In the well known Copenhagen interpretation of Quantum mechanics, advocated by N. Bohr, the physical objects and the experimental results can be described only in a macroscopic language, leaving any possible microscopic description as `unspeakable’. This point of view has been deepened by C. Rovelli in the `relational interpretation’ of Quantum mechanics. Most of the alternative interpretations, which try a detailed microscopic description of physical phenomena and of their evolution, have in common the explicit introduction of the wave function as the basic element of the theory. These interpretations require the notion of `quantum state’ as the fundamental concept of the theory, which is the typical `unspeakable’ physical element according to the Copenhagen interpretation. The two basic physical entities are intimately bound together by the integrity of the wave function. These interpretations are usually indicated as “realistic”. It is well known that the use of the wave function and its time evolution in the description of the physical processes leads unavoidably to some difficulties or so-called `paradoxes’. The measurement problem is at the center of these difficulties, mainly because it requires the introduction of the reduction process of the wave function, which is not included explicitly within the mathematical formalism of Quantum Mechanics. In this paper we build up and propose a model which goes beyond the standard formalism and which is able to solve the measurement problem and all the other difficulties which, in a way or in another, are related to it.

]]>It is shown that the probability density satisfies a hyperbolic equation of motion with the unique characteristic that in its many-particle form it contains derivatives acting at spatially remote regions. Based on this feature we explore inter-particle correlations and the relation between the quantum equilibrium condition and the permutation invariance of the probability density. Some remarks concerning the quantum to classical transition are also presented.

]]>In this paper we examine the quantum wave equations for an observer experiencing constant gravity acceleration. For non-relativistic Newtonian gravity by using a thought experiment (along with related derivation method) and the weak equivalence principle, we derive the Schrodinger wave equation for a “local observer” (located in a small spatial interval), stationary with respect to a static gravitational field. In the case of curved space time with a static space time metric, by using the same procedure and applying the equivalence principle, we derive the Dirac and the Klein-Gordon wave equations for a local observer, stationary with respect to the static space time metric background.

]]>The central mystery of quantum mechanics is the principle of quantization. The Heisenberg uncertainty principle is a consequence of quantization, as are the interpretative problems of quantum mechanics, such as the measurement problem and wave-particle duality. John Wheeler expressed the mystery of quantization in the question: “How come the quantum? What is the deeper principle that lies behind the strange quantum behavior that rules our world?” The present article proposes a deeper principle that offers an answer to Wheeler’s question. At its core are two closely related elements. One is Sciama’s 1958 suggestion that one half of the causal determinants of systems always lie in their future—quantization simply reflecting our ignorance of that future half. The other is the postulation of an underlying periodic process that every spin-half particle undergoes in the ‘shadow’ of the Heisenberg uncertainty principle. It is an extension of an early idea of Dirac’s. The deeper principle also suggests an answer to a related mystery: to *what* exactly might the frequency and the wavelength actually refer in the Einstein-de Broglie relations (besides, trivially, to the frequency and wavelength of a quantum system represented by the wave function)? In other words, what are they the frequency and wavelength *of?* And how does the frequency (whatever it’s the frequency of) entail, *physically*, an energy, i.e. require Planck’s constant as a conversion factor when energy is expressed in conventional units?

In this paper I inquire into the applicability of topological structures in the mathematical modeling of certain quantum situations and attempt an interpretation, on the level of metatheory, of phenomena associated with the time evolution of quantum processes and the individuality of quantum objects upon observation. Accordingly the paper engages, on the one hand, in an epistemologically oriented discussion of the merits of topological approaches concerning natural science in general and certain questions of quantum theory in particular, and on the other, in an elaboration of a proper topological structure to deal with the mathematical aspects of an open question of the theory of quantum histories, the latter as developed mainly by C. J. Isham and co. On this motivation a brief discussion concerning the topological nature of the Bohm-Aharonov effect is thought to be in order. Overall the primary focus is to discuss the relevance of topology, as a pure mathematical theory of structures, with the quantum context and in particular of the quantum histories processes over temporal points and continuous time intervals.

]]>In this paper, we analyze the thought experiment of “Wigner’s friend” and point out that new understanding should be made to Born’s rule and measurement process: Born’s rule is no longer seen as a rule based on the history of the quantum system’s, and the measurement results are no longer directly related to the state of the measured object before the measurement. Inspired by Everett III and H. Zurek’s views, we believe that Born’s rule reflects the coordination between states of different parts in quantum entanglement systems, so it has nothing to do with the history of particles themselves but rather with the historical records. A new formulation of pilot wave theory, objective relative state formulation, or ORSF is suggested. Under this interpretation, micro-particles can also be assigned definite states before being observed. Based on this formulation, Wigner’s friend-like scenarios can be effectively explained. We also notice that our universe can be totally retrocausal by the new formulation. The new interpretation brings new perspectives to many quantum phenomena.

]]>This article is a sequel to a recently published article by the present author (IJQF, 9,4). That article seemed to go some way towards providing a physical explanation of the mysterious probability amplitude nature of quantum mechanics’ psi waves, and in that way towards a possible solution to the measurement problem of quantum mechanics. This article begins where the previous article finished. It puts forward a ‘local’, causally deterministic, additional variable model of a quantum system’s transformation from the potentiality described by the psi function into actuality. The model’s key element is the deeper-level, periodic physical process (double transition\basic process) postulated in the previous article. The model specifies what the additional variables are and how they work—and the sense in which they are ‘local’. It explains the ontology of the potentiality represented by the psi function in terms of the underlying double transition\basic process. The model is time-reversal invariant, and encompasses both fermionic and bosonic systems. Because the model is explicitly retrocausal—the possibility of retrocausality already latent in the basic process—it readily evades the various ‘no-go’ theorems, such as Bell’s theorem, usually taken to show the impossibility of a local hidden variable model that agrees with the predictions of quantum mechanics.

]]>We present a set of exact system solutions to a model we developed to study wave function collapse in the quantum spin measurement process. Specifically, we calculated the wave function evolution for a simple harmonic oscillator of spin 1/2, with its magnetic moment in interaction with a magnetic field, coupled to an environment that is a bath of harmonic oscillators. The system’s time evolution is described by the direct product of two independent Hilbert spaces: one that is defined by an effective Hamiltonian, which represents a damped simple harmonic oscillator with its potential well divided into two, based on the spin and the other that represents the effect of the bath, i.e., the Brownian motion. The initial states of this set of wave functions form an orthonormal basis, defined as the eigenstates of the system. If the system is initially in one of these states, the final result is predetermined, i.e., the measurement is deterministic. If the bath is initially in the ground state,and the wave function is initially a wave packet at the origin, it collapses into one of the two potential wells depending on the initial spin. If the initial spin is a vector in the Bloch sphere not parallel to the magnetic field, the final distribution among the two potential wells is given by the Born rule applied to the initial spin state with the well-known ground state width. Hence, the result is also predetermined. We discuss its implications to the Bell theorem. We end with a summary of the implications for the understanding of the statistical interpretation of quantum mechanics.

]]>Quantum entanglement is a unique property of quantum systems, where the states of two particles become correlated in such a way that the state of one particle cannot be described independently of the other. Entangled quantum systems can connect to the environment via a Bell state measurement. This applies, for example, to teleportation and entanglement swapping. Although the results are well understood, it is not entirely clear whether they involve nonlocal action or whether they are predetermined because quantum mechanics does not provide this information. The best way to clarify this is to use a model, provided that it predicts the key measurement results. Models based on the fact that the partners of an entangled pair have the same value of a statistical parameter cannot be applied here. This is because the partner particles of the resulting entangled states after a teleportation or an entanglement swapping never had contact before. The question then is, what connects entangled photons? Therefore, this paper presents a local realistic model that reproduces the quantum mechanical predictions for expectation values with polarization measurements, but is not based on shared statistical parameters. Instead, the coupling of the entangled particles is based on initial conditions and conservation of spin angular momentum. The model refutes Bell’s theorem and also explains teleportation and entanglement swapping in a local way. It is also shown which error in Bell’s derivation leads to Bell’s inequality failing to correctly describe the relationships between expectation values from quantum mechanics. The manuscript is thus a step forward toward a complete theory describing quantum physical reality as thought possible by Einstein, Podolsky, and Rosen.

]]>What is it that ‘waves’ in wave mechanics? It is thought that the waves represented by the wave function are not waves *of* anything. But this sits uneasily with the seeming physical significance of the phase relations between the linearly superposed elements of the wave function. For example, motion in quantum mechanics is described by the interference of superposed wave functions belonging to different energies, controlled by the phase relations between them. Quantum field theory, too, remains rooted in the ‘harmonic paradigm’ of waves and wave packets. So some think there is more to be said. The present article seeks to contribute to the ongoing debate about the ontology and meaning of the wave function by offering a new perspective on what it is that ‘waves’ in quantum mechanics. It postulates an underlying periodic physical process that all spin-half particles are taken to undergo in the ‘shadow’ of the Heisenberg uncertainty principle. It shows how the underlying process can account for the waves and wave packets of the quantum-mechanical formalism (including in the spin-one case)—the mathematical formalism ‘modelling’ the underlying actual physical process. The new perspective seems to provide insight into other aspects of quantum mechanics as well, including its linear superposition principle, the Schrödinger *Zitterbewegung*—and, rather unexpectedly, into the quantum field-theoretical problem of why a finite particle mass and charge is always observed despite the potentially infinite field energy surrounding a particle.

Bell inequalities violation is generally interpreted to rule out local and/or non-contextual hidden variables theories. Recently, an actual hidden variables model in matrix mechanics formulation was presented which is based on ontologically classical endogenous motion. All results of standard matrix mechanics are reproduced. A critical feature of the model is that it reproduces the mathematics of quantum observables including measurability, and hence quantum experiments. This feature can be a characteristic of a given class of hidden variables theories. There is then a direct conflict with the consensus interpretation of violation suggesting a need to reconsider Bell’s theorem. It is found there is an additional assumption restricting the type of hidden variables theories inequalities represent by excluding those which reproduce quantum mathematics. Any theory which reproduces the mathematics of quantum observables is thereby not subject to Bell-type constraints.

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