates the integrated quantum flux to the usual quantum mechanical formula for the cross section. The integrated quantum flux is equal to the probability of outward crossings of surfaces by Bohmian trajectories in the scattering regime.
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  27. Martin Daumer, Detlef Dürr, Sheldon Goldstein & Nino Zanghì (1996). Naive Realism About Operators. Erkenntnis 45 (2-3):379 - 397.
    A source of much difficulty and confusion in the interpretation of quantum mechanics is a naive realism about operators. By this we refer to various ways of taking too seriously the notion of operator-as-observable, and in particular to the all too casual talk about measuring operators that occurs when the subject is quantum mechanics. Without a specification of what should be meant by measuring a quantum observable, such an expression can have no clear meaning. A definite specification is provided by (...)
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  28. Michael Dickson (1996). Antidote or Theory? Studies in History and Philosophy of Science Part B 27 (2):229-238.
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  29. W. Michael Dickson (1996). Determinism and Locality in Quantum Systems. Synthese 107 (1):55 - 82.
    Models of the EPR-Bohm experiment usually consider just two times, an initial time, and the time of measurement. Within such analyses, it has been argued that locality is equivalent to determinism, given the strict correlations of quantum mechanics. However, an analysis based on such models is only a preliminary to an analysis based on a complete dynamical model. The latter analysis is carried out, and it is shown that, given certain definitions of locality and determinism for completely dynamical models, locality (...)
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  30. Mauro Dorato & Federico Laudisa (forthcoming). Realism and Instrumentalism About the Wave Function. How Should We Choose? In Shao Gan (ed.), Protective Measurements and Quantum Reality: Toward a New Understanding of Quantum Mechanics. CUP.
    The main claim of the paper is that one can be ‘realist’ (in some sense) about quantum mechanics without requiring any form of realism about the wave function. We begin by discussing various forms of realism about the wave function, namely Albert’s configuration-space realism, Dürr Zanghi and Goldstein’s nomological realism about Ψ, Esfeld’s dispositional reading of Ψ Pusey Barrett and Rudolph’s realism about the quantum state. By discussing the articulation of these four positions, and their interrelation, we conclude that instrumentalism (...)
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  31. Cian Dorr, Finding Ordinary Objects in Some Quantum Worlds.
    cation we have in mind is that of formulating the laws of a classical meration space to the complex numbers. But what is it for such a function chanics of point-particles living in Newtonian absolute space, one espe-.
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  32. D. Durr, S. Goldstein & N. Zanghi (1995). Quantum Physics Without Quantum Philosophy. Studies in History and Philosophy of Science Part B 26 (2):137-149.
    Quantum philosophy, a peculiar twentieth-century malady, is responsible for most of the conceptual muddle plaguing the foundations of quantum physics. When this philosophy is eschewed, one naturally arrives at Bohmian mechanics, which is what emerges from Schrodinger's equation for a nonrelativistic system of particles when we merely insist that 'particles' means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. The quantum formalism emerges when measurement situations are (...)
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  33. Detlef Dürr, Sheldon Goldstein, Roderich Tumulka & Nino Zanghí (2005). On the Role of Density Matrices in Bohmian Mechanics. Foundations of Physics 35 (3):449-467.
  34. Detlef Dürr, Sheldon Goldstein & Nino Zanghí (1993). A Global Equilibrium as the Foundation of Quantum Randomness. Foundations of Physics 23 (5):721-738.
    We analyze the origin of quantum randomness within the framework of a completely deterministic theory of particle motion—Bohmian mechanics. We show that a universe governed by this mechanics evolves in such a way as to give rise to the appearance of randomness, with empirical distributions in agreement with the predictions of the quantum formalism. Crucial ingredients in our analysis are the concept of the effective wave function of a subsystem and that of a random system. The latter is a notion (...)
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  35. F. T. Falciano, M. Novello & J. M. Salim (2010). Geometrizing Relativistic Quantum Mechanics. Foundations of Physics 40 (12):1885-1901.
    We propose a new approach to describe quantum mechanics as a manifestation of non-Euclidean geometry. In particular, we construct a new geometrical space that we shall call Qwist. A Qwist space has a extra scalar degree of freedom that ultimately will be identified with quantum effects. The geometrical properties of Qwist allow us to formulate a geometrical version of the uncertainty principle. This relativistic uncertainty relation unifies the position-momentum and time-energy uncertainty principles in a unique relation that recover both of (...)
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  36. Bruno Galvan (2007). Typicality Vs. Probability in Trajectory-Based Formulations of Quantum Mechanics. Foundations of Physics 37 (11):1540-1562.
    Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown that the explanation does not make use of the full probability measure, but rather of a suitable set function deriving from it, which defines relative typicality between single-time cylinder sets. Such a set function can also be derived directly (...)
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  37. Shan Gao, Protective Measurement and the de Broglie-Bohm Theory.
    We investigate the implications of protective measurement for de Broglie-Bohm theory, mainly focusing on the interpretation of the wave function. It has been argued that the de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions. But this premise turns out to be wrong according to protective measurement; a charged quantum system (...)
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  38. Shan Gao, Why the de Broglie-Bohm Theory is Probably Wrong.
    We investigate the validity of the field explanation of the wave function by analyzing the mass and charge density distributions of a quantum system. It is argued that a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. This is also a consequence of protective measurement. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously (...)
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  39. GianCarlo Ghirardi & Raffaele Romano (2013). About Possible Extensions of Quantum Theory. Foundations of Physics 43 (7):881-894.
    Recently it has been claimed that no extension of quantum theory can have improved predictive power, the statement following, according to the authors, from the assumptions of free will and of the correctness of quantum predictions concerning the correlations of measurement outcomes. Here we prove that the argument is basically flawed by an inappropriate use of the assumption of free will. In particular, among other implications, the claim, if correct, would imply that Bohmian Mechanics is incompatible with free will. This (...)
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  40. Sheldon Goldstein, On the Weak Measurement of Velocity in Bohmian Mechanics.
    In a recent article [1], Wiseman has proposed the use of so-called weak measurements for the determination of the velocity of a quantum particle at a given position, and has shown that according to quantum mechanics the result of such a procedure is the Bohmian velocity of the particle. Although Bohmian mechanics is empirically equivalent to variants based on velocity formulas different from the Bohmian one, and although it has been proven that the velocity in Bohmian mechanics is not measurable, (...)
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  41. Sheldon Goldstein, Are All Particles Identical?
    We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same particle, just as spin-up and spin-down do. The implications of this viewpoint can be best appreciated within Bohmian mechanics, a precise formulation of quantum mechanics with particle trajectories. The implementation of this viewpoint in such a theory leads to trajectories different from those of the (...)
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  42. Sheldon Goldstein, Quantum Hamiltonians and Stochastic Jumps.
    With many Hamiltonians one can naturally associate a |Ψ|2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it is typically a jump process on the configuration space of a variable number of particles. We define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [3] and of ourselves [11]. We introduce a formula expressing the jump rates (...)
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  43. Sheldon Goldstein, Absence of Chaos in Bohmian Dynamics.
    In a recent paper [1], O. F. de Alcantara Bonfim, J. Florencio, and F. C. S´ a Barreto claim to have found numerical evidence of chaos in the motion of a Bohmian quantum particle in a double square-well potential, for a wave function that is a superposition of five energy eigenstates. But according to the result proven here, chaos for this motion is impossible. We prove in fact that for a particle on the line in a superposition of n + (...)
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  44. Sheldon Goldstein, Bohmian Trajectories as the Foundation of Quantum Mechanics.
    Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schr¨ odinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for: to serve as the foundation of quantum mechanics, i.e., to explain quantum mechanics in terms of a theory that is free of paradoxes and allows an understanding that is as clear as that of classical mechanics. Indeed, they succeed in serving that purpose in the context of a (...)
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  45. Sheldon Goldstein (2010). Bohmian Mechanics and Quantum Information. Foundations of Physics 40 (4):335-355.
    Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and (...)
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  46. Sheldon Goldstein, Bohmian Mechanics. Stanford Encyclopedia of Philosophy.
    Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952. It is the simplest example of what is often called a hidden variables interpretation of quantum mechanics. In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's equation. However, the (...)
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  47. Sheldon Goldstein (1996). Review Essay: Bohmian Mechanics and the Quantum Revolution. [REVIEW] Synthese 107 (1):145 - 165.
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  48. Sheldon Goldstein (1996). Bohmian Mechanics and the Quantum Revolution. [REVIEW] Synthese 107 (1):145 - 165.
    When I was young I was fascinated by the quantum revolution: the transition from classical definiteness and determinism to quantum indeterminacy and uncertainty, from classical laws that are indifferent, if not hostile, to the human presence, to quantum laws that fundamentally depend upon an observer for their very meaning. I was intrigued by the radical subjectivity, as expressed by Heisenberg’s assertion [3] that “The idea of an objective real world whose smallest parts exist objectively in the same sense as stones (...)
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  49. Sheldon Goldstein, D. Dürr, J. Taylor, R. Tumulka & and N. Zanghì, Quantum Mechanics in Multiply-Connected Spaces.
    J. Phys. A, to appear, quant-ph/0506173.
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  50. Sheldon Goldstein, D. Dürr & N. Zanghì, Bohmian Mechanics and Quantum Equilibrium.
    in Stochastic Processes, Physics and Geometry II, edited by S. Albeverio, U. Cattaneo, D. Merlini (World Scientific, Singapore, 1995) pp. 221-232.
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