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Qeios

A Complete Quantum Mechanics That Is Also Visualizable

Richard Joseph Oldani

Published Nov 5, 2024• 0 citations
Publisher

Abstract

We hypothesize that quantum mechanics is incomplete because it does not take into consideration the absorption of energy by quantum systems as described by matrix mechanics. To be complete quantum mechanics must include both matrix and wave mechanics, and due to the conservation of energy the first (absorption) must be carried out to completion before the second one (emission) can begin. The combined model of matrix and wave mechanics integrates naturally with Einstein’s use of independent coordinate systems K and K’ to describe the absorption and emission of radiation. All subsequent mathematical models are versions of this physical model.

DOI
10.32388/pq5jzl.2

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We hypothesize that quantum mechanics is incomplete because it does not take into consideration the absorption of energy by quantum systems as described by matrix mechanics. To be complete quantum mechanics must include both matrix and wave mechanics, and due to the conservation of energy the first (absorption) must be carried out to completion before the second one (emission) can begin. The combined model of matrix and wave mechanics integrates naturally with Einstein’s use of independent coordinate systems K and K’ to describe the absorption and emission of radiation. All subsequent mathematical models are versions of this physical model.
We hypothesize that quantum mechanics is incomplete because it does not take into consideration the absorption of energy by quantum systems as described by matrix mechanics. To be complete quantum mechanics must include both matrix and wave mechanics, and due to the conservation of energy the first (absorption) must be carried out to completion before the second one (emission) can begin. The combined model of matrix and wave mechanics integrates naturally with Einstein’s use of independent coordinate systems K and K’ to describe the absorption and emission of radiation. All subsequent mathematical models are versions of this physical model.
Although quantum mechanics correctly predicts what it is possible to observe (the emissions) it ignores the other half of natural phenomena, what cannot be observed (the absorptions), thereby violating the conservation laws. By describing only one-half of quantum mechanics conceptual difficulties such as wave function collapse, infinite paths, non-locality, and abstract mathematical models appear out of nowhere. The deficiencies are corrected in non-relativistic theory by showing that the unobserved absorption energies of off-diagonal elements in matrix mechanics are essential and that matrix and wave mechanics are equally important for formulating a complete quantum mechanics. Due to the conservation of energy absorption must be carried out to completion before energy emission can begin. When relativistically correct equations of motion are derived they show that the wave function is incomplete because it describes the excitation and decay of an electron with twice the allowable action minimum. Einstein’s unfinished quantum theory forms the mathematical foundation leading up to and underlying the proposed mathematical model. Keywords Conservation laws; Quantum mechanics; Hamilton’s principle; Energy; Momentum; Path integral formulation; Matrix mechanics
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.
Is often claimed that Einstein is wrong about quantum mechanics. However, when compared 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) it ignores the other half of natural phenomena, what cannot be observed (the absorptions), thereby violating the conservation laws. By describing only one-half of quantum mechanics conceptual difficulties such as wave function collapse, infinite paths, and inscrutable mathematics seem to appear out of nowhere. The deficiencies are corrected by introducing Hamilton’s principle S = ∫ Ldt and applying the methods of quantum field theory to derive relativistic equations of motion. The calculus of variations is used to show that the wave function represents an incomplete equation of motion because it equals 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 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.
Matrix mechanics describes the spectral emissions of hydrogen gas, but quantum mechanics concerns the emission and absorption of radiation by a single atom. To obtain the spectral emissions of a single hydrogen atom we reformulate matrix mechanics by introducing thermal energy in infinitesimal increments and registering the spectral lines one by one until a complete spectrum is obtained. Wave mechanics is reformulated from a conservative to a non-conservative system by linking the output of matrix mechanics to the input of wave mechanics. To describe the gradual increase and decrease of energy by a quantum system we integrate between two specific endpoints, the atomic orbitals, and two specific times, the period τ, which are the conditions necessary for Hamilton’s principle. The Lagrangian method is shown to be superior for analyzing quantum theory because it describes quantum systems relativistically as evolutions in time.