fredag 30 december 2022

The Quantum Kabbalah

Kabbalah picture of the noble gas Oganesson with 118 electrons structured into shells.

The foundation of the quantum mechanics of atom physics is the Schrödinger equation 

  • $i\frac{\partial\Psi}{\partial t} =H\Psi$   (S) 

in a wave function $\Psi$, with $H$ a Hamiltonian linear operator. (S) can be seen as the sign of a Kabbalah, which is a school of thought of Jewish mysticism or more generally an esoteric method within Western mystery tradition. For a system with $N$ electrons the wave function $\Psi$ depends on $3N$ space variables and evolves over time $t$ from one time instant to the next. 

The Kabbalah connection is natural because physicists have made it very clear that (S) is a true mystery, which cannot be understood as physics, but nevertheless has to be accepted as a perfect model of physics with predictions always in exact agreement with observed reality. 

In a conversation/dispute you can always bring in the wave function $\Psi$ as a complete description of the subject at hand, ultimately "the wave function of the World" which will give you an advantage in the discussion. 

The reason that (S) cannot be understood as physics, is that it is derived by a purely formal mathematical generalisation without physical basis of a model for the Hydrogen atom with $N=1$ with physical basis, to all the atoms in the periodic table with $N=2, 3,...,118$. The $3N$-dimensionality of $\Psi$ asks for $100^{3N}$ mesh points in computational resolution, which makes $\Psi$ uncomputable already for $N=4$. 

This makes (S) into a symbol carrying a secret which cannot be revealed, thus into a modern physics version the Ein Sof (Endless One) of Kabbalah with connection in the above picture.

The fact that $\Psi$ cannot be computed has split the physics community into chemical physicists at chemistry departments using electronic "orbitals" to reduce dimensions in practical computations filling supercomputers, and philosophers at philosophy departments seeking to understand the mystery of (S) as foundational quantum mechanics without computation, while physicists at physics departments since long have left (S) for deeper theories of quantum field theory and string theory deeper into a mystery far beyond any form of computability. This is the crisis of modern physics witnessed by many.                

PS Erwin Schrödinger formulated the Schrödinger equation for Hydrogen (with physical basis) in 1925, but could not accept the generalisation to $N>1$ because it was not physical, and sought for help in Indian Philosophy from his standpoint expressed in the opening of The Interpretation of Quantum Mechanics (Dublin Seminars 1949-1955):

  • Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics held today, I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody.
  • The view I am opposing is so widely accepted, without ever being questioned, that I would have some difficulties in making you believe that I really, really consider it inadequate and wish to abandon it. 
  • It is, as I said, the probability view of quantum mechanics. You know how it pervades the whole system. It is always implied in every thing a quantum theorist tells you. Nearly every result he pronounces is about the probability of this or that or that ... happening with usually a great many alternatives. 
  • The idea that they be not alternatives but all really happen simultaneously seems lunatic to him, just impossible (Many Worlds Theory)
  • He thinks that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish. 

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