Results 1  10
of
828
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 ..."
Abstract

Cited by 166 (52 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 73 (16 self)
 Add to MetaCart
(Show Context)
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
Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems
 Am. J. Phys
, 2001
"... This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these cor ..."
Abstract

Cited by 54 (1 self)
 Add to MetaCart
This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible
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 ..."
Abstract

Cited by 51 (13 self)
 Add to MetaCart
(Show Context)
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.
On the Common Structure of Bohmian Mechanics and the GhirardiRiminiWeber Theory
, 2006
"... 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 nonline ..."
Abstract

Cited by 50 (17 self)
 Add to MetaCart
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 spacetime, or a discrete set of spacetime points. The role of the wave function then is to govern the motion of the matter.
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 ..."
Abstract

Cited by 48 (17 self)
 Add to MetaCart
(Show Context)
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.
Bohmian mechanics
 Chance in Physics: Foundations and Perspectives
, 2001
"... Quantum Mechanics and Reality. While quantum mechanics, as presented in physics textbooks, provides us with a formalism, it does not attempt to provide a description of reality. The formalism is a set of rules for computing the probability distribution of the outcome of essentially any experiment (w ..."
Abstract

Cited by 44 (6 self)
 Add to MetaCart
(Show Context)
Quantum Mechanics and Reality. While quantum mechanics, as presented in physics textbooks, provides us with a formalism, it does not attempt to provide a description of reality. The formalism is a set of rules for computing the probability distribution of the outcome of essentially any experiment (within the realm of quantum mechanics). A description of reality, in contrast, would tell us what processes take place on the microscopic level that lead to the random outcomes that we observe, and would thus explain the formalism. While the correctness of the formalism is almost universally agreed upon, the description of the reality behind the formalism is controversial. It has also been doubted whether a description of reality needs to conform with ordinary standards of logical consistency, and whether to have such a description is desirable at all. Indeed, it has often been claimed that quantum theory forces us to reject the reality of an external world that exists objectively, independently of the human mind. Bohmian Mechanics and Quantum Mechanics. Bohmian mechanics, which is also called the de BroglieBohm theory, the pilotwave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 (de
Geometrical Formulation of Quantum Mechanics
, 1997
"... ..., has a very different appearance. In particular, states are now represented bypointsofasymplecticmanifold (whichhappenstohaveinadditionacomplecticowgeneratedbya Hamiltonianfunction. Thereisthusaremarkablepatible Riemannian metric), observablesarerepresentedbycertain realvalued functionsonthissp ..."
Abstract

Cited by 42 (0 self)
 Add to MetaCart
(Show Context)
..., has a very different appearance. In particular, states are now represented bypointsofasymplecticmanifold (whichhappenstohaveinadditionacomplecticowgeneratedbya Hamiltonianfunction. Thereisthusaremarkablepatible Riemannian metric), observablesarerepresentedbycertain realvalued functionsonthisspaceandthe Schrödingerevolutioniscapturedbythesym similaritywiththestandardsymplecticformulationofclassicalmechanics. FeaturessuchasuncertaintiesandstatevectorreductionswhicharespeclassicalconsiderationsandtheWKBapproximation.Moreimportantly,it Thegeometricalformulationshedsconsiderablelightonanumberofissues cictoquantummechanicscanalsobeformulatedgeometricallybutnowrefer totheRiemannianmetricastructurewhichisabsentinclassicalmechanics. ture.Thegeometricalreformulationprovidesauniedframeworktodiscuss suggestsgeneralizationsofquantummechanics. Thesimplestamongtheseare suchasthesecondquantizationprocedure,theroleofcoherentstatesinsemi theseandtocorrectamisconception. Finally,italsosuggestsdirectionsin equivalenttothedynamicalgeneralizations thathaveappearedintheliterahasanastonishingrangeofapplicationsfromquarksandleptonstoneutronstarsand Quantummechanicsisprobablythemostsuccessfulscientictheoryeverinvented.It whichmoreradicalgeneralizationsmaybe found.
Quantum Probability from Subjective Likelihood: improving on Deutsch’s proof of the probability rule
 STUDIES IN THE HISTORY AND PHILOSOPHY OF PHYSICS, FORTHCOMING
, 2005
"... I present a proof of the quantum probability rule from decisiontheoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch’s recent proof of the probability rule, but the proof is simpler and proceeds from weaker decisiontheor ..."
Abstract

Cited by 40 (9 self)
 Add to MetaCart
I present a proof of the quantum probability rule from decisiontheoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch’s recent proof of the probability rule, but the proof is simpler and proceeds from weaker decisiontheoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.
Between classical and quantum
, 2008
"... The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, inclu ..."
Abstract

Cited by 37 (5 self)
 Add to MetaCart
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is Heisenberg’s ‘quantumtheoretical Umdeutung (reinterpretation) of classical observables’, which lies at the basis of quantization theory. Similarly, Bohr’s correspondence principle (in somewhat revised form) and Schrödinger’s wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely