söndag 18 augusti 2013

Quantum Contradictions 10: Symmetric and Antisymmetric Wave Functions

The wave function as solution of the Schrödinger equation as the basis of quantum mechanics, has 3N spatial dimensions for an N-particle system. As such it is a computational impossibility as noted by Nobel Laureate Walter Kohn in his Nobel Lecture 1998:
  • In general the many-dimensional wave function of a system of N electrons is not a legitimate scientific concept (for N > 10 say). 
But if the 3N-dimensional wave function is a computational impossibility, or monstrosity, it is also a physical monstrosity; at least if physics is viewed as some form of analog computation, which appears to be the only possibility beyond mysticism.

Nevertheless, physicists worship the 3N-dimensional wave function and believe it has a deep physical significance. In particular, it is believed that the atomic world consists of bosons represented by fully symmetric wave functions and fermions represented by fully anti-symmetric wave functions. In particular the periodic table is believed to result from the fact that electrons are fermions satisfying Pauli's exclusion principle as a consequence of anti-symmetry.

A periodic table based on bosons (such as photons) would be a trivial table with only one kind of atom.

But if the 3N-dimensional wave function is a monstrosity, then so must be the subdivision into fully symmetric and anti-symmetric wave functions and then also Pauli's exclusion principle.

In the alternative model under study in this sequence of posts, another explanation of the periodic table presents itself: In this model it is the repulsion between electrons which shapes the atomic shell structure starting from the Helium atom with two electrons repelled into opposite position around the kernel.

In other words, atoms with electrons without repulsion would be of one kind and thus correspond to bosonic atoms of one kind only capable of creating a trivial dull world.

We are thus led to the idea that it is the repulsion between electrons, which forms the atomic world of great variability creating a far from dull world of even greater variability by upscaling, and not any mystery of anti-symmetric wave functions which cannot explain e.g. the electron structure of Plutonium with N = 94.

2 kommentarer:

  1. What in your opinion is the computational compexity of simulating (solving numerically) the partial differential equations for N=10?

    How does the complexity increase as a function of N?

  2. With a resolution of 100 grid points in one dimension a total of 100^30 = 10^300 is needed for 3N dimensions, beyond the capacity of any thinkable computer.