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The Alternate Interpretation of the Quantum Theory Utilizing Indefinite Metric

M. Morimoto

Published Oct 1, 2020• 0 citations
OpenAlex

Abstract

In this paper, we propose an alternate interpretation of the quantum theory using objective physical reality that does not depend on the conventional probability interpretation. As typical physical phenomena for the probability interpretation, we consider the single-photon interference, single-electron interference, and EPR correlation experiments using photon polarization. For the calculation using the alternate interpretation, the minus sign derived from the covariant quantization of Maxwell's equations, which is associated with the scalar potential of time axis component of four-vector, is taken as it is as an inevitable request from the theory. We show that both conventional and alternate interpretation derive the identical calculation results for these single photon, single electron interference, and EPR correlation. These alternate calculation processes describe that there is the scalar potential in whole space-time and when there is some geometrical arrangement in the space, the scalar potential forms the oscillatory field of the potential according to the arrangement. It reveals the objective physical reality that the single-photon, single-electron interference, and EPR correlation are generated by the movement of the photons and electrons in the oscillatory field with interference. In addition, we show that the oscillatory field formation of the scalar potential depending on the geometrical arrangement causes energy fluctuation in the space, which enables removal of infinite zero-point energy and causes spontaneous symmetry breaking and Casimir effect. By recognizing the electromagnetic field as an unitary U(1) gauge field and generalizing it to a special unitary SU(2), we also show the uncharged particle, e.g. neutron, interferences are generated by the geometrical arrangement of the SU(2) gauge field. Furthermore, we discuss the origin of the scalar potential by distinguishing the space where the substance exists and the vacuum. Finally, by introducing the extended Lorentz gauge, we propose the alternate solution without physical state and subsidiary condition for the contradiction between Lorentz gauge as an operator equation and the commutation relation in the covariant canonical quantization of Maxwell's equations with the conventional Lorentz gauge. This paper contains the compilation of published author's papers \cite{Morimoto1,Morimoto2} in addition to featured discussions such as the physical reality, uncharged particle interference and alternate proposal for the contradiction between Lorentz gauge as an operator equation and commutation relation.

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In this paper, we propose an alternate interpretation of the quantum theory using objective physical reality that does not depend on the conventional probability interpretation. As typical physical phenomena for the probability interpretation, we consider the single-photon interference, single-electron interference, and EPR correlation experiments using photon polarization. For the calculation using the alternate interpretation, the minus sign derived from the covariant quantization of Maxwell's equations, which is associated with the scalar potential of time axis component of four-vector, is taken as it is as an inevitable request from the theory. We show that both conventional and alternate interpretation derive the identical calculation results for these single photon, single electron interference, and EPR correlation. These alternate calculation processes describe that there is the scalar potential in whole space-time and when there is some geometrical arrangement in the space, the scalar potential forms the oscillatory field of the potential according to the arrangement. It reveals the objective physical reality that the single-photon, single-electron interference, and EPR correlation are generated by the movement of the photons and electrons in the oscillatory field with interference. In addition, we show that the oscillatory field formation of the scalar potential depending on the geometrical arrangement causes energy fluctuation in the space, which enables removal of infinite zero-point energy and causes spontaneous symmetry breaking and Casimir effect. By recognizing the electromagnetic field as an unitary U(1) gauge field and generalizing it to a special unitary SU(2), we also show the uncharged particle, e.g. neutron, interferences are generated by the geometrical arrangement of the SU(2) gauge field. Furthermore, we discuss the origin of the scalar potential by distinguishing the space where the substance exists and the vacuum. Finally, by introducing the extended Lorentz gauge, we propose the alternate solution without physical state and subsidiary condition for the contradiction between Lorentz gauge as an operator equation and the commutation relation in the covariant canonical quantization of Maxwell's equations with the conventional Lorentz gauge. This paper contains the compilation of published author's papers \cite{Morimoto1,Morimoto2} in addition to featured discussions such as the physical reality, uncharged particle interference and alternate proposal for the contradiction between Lorentz gauge as an operator equation and commutation relation.
We show single photon and electron interferences can be calculated without quantum-superposition states by using tensor form (covariant quantization). From the analysis results, the scalar potential which correspond to an indefinite metric vector forms an oscillatory field and causes the interferences. The results clarify the concept of quantum-superposition states is not required for the description of the interference, which leads to an improved understanding of the uncertainty principle and resolution of paradox of reduction of the wave packet, elimination of infinite zero-point energy and derivation of spontaneous symmetry breaking. The results conclude Quantum theory is a kind of deterministic physics without "probabilistic interpretation".
We examine a covariant quantization of electromagnetic fields by using an operator derived from a constant scalar that can be called extended Lorentz gauge. The quantization can avoid an inconsistency between Lorentz gauge and a commutation relation, which can eliminate the need for introduction of physical state defined by a subsidiary condition and auxiliary field in Lagrangian density in Lorentz gauge. By using this quantization and indefinite metric straightforwardly, all quantum phenomena can be provided without enigmatic and paradoxical "probability interpretation".
Classically, electromagnetic pulses are described by real fields that couple to charged matter and propagate causally. We will show here that real fields of the form used in standard classical electromagnetic theory have a quantum mechanical interpretation in which the probability density for a photon to be at x\mathbf{x}x is positive definite and operators representing all of the standard physical observables exist. A covariant alternative to the ${\ensuremath{\omega}}_{k}^{1/2}$ dependence that appears in most (but not all) presentations of quantum optics and quantum field theory is presented and real Lorentz scalar one-photon advanced and retarded potentials are derived.
This is the second of the two related papers analyzing the origins and possible explanations of a paradoxical phenomenon of the quantum potential (QP). It arises in quantum mechanics (QM) of a particle in a Riemannian n-dimensional configurational space obtained by various procedures of quantization of non-relativistic natural Hamilton systems. Now, two questions are investigated: 1) Does a QP appear in non-relativistic QM generated by the quantum theory of a scalar field (QFT) non-minimally coupled to the space-time metric? 2) To which extent is it in accord with quantization of natural systems? To this end, the asymptotic non-relativistic equation for particle-interpretable wave functions and operators of canonical observables are obtained from the primary QFT objects. It is shown that, in globally static space-time, the Hamilton operators coincide at the origin of the quasi-Euclidean space coordinates in both alternative approaches for any non-minimality constant ξ~\tilde \xiξ~​ , but a certain requirement of the Equivalence Principle to the quantum field propagator distinguishes the unique value ξ~=1/6\tilde \xi = 1/6ξ~​=1/6 = 1/6. Just the same value had the constant ζ in the quantum Hamiltonians arising from the traditional quantizations of natural systems: the DeWitt canonical, Pauli-DeWitt quasiclassical, geometric and Feynman ones, as well as in the revised Schrödinger variational quantization. Thus, the QP generated by mechanics is tightly related to non-minimality of the quantum scalar field. Meanwhile, an essential discrepancy exists between the non-relativistic QMs derived from the two alternative approaches: QFT generates a scalar QP, whereas various quantizations of natural mechanics lead to QPs depending on the choice of space coordinates as physical observables and nonvanishing even in flat space if the coordinates are curvilinear.
We present a quantum framework grounded in micro-causality and spacetime quantization, where spacetime is composed of discrete, causally ordered units rather than a continuous manifold. This intrinsic structure naturally generates fundamental quantum features—wave–particle duality, energy quantization, and the Heisenberg uncertainty principle—without invoking canonical quantization, matter-wave postulates, or harmonic-oscillator models. Consequently, this paradigm eliminates the long-standing paradoxes of wavefunction collapse, self-interference, and non-local spooky correlations in entanglement.Within this causal lattice spacetime, quantum commutation relations emerge from finite shift operators, and the uncertainty principle arises geometrically from non-commutativity at the fundamental level. Unlike standard quantum field theory (QFT), which predicts infinite vacuum energy and requires renormalization, the present framework removes zero-point energy, ultraviolet divergences, and fine-tuning. Moreover, U(1) symmetry is broken geometrically on the lattice, leading to mass generation without a Higgs mechanism.The Casimir effect is reinterpreted as a temperature-dependent imbalance in thermal radiation pressure rather than the consequence of vacuum fluctuations, predicting that the Casimir force should vary with ambient temperature. Experimental confirmation of such dependence would directly support the lattice interpretation and challenge the QFT view of vacuum energy.By unifying key quantum behaviors through discrete causal geometry, this model offers a divergence-free and physically grounded alternative to continuum-based QFT. It opens new avenues for quantum unification, cosmology, and the understanding of fundamental constants, without speculative constructs, singularities, or infinities.
By expanding the research paradigm and reconciling the two binary oppositions of "relative and absolute" and "quantum and classical" in physics, a new theoretical framework that is compatible with relativity and quantum mechanics is proposed. Firstly, excavate and establish three universal axioms: Axiom 1 (consensus guarantees equal rights), Axiom 2 (objective existence independent of measurement), and Axiom 3 (universality of causality and dialectical logic), based on which to criticize the logical contradictions of existing theories. In the field of relativity, this article points out that there is a logical paradox in the explanation of "clock slowing down depends on relative motion" in special relativity (A clock is both faster and slower than B clock), and proposes a relative absolute spacetime view that "absolute motion leads to clock slowing down". By extending the Lorentz transformation, absolute motion and relative motion are unified, solving problems such as the twin paradox. At the same time, based on the prediction of the Dirac equation for negative mass matter, the "negative mass spacetime curvature paradox" is proposed, challenging Einstein's physical explanation of spacetime curvature and arguing that it is only a mathematical tool (the mathematical expression of gravity) rather than a physical reality. In the field of quantum mechanics, this article criticizes the Copenhagen interpretation for violating Axiom 2 (denying the independent eigenstates of microscopic particles). By modifying the Schrödinger equation twice (For the first time, electromagnetic potential energy was replaced with gravitational potential energy, and the Schrödinger-Tu equation was established to describe macroscopic objects such as the Earth's revolution; The second step is to convert potential energy into electromagnetic/gravitational force and derive the wave mechanics equation of classical mechanics laws, such as Newton's second law with force operator), proves that quantum and classical theories are compatible within the same mathematical framework. In the experiment, it was demonstrated through the "anti-interference electron diffraction experiment" that a strong magnetic field only changes the shape of diffraction fringes without causing them to disappear, denying the inevitability of quantum decoherence. The establishment of "generalized wave dynamics" and "relative absolute spacetime view" breaks the binary opposition of traditional theories and provides a new paradigm for the unity of relativity and quantum mechanics. The core value of these jobs lies in: In terms of theoretical innovation, reconstruct the space-time and quantum interpretation system, while retaining the original mathematical form system; In terms of experimental verification, design feasible schemes such as hollow glass disk Jones experiment and geometric optical velocimetry experiment; In terms of philosophical significance, replacing "mathematical symmetry" with "content unity" and returning to the objectivity of physical mechanisms. The research conclusion indicates that by expanding paradigms and axiomatic constraints, the contradiction between relativity and quantum mechanics can be transformed into a complementary relationship, laying the foundation for the great unity of physics theory