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178
Quantum Equilibrium and the Origin of Absolute Uncertainty
, 1992
"... The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when ..."
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Cited by 112 (47 self)
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The quantum formalism is a "measurement" formalisma phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schr6dinger's equation for a system of particles when we merely insist that "particles " means particles. While distinctly nonNewtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that an appearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by "p = IV [ 2.,, A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.
Bohmian mechanics as the foundation of quantum mechanics
"... In order to arrive at Bohmian mechanics from standard nonrelativistic quantum mechanics one need do almost nothing! One need only complete the usual quantum description in what is really the most obvious way: by simply including the positions of the particles of a quantum system as part of the state ..."
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Cited by 42 (13 self)
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In order to arrive at Bohmian mechanics from standard nonrelativistic quantum mechanics one need do almost nothing! One need only complete the usual quantum description in what is really the most obvious way: by simply including the positions of the particles of a quantum system as part of the state description of that system, allowing these positions to evolve in the most natural way. The entire quantum formalism, including the uncertainty principle and quantum randomness, emerges from an analysis of this evolution. This can be expressed succinctly—though in fact not succinctly enough—by declaring that the essential innovation of Bohmian mechanics is the insight that particles move! 1 Bohmian Mechanics is Minimal Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference 1 patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes.
Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory
, 2003
"... Bohmian mechanics is the most naively obvious embedding imaginable of Schrödinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly nonNewtonian sort of way, one which may at first appear to have little to do with the spectrum of predict ..."
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Cited by 29 (14 self)
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Bohmian mechanics is the most naively obvious embedding imaginable of Schrödinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly nonNewtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically random, with probability density ρ given by ψ², the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements. ” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas.
A Relativistic Version of the GhirardiRiminiWeber Model
, 2004
"... Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi–Rimini–Weber (GRW) model of spontaneous wavefunction collapse. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of spacetime ..."
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Cited by 25 (12 self)
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Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi–Rimini–Weber (GRW) model of spontaneous wavefunction collapse. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of spacetime points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. The model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of spacetime or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski spacetime as well as in (wellbehaved) curved background spacetimes. PACS numbers: 03.65.Ta; 03.65.Ud; 03.30.+p. Key words: spontaneous wavefunction collapse; relativity; quantum theory without observers. 1
Spacetime Physics with Geometric Algebra
 Am. J. Phys
, 2003
"... This is an introduction to spacetime algebra (STA) as a unified mathematical language for physics. STA simplifies, extends and integrates the mathematical methods of classical, relativistic and quantum physics while elucidating geometric structure of the theory. For example, STA provides a single, m ..."
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Cited by 22 (5 self)
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This is an introduction to spacetime algebra (STA) as a unified mathematical language for physics. STA simplifies, extends and integrates the mathematical methods of classical, relativistic and quantum physics while elucidating geometric structure of the theory. For example, STA provides a single, matrixfree spinor method for rotational dynamics with applications from classical rigid body mechanics to relativistic quantum theory – thus significantly reducing the mathematical and conceptual barriers between classical and quantum mechanics. The entire physics curriculum can be unified and simplified by adopting STA as the standard mathematical language. This would enable early infusion of spacetime physics and give it the prominent place it deserves in the curriculum. I.
On the global existence of Bohmian mechanics
 Comm. Math. Phys
, 1995
"... Abstract. We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substant ..."
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Cited by 20 (12 self)
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Abstract. We show that the particle motion in Bohmian mechanics, given by the solution of an ordinary differential equation, exists globally: For a large class of potentials the singularities of the velocity field and infinity will not be reached in finite time for typical initial values. A substantial part of the analysis is based on the probabilistic significance of the quantum flux. We elucidate the connection between the conditions necessary for global existence and the selfadjointness of the Schrödinger Hamiltonian.
Trajectories and Particle Creation and Annihilation in Quantum Field Theory
 arXiv:quantph/0208072 18 Dürr, D., Goldstein, S., Tumulka, R., and Zanghì, N.: Bohmian Mechanics and Quantum
, 2003
"... We develop a theory based on Bohmian mechanics in which particle world lines can begin and end. Such a theory provides a realist description of creation and annihilation events and thus a further step towards a “beablebased ” formulation of quantum field theory, as opposed to the usual “observable ..."
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Cited by 15 (12 self)
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We develop a theory based on Bohmian mechanics in which particle world lines can begin and end. Such a theory provides a realist description of creation and annihilation events and thus a further step towards a “beablebased ” formulation of quantum field theory, as opposed to the usual “observablebased ” formulation which is plagued by the conceptual difficulties—like the measurement problem—of quantum mechanics. PACS numbers 03.65.Ta (foundations of quantum mechanics) 42.50.Ct (quantum description of interaction of light and matter) 1
Subquantum Information and Computation
, 2002
"... It is argued that immense physical resources – for nonlocal communication, espionage, and exponentiallyfast computation – are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time ..."
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Cited by 15 (6 self)
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It is argued that immense physical resources – for nonlocal communication, espionage, and exponentiallyfast computation – are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that ‘nonquantum ’ or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish nonorthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NPcomplete problems in polynomial time).
On the FluxAcrossSurfaces Theorem
 Letters in Mathematical Physics 38
, 1996
"... 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 integrate ..."
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Cited by 13 (8 self)
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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. 1 Introduction Timedependent scattering theory is concerned with the longtime behavior of wave packets / t . Dollard's scatteringintocones theorem [2, 3] asserts that, assuming, say, asymptotic completeness, the probability of finding a particle with a wave function / 2 H ac (H), the absolutely continuous subspace for the Hamiltonian H, in the far future in a given cone C ae IR 3 (with vertex at the origin) equals the probability that the quantum mechanical momentum of\...
R.: A Simple Proof for Global Existence of Bohmian Trajectories
 Commun. Math. Phys
, 2005
"... We address the question whether Bohmian trajectories exist for all times. Bohmian trajectories are solutions of an ordinary differential equation involving a wavefunction obeying either the Schrödinger or the Dirac equation. Some trajectories may end in finite time, for example by running into a nod ..."
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Cited by 13 (3 self)
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We address the question whether Bohmian trajectories exist for all times. Bohmian trajectories are solutions of an ordinary differential equation involving a wavefunction obeying either the Schrödinger or the Dirac equation. Some trajectories may end in finite time, for example by running into a node of the wavefunction, where the law of motion is illdefined. The aim is to show, under suitable assumptions on the initial wavefunction and the potential, global existence of almost all solutions. We provide a simpler and more transparent proof of the known global existence result for spinless Schrödinger particles and extend the result to particles with spin, to the presence of magnetic fields, and to Dirac wavefunctions. Our main new result are conditions on the current vector field on configurationspacetime which are sufficient for almostsure global existence. MSC (2000): 34A12; 81P99. PACS: 02.30.Hq; 03.65.Ta; 03.65.Pm. Key words: Bohmian mechanics; ordinary differential equations: existence of solutions; equivariant probability distribution; current vector field; Schrödinger equation; Dirac equation. 1