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.

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.  

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.

---

✅ 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