In discussing Quantum Mechanics (QM), I shall restrict myself here to Schroedinger's Non-Relativistic Wave Mechanics (WM), as Dirac showed (in his 1930 text) [using Hilbert State Vectors] that Heisenberg's Matrix Mechanics (MM) was simply mathematically equivalent.
WM was invented in 1925 when Schroedinger adopted de Broglie's radical proposal that a quantum particle, like an electron, could "have" both contradictory point particle properties (like momentum, P) and wave properties, like a wave-length or wave-number K) by: K = h P; where h is Planck's constant (smuggling in quantization). Next he ASSUMED that a free electron could be represented as a spherical wave described by the Wave Equation. Then, he "joined the QM Club" by restricting his math approach to an isolated hydrogen atom, with its one orbital electron moving around the single proton (each with only one electron charge,e) at a spatial separation r at time t (i.e. x;t). He then linearized out the time by assuming a harmonic form: Exp{i w t) along with Einstein's EM frequency (photon) rule: E = h w. This gave him his famous Wave Equation [using W instead of Greek letter, psi]: H W = E W where H was the classical particle Hamiltonian H =K+U with K the kinetic energy [K= p2/2m] and U the Coulomb potential energy [U = e2/r]. Replacing the quadratic momentum term gave the Laplacian in 3D spherical polar co-ordinates [r, theta, phi]. He then remembered this resembled the 19th century oscillating sphere model with its known complete (infinite series) solution for n=1 to N=infinity for W=Y(l:cos theta) exp[i m phi] introducing the integer parameters l [angular momentum] and m [rotation around the Z axis]. By assuming the math solution is separable, he was left with the linear radial equation that could be solved [with difficulty] but approximated to Bohr's 1913 2D circular [planetary] model E values.
The "TRICK" was to isolate out from the infinite sums, all terms that only included EACH of the finite n terms [measured from n=1 to 6]. This was Dirac's key to match the nth wave function W(n:x,t) with his own Hilbert ket vector: W(n:x,t) = |n, x, t>.
So, I maintain that QM has failed to map its mathematics to a SINGLE hydrogen atom [the physical assumptions used therein] but to the full [almost infinite] collection of atoms present in real experiments. This then results in multiple epistemological nonsense such as Born's probability theory, wave function collapse and the multiverse theory.
This is NOT needed IF we reject the Continuum Hypothesis [imported from Classical Mechanics] and stick to finite difference mathematics.
have you ever investigated the Fibonacci meta cycle and it's association with the meta physics of time and space? It appears that Einstein did by his creation of the power function.
Here is an Elsevier article that classically explains the electron and electric force without adding any new physics. It can also account for the weird behavior of the electron in a classical manner.
Article Mechanisms explaining Coulomb’s electric force & Lorentz’s m...
Dan S Correnti
Dear Dan:
Coulomb's Law is only a statistical macro average with NO evidence that it applies at the level of a single electron; similarly for the Lorentz "force" where EVERYONE has misinterpreted Newton's vis concept (Law II of Motion) as human analogy 'force' that was actually IMPULSE between 2 bodies that does still work at the electron level, as I will show with a new QM theory.
Physics has been fatally flawed since Newton adopted Descartes' Reference Scheme for mapping algebra to geometry. The Reason:
The Origin of an Inertial Reference Frame (IRF) is arbitrary but as we usually measure differences in spatial locations then this does NOT matter experimentally. However, Newton zeroed in on the concept of velocity as the ratio of spatial difference divided by temporal difference; the IRF scheme is OK if both differences are finite but Newton accepted the controversial idea of infinitesimal, where differences shrink to zero. Math guys created an abstract Limit Definition that allowed THEM to proceed BUT there has never been an equivalent solution in the world of physical measurements. So, physics has proceeded merrily along with its bogus ideas of instantaneous velocity and momentum, along with the bogus, related ideas of instantaneous values of all single point variables, like kinetic energy and WORSE, Lagrange's Potential Energy.
Now, we can investigate the micro-world of atoms and electrons, are assumptions are surfacing to haunt us. In particular, these CONTINUUM ideas are still the foundation of Quantum Mechanics (QM) that always begins by assuming IRF.
Even here, experimentalists measure interactions between the Zillions of atoms in their equipment and the Zillions of atoms in the energy source, beginning by assuming the origin of the IRF coincides with one hydrogen atom's nucleus. Meanwhile, the theorists calculate their AVERAGES by integrating instantaneous values over ALL space and time. Wave Mechanics began by Schroedinger adopting de Broglie's Wave/Particle equation that smuggled in the quantum along with the bogus idea of instantaneous momentum so map to differential operators.
Or, we need to use multiple valued 'Variables' (arrays) to map both space and time (aka Hilbert Vectors) and invent bizarre interpretations of the math, such as Born's Probability view or Everett's Multiverse and Entanglement.
ENOUGH ALREADY. Until we fix our foundations, physics is building on sand !!!
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