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Pure and applied physics

Incompleteness of Quantum Theory on EinsteinâÂÂs Program

D. Elbaz

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

Adiabatic variations of frequencies lead to electromagnetic interaction constituted by progressive waves. By comparison, the consistent quantum theory, based upon time-like equations, of Dirac for fermions and of Klein- Gordon for bosons, is incomplete since it does not take account of a spacelike function u0(k0r0) to describe massive particle extension. It leads to Dirac’s distribution δ(r0) in the geometrical optics approximation, in order to handle a particle as a singularity within a continuous field, and to energymomentum conservation laws, and to least action law, with determination of the Lagrangian.

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Adiabatic variations of frequencies lead to electromagnetic interaction constituted by progressive waves. By comparison, the consistent quantum theory, based upon time-like equations, of Dirac for fermions and of Klein- Gordon for bosons, is incomplete since it does not take account of a spacelike function u0(k0r0) to describe massive particle extension. It leads to Dirac’s distribution δ(r0) in the geometrical optics approximation, in order to handle a particle as a singularity within a continuous field, and to energymomentum conservation laws, and to least action law, with determination of the Lagrangian.
The Einstein's program forms a consistent system for universe description, beside the standard model of particles. It is founded upon a scalar field propagating at speed of light c, which constitutes a common relativist framework for classical and quantum properties of matter and interactions. Matter corresponds to standing waves. Classical domain corresponds to geometrical optics approximation, when frequencies are infinitely high, and then hidden. Quantum domain corresponds to wave optics approximation. Adiabatic variations of frequencies lead to electromagnetic interaction constituted by progressive waves. It leads to theoretical economy for Quantum Theory, with unification of first and second quantifications for interactions and matter, to the wave-particle duality by reduction of the introduced amplitude space-like function ( ), , t r u which completes the usual time-like function ( ), , t r ψ with hidden variables.
The Einstein’s program forms a consistent system for universe description, beside the standard model of particles. It is founded upon a scalar field propagating at speed of light c, which constitutes a common relativist framework for classical and quantum properties of matter and interactions. Matter corresponds to standing waves. Classical domain corresponds to geometrical optics approximation, when frequencies are infinitely high, and then hidden. Quantum domain corresponds to wave optics approximation. Adiabatic variations of frequencies yield electromagnetic interaction. They lead also to Classical and Quantum Mechanics equations, with unification of first and second quantifications for interactions and matter, and to the wave-particle duality, by space reduction of the introduced space-like amplitude function u(r,t), which completes the usual time-like function ψ(r,t).
The Einstein’s program enables a theoretical economy for quantum double slit experiment, in its wave-particle duality behavior, with the unification of first and second quantifications for light and matter. It introduces a space-like amplitude function u(r,t), which completes the usual time-like functions ψ(r,t) of quantum mechanics and quantum fields. The Einstein’s program is founded upon a scalar field propagating at speed of light c. It forms a common relativist framework, for classical and quantum properties of matter and interactions. Matter properties derive from standing waves, and interactions from progressive waves. The classical domain arises in the geometrical optics approximation, when frequencies are infinitely high, and then hidden. The quantum domain corresponds to wave optics approximation. Adiabatic variations of frequencies yield electromagnetic interaction and dynamical laws of energy-momentum conservation and least action principle.
It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Although quantum mechanics correctly describes energy exchange due to emissions with remarkable accuracy it ignores momentum exchange (the absorptions), thereby failing to recognize their causal relationship due to the conservation laws. The deficiencies in non-relativistic theory are corrected by introducing Hamilton’s principle and deriving relativistic equations of motion. This allows wave function behavior to be described as the combined action of a particle and an associated localized field. The calculus of variations is applied to the Schrödinger wave equation to show that it is incomplete because it yields twice the allowable action minimum.
It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Although statistical formulations of quantum mechanics correctly describe energy and momentum exchange with remarkable accuracy there are individual cases, paradoxically, that violate the conservation laws. A recent study finds that in order to account for observed violations frames of reference involved in preparation of the initial state must be explicitly taken into account [1]. We show here that the same conclusion was arrived at in a much simpler way by Einstein over 100 years ago. Deficiencies in the foundations of non-relativistic theory are corrected by introducing Hamilton’s principle and deriving relativistic equations of motion. This allows quantum mechanical formalism in abstract space to be replaced by the superposition of particle field geometries in real space. Applying the calculus of variations to the Schrödinger wave equation reveals that the wave function is incomplete because it requires twice the allowable action minimum.
It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Although quantum mechanics correctly predicts what it is possible to observe (the emissions) with remarkable accuracy it ignores the other half of natural phenomena, that which cannot be observed (the absorptions), thereby violating the conservation of energy. Similarly, the conservation of momentum is violated by disregarding unobservable molecular impulses. Despite irrefutable proof that molecular impulses transfer momentum asymmetrically as shown by Einstein’s derivation of the A and B coefficients, the wave function is assumed to apply symmetrically in time. The deficiencies are corrected by introducing Hamilton’s principle and deriving relativistic equations of motion. This allows non-relativistic quantum mechanics to be described with a physical model and wave function behavior to be interpreted as the combined action of a particle and its associated quantized field. The calculus of variations is applied to the wave function to show that it is an incomplete equation of motion because it yields twice the allowable action minimum. The concept of reality is redefined by showing that reductionism applies to classical phenomena, but not quantum phenomena.