söndag 29 maj 2016

Restart of Quantum Mechanics: From Observable/Measurable to Computable

Schrödinger and Heisenberg receiving the Nobel Prize in Physics in 1933/32..

If modern physics was to start today instead of as it did 100 years ago with the development of quantum mechanics as atomistic mechanics by Bohr-Heisenberg and Schrödinger, what would be the difference?

Bohr-Heisenberg were obsessed with the question:
• What can be observed?
motivated by Bohr's Law:
• We are allowed to speak only about what can be observed.
Today, with the computer to the service of atom physics, a better question may be:
• What can be computed?
possibly based on an idea that
• It may be meaningful to speak about what can be computed.
Schrödinger as the inventor of the Schrödinger equation as the basic mathematical model of quantum mechanics, never accepted the Bohr-Heisenberg Copenhagen Interpretation of quantum mechanics with the Schrödinger wave function as solution of the Schrödinger equation interpreted as a probability of particle configuration, with collapse of the wave function into actual particle configuration under observation/measurement.

Schrödinger sought an interpretation of the wave function as a physical wave in a classical continuum mechanical meaning, but had to give in to Bohr-Heisenberg, because the multi-dimensionality of the Schrödinger equation did not allow a direct physical interpretation, only a probabilistic particle interpretation. Thus the Schrödinger equation to Schrödinger became a monster out of control, as expressed in the following famous quote:
• If we have to go on with these damned quantum jumps, then I'm sorry that I ever got involved.
And Schrödinger's equation is a monster also from computational point of view, because solution work scales severely exponentially with the number of electrons and thus is beyond reach even for small $N$.

But the Schrödinger equation is an ad hoc model with only weak formal unphysical rationale, including the basic ingredients of (i) linearity and (ii) multi-dimensionality.

Copenhagen quantum mechanics is thus based on a Schrödinger equation, which is an ad hoc model and which cannot be solved with any assessment of accuracy because of its multi-dimensionality and thus cannot really deliver predictions which can be tested vs observations, except in very simple cases.

The Copenhagen dogma is then that predictions of the standard Schrödinger equation always are in perfect agreement with observation, but a dogma which cannot be challenged because predictions cannot be computed ab initio.

In this situation it is natural to ask, in the spirit of Schrödinger, for a new Schrödinger equation which has a direct physical meaning and to which solutions can be computed ab initio, and this is what I have been exploring in many blog posts and in the book (draft) Many-Minds Quantum Mechanics.

The basic idea is to replace the linear multi-d standard Schrödinger equation with a computable non-linear system in 3d as a basis of a new form of physical quantum mechanics. I will return with more evidence of the functionality of this approach, which is very promising...

Note that a wonderful thing with computation is that it can be viewed as a form of non-destructive testing, where the evolution of a physical system can be followed in full minute detail without any form of interference from an observer, thus making Bohr's Law into a meaningless limitation of scientific thinking and work from a pre-computer era preventing progress today.

PS It is maybe wise to be a little skeptical to assessments of agreement between theory and experiments to an extremely high precision. It may be that things are arranged or rigged so as to give exact agreement, by changing computation/theory or experiment.