Chemistry as Emergent Quantum Physics?

A physical phenomenon may be called emergent if it is a non-obvious consequence of the assumptions of a physical theory revealed by symbolic or digital computation, and can then be seen to be a consequence of theory + computation, where computation in general adds essential new theory. 

A key example is turbulence which is an emergent aspect of solutions of Euler's equations for incompressible inviscid fluid flow computed as best possible in a specific sense specified in the book Computational Turbulent Incompressible Flow. 

Let us ask:

• Does chemistry as science of molecules composed of atoms, emerge from quantum physics as science of atoms? 

Assume first that quantum physics is textbook Standard Quantum Mechanics StdQM. A physicists in the foot steps of Dirac will say that chemistry is applied quantum physics and so that 

• Chemistry emerges from StdQM, in principle.                                                 (1)

A chemist will object and say that 

• Chemical bonding as essence of chemistry does not emerge from StdQM.      (2)   

Let us assume that (2) based on experience is true, noting that (1) is speculation. 

But if (2) is true, then chemistry needs more of physics than what is in StdQM, but then more precisely what?

We now compare with RealQM as an alternative to StdQM, with the following ambition:

• Chemistry and chemical bonding emerges from RealQM.                                  (3)

RealQM has computational form of linear complexity, which allows chemistry to emerge from computation with RealQM, without need of any extra physics. Want to try?

Recall that RealQM is ab initio, with mesh resolution as only parameter, which means that all theory is already within RealQM in transparent form.

This is not the case for StdQM, where computation implicitly adds new physics without transparency. 

Computational Emergence: New Paradigm

Computation has turned the philosophical idea of emergence into a virtual laboratory for exploration of large scale complex structures developing in systems formed by small scale simple components. The laboratory is realised in efficient form by the Finite Element Method FEM covering all areas of continuum physics including fluids, solids and electro-magnetics modeled by the classical partial differential equations of Euler, Navier and Maxwell.

Computation thus brings new life into the classical models of continuum mechanics describing small scale simple local physics in terms of differential equations, by exhibiting the large scale global result as emergence by solving the equations typically by time stepping. In particular, the turbulent flow of a fluid with small viscosity like air and water can be simulated by computational solution of the Euler equations (expressing Newton's 2nd law and incompressibility in local form).

In general, emergence can be explored if solutions can be computed. With increasing computational power more of continuum physics can be explored as emergence in a FEM laboratory. 

Quantum Mechanics QM as the physics of atoms and molecules appears to fall outside this paradigm, because the basic mathematical model in the form of  Schrödinger's equation is uncomputable by involving $3N$ spatial dimensions for a system with $N$ electrons bringing in exponential computational complexity. Exploration of emergence in systems of atoms and molecules is thus not possible by computation because of exponential complexity, which can only be a big disappointment for a physicist seeking to understand emergence in atomic systems. 

There is however a version of QM named RealQM which is a computable because it has the form of classical continuum physics in 3 space dimensions. RealQM opens the possibility of exploration of emergence in systems of atoms as forms of chemistry and protein folding. 

Emergence emerges as a central concept of physics, open to  exploration by computation. Effective large scale models may be formed once emergence is uncovered.

Protein folding is an example of emergence in all forms of life based on proteins formed (from chains of simple amino acids specified by the genetic code) in a folding process into 3d structures determining the function of the protein. Protein folding has exponential complexity with QM, but only polynomial with RealQM which opens new possibilities of computational simulation of the emergence of life. 

Reductionism + Emergence vs Quantum Mechanics

Reductionism and emergence are two basic principles of science:

• Decomposition of a complex system into simpler parts.

• Composition of simple parts into complex system.

Combination of these principles allows simulation and control of complex systems. The Finite Element Method FEM is a realisation of this combination covering the vast area of Continuum Mechanics CM. See also this recent post. The canonical example is the formation of a moving large scale coherent wave from small scale motion up and down of water particles. 

FEM decomposes a structure like a bridge into finite elements as beams, columns and cables with simple behaviour captured by analytical mathematics, which are then put together into the structure represented by a system of equations describing the coupling of the finite elements. The action of the structure under loads can then be simulated by computing solutions to the system of equations. 

The finite elements represent reductionism and emergence comes from assembly into structure. FEM is a powerful methodology covering all of CM by digital computing made into a very powerful tool for scientists and engineers. The key is that finite elements are described by simple analytical mathematics while the the structure is made to emerge by powerful computing, as a synthesis of analysis and computation. 

It is essential that the physics of the element is simpler to describe mathematically than that of the whole structure composed of elements. Elements more complicated than the whole structure destroys the whole idea of combined reduction and emergence. 

CM represents macroscopic physics while microscopic physics of atoms and molecules is described by Quantum Mechanics QM. Modern physics consists of CM + QM.

Does QM represent a reduction of CM into elements in the form of atoms and molecules of simpler mathematical form? No, it is the opposite: The QM mathematical model of atoms and molecules is  Schrödinger's equation in $3N$ spatial dimensions for a system with $N$ electrons, which contains immensely more of complexity than the 3 spatial dimensions of CM.  

This means that QM does no appear by reduction of CM, and CM does not emerge by assembly of QM. In other words, the grand scheme of reduction-emergence so successful in CM cannot be applied when including QM to the picture. 

Real Quantum Mechanics RealQM is a reduced form of QM with the same complexity as CM which opens to 

• reduction of molecules to atoms 
• emergence of molecules from atoms 
• reduction of CM to QM molecules 
• emergence of CM from QM molecules.  

RealQM thus (in principle) connects to CM into a synthesis covering (in principle) all scales from micro to macro following the scheme of reduction-emergence. 

QM does not combine with CM in the same constructive way since the models of QM are vastly more mathematically complex and computationally demanding than CM. 

RealQM thus offers an alternative to QM which combines with CM into a synthesis over all scales. 

In particular, RealQM represents Structural Mechanics of the Atom.

QM was loaded from start in 1926 with complications which have never been resolved including exponential complexity defying computation and wave-particle contradiction. To the already long list of complications, we can now add the gulf between CM and QM preventing the use of the principle of reductionism + emergence.

Here is a comment to the post by chatGPT:

Key Claims of the Post

From what I can tell (based on the blog post and previously quoted material) the major claims include:

1. Reductionism (breaking things down into simpler parts) has been undermined in modern physics because the microscopic theory (quantum mechanics) is more complex than the macroscopic (classical/continuum) theory.

2. The usual expectation of reductionism (“the part is simpler than the compound”) fails: in that sense, QM is not “simpler” than classical or continuum mechanics.

3. Therefore the standard reductionist/emergent framework—that macroscopic phenomena emerge from simpler microscopic laws—doesn’t hold in the straightforward way often assumed.

4. The author points toward an alternative theory (he calls it “RealQM”) that would restore a simpler microscopic basis to make the reduction → emergence ladder more conventional.

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✅ Where the Argument Has Strength

• It’s true that the microscopic quantum description (especially for many-body systems) is extremely complex and difficult to solve. The sheer mathematical/or computational complexity of going from many interacting quantum particles to a full continuum description is daunting. That fact backs up the observation that the “part” (quantum many-body) can be harder to handle than the “whole” (classical continuum) in practice.

• It’s legitimate to highlight the practical gap between microscopic laws and macroscopic descriptions — the “how do you get from A to B” question is real and non-trivial.

• The post raises a useful philosophical point: just because a theory is “fundamental” doesn’t guarantee we can easily derive all higher-level behaviour from it in practice. This aligns with mainstream philosophy of science (see e.g., discussions of emergence + reduction). arXiv+1

Emergence vs Playing Dice

Follow the emergence of structure when dropping a stone in a pond  in this code from Model Workshop Leibniz World of Math exhibiting a very rich world of emerging from simple basic laws with playing dice.

The wisdom of modern physicists since 100 years is that the Schrödinger wave function of quantum mechanics supposedly describing atom physics, represents a probability distribution as if electrons and protons forming atoms play dice or roulette to evolve in time from which the World emerges with all its amazing features. 

In other words (connecting to the previous post), modern physicists embrace an idea of:

• Emergence of complex coordinated ordered phenomena from playing dice. 

But is it possible that order can emerge from playing dice? This question was addressed in the book The Dice Man by George Cockcroft and the answer was No. It does not work to play dice to take the decisions required to go through life. It ends in chaos without order. 

The same result is to be expected concerning the physics of atoms forming the world. The idea of atoms playing dice lacks scientific logic. An atom is an elementary simple thing and as such, cannot include a roulette wheel/ball as something complex and so unpredictable. An atom does not have the capacity to play roulette! RealQM offers an new Schrödinger equation as a continuum model in 3 space dimension which is free of roulette statistics. 

The emergence of a surface wave of water comes from coordinated motion of water particles reacting to forces without the help of any dice playing. Emergence of patterns in physical systems is the result of increasing difference while playing dice represents decreasing difference. 

In real physics both play a role: Increasing difference without limit leads to break-down. Without difference no structures. This aspect is investigated in setting accessible for a general audience in The Clock and the Arrow, 

There is a connection to Darwin's theory of Evolution as emergence of complex living organisms from playing dice combined with selection of fittest. This is a very simple theory and as such cannot explain much. In particular, there is evidence that evolution of life is driven by environmental pressure as if there is presence of some form of intelligent design.