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.

]]>A brief philosophical inquiry into the foundations of quantum mechanics is presented here. In particular, the direct relationship between granularity, discontinuity, and the presence of quantum effects will be argued. Furthermore, an “interpretation of relational interpretation” will be supported, which, in combination with the problem of logical undecidability, produces a promising approach that places the apparent illogicality of QM within the realm of logic and effectively addresses its usual paradoxes.

]]>A codification of the internal degrees of freedom of the elementary fermions of the Standard Model is proposed in terms of overlapped triads of semiaxes in a three-dimensional Euclidean pre-space. The common orientation of these triads and the common length of their semiaxes in turn encode the fermion position in spacetime. The connection between the pre-spatial description of the fermion and its quantum description adopted by the Standard Model is established through a one-to-one correspondence between configurations of the system of triads and positional eigenstates of the fermion. The effect of the discrete symmetries $C$, $P$, $T$ on triadic configurations in pre-space is discussed, and it is shown that the connection between the chirality of triads and ordinary space provides an intuitive explanation of the violation of parity in the weak interactions and of its conservation in the strong interactions.

]]>In this paper, by using a hyperfinite dimensional space and time lattice (ST -lattice) of nonstandard analysis, we present a variant of Bohmian interpretation of quantum mechanics which we call probabilistic Bohmian mechanics, PBM. We describe the model for non-relativistic quantum mechanics in detail and elaborate on its relativistic extension. The assumption of quantum equilibrium does not exist in the PBM model and its absence is compensated for by assuming that the particles are moving with infinite speed on a space time lattice according to probability density, which in PBM is regarded as density of space and time position states. In relativistic extension the PBM model assumes that Lorentz symmetry of space and time is just a wave phenomenon related to the space time symmetry of wave equations on real standard axes, whereas the motion of particles with infinite speed can only be described within the hyperfinite dimensional time and space lattice of preferred space time foliation (PST -lattice). In the PBM model the particle trajectories do not exist on the standard real time and space axes of any Lorentz frame and thus the assumption of wave function collapse is necessary. The wave function collapse is considered as a two-step process of decoherence (on standard real axes) and the subsequent particle jump (on the ST -lattice). For the PBM model, as an objective collapse theory, the causality problem, related to wave function collapse, is addressed by the preferred space-time foliation.

]]>A preliminary hidden variables matrix mechanics treatment of the harmonic oscillator has been previously presented based on classical endogenous periodic motion. This work extends to incorporating the model into the mathematics of matrix mechanics. Although initially motivated by EPR-Bell analysis, the proposed model is based on re-examining the physical assumptions of Heisenberg and Born. All assumptions are maintained except for Bohr’s state-to-state instantaneous transition which has been experimentally invalidated, and Heisenberg’s non-path postulate which is replaced by classical endogenous periodic paths. Matrix elements of standard matrix mechanics are modified to replace transition amplitudes by transition paths. The redefined elements generate eigenvalues-eigenstates which then characterise eigenpaths. Since the endogenous motion averages out over a cycle it is unseen by the wave function. Nevertheless, mathematical equivalence with position and momentum non-commutation in Schrodinger operators is preserved. The modified matrix mechanics is shown to be mathematically equivalent to that of Born-Jordan reproducing all standard results. Generic quantum equations of motion are obtained following the quantization procedures of Born-Jordan and Dirac’s Poisson Bracket equation. These new relations meet the benchmark criteria of reproducing conservation of energy and the quantum frequency condition. Since the endogenous paths are ontologically classical no radical metaphysical interpretations are needed for spatial-temporal movement. Quantum randomness is not explained by the proposed model but is attributed to endogenous structures of quantum matter.

]]>Roderich Tumulka’s GRWf theory offers a simple, realist and relativistic solution to the measurement problem of quantum mechanics. It is achieved by the introduction of a stochastic dynamical collapse of the wavefunction. An issue with dynamical collapse theories is that they involve an amendment to the Schrodinger equation; amending the dynamics of such a tried and tested theory is seen by some as problematic. This paper proposes an alteration to GRWf that avoids the need to amend the Schrodinger equation via what might be seen as a primary set of solutions to the Schrodinger equation that satisfy a normalisation condition over space and time. The traditional Born-normalised solutions are shown to be conditionalisations of these primary solutions.

]]>The purpose of this paper is to show that the mathematics of quantum mechanics (QM) is the vector (Hilbert) space version of the mathematics of partitions at the set level. Since partitions are the math tool to describe indefiniteness and definiteness, this shows how the reality so well described by QM is a non-classical reality featuring the objective indefiniteness of superposition states. The lattice of partitions gives a skeletal model of quantum reality with the partition versions of pure states, non-classical mixed states (i.e., including a superposition state), and the completely distinguished classical state that satisfies the partition logic version of the Principle of Identity of Indistinguishables. Both the key notions of quantum states and quantum observables are respectively the (density) matrix versions of partitions and vector space version of a numerical attributes. The operation of projective measurement given by the Lüders mixture operation is the vector space version of the partition join operation between the partition prefiguring the density matrix of the state being measured and the partition prefiguring the observable being measured. All this adds specific key concepts and structure to Abner Shimony’s idea of a literal understanding of QM to form what might be called the “Objective Indefiniteness Interpretation” of QM.

]]>By subjecting the de Broglie wave to an inverse Lorentz transformation, an attempt is made to return this mysterious wave to a form that is physically viable in the rest frame of the associated particle. The attempt is unsuccessful: it is found that in that frame, the wave becomes an oscillation that varies in time, but not in space, and cannot be identified with the spatially-extended sinusoidal wave that accompanies the moving particle. It is shown that this difficulty is a consequence of the restricted manner in which de Broglie reconciled the phases of particle and wave in his doctoral thesis of 1924. Although he assumed that the particle is surrounded in its rest frame by a spatially extended “periodic phenomenon”, he applied his “theorem of the harmony of phases”, not to that extended waveform, but to a single oscillating point within the waveform. As such a point moves, it does describe a sinusoidally varying phase, but this is the varying phase, not of a wave, but of a moving and oscillating point. Had de Broglie applied his harmonizing of phase to the full underlying waveform, a wave with the characteristics of the de Broglie wave would have emerged, in a physically reasonable manner, as the relativistically induced modulation (a dephasing) of the underlying wave structure. After showing that there is considerable support for this interpretation in de Broglie’s thesis, consideration is given to the implications of such an interpretation for relativity, quantum mechanics and particle structure.

]]>The process approach to NRQM offers a fourth framework for the quantization of physical systems. Unlike the standard approaches (Schrodinger-Heisenberg, Feynman, Wigner-Gronewald-Moyal), the process approach is *not* equivalent to NRQM and is *not* merely a re-interpretation. The process approach provides a dynamical *completion* of NRQM. Standard NRQM arises as a asymptotic quotient by means of a set-valued process covering map, which links the process algebra to the usual space of wave functions and operators on Hilbert space. The process approach offers an emergentist, discrete, finite, quasi-non-local and quasi-non-contextual realist interpretation which appears to resolve many of the paradoxes and is free of divergences. Nevertheless, it retains the computational power of NRQM and possesses an emergent probability structure which agrees with NRQM in the asymptotic quotient. The paper describes the process algebra, the process covering map for single systems and the configuration process covering map for multiple systems. It demonstrates the link to NRQM through a toy model. Applications of the process algebra to various quantum mechanical situations – superpositions, two-slit experiments, entanglement, Schrodinger’s cat – are presented along with an approach to the paradoxes and the issue of classicality.