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Particle density of the electron in a hydrogen atom in the bound 3 d ( m = 0) state. In the interpretation of the proposed theory, this “electron cloud” depicts a cloud of worlds projected to physical space. In each world, the electron is in a well-defined position, moving around in a nonclassical manner on its Bohmian trajectory.
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A non-relativistic quantum mechanical theory is proposed that combines
elements of Bohmian mechanics and of Everett's "many-worlds" interpretation.
The resulting theory has the advantage of resolving known issues of both
theories, as well as those of standard quantum mechanics. It has a clear
ontology and a set of precisely defined postulates from...
Context in source publication
Context 1
... the expected number of particles in a region X in physical space. Thus when we look at, say, a graphical representation of the particle density of an electron, the so-called “electron cloud”, then we are actually looking at a cloud of worlds projected to physical space, where in each of these worlds the electron is in a well-defined position, moving around in a nonclassical manner on its Bohmian trajectory ( Figure 3). The appearance of particles as point-like entities at a definite location in three-dimensional space, results from the subjective experience of the metaworld from the perspective of a single point, a world , within this metaworld. Consider the appearance of time: Physically, time is just a continuous parameter in an extra dimension, with none of its constituting points being preferred, but in our experience time appears as a single point-like temporal entity, termed “now”, that moves on from past to future. In much the same way, we experience the wave-like, continuous, high-dimensional metaworld as a set of discrete point-like “particles” that move through a three-dimensional space. This question bears on a typical misconception concerning the probability concept in measure theory. The probability measure of some given set is not “the” probability of this set, but precisely the probability to randomly pick out an element from this set . In contrast to that, the world that is actual to a given person, is, well, given and therefore does not have a probability (other than 1) assigned to it. Consider an analogy to classical statistical mechanics: Here, the actual state of a system always corresponds to a point in phase space, that is, its microstate . Nonetheless, the system may possess certain macroscopic properties like volume, temperature and pressure. If only these are given, then this incomplete information is accounted for by describing “the state” of the system, its macrostate , that is, by a probability density on phase space. Actually, this is a rather sloppy talk and potentially misleading, for the probability density actually is not “the state” ...
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Citations
... Here I examine the problem of explaining the symmetry dichotomy within two interpretations of quantum mechanics which clarify the connection between particles and the wave function by including particles following definite trajectories through space in addition to, or in lieu of, the wave function: (1) Bohmian mechanics and (2) a hydrodynamic interpretation that posits a multitude of quantum worlds interacting with one another, which I have called " Newtonian quantum mechanics " (Hall et al. , 2014 have called this kind of approach " many interacting worlds " ). Versions of this second interpretation have recently been put forward by Tipler (2006); Poirier (2010); Schiff & Poirier (2012); Boström (2012); Boström (2015); Hall et al. (2014); Sebens (2015); it builds on the hydrodynamic approach to quantum mechanics (see Madelung, 1927; Wyatt, 2005; Holland, 2005). Bohmian mechanics and Newtonian quantum mechanics are often called " interpretations " of quantum mechanics, but should really be thought of as distinct physical theories which seek to explain the same body of data (those experiments whose statistics are successfully predicted by the standard methods of non-relativistic quantum mechanics). ...
I address the problem of explaining why wave functions for identical particles must be either symmetric or antisymmetric (the symmetry dichotomy) within two interpretations of quantum mechanics which include particles following definite trajectories in addition to, or in lieu of, the wave function: Bohmian mechanics and Newtonian quantum mechanics (a.k.a. many interacting worlds). In both cases I argue that, if the interpretation is formulated properly, the symmetry dichotomy can be derived and need not be postulated.
... A continuous infinity of worlds is also postulated by Boström (2012), who tries to combine the approaches of Everett and Bohm. Boström considers the configuration space of N pointlike particles and associates, at a given time, a distinct world with each configuration. ...
Everett's interpretation of quantum mechanics was proposed to avoid problems
inherent in the prevailing interpretational frame. It assumes that quantum
mechanics can be applied to any system and that the state vector always evolves
unitarily. It then claims that whenever an observable is measured, all possible
results of the measurement exist. This notion of multiplicity has been
understood in different ways by proponents of Everett's theory. In fact the
spectrum of opinions on various ontological questions raised by Everett's
approach is rather large, as we attempt to document in this critical review. We
conclude that much remains to be done to clarify and specify Everett's
approach.
... My proposal is different from Bohmian mechanics in that the wavefunction does not represent a physical field existing in addition to particles, and it is different from Everettian mechanics in that the worlds are precisely defined and do not split (Fig. 1). The theory is based on ideas initially published as a preprint draft [5], which has been completely re-worked and enhanced, in particular by adding a logical framework to properly deal with propositions about physical systems in a multiplicity of worlds, and by providing the conceptual prerequisites for treating the collection of worlds as a continuous substance. After having finished and submitted an earlier version of this manuscript, I noticed that essentially the same theory, though with a stronger focus on formal aspects and less focus on ontological and epistemological matters, has independently been put forward by Poirier and Schiff [35,39]. ...
... What happens is that due to the measurement process, the configuration space is partitioned into smaller volumes that contain those worlds where the individual measurement outcomes occur. As the theory is deterministic at the level of individual worlds, which follows from the unique solvability of the Bohr equation (33), the measurement result obtained in each individual world is determined from the very beginning (see [48] for a similar view on determinism in quantum mechanics, including a critical review on the ideas proposed in [5]). It only appears to be random to the individual observer who spends their lifetime in a particular trajectory without knowing which one. ...
... In a recent paper, Vaidman [48] discusses numerous formulations and interpretations of quantum mechanics, and in particular the idea put forward in [43] and in [5], of a continuum of worlds existing in parallel. Although Vaidman strongly argues for a multiplicity of worlds, he rejects the idea that there is a continuum of them. ...
A non-relativistic quantum mechanical theory is proposed that describes the
universe as a continuum of worlds whose mutual interference gives rise to
quantum phenomena. A logical framework is introduced to properly deal with
propositions about objects in a multiplicity of worlds. In this logical
framework, the continuum of worlds is treated similarly to the continuum of
time points; both "time" and "world" are considered as mutually independent
modes of existence. The theory combines elements of Bohmian mechanics and of
Everett's many-worlds interpretation; it has a clear ontology and a set of
precisely defined postulates from where the predictions of standard quantum
mechanics can be derived. Probability as given by the Born rule emerges as a
consequence of insufficient knowledge of observers about which world it is that
they live in. The theory describes a continuum of worlds rather than a single
world or a discrete set of worlds, so it is similar in spirit to many-worlds
interpretations based on Everett's approach, without being actually reducible
to these. In particular, there is no splitting of worlds, which is a typical
feature of Everett-type theories. Altogether, the theory explains 1) the
subjective occurrence of probabilities, 2) their quantitative value as given by
the Born rule, 3) the identification of observables as self-adjoint operators
on Hilbert space, and 4) the apparently random "collapse of the wavefunction"
caused by the measurement, while still being an objectively deterministic
theory.
... All of them are trying to assign ontology to " worlds " in this or other form and remove the wave function from being ontological. Boström defines [124]: A world is a collection of finitely many particles having a definite mass and a definite position. ... A metaworld is a temporally evolving superposition of worlds of the same kind. ...
... yields the amount or volume of worlds whose configuration is contained within the set Q... ... the wavefunction is interpreted as describing a physically existing field, and its absolute square is taken to represent the density of this field, hence a density of worlds. (Boström, 2012). I will analyze below the possibility to view the wave function as a density of worlds. ...
Historically, appearance of the quantum theory led to a prevailing view that
Nature is indeterministic. The arguments for the indeterminism and proposals
for indeterministic and deterministic approaches are reviewed. These include
collapse theories, Bohmian Mechanics and the many-worlds interpretation. It is
argued that ontic interpretations of the quantum wave function provide simpler
and clearer physical explanation and that the many-worlds interpretation is the
most attractive since it provides a deterministic and local theory for our
physical Universe explaining the illusion of randomness and nonlocality in the
world we experience.
Here I explore a novel no-collapse interpretation of quantum mechanics that combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds. © 2015 by the Philosophy of Science Association. All rights reserved.
