Corruption of Modern Physics 5: Microscopic Statistics

The number of births, deaths or murders in say Sweden do not vary much from year to year and so are more or less predictable, while it is impossible to predict exactly which person will die from a natural cause or get murdered. This does not say that deaths/murders are completely random as if decided by throwing a dice. In all cases there are very specific conditions which predictably lead to a particular outcome as predictable microscopics of a macroscopic event such as death/murder. If the predictable microscopics was known in full detail, then the macroscopic event would also be predictable. A killed B because of a specific reason.

But with unknown microscopics as hidden variables, macroscopics appear random. This is how a roulette table works.   

This connects to the basic unsolved problem of modern atom physics as the statistical/random nature of the Copenhagen Interpretation CI of quantum mechanics, which Bohr imprinted into the minds of all modern physicists with strong support from Born and Heisenberg, except a few like Schrödinger (inventor of quantum mechanics) and Einstein protesting with his famous God Does Not Play Dice.  

CI postulates that quantum mechanics can only make microscopic predictions of statistical nature such as the probability that an electron as a particle will be at a specific point is space and time. In other words, in CI there can be no hidden variables allowing prediction of microscopics.  In CI an electron really plays dice, something Einstein never accepted. 

Bohr supported CI by the observation that in the decay of radioactive atoms the half-life, as the time after which half of the atoms have decayed, is predictable, while it is impossible to predict precisely which atoms will decay and when. The basic CI conviction is that atoms play roulette to decide to decay or not. There can be no hidden variables, to be compared with the deaths/murders in a population containing hidden variables. 

But random microscopics is is an awkward idea from scientific point of view. Conceptually macroscopics can be complex as an agglomeration of microscopics, while the very idea of microscopics is that it is something simple. Complex microscopics must build on microscopics of microscopics and so on in an endless regression. Thus microscopics as an elementary piece of something bigger must be simple, and simple in general means predictable. When Bohr speaks about an electron playing roulette as random microscopics, it appears self contradictory or at least confusing and mystical as the signum of quantum mechanics: 

• How does single electron play roulette? 
• What is the origin of this strange idea?

An answer is given in Corruption of Physics 3. There we recall that quantum mechanics was created in 1920s when Schrödinger formulated a new model for the Hydrogen atom as a negatively charged electron cloud attracted by a positively charged kernel. The model takes the the form of a partial differential equation named Schrödinger's equation in terms of a wave function $\Psi (x,t)$ depending on a three-dimensional space variable $x$ and a time variable $t$ with $\vert\Psi (x,t)\vert^2$ representing electron density at $(x,t)$. 

This model is fully predicatble/computable and produces an atomic spectrum in direct correspondence with observation as the first model of predictable microscopics of atom physics in parity with Newton's predictable model of the motion of celestial objects. 

That was a wonderful achievement of rational thinking, but what would a Schrödinger equation look like for an atom with more than one electron? It was far from obvious how to generalise from one to many. and Schrödinger hesitated. Of course, a direct formal generalisation could be made with a pen stroke into a wave function $\Psi (x1,x2,....,xN,t)$ depending on $N$ three-dimensional space variables $x1, x2,...,xN$ for an atom with $N$ electrons, thus into a wave function depending on $3N$ space variables, however without direct physical meaning for $N>1$. The only way out was to give this multi-dimensional wave-function a statistical meaning as a probability. That was what Born did followed by Bohr, while Schrödinger protested, and that ended the search for a generalisation of Schrödinger's equation with direct physical meaning. Modern physics was stuck with multi-dimensional Schrödinger equation without physical meaning, which in addition was uncomputable for a multi-electron atom as pointed out by Nobel Laureate Walter Kohn when receiving the Prize. 

There modern physics stands today. Electrons play roulette. Atom microscopics is random with self-contradictory microscopics upon microscopics. Hidden variables are forbidden like the fruits of Knowledge in Paradise. Bohr dictates that physics is not what is, but what we can say. The multi-dimensional Schrödinger equations without hidden variables contains everything that can be said, which however is not much since it is uncomputable. 

A way out of this dead end is opened by Real Quantum Mechanics presenting a different generalisation of Schrödinger's one-electron equation into a computable many-electron wave equation in three space dimensions with physical meaning. With such a model it would in principle be possible to predict which atom would decay because of specific conditions of its nucleus and surrounding electron configuration, although in practice they would appear like hidden variables. 

One thing is to say like Bohr that there can be no hidden variables, only microscopic roulettes without physics, another to say that they may exist and may be revealed into deterministic physics.