torsdag 15 december 2022

Bohm and the Nobel Prize in Physics 2022


David Bohm struggles in Causality and Chance in Modern Physics to give a meaning to Quantum Mechanics in its probabilistic Copenhagen Interpretation CI based on Schrödinger's equation advocated by Bohr/Born/Heisenberg. Bohm expresses his main hang-up, which he shares with Schrödinger and Einstein (and myself), as follows:

  • The Schrödinger wave equation does not describe a wave in ordinary 3d space, but instead a wave in an abstract $3N$-dimensional space with $N$ the number of particles.
  • This is not really acceptable in a physical theory, and should at least be regarded as an artifice that one uses provisionally until one obtains a better theory in which everything is expressed once more in ordinary 3d space. 
The wave function $\Psi (x1,x2,...,xN;t)$ as (complex/real-valued) solution to Schrödinger's equation thus depends on $N$ 3d particle position variables/coordinates $x1$ to $xN$ thus on $3N$ spatial variables (plus time $t$), which for $N>1$ do not represent any reality of physical 3d space. 

100 years ago Born came up with the idea of letting the 3N-dimensional coordinates $(x1,...,xN)$ represent possibility of particle positions rather than actuality of reality, with $\vert\Psi (x1,x2,...,xN;t)\vert^2$ the probability of a particle configuration at time $t$ with particle $i$ at position $xi$ for $i=1,...,N$. 

This is still today the doctrine of the physics community serving as background to the Physics Prize 2022, and the protests from Bohm, Schrödinger and Einstein are no longer voiced. The Prize 2022 is meant to give final blow to Einstein's "God does not play dice" still haunting modern physics with the question: How is it possible that atoms always show exactly the same spectrum if their electrons are simply gambling?  How come that the periodic table appears to be written in stone, when electrons are jumping around playing roulette?   

But CI is filled with unresolved questions and contradictions:
  1. By multidimensionality the wave function is uncomputable on any foreseeable computer. Claims that CI always agrees with observation cannot be verified. 
  2. Atoms have fully deterministic excited states/energies with stable ground state/energy. No role for probabilities here.
  3. The generalisation of Schrödinger's equation to $N>1$ from the physical model for the Hydrogen atom with $N=1$ is performed with a stroke of a pen as a mathematical formality without physical reality. Real Quantum Mechanics presents a different generalisations with physical meaning. Real QM is computable and so elevates simulation and not observation as in CI to focal interest.
  4. Bohm tried to give a physical meaning to CI in the form of a pilot wave theory, but retained the uncomputable multidimensional wave function. Wheeler tried the idea of giving possibility the same reality as actuality in his Many-Worlds version of QM. The physics community could not embrace Bohm nor Wheeler although both tried (but without success) to give meaning to CI.
  5. The Nobel Physics Prize 2022 sells the idea of a 2nd quantum revolution into quantum information/computing based on multidimensional wave functions of immense richness/power, but reality may be lacking. Will it be a quantum jump into the void? Who will call the bet?   

Here is Sabine Hossenfelder's explanation of Bohmian Mechanics:




  

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