Exploring Microscopics by Computation

Modern physics appeared after a long success story initiated by the scientific revolution culminating at the end of the 19th century in a combination of Newton's mechanics and Maxwell's electromagnetics in full harmony appearing to capture macroscopic physics. 

Of course there were open problems asking for resolution including the ultra-violet catastrophe of black-body radiation viewed to be of particular importance. The start was the Rayleigh-Jeans radiation law stating that radiation intensity scales quadratically with frequency $\nu$, which asks for an upper bound $\nu_{max}$ on frequency to avoid infinite intensity by summation over frequencies. Such a bound was available as Wien's displacement law stating that $\nu_{max}$ scales linearly with temperature $T$. 

The theoretical challenge was to explain the bound $\nu <\nu_{max}$ with $\nu_{max}\sim T$. Planck as leading physicist of the German Empire took on the challenge but was unable to find an answer within classical physics and so resorted to a form of statistical physics inspired by Boltzmann's statistical  thermodynamics. Under much agony Planck thereby took a step out of classical physics into a new form of statistical physics, which then evolved in the quantum mechanics as the essence of modern physics.

The fundamental step away from classical physics as deterministic physics about existing realities, was the introduction of statistical physics about probabilities of possibilities. From specific existing realities to infinite possibilities.  

In the new digital world the distinction between existing unique reality and virtual realities is blurred which means that difference between classical deterministic reality and modern probabilistic possibility is also blurred. 

It is thus of interest to seek to pin down the difference between (i) classical physics as existing realities and (ii) modern physics as probabilities of possibilities. A striking aspect is that (i) does not require any human minds/observers (the Moon is there even when nobody looks at it), while (ii) requires some form of mind to carry/represent thinkable possibilities.  

Quantum Mechanics QM emerged before the computer and so computational aspects were not in the minds of the pioneers Bohr-Born-Heisenberg, who came to develop the Copenhagen Interpretation CI formed in the 1920s based on a multi-dimensional wave function $\Psi (x,t)$ depending on a spatial coordinate $x$ with $3N$ dimensions for an atomic system with $N$ electrons satisfying a linear Schrödinger Equation SE (and $t$ is a time coordinate), with $\vert\Psi (x,t)\vert^2$ interpreted as a probability density over configuration space with coordinate $x$. This is still the text book version as Standard QM StdQM.

The many dimensions makes the wave function $\Psi (x,t)$ uncomputable and so has existence only in the mind of a CI physicist with unlimited fantasy. The grand project of StdQM can thus be put in question from computational point of view, and also from realistic point of view if we think that the evolution of the World from one time instant to a next is the result of some form of analog computational process performed by real atoms.

The World is thus equipped with (analog) computational power allowing evolution in time of the existing reality, but it is hard to believe that it has capacity for exploration of all possibilities to form probabilities of possibilities, unless you are believer in the Many-Worlds Interpretation as an (unthinkable) alternative to CI.

From computational point of view StdQM as all possibilities is thus hopeless. The evolution of the multi-dimensional wave function $\Psi (x,t)$ in time is an impossible project. What is today possible is exploration of thinkable realities as long as they are computable.

The exploration can be done starting from RealQM as a computable alternative to StdQM. To see that it is not necessary to take the full step into the the impossibility of StdQM, we need explanations of in particular (1) Wien's Displacement Law and (2) Photoelectric effect, in terms of classical deterministic physics. This is offered on Computational Blackbody Radiation in the form of classical threshold effects.

It thus appears possible to stay within a framework of deterministic classical computable physics and so open to exploration of thinkable worlds of microscopics by computation, which is not possible starting from StdQM.  

Summary: There is a distinction between (a) specific computable (thinkable) realities, and (b) probabilities of uncomputable possibilities. Your choice! As Schrödinger put it: There is a difference between a specific blurred picture and a precise picture of a fog bank.