Here, we show that by accepting Fuzzy time-Particle interpretation of Quantum Mechanics, the singularities in the new Model are vanished.

The major point in [1] chapter 2 is the following claim: “Any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction.” So, in the case we wish to save Classical Logic we should change our Computational Model. As we see in chapter two, the mentioned contradiction is about and around the concept of time, as it is in the contradiction of modified version of paradox. It is natural (...) to try fabricating the paradox not by time but in some other linear ordering or the concept of space. Interestingly, the attempts to have similar contradiction by the other concepts like space and linear ordering, is failed. It is remarkable that, the paradox is considered either Epistemological or Logical traditionally, but by new considerations the new version of paradox should be considered as either Logical or Physical paradox. Hence, in order to change our Computational Model, it is natural to change the concept of time, but how? We start from some models that are different from the classical one but they are intuitively plausible. The idea of model is somewhat introduced by Brouwer and Husserl [3]. This model doesn’t refute the paradox, since the paradox and the associated contradiction would be repeated in this new model. The model is introduced in [2]. Here we give some more explanations. (shrink)

Throughout this paper, in a nutshell we try to show a way to check Fuzzy time in general and Fuzzy time-Particle interpretation of Quantum Mechanics, experimentally. . -/- .

The question of some of the friends is: -/- How is it possible to explain “Double slit experiment” by “Fuzzy time-Particle Interpretation”?

A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion, field evolution and conservation laws can all be deduced from a single Lagrangian density expression. The formalism presented is Lorentz invariant. This paper follows on from a previous one which was limited to the single-particle case. The present paper treats (...) the more general case of many particles in an entangled state. It is found that describing more than one particle while maintaining a relativistic description requires the specification of final boundary conditions as well as the usual initial ones, with the experimenter’s controllable choice of the final conditions thereby exerting a backwards-in-time influence. This retrocausality then allows an important theoretical step forward to be made, namely that it becomes possible to dispense with the usual, many-dimensional description in configuration space and instead revert to a description in space–time using separate, single-particle wavefunctions. (shrink)

We consider time as a fuzzy concept. Based on this, the Fuzzy Time-Particle interpretation Of Quantum Mechanics is introduced as an interpretation of Quantum Mechanics [4],[5],[6]. Here, we show how to compute the function associated to Fuzzy time.

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change (...) this picture and show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

In conceptual debates involving the quantum gravity community, the literature discusses the so-called “emergence of space–time”. However, which interpretation of quantum mechanics (QM) could be coherent with such claim? We show that a modification of the Copenhagen Interpretation of QM is compatible with the claim that space–time is emergent for the macroscopic world of measurements. In other words, pure quantum states do not admit space–time properties until we measure them. We call (...) this approach “Achronotopic” (ACT) Interpretation of QM, which yields a simple and natural interpretation of the most puzzling aspects of QM, such as particle-wave duality, wave function collapse, entanglement, and quantum superposition. Our interpretation yields the same results in all measurements as the Copenhagen Interpretation, but provides clues toward the sub-Planckian physics. In particular, it suggests the non-existence of quantum gravity in the conventional sense understood as the quantization of a classical theory. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change (...) this picture and show why it is helpful to consider the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

We propose the Prototime Interpretation of quantum mechanics, which claims that quantum entanglement occurs in a "prototemporal" realm which underlies spacetime. Our paper is tentative and exploratory. The argument form is inference to the best explanation. We claim that the Prototime Interpretation (PI) is worthy of further consideration as a superior explanation for perplexing quantum phenomena such as delayed choice, superposition, the wave-particle duality and nonlocality. In Section One, we introduce the Prototime (...) class='Hi'>Interpretation. Section Two identifies its advantages. Section Three discusses several implications of the view, such as its deterministic nature and relation to the simulation hypothesis. (shrink)

E. Schrödinger's ideas on interpreting quantum mechanics have been recently re-examined by historians and revived by philosophers of quantum mechanics. Such recent re-evaluations have focused on Schrödinger's retention of space–time continuity and his relinquishment of the corpuscularian understanding of microphysical systems. Several of these historical re-examinations claim that Schrödinger refrained from pursuing his 1926 wave-mechanical interpretation of quantum mechanics under pressure from the Copenhagen and Göttingen physicists, who misinterpreted his ideas in their (...) dogmatic pursuit of the complementarity doctrine and the principle of uncertainty. My analysis points to very different reasons for Schrödinger's decision and, accordingly, to a rather different understanding of the dialogue between Schrödinger and N. Bohr, who refuted Schrödinger's arguments. Bohr's critique of Schrödinger's arguments predominantly focused on the results of experiments on the scattering of electrons performed by Bothe and Geiger, and by Compton and Simon. Although he shared Schrödinger's rejection of full-blown classical entities, Bohr argued that these results demonstrated the corpuscular nature of atomic interactions. I argue that it was Schrödinger's agreement with Bohr's critique, not the dogmatic pressure, which led him to give up pursuing his interpretation for 7 yr. Bohr's critique reflected his deep understanding of Schrödinger's ideas and motivated, at least in part, his own pursuit of his complementarity principle. However, in 1935 Schrödinger revived and reformulated the wave-mechanical interpretation. The revival reflected N. F. Mott's novel wave-mechanical treatment of particle-like properties. R. Shankland's experiment, which demonstrated an apparent conflict with the results of Bothe–Geiger and Compton–Simon, may have been additional motivation for the revival. Subsequent measurements have proven the original experimental results accurate, and I argue that Schrödinger may have perceived even the reformulated wave-mechanical approach as too tenuous in light of Bohr's critique. (shrink)

A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the “virtual” paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born’s (...) rule; therefore, Bell’s type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system. (shrink)

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv 0 =m 0 c 2 ; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon (1) ) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to the (...) nonlinear soliton wave U 0 introduced by him in his double solution model of wave mechanics. (2) Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic “aether,” (3) these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments. (shrink)

In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general (...) discussion about paradoxes, as Philosophical back ground of the subject and in this way, we introduce the concepts of General View, the first picture, BBF-General View. (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 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 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 wave function, 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 wave function is supplemented by the information provided by the configuration of the particles. The second possibility consists in assuming that, while the wave function 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 wave function ontologically seriously and avoid the problem of macroscopic superpositions just allowing for quantum jumps. In this paper we will argue that such "bare" wave function ontology is not possible, neither for GRW nor for any other quantum theory: quantum mechanics cannot be about the wave function simpliciter. That is, we need more structure than the one provided by the wave function. As a response, quantum theories about the wave function can be supplemented with structure, without taking it as an additional ontology. We argue in reply that such "dressed-up" versions of wave function 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 wave function; 2- Even if the wave function 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)

Quantum mechanics portrays the universe as involving non-local influences that are difficult to reconcile with relativity theory. By postulating backward causation, retro-causal interpretations of quantum mechanics could circumvent these influences and accordingly reconcile quantum mechanics with relativity. The postulation of backward causation poses various challenges for the retro-causal interpretations of quantum mechanics and for the existing conceptual frameworks for analyzing counterfactual dependence, causation and causal explanation. In this chapter, we analyze the nature (...) of time, causation and explanation in a local, deterministic retro-causal interpretation of quantum mechanics that is inspired by Bohmian mechanics. This interpretation of quantum mechanics offers a deterministic, local ‘hidden-variables’ model of the Einstein-Podolsky-Rosen experiment that poses a new challenge for Reichenbach’s principle of the common cause. In this model, the common cause – the state of particles at the emission from the source – screens off the correlation between its effects – the distant measurement outcomes – but nevertheless fails to explain the correlation between the effects. (shrink)

Elaboramos aquí una nueva interpretación propuesta recientemente de la teoría cuántica, según la cual las partículas cuánticas son consideradas como entidades conceptuales que median entre los pedazos de materia ordinaria los cuales son considerados como estructuras de memoria para ellos. Nuestro objetivo es identificar qué es lo equivalente para el ámbito cognitivo humano de lo que el espacio-tiempo físico es para el ámbito de las partículas cuánticas y de la materia ordinaria. Para ello, se identifica la noción de "historia" como (...) el equivalente en la esfera cognitiva humana de lo que la materia ordinaria es en el ámbito físico cuántico. Analizamos también el papel desempeñado por los conectivos lógicos de disyunción y de conjunción con respecto a la noción de localidad. De manera similar a lo que hemos hecho en investigaciones anteriores referidas a esa nueva interpretación de la teoría cuántica, se utiliza el entorno cognitivo específico de la Internet para dilucidar las comparaciones que hacemos entre el ámbito cognitivo humano y el ámbito físico cuántico. We elaborate the new interpretation of quantum theory that we recently proposed, according to which quantum particles are considered conceptual entities mediating between pieces of ordinary matter which are considered to act as memory structures for them. Our aim is to identify what is the equivalent for the human cognitive realm of what physical space-time is for the realm of quantum particles and ordinary matter. For this purpose, we identify the notion of 'story' as the equivalent within the human cognitive realm of what ordinary matter is in the physical quantum realm, and analyze the role played by the logical connectives of disjunction and conjunction with respect to the notion of locality. Similarly to what we have done in earlier investigations on this new interpretation of quantum theory, we use the specific cognitive environment of the Internet to elucidate the comparisons we make between the human cognitive realm and the physical quantum realm. (shrink)

Quantum mechanics, which describes the behavior of subatomic particles, seems to challenge common sense. Waves behave like particles; particles behave like waves. You can tell where a particle is, but not how fast it is moving--or vice versa. An electron faced with two tiny holes will travel through both at the same time, rather than one or the other. And then there is the enigma of creation ex nihilo, in which small particles appear with their so-called (...) antiparticles, only to disappear the next instant in a tiny puff of energy. Since its inception, physicists and philosophers have struggled to work out the meaning of quantum mechanics. Some, like Niels Bohr, have responded to quantum mechanics' mysteries by replacing notions of position and velocity with probabilities. Others, like Einstein and Penrose, have disagreed and think that the entire puzzle reflects not a fundamental principle of nature but our own ignorance of basic scientific processes. Sneaking a Look at God's Cards offers the general reader a deep and real understanding of the problems inherent to the interpretation of quantum mechanics, from its inception to the present. The book presents a balanced overview of current debates and explores how the theory of quantum mechanics plays itself out in the real world. Written from the perspective of a leading European physicist, the book looks extensively at ideas from both sides of the Atlantic and also considers what philosophers have contributed to the scientific discussion of this field. Sneaking a Look at God's Cards sets out what we know about the endlessly fascinating quantum world, how we came to this understanding, where we disagree, and where we are heading in our quest to comprehend the seemingly incomprehensible. (shrink)

Here, we continue the discussion in [1], about infinities in Physics. Our goal is to create a Mathematical system to give a probable explanation for infinities in QED, based on Fuzzy time. This Mathematical system should be sufficiently satisfactory and Simple. In general, our goal of these series, is to provide more reasons to consider time as a fuzzy concept in a way that is explained in [4], [5], [6].

An axiomatic framework for describing general space-time models is presented. Space-time models to which irreducible propositional systems belong as causal logics are quantum (q) theoretically interpretable and their event spaces are Hilbert spaces. Such aq space-time is proposed via a “canonical” quantization. As a basic assumption, the time t and the radial coordinate r of aq particle satisfy the canonical commutation relation [t,r]=±i $h =$ . The two cases will be considered simultaneously. In that (...) case the event space is the Hilbert space L2(ℝ3). Unitary symmetries consist of Poincaré-like symmetries (translations, rotations, and inversion) and of gauge-like symmetries. Space inversion implies time inversion. Thisq space-time reveals a confinement phenomenon: Theq particle is “confined” in an $h =$ size region of Minkowski space $\mathbb{M}^4$ at any time. One particle mechanics overq space-time provides mass eigenvalue equations for elementary particles. Prugovečki's stochasticq mechanics andq space-time offer a natural way for introducing and interpreting consistently such aq space-time andq particles existing in it. The mass eigenstates ofq particles generate Prugovečki's extended elementary particles. When $h =$ →0, these particles shrink to point particles and $\mathbb{M}^4$ is recovered as the classical (c) limit ofq space-time. Conceptual considerations favor the case [t,r]=+i $h =$ , and applications in hadron physics give the fit $h =$ ⋍2/5 fermi/GeV. (shrink)

A Lagrangian description is presented which can be used in conjunction with particle interpretations of quantum mechanics. A special example of such an interpretation is the well-known Bohm model. The Lagrangian density introduced here also contains a potential for guiding the particle. The advantages of this description are that the field equations and the particle equations of motion can both be deduced from a single Lagrangian density expression and that conservation of energy and momentum (...) are assured. After being developed in a general form, this Lagrangian formulation is then applied to the special case of the Bohm model as an example. It is thereby demonstrated that such a Lagrangian description is compatible with the predictions of quantum mechanics. (shrink)

A formulation of relativistic quantum mechanics is presented independent of the theory of Hilbert space and also independent of the hypothesis of spacetime manifold. A hierarchy is established in the nondistributive lattice of physical ensembles, and it is shown that the projections relating different members of the hierarchy form a semigroup. It is shown how to develop a statistical theory based on the definition of a statistical operator. Involutions defined on the matrix representations of the semigroup are interpreted (...) in terms ofCPT conjugations. The theory of particles of spin one-half and systems with higher spin is developed from first principles. Methods are also developed for defining energy, momentum, orbital angular momentum, and weighted spacetime coordinates without reference to a manifold. (shrink)

The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism (...) of quantum mechanics is only partly relevant to its problem, which is ostensibly known. The paper accepts just the opposite: The mathematical solution is absolute relevant and serves as an axiomatic base, from which the real and yet hidden problem is deduced. Wave-particle duality, Hilbert space, both probabilistic and many-worlds interpretations of quantum mechanics, quantum information, and the Schrödinger equation are included in that base. The Schrödinger equation is understood as a generalization of the law of energy conservation to past, present, and future moments of time. The deduced real problem of quantum mechanics is: “What is the universal law describing the course of time in any physical change therefore including any mechanical motion?”. (shrink)

The purpose of the paper is to explore different aspects of the covariance of non-relativistic quantum mechanics. First, doubts are expressed concerning the claim that gauge fields can be 'generated' by way of imposition of gauge covariance of the single-particle wave equation. Then a brief review is given of Galilean covariance in the general case of external fields, and the connection between Galilean boosts and gauge transformations. Under time-dependent translations the geometric phase associated with Schrödinger evolution (...) is non-invariant, and the significance of this result is briefly analysed. The covariance properties of Schrödinger dynamics are then brought to bear on certain versions of the modal interpretation of quantum mechanics. The conclusion that it is only relational properties that can be considered coordinate- or gauge-independent elements of reality is reinforced by appeal to the theory of quantum reference frames due to Aharonov and Kauffher. , Cambridge University Press ; pp. 45-70.). (shrink)

The single-particle wave function ψ=ReiS/h has been interpreted classically: At a given point the particle momentum is ▽S, and the relative particle density in an ensemble is R 2 . It is first proposed to modify this interpretation by assuming that physical variables undergo rapid fluctuations, so that ▽S is the average of the momentum over a short time interval. However, it appears that this is not enough. It seems necessary to assume that the density (...) also fluctuates. The fluctuations are taken to be random and to satisfy conditions required for agreement with quantum mechanics. In some cases the fluctuating density may take on instantaneous negative values. One gets agreement with quantum mechanics for the spin correlations of two particles in a singlet state. This comes about because of the correlations between the fluctuations of the variables of the two particles, the effect of which is equivalent to an action at a distance. The relation to Bell's inequality is discussed. (shrink)

Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time–space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein–Gordon–Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space–time curvatures. Interpretation of some important issues of quantum (...) mechanical reality is carried out in comparison with the 5D space–time–matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally. (shrink)

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the (...) problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research. (shrink)

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of “myths”, that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the (...) problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research. (shrink)

A mapping of a finite directed graph onto a curve in space-time is considered. The mapping induces the dynamics of a free particle moving along the curve. The distinction between the Lagrangian and the Hamiltonian formulation of particle mechanics is expressed in terms of the distinction between referring to a particle in space and time and referring to the points in space which the particle occupies, respectively. These elements are combined to yield an (...) interpretation of Feynman's path integral formulation of quantum mechanics. Describing a bound state of a system as a particle is discussed. (shrink)

Time-symmetric formulation of quantum mechanics—the two-state vector formalism—is presented as a tool for studying past behaviour of quantum systems. A role of weak measurement and weak values in the Cheshire Cat effect and a nested (Vaidman) three-path interferometer are discussed. Interpretation of a particle’s faint trace indicating possibility of discontinuous paths of particles passing the Vaidman interferometer is given. Consistent histories are presented as one of alternative approaches. Multitude of controversial issues is briefly reviewed (...) and discussed. (shrink)

The usual quantum mechanical treatment of a Schrödinger particle is translated into manifestly Galilean-invariant language, primarily through the use of Wigner-distribution methods. The hydrodynamical formulation of quantum mechanics is derived directly from the Wigner-distribution formulation, and the two formulations are compared. Wigner distributions are characterized directly, i.e., without reference to wave functions, and a heuristic interpretation of Wigner distributions and their evolution is developed.

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in the classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations: Δq>0 and Δp>0, i.e. the uncertainty (errors of observation) in the determination of coordinate (...) and momentum is always positive (non zero).A “functional” formulation of classical mechanics was suggested. The fundamental equation of the microscopic dynamics in the functional approach is not the Newton equation but the Liouville equation for the distribution function of the single particle. Solutions of the Liouville equation have the property of delocalization which accounts for irreversibility. The Newton equation in this approach appears as an approximate equation describing the dynamics of the average values of the position and momenta for not too long time intervals. Corrections to the Newton trajectories are computed. An interpretation of quantum mechanics is attempted in which both classical and quantum mechanics contain fundamental randomness. Instead of an ensemble of events one introduces an ensemble of observers. (shrink)

We expound an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. The ψ function is no longer interpreted as a probability amplitude of the observed behaviour of elementary particles but as an objective physical field representing the particles themselves. The particles are thus extended objects whose extension varies (...) in time according to the variation of ψ. They are considered as fundamental regions of space with some kind of nonlocality. Special consideration is given to the Heisenberg relations, the Einstein-Podolsky- Rosen correlations, the reduction process, the problem of measurement, and the quantum-statistical distributions. (shrink)

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems (...) are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics.These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble.Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the center of masses of large macroscopic systems do satisfy Newton’s laws. (shrink)

Certain modifications, by way of improvement, are proposed for the Feynman postulates in quantum mechanics. These modifications incorporate a criterion for the applicability of the principle of superposition. It is shown that the modified postulates, together with certain assumptions regarding the trajectory of a particle, lead to an expression for the position-momentum uncertainty relationship which is broadly in agreement with the conventional expression. The time-energy uncertainty relationship is, however, found to have a likely place only in (...) the relativistic theory. A criterion, in the form of a ratio involving the linear dimensions of the particle, is obtained for the validity of the classical mechanics approximation. The modified postulates are suggested to favor the statistical interpretation of quantum mechanics over the Copenhagen interpretation. (shrink)

Recent double-slit type neutron experiments (1) and their theoretical implications (2) suggest that, since one can tell through which slit the individual neutrons travel, coherent wave packets remain nonlocally coupled (with particles one by one), even in the case of wide spatial separation. Following de Broglie's initial proposal, (3) this property can be derived from the existence of the persisting action of real superluminal physical phase waves considered as building blocks of the real subluminal wave field packets which surround individual (...) particle paths in the Einstein-de Broglie-Bohm interpretation of quantum mechanics. (shrink)

Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory (...) require us to abandon classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an example of just what it is to do the philosophy of physics. (shrink)

The realist interpretations of quantum theory, proposed by de Broglie and by Bohm, are re-examined and their differences, especially concerning many-particle systems and the relativistic regime, are explored. The impact of the recently proposed experiments of Vigier et al. and of Ghose et al. on the debate about the interpretation of quantum mechanics is discussed. An indication of how de Broglie and Bohm would account for these experimental results is given.

We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle–wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources. The final world model treated here contains only gravonons and a scalar matter field. The (...) gravonons are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: There is a chooser mechanism for the selection of the localization site. The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schrödinger’s equation without the need of introducing a probabilistic interpretation. (shrink)

The simplest nonlinear spinor field equation admitting regular stationary solutions is considered. Following a causal interpretation of quantum mechanics, given by de Broglie in his double solution theory, these regular solutions must be regarded as describing the internal particle structure. Using this spinor field model, an attempt is made to give a statistical description of one-particle experiments by means of a Gibbsian assemblage method. It is shown that in the limiting case of pointlike nonrelativistic particles (...) this method is equivalent to the quantum mechanical one, that is, the probability amplitude can be introduced satisfying all postulates of quantum mechanics. (shrink)

We present a new approach on the interpretation of the quantum mechanism. The derivation is phenomenological and incorporates an energetic vacuum which interacts with elementary particles. We consider a classical ensemble average for the square of 4-velocities of identical elementary particles with the same initial conditions in Minkowski space. The relativistic extension of a result in Brownian motion allows the variance to be identified with Bohm's quantum potential. A simple relation between 4-velocities and 4-momenta at a specific (...) 4-position with given proper time leads to one of two statistical equations that constitute our quantum theory, the other being the continuity equation. The Klein-Gordon equation is a consequence of these two statistical equations. (shrink)

How long does a quantum particle take to traverse a classically forbidden energy barrier? In other words, what is the correct expression for quantum tunnelling time? This seemingly simple question has inspired widespread debate in the physics literature. I argue that we should not expect the orthodox interpretation of quantum mechanics to provide a unique correct expression for quantum tunnelling time, because to do so it would have to provide a unique (...) correct answer to a question whose assumptions are in tension with its core interpretational commitments. I explain how this conclusion connects to time’s special status in quantum mechanics, the meaningfulness of classically inspired concepts in different interpretations of quantum mechanics, the prospect of constructing experimental tests to distinguish between different interpretations, and the status of weak measurement in resolving questions about the histories of subensembles. (shrink)

In a recently proposed interpretation of quantum mechanics, U. Mohrhoff advocates original and thought-provoking views on space and time, the definition of macroscopic objects, and the meaning of probability statements. The interpretation also addresses a number of questions about factual events and the nature of reality. The purpose of this note is to examine several issues raised by Mohrhoff's interpretation, and to assess whether it helps providing solutions to the long-standing problems of quantum (...) mechanics. (shrink)

Over many years, Aharonov and co-authors have proposed a new interpretation of quantum mechanics: the two-time interpretation. This interpretation assigns two wavefunctions to a system, one of which propagates forwards in time and the other backwards. In this paper, I argue that this interpretation does not solve the measurement problem. In addition, I argue that it is neither necessary nor sufficient to attribute causal power to the backwards-evolving wavefunction ⟨Φ| and thus its (...) existence should be denied, contra the two-time interpretation. Finally, I follow Vaidman in giving an epistemological reading of ⟨Φ|. (shrink)

It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from “Copenhagen” to “many worlds” are critically revisited. The difficulties for intuitive models of quantum physics are pointed out and possible solutions proposed. In particular the existence of discrete states, the quantum jumps, the alleged lack of objective properties, measurement theory, the probabilistic character of quantum physics, the wave–particle duality and the Bell inequalities are analyzed. The sketch (...) of a realistic picture of the quantum world is presented. It rests upon the assumption that quantum mechanics is a stochastic theory whose randomness derives from the existence of vacuum fields. They correspond to the vacuum fluctuations of quantum field theory, but taken as real rather than virtual. (shrink)

The Conditional Probability Interpretation of Quantum Mechanics replaces the abstract notion of time used in standard Quantum Mechanics by the time that can be read off from a physical clock. The use of physical clocks leads to apparent non-unitary and decoherence. Here we show that a close approximation to standard Quantum Mechanics can be recovered from conditional Quantum Mechanics for semi-classical clocks, and we use these clocks to compute the (...) minimum decoherence predicted by the Conditional Probability Interpretation. (shrink)

The interpretation of quantum mechanics presented in this paper is inspired by two ideas that are fundamental in Bohr’s writings: indivisibility and complementarity. Further basic assumptions of the proposed interpretation are completeness, universality and conceptual economy. In the interpretation, decoherence plays a fundamental role for the understanding of measurement. A general and precise conception of complementarity is proposed. It is fundamental in this interpretation to make a distinction between ontological reality, constituted by everything that (...) does not depend at all on the collectivity of human beings, nor on their decisions or limitations, nor on their existence, and empirical reality constituted by everything that not being ontological is, however, intersubjective. According to the proposed interpretation, neither the dynamical properties, nor the constitutive properties of microsystems like mass, charge and spin, are ontological. The properties of macroscopic systems and space-time are also considered to belong to empirical reality. The acceptance of the above mentioned conclusion does not imply a total rejection of the notion of ontological reality. In the paper, utilizing the Aristotelian ideas of general cause and potentiality, a relation between ontological reality and empirical reality is proposed. Some glimpses of ontological reality, in the form of what can be said about it, are finally presented. (shrink)

Einstein’s unpublished 1927 deterministic trajectory interpretation of quantum mechanics is critically examined, in particular with regard to the reason given by Einstein for rejecting his theory. It is shown that the aspect Einstein found objectionable—the mutual dependence of the motions of particles when the (many-body) wavefunction factorises—is a generic attribute of his theory but that this feature may be removed by modifying Einstein’s method in either of two ways: using a suggestion of Grommer or, in a physically (...) important special case, using a simpler technique. It is emphasized though that the presence or absence of the interdependence property does not determine the acceptability of a trajectory theory. It is shown that there are other grounds for rejecting Einstein’s theory (and the two modified theories), to do with its domain of applicability and compatibility with empirical predictions. That Einstein’s reason for rejection is not a priori grounds for discarding a trajectory theory is demonstrated by reference to an alternative deterministic trajectory theory that displays similar particle interdependence yet is compatible with quantum predictions. (shrink)

We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects without having to invoke the existence of measurable classical quantities like the time in ordinary quantum mechanics. The formulation eliminates any (...) privileged role to the measurement process giving an objective definition of when an event occurs in a system. (shrink)

A drastic resolution of the quantum paradoxes is proposed, combining (I) von Neumann's postulate that collapse of the state vector is due to the act of observation, and (II) my reinterpretation of von Neumann's quantal irreversibility as an equivalence between wave retardation and entropy increase, both being “factlike” rather than “lawlike” (Mehlberg). This entails a coupling of the two de jure symmetries between (I) retarded and (II) advanced waves, and between Aristotle's information as (I) learning and (II) willing awareness. (...) Symmetric acceptance of cognizance as a source of retarted waves, and of will as a sink of advanced waves, is submitted as a central “paradox” of the Copernican or Einsteinian sort, out of which new light is shed upon previously known paradoxes, such as the EPR paradox, Schrödinger's cat, and Wigner's friend. Parapsychology is thus found to creep into the picture. (shrink)