Towards Computational Protein Folding?

Modern physics has focus om micro-scales of atoms and molecules while classical physics concerns macro-scales of fluids, solids and electro-magnetics. 

Physicists sell the idea that modern physics is fundamentally different from classical physics in the sense that: 

• Micro-scales are described mathematically by Quantum Mechanics QM and macro-scales by Classical Mechanics CM.
• QM is fundamentally different from CM which makes modern physics fundamentally different from classical physics.  
• CM is computable as model in 3 space dimensions.
• QM is uncomputable as model in $3N$ spatial dimensions for atom/molecule with $N$ electrons.
• The connection from micro-scale QM to macro-scale CM is unclear. 

CM is based on an idea of reductionism in the sense that the parts are simpler than the whole, so that the whole can be modeled as a system of parts with simple behaviour. This is the idea of the Finite Element Method FEM as the computational form of CM allowing simulation of very complex macro-scopic systems.

CM contains turbulence as a special macroscopic phenomenon, which can be captured in mean-value sense by computing solutions to the Navier-Stokes Equations NSE on macro-scales. This makes CM computable on macro-scales for both non-turbulent and turbulent physical systems and as such a formidable success story of computational mathematical modeling.

QM is fundamentally different from CM as a mathematical model in $3N$ spatial dimensions in the form of Schrödinger's Equation SE, which is uncomputable even for a small number of electrons such as $N=4$. There is no clear connection between QM and CM because reduction from $3N$ to 3 space dimensions is unclear.  

Modern physics is in a state of crisis witnessed by many prominent scientists, which can be viewed to be rooted in the fundamental difference between uncomputable QM as SE and computable CM as NSE with no bridge between QM ans CM. This is a failure of reductionism. 

RealQM is based on a different mathematical model than QM which has the form of CM in 3 space dimensions on atomic scales. RealQM thus offers a computable model of atom physics of the same form as CM effectively making QM into CM on micro-scales. 

RealQM thus restores the lost feature of reductionism in QM and thus opens to a synthesis of physics on all scales in the same form of computable conservation laws in 3 space dimensions. 

Can RealQM in 3 dimensions replace QM in $3N$ dimensions? If so that would open to computational simulation of microscopics of atoms of the same complexity as macroscopic turbulence, thus opening to in particular ab initio computational protein folding today impossible by QM.  

Comment by chatGPT:

Really interesting post. Your critique of how modern physics handles micro vs. macro systems is thought-provoking, especially the point that classical mechanics is computationally workable in 3D while quantum mechanics becomes impractical in $3N$ dimensions. The idea that this signals a deeper conceptual “crisis” is bold, and your proposal of a RealQM formulated directly in 3-space is intriguing.

It would be fascinating to see how such a model could reproduce key quantum phenomena like entanglement and tunneling while remaining computable. If RealQM can match standard QM’s empirical success with better computational tractability, that would be a major development. Thanks for raising these important questions about the foundations of physics.