måndag 14 april 2025

Where Quantum Mechanics Went Wrong in 1926

The physics of atoms and molecules as the essence of modern physics was born from Schrödinger's wave equation for the Hydrogen atom in 1926. Let me cite from Epistemology and Probability, Bohr, Heisenberg, Schrödinger and the Nature of Quantum Theoretical Thinking by A Plotnitsky:

  • Schrödinger’s wave mechanics aimed at offering, and initially appeared to be able to offer, a theory that would be realist and causal and thus would conform to the  "classical ideal". 
  • It was expected to be able, just as classical mechanics did, both to describe the physical processes at a subatomic level (as wave-like processes) and to predict, on the basis of this description, the outcomes of the experiments involving these processes. 
  • While Schrödinger’s hopes concerning the descriptive capacity of his theory 
  •  did not materialize, on the predictive side the theory was spectacularly successful.
  • Schrödinger’s equation does not describe any physical waves, as Schrödinger initially hoped it would. Instead, quantum probabilistic predictions—enabled by Born’s rules for deriving probabilities from quantum amplitudes.
  • Schrödinger did not change his philosophy. Instead, he came to doubt and even to repudiate quantum mechanics, at least as a desirable way of doing physics, although he acknowledged that the theory and even understanding it in ‘‘the spirit of Copenhagen’’ (which remained philosophically deplorable to him) may have been imposed on us by nature itself.


We understand that Schrödinger from start was searching for mathematical model within classical continuum mechanics as a wave equation describing the mechanics of an atom, including radiation spectrum. The Schrödinger equation for a Hydrogen atom with one electron has this form. Schrödinger never gave up his hope that his model somehow could be generalised to atoms with many electrons within the same frame of classical physics, with thus atom mechanics as a form of macroscopic mechanics just on a smaller scale.

But what would such a generalisation look like for the Helium atom with two electrons? Schrödinger hesitated, but ended up taking the easy ride resorting to formal mathematics just adding a new 3d variable for the second electron, thus ending up with a differential equation in six spatial dimensions with unclear physical realistic meaning. 

This was the critical point in 1926 when Max Born stepped in to shape modern physics until our days by giving the six-dimensional wave function for Helium a probabilistic meaning thus leaving deterministic reality, which all leading modern physicists have described as weird, and Schrödinger refused to teach from 1928 to essentially give up quantum mechanics in despair.  

Today 100 years later there is a generalisation of Schrödinger's equation for the Hydrogen atom to atoms and molecules with many electrons in the original spirit of Schrödinger in the form of Real Quantum Mechanics RealQM. 

Why did not Schrödinger take this route, which is very natural,  and instead let himself be overpowered by Born (boosted by Bohr and Heisenberg)? 

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