- The need for an improved understanding of what Quantum Mechanics really is, needs hardly be explained in this meeting.
- My primary concern is that Quantum Mechanics, in its present state, appears to be mysterious.
- It should always be the scientists’ aim to take away the mystery of things.
- It is my suspicion that there should exist a quite logical explanation for the fact that we need to describe probabilities in this world quantum mechanically.
- This explanation presumably can be found in the fabric of the Laws of Physics at the Planck scale.
- However, if our only problem with Quantum Mechanics were our desire to demystify it, then one could bring forward that, as it stands, Quantum Mechanics works impeccably.
- It predicts the outcome of any conceivable experiment, apart from some random ingredient. This randomness is perfect. There never has been any indication that there would be any way to predict where in its quantum probability curve an event will actually be detected.
- Why not be at peace with this situation?
- One answer to this is Quantum Gravity. Attempts to reconcile General Relativity with Quantum Mechanics lead to a jungle of complexity that is difficult or impossible to interpret physically. In a combined theory, we no longer see “states” that evolve with “time”, we do not know how to identify the vacuum state, and so on.
- What we need instead is a unique theory that not only accounts for Quantum Mechanics together with General Relativity, but also explains for us how matter behaves.
- We should find indications pointing towards the correct unifying theory underlying the Standard Model, towards explanations of the presumed occurrence of supersymmetry, as well as the mechanism(s) that break it. We suspect that deeper insights in what and why Quantum Mechanics is, should help us further to understand these issues.
Hooft then proceeds to seek a determinism behind quantum mechanics in the form of cellular automatons (also here).
I am pursuing another route to an understandable form of quantum mechanics as analog computation with finite precision, which in a way connects to Hooft's cellular automaton's, but is expressed by Schrödinger type wave equations in a continuum mechanics framework.
In this framework the finite precision computation makes a difference between smooth (strong) solutions and non-smooth (weak) solutions of the wave equations: Smooth solutions satisfy the wave equations exactly (with infinite precision), while non-smooth solutions satisfy the equations only in a weak sense with finite precision and loss of information as a form of dissipative radiation.
This allows the ground state of an atom as a smooth solution without dissipation to be stable over time without dissipation, while an excited state as a non-smooth solution will return to the ground state under dissipative radiation.
The situation is analogous to that described in my work together with Johan Hoffman on fluid mechanics, with turbulent solutions as non-smooth dissipative solutions of formally inviscid Euler equations, which allowed us to resolve d'Alembert's paradox (J Math Fluid Mech 2008) and formulate a new theory of flight (to appear in J Math Fluid Mech 2015), among other things.