torsdag 18 september 2025

Unified Field Model as Macro-Micro Continuum Model

It was Niels Bohr who in the 1920s implanted the idea into modern physics that the microscopic world of atoms cannot be understood/described using the concepts of classical physics, which had served so well to describe the macroscopic world we can directly experience. The new understanding/description took the form of Quantum Mechanics QM based on a multi-dimensional Schrödinger Equation SE of a non-classical form. 

With the help of Heisenberg Bohr managed to let his idea take over modern physics into our days, on the way crushing Schrödinger asking for "Anschaulichkeit" or "possible to visualise" as understanding in terms of classical physics. The essence of the Bohr-Heisenberg dogma was:

  • Only observation/measurement counts. Underlying ontology left out. Visualisation impossible.
  • Complementarity: Contradicting physics allowed. Both particle and wave.
  • Uncertainty Principle: Limit to what can be measured.
  • Separation ontology (classic, what is) and epistemology (new, what we can say)

The result today is a science of physics in a state of crisis. The new concepts required by Bohr could never be clarified resulting in a QM which "nobody can understand" in the words of Richard Feynman. The basic form of a classical mathematical model of the physics of a solid, fluid or gasses is a partial differential equation involving functions $u(x,t)$ depending on a real variable/spatial coordinate $x$ ranging over some domain in 3d space and a time coordinate $t$. This is a continuum mechanics model with the set of real numbers offering space as a continuum without preset smallest spatial scale. The function $u(x,t)$ could represent the density at time $t$ of a fluid with $x$ ranging over the 3d domain occupied by the fluid.

Continuum mechanics as classical physics is described by a mathematical model covering all physical scales from micro to macro and thus does not single out micro-scopics as conceptually different from macro-scopics, which could be the case if macro-scopics is "continuous" and microscopics "discrete".

In continuum mechanics both micro- and macro-scopics are "continuous". Nothing is "discrete". No "particles". The continuum of real numbers can represent a continuum mechanics without smallest scale.

The multi-d SE depends on continuous spatial variables, and in this sense is a continuum model, but not a classical continuum model since the continuum is not 3d (for system with more than one electrons). 

RealQM offers a different Schrödinger equation as a non-linear system of non-overlapping charge densities in 3d thus in the form of classical continuum mechanics with a seamless connection to macro-scopics. 

It is thus possible to formulate a Unified Field Model combining classical Newtonian continuum models like Navier-Stokes and Maxwell's equations with a Schrödinger equation of the same principal form. This was what Einstein tried to accomplish, but did not succeed with because he was stuck with a perceived incompatibility between General Relativity and QM.  

 

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