The meaning of the wavefunction and its evolution are investigated. First, we argue that the wavefunction in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wavefunction gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wavefunction of an isolated system obeys the free Schrödinger equation due (...) to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wavefunction. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)
This article analyzes the implications of protective measurement for the meaning of the wavefunction. According to protective measurement, a charged quantum system has mass and charge density proportional to the modulus square of its wavefunction. It is shown that the mass and charge density is not real but effective, formed by the ergodic motion of a localized particle with the total mass and charge of the system. Moreover, it is argued that the ergodic motion (...) is not continuous but discontinuous and random. This result suggests a new interpretation of the wavefunction, according to which the wavefunction is a description of random discontinuous motion of particles, and the modulus square of the wavefunction gives the probability density of the particles being in certain locations. It is shown that the suggested interpretation of the wavefunction disfavors the de Broglie-Bohm theory and the many-worlds interpretation but favors the dynamical collapse theories, and the random discontinuous motion of particles may provide an appropriate random source to collapse the wavefunction. (shrink)
We investigate the meaning of the wavefunction by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wavefunction. In a realistic interpretation, the wavefunction of a quantum system can be taken as a description of either a physical field or the ergodic motion (...) of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wavefunction is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wavefunction. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wavefunction cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wavefunction. Which kind of ergodic motion of particles then? It is argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wavefunction is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wavefunction not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. We show that this new interpretation of the wavefunction provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed. (shrink)
We show that the physical meaning of the wavefunction can be derived based on the established parts of quantum mechanics. It turns out that the wavefunction represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.
The possibility of consistency between the basic quantum principles of quantum mechanics and wavefunction collapse is reexamined. A specific interpretation of environment is proposed for this aim and is applied to decoherence. When the organization of a measuring apparatus is taken into account, this approach leads also to an interpretation of wavefunction collapse, which would result in principle from the same interactions with environment as decoherence. This proposal is shown consistent with the non-separable character (...) of quantum mechanics. (shrink)
I argue that the wavefunction ontology for quantum mechanics is an undesirable ontology. This ontology holds that the fundamental space in which entities evolve is not three-dimensional, but instead 3N-dimensional, where N is the number of particles standardly thought to exist in three-dimensional space. I show that the state of three-dimensional objects does not supervene on the state of objects in 3N-dimensional space. I also show that the only way to guarantee the existence of the appropriate mental (...) states in the wavefunction ontology has undesirable metaphysical baggage: either mind/body dualism is true, or circumstances which we take to be logically possible turn out to be logically impossible.While our theory can be extended formally in a logically consistent way by introducing the concept of a wave in a 3N-dimensional space, it is evident that this procedure is not really acceptable in a physical theory... (Bohm 1957, 117). (shrink)
Two different concepts of distinguishability are often mixed up in attempts to derive in quantum mechanics the (anti)symmetry of the wavefunction from indistinguishability of identical particles. Some of these attempts are analyzed and shown to be defective. It is argued that, although identical particles should be considered as observationally indistinguishable in (anti)symmetric states, they may be considered to be conceptually distinguishable. These two notions of (in)distinguishability have quite different physical origins, the former one being related to observations (...) while the latter has to do with the preparation of the system. (shrink)
An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct Klein-Gordon equations and two distinct Dirac-type equations in a general metric, depending on the connection used. Each of (...) these two equations is generally-covariant, transforms the wavefunction as a four-vector, and differs from the Fock-Weyl gravitational Dirac equation (DFW equation). One obeys the equivalence principle in an often-accepted sense, whereas the DFW equation obeys that principle only in an extended sense. (shrink)
The following introduction offers a broad survey of the history of quantum physics. It then outlines the position of each contributor in this Special Focus Section concerning the collapse of the quantum wavefunction and defines three important terms (Hilbert space, Schrödinger’s cat, and decoherence) used in discussing this topic.
We investigate and develop further two models, the GRW model and the K model, in which the Schrödinger evolution of the wavefunction is spontaneously and repeatedly interrupted by random, approximate localizations, also called “self-reductions” below. In these models the center of mass of a macroscopic solid body is well localized even if one disregards the interactions with the environment. The motion of the body shows a small departure from the classical motion. We discuss the prospects and the (...) difficulties of observing this anomaly. As far a the influence of the surroundings on submacroscopic objects (like dust particles) is concerned, we show that the estimates obtained recently in the theory of continuous measurements and in the K model are compatible. Also, we elaborate upon the relationship between the models. Firstly, borrowing a line of thought from the K model, we find the transition region between macroscopic and microscopic behaviors in the GRW model. Secondly, we refine the propagation rule of the wavefunction in the K model with the help of the time-evolution equation proposed in the GRW model. (shrink)
Probability distributions are seen to be observer dependent. The probability function ψ†ψ can be put into an observer-dependent form. This eliminates the acausal behavior of the collapse of the wavefunction.
A brief review of the conceptual difficulties met by the quantum formalism is presented. The main attempts to overcome these difficulties are considered and their limitations are pointed out. A recent proposal based on the assumption of the occurrence of a specific type of wavefunction collapse is discussed and its consequences for the above-mentioned problems are analyzed.
The many-Hilbert-spaces approach to the measurement problem in quantum mechanics is reviewed, and the notion of wavefunction collapse by measurement is formulated as a dephasing process between the two branch waves of an interfering particle. Following the approach originally proposed in Ref. 1, we introduce a “decoherence parameter,” which yields aquantitative description of the degree of coherence between the two branch waves of an interfering particle. By discussing the difference between the wavefunction collapse and (...) the orthogonality of the apparatus' wave functions, we analyze critically two proposals, recently appeared in the literature, (2, 3) and argue that neither one describes a dephasing process. We conclude that the concept of “wavefunction collapse,” according to the conventional Copenhagen interpretation, is to be replaced by that of a statisticallydefined dephasing process. (shrink)
We suggest scattering experiments which implement the concept of “protective measurements” allowing the measurement of the complete wavefunction even when only one quantum system (rather than an ensemble) is available. Such scattering experiments require massive, slow, projectiles with kinetic energies lower than the first excitation of the system in question. The results of such experiments can have a (probabilistic) distribution (as is the case when the Born approximation for the scattering is valid) or be deterministic (in a (...) semiclassical limit). (shrink)
It is pointed out that ordinary quantum mechanics as a classical field theory cannot account for the wavefunction collapse if it is not seen within the framework of field quantization. That is needed to understand the particle structure of matter during wavefunction evolution and to explain the collapse as symmetry breakdown by detection. The decay of a two-particle bound s state and the Stern-Gerlach experiment serve as examples. The absence of the nonlocality problem in (...) Bohm’s version of the EPR arrangement favours the approach described. (shrink)
We introduce a theoretical model to scrutinize the conductivity of small polarons in 1D disordered systems, focusing on two crucial ? as will be demonstrated ? factors: the density of states and the spatial extent of the electronic wavefunction. The investigation is performed for any temperature up to 300 K and under electric field of arbitrary strength up to the polaron dissociation limit. To accomplish this task, we combine analytical work with numerical calculations.
Under certain conditions private information can be a source of trade. Arbitrage for instance can occur as a result of the existence of private information. In this paper we want to explicitly model information. To do so we define an ‘information function’. This information function is a mathematical object, also known as a so called ‘wavefunction’. We use the definition of wavefunction as it is used in quantum mechanics and we attempt to (...) show the usefulness of this wavefunction in an economic context. We attempt to answer the following questions. How does the information function relate to private information? How can we use the information function to define the ‘quantity’ of information? How can we use the information function in arbitrage-based option pricing? How can the information function be used in the formulation of a so called Universal Brownian motion? (shrink)
The inherent necessity of wave functions may be determined in either of two ways. One way, frequently presupposed, states that the fundamental validity of wave functions is determined generically: The nature of the system determines the assignability of inherently necessary wave functions. The other approach holds that it is the specific experiment which determines the systems for which description by use of wave functions is fundamentally valid. A guideline based on this contextual approach is proposed and (...) tested in three experimental situations. (shrink)
We study here the properties of some quantum mechanical wave functions, which, in contrast to the regular quantum mechanical wave functions, can be predetermined with certainty (probability 1) by performing dense measurements (or continuous observations). These specific “certain” states are the junction points through which pass all the diverse paths that can proceed between each two such neighboring “sure” points. When we compare the properties of these points to the properties of the well-known universal wave functions of (...) Everett we find a strong similarity between these two apparently uncorrelated entities, and in this way find the same similarity between the Feynman path integrals and Everett's universal wave functions. (shrink)
We propose a simple classical model of the zitterbewegung. In this model spin is proportional to the velocity of the particle, the component parallel top is constant and the orthogonal components are oscillating with2p frequency. The quantization of the system gives wave equations for spin,0, 1/2, 1, 3/2,…, etc. respectively. These equations are convenient for massless particles. The wave equation of the spin-1, massless free particle is equivalent to the Maxwell equations and the state functions have a probability (...) interpretation and exhibit conserved current densities. The ground state has zero energy. (shrink)
Scientific endeavour has often tried to localize superior cerebral functions either in areas like the ones described by Broca as being those connected with language in the left hemisphere, or in the huge array of the hundred billion of interconnected neurons. But in this last case the coined description of the grandmother neuron, tends to show humorously that hopes have fallen short of their target.Along the same lines, the specific timing of electric neural activity is known to take place around (...) a few milliseconds, which seems to be insufficient to account for the high potential speed necessary to sustain the very massive and complex process which is involved in mental activity. (shrink)
We investigate the validity of the field explanation of the wavefunction 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 wavefunction. This is also a consequence of protective measurement. If the wavefunction is a physical field, then the mass and charge density (...) will be distributed in space simultaneously for a charged quantum system, and thus there will exist a remarkable electrostatic self-interaction of its wavefunction, though the gravitational self-interaction is too weak to be detected presently. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus we conclude that the wavefunction cannot be a description of a physical field. In the second part of this paper, we further analyze the implications of these results for the main realistic interpretations of quantum mechanics, especially for de Broglie-Bohm theory. It has been argued that 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 wavefunction, regarded as a Ψ-field, has no mass and charge density distributions, which turns out to be wrong according to the above results. For a charged quantum system, both Ψ-field and Bohmian particle have charge density distribution. This then results in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which contradicts both the predictions of quantum mechanics and experimental observations. Therefore, de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is probably wrong. Lastly, we suggest that the wavefunction is a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles, and we also briefly analyze the implications of this suggestion for other realistic interpretations of quantum mechanics including many-worlds interpretation and dynamical collapse theories. (shrink)
It is shown that the superposed wavefunction of a measuring device, in each branch of which there is a definite measurement result, does not correspond to many mutually unobservable but equally real worlds, as the superposed wavefunction can be observed in our world by protective measurement.
We investigate the implications of protective measurement for de Broglie-Bohm theory, mainly focusing on the interpretation of the wavefunction. 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 wavefunction, 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 has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wavefunction. Then in the de Broglie-Bohm theory both Ψ-field and Bohmian particle will have charge density distribution for a charged quantum system. This will result in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Therefore, the de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is problematic according to protective measurement. Lastly, we briefly discuss the possibility that the wavefunction is not a physical field but a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles. (shrink)
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 wavefunction ontology: the view according to which the wavefunction 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 (...)wavefunction evolves in time according to the equations that has his name). The Many-Worlds interpretation1 accepts the existence of such macroscopic superpositions but takes it that they can never be observed. Superposed objects and superposed observers split together in different worlds of the type of the one we appear to live in. For these who, like Schroedinger, think that macroscopic superpositions are a problem, the common wisdom is that there are two alternative views: "Either the wavefunction, as given by the Schroedinger equation, is not everything, or is not right" [Bell 1987]. The deBroglie-Bohm theory, now commonly known as Bohmian Mechanics, takes the first option: the description provided by a Schroedinger-evolving wavefunction is supplemented by the information provided by the configuration of the particles. The second possibility consists in assuming that, while the wavefunction provides the complete description of the system, its temporal evolution is not given by the Schroedinger equation. Rather, the usual Schroedinger evolution is interrupted by random and sudden "collapses". The most promising theory of this kind is the GRW theory, named after the scientists that developed it: Gian Carlo Ghirardi, Alberto Rimini and Tullio Weber.. It seems tempting to think that in GRW we can take the wavefunction ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper we will argue that such "bare" wavefunction ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wavefunction simpliciter. That is, we need more structure than the one provided by the wavefunction. As a response, quantum theories about the wavefunction can be supplemented with structure, without taking it as an additional ontology. We argue in reply that such "dressed-up" versions of wavefunction ontology are not sensible, since they compromise the acceptability of the theory as a satisfactory fundamental physical theory. Therefore we maintain that: 1- Strictly speaking, it is not possible to interpret quantum theories as theories about the wavefunction; 2- Even if the wavefunction is supplemented by additional non-ontological structures, there are reasons not to take the resulting theory seriously. Moreover, we will argue that any of the traditional responses to the measurement problem of quantum mechanics (Bohmian mechanics, GRW and Many-Worlds), contrarily to what commonly believed, share a common structure. That is, we maintain that: 3- All quantum theories should be regarded as theories in which physical objects are constituted by a primitive ontology. The primitive ontology is mathematically represented in the theory by a mathematical entity in three-dimensional space, or space-time. (shrink)
We give a new argument supporting a gravitational role in quantum collapse. It is demonstrated that the discreteness of space-time, which results from the proper combination of quantum theory and general relativity, may inevitably result in the dynamical collapse of thewave function. Moreover, the minimum size of discrete space-time yields a plausible collapse criterion consistent with experiments. By assuming that the source to collapse the wavefunction is the inherent random motion of particles described by the (...) class='Hi'>wavefunction, we further propose a concrete model of wavefunction collapse in the discrete space-time. It is shown that the model is consistent with the existing experiments and macroscopic experiences. (shrink)
The literature on physicalism often fails to elucidate, I think, what the word physical in physical ism precisely means. Philosophers speak at times of an ideal set of fundamental physical facts, or they stipulate that physical means non-mental , such that all fundamental physical facts are fundamental facts pertaining to the non-mental. In this article, I will probe physicalism in the very much tangible framework of quantum mechanics. Although this theory, unlike “ideal physics” or some “final theory of non-mentality”, is (...) an incomplete theory of the world, I believe this analysis will be of value, if for nothing else, at least for bringing some taste of physical reality, as it were, back to the debate. First, I will introduce a broad characterization of the physicalist credo. In Sect. 2, I will provide a rather quick review of quantum mechanics and some of its current interpretations. In Sect. 3, the notion of quantum non-separability will be analyzed, which will facilitate a discussion of the wavefunction ontology in Sect. 4. In Sects. 5 and 6, I will explore competing views on the implications of this ontology. In Sect. 7, I will argue that the prior results, based on a thoroughly realist interpretation of quantum mechanics, support only a weak version of non-reductive physicalism. (shrink)
When a quantum system is macroscopic and becomes entangled with a microscopic one, entanglement is not immediately total, but gradual and local. A study of this locality is the starting point of the present work and shows unexpected and detailed properties in the generation and propagation of entanglement between a measuring apparatus and a microscopic measured system. Of special importance is the propagation of entanglement in nonlinear waves with a finite velocity. When applied to the entanglement between a macroscopic system (...) and its environment, this study yields also new results about the resulting disordered state. Finally, a mechanism of wavefunction collapse is proposed as an effect of perturbation in the growth of local entanglement between a measuring system and the measured one by waves of entanglement with the environment. (shrink)
In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wavefunction collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wavefunction as a space-time probability density. The particle’s configurations evolve in space-time in terms of a parameter σ with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction (...) with an external electromagnetic field. The physical meaning of σ is explored. Two special situations are studied in depth: (1) the classical limit, where the Einsteinian Mechanics of Special Relativity is recovered and the parameter σ is shown to tend to the particle’s proper time; and (2) the non-relativistic limit, where it is obtained a model very similar to the usual non-relativistic Bohmian Mechanics but with the time of the frame of reference replaced by σ as the dynamical temporal parameter. (shrink)
We review the relation between spacetime geometries with trace-torsion fields, the so-called Riemann–Cartan–Weyl (RCW) geometries, and their associated Brownian motions. In this setting, the drift vector field is the metric conjugate of the trace-torsion one-form, and the laplacian defined by the RCW connection is the differential generator of the Brownian motions. We extend this to the state-space of non-relativistic quantum mechanics and discuss the relation between a non-canonical quantum RCW geometry in state-space associated with the gradient of the quantum-mechanical expectation (...) value of a self-adjoint operator given by the generalized laplacian operator defined by a RCW geometry. We discuss the reduction of the wavefunction in terms of a RCW quantum geometry in state-space. We characterize the Schroedinger equation in terms of the RCW geometries and Brownian motions. Thus, in this work, the Schroedinger field is a torsion generating field, both for the linear and non-linear cases. We discuss the problem of the many times variables and the relation with dissipative processes, and the role of time as an active field, following Kozyrev and a recent experiment in non-relativistic quantum systems. We associate the Hodge dual of the drift vector field with a possible angular-momentum source for the phenomenae observed by Kozyrev. (shrink)
We discuss the issue of quantum-classical transition in a system of a single particle with and without external potential. This is done by elaborating the notion of self-trapped wavefunction recently developed by the author. For a free particle, we show that there is a subset of self-trapped wave functions which is particle-like. Namely, the spatially localized wave packet is moving uniformly with undistorted shape as if the whole wave packet is indeed a classical free (...) particle. The length of the spatial support of the wave packet is given by the Compton wavelength so that the wave packet is more localized for particle with larger mass. Whereas for a particle of mass m in a macroscopic external potential, we show that the time needed by the corresponding self-trapped wavefunction to depart from a classical trajectory is of the order ∼m 2 c/ℏ. We argue that it is the Compton wavelength that matters and not the de Broglie wavelength as in conventional semiclassical approach. (shrink)
It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wavefunction (“statistical mixture”) or a system that is entangled with another system (“reduced density matrix”). We point out another role, previously unnoticed in the literature, that a density matrix can play: it can be the “conditional density matrix,” conditional on the configuration of the environment. A precise definition can be (...) given in the context of Bohmian mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp definition, except perhaps in special cases. In contrast to statistical and reduced density matrices, forming the conditional density matrix involves no averaging. In Bohmian mechanics with spin, the conditional density matrix replaces the notion of conditional wavefunction, as the object with the same dynamical significance as the wavefunction of a Bohmian system. (shrink)
Knowledge of the entanglement properties of the wave functions commonly used to describe quantum many-particle systems can enhance our understanding of their correlation structure and provide new insights into quantum phase transitions that are observed experimentally or predicted theoretically. To illustrate this theme, we first examine the bipartite entanglement contained in the wave functions generated by microscopic many-body theory for the transverse Ising model, a system of Pauli spins on a lattice that exhibits an order-disorder magnetic quantum phase (...) transition under variation of the coupling parameter. Results for the single-site entanglement and measures of two-site bipartite entanglement are obtained for optimal wave functions of Jastrow-Hartree type. Second, we address the nature of bipartite and tripartite entanglement of spins in the ground state of the noninteracting Fermi gas, through analysis of its two- and three-fermion reduced density matrices. The presence of genuine tripartite entanglement is established and characterized by implementation of suitable entanglement witnesses and stabilizer operators. We close with a broader discussion of the relationships between the entanglement properties of strongly interacting systems of identical quantum particles and the dynamical and statistical correlations entering their wave functions. (shrink)
Some wave functions separate into two or more distinct regions in phase space. Each region is characterized by a trajectory and a spread about that trajectory. The trajectory is the quantum mechanical current. We show that these regions correspond to parts of the wavefunction and that these parts are generally nonorthogonal.
Sum rules are derived for the quantum wave functions of the Hadamard billiard in arbitrary dimensions. This billiard is a strongly chaotic (Anosov) system which consists of a point particle moving freely on a D-dimensional compact manifold (orbifold) of constant negative curvature. The sum rules express a general (two-point)correlation function of the quantum mechanical wave functions in terms of a sum over the orbits of the corresponding classical system. By taking the trace of the orbit sum rule (...) or pre-trace formula, one obtains the Selberg trace formula. The sum rules are applied in two dimensions to a compact Riemann surface of genus two, and in three dimensions to the only non-arithmetic tetrahedron existing in hyperbolic 3-space. It is shown that the quantum wave functions can be computed from classical orbits. Conversely, we demonstrate that the structure of classical orbits can be extracted from the quantum mechanical energy levels and wave functions (inverse quantum chaology). (shrink)
The phase space formulation of quantum mechanics is based on the use of quasidistribution functions. This technique was pioneered by Wigner, whose distribution function is perhaps the most commonly used of the large variety that we find discussed in the literature. Here we address the question of how one can obtain distribution functions and hence do quantum mechanics without the use of wave functions.
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 (...) should we be realist regarding these theories? Two different proposals have been made: on the one hand, there are those who insist on a direct ontological interpretation of the wavefunction as representing physical bodies, and on the other hand there are those who claim that quantum mechanics is not really about the wavefunction. In this paper we will present and discuss one proposal of the latter kind that focuses on the notion of primitive ontology. (shrink)
Under so-called primitive ontology approaches, in fully describing the history of a quantum system, one thereby attributes interesting properties to regions of spacetime. Primitive ontology approaches, which include some varieties of Bohmian mechanics and spontaneous collapse theories, are interesting in part because they hold out the hope that it should not be too difficult to make a connection between models of quantum mechanics and descriptions of histories of ordinary macroscopic bodies. But such approaches are dualistic, positing a quantum state as (...) well as ordinary material degrees of freedom. This paper lays out and compares some options that primitive ontologists have for making sense of the quantum state. (shrink)
A simple quantum model describing the onset of time is presented. This is combined with a simple quantum model of the onset of space. A major purpose is to explore the interpretational issues which arise. The state vector is a superposition of states representing different “instants.” The sample space and probability measure are discussed. Critical to the dynamics is state vector collapse: it is argued that a tenable interpretation is not possible without it. Collapse provides a mechanism whereby the universe (...) size, like a clock, is narrowly correlated with the quantized time eigenvalues. (shrink)
This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein’s bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies (...) of the CI, and gives intuitive explanations of some previously mysterious quantum effects. (shrink)
The aim of this note is to complete the discussion on the possibility of creation of quantum-like (QL) representation for the question order effect which was presented by Wang and Busemeyer (2013). We analyze the role of a fundamental feature of mental operators (given, e.g., by questions), namely, their complementarity.