Regarding quantum physics ”The
Copenhagen interpretation was recently summarized as “Shut up and calculate!”
That’s blunt, but not completely unfair. It is, in fact, the right
injunction

for
most physicists most of the time.” say Rosenblum and Kuttner
(2006).

A very simplified discussion on molecular orbitals excerpted
from Levine (1977) follows. A Slater type orbital (for example, for a
1s orbital) has the form:

Following
the Hellmann-Feynman theorem

it
is possible then to calculate the molecular orbital energies.
Levine(1977) cites Parr (1963) saying “We have at our reach precise
descriptions of molecules”. That is, Parr's position is that
advanced quantum chemistry provides a view of how molecules behave.
However, we can see that the energy of an electron in an orbital is
calculated by an operator which calculates a number of exponential
functions

*f*, whose addition multiplied by a set of parameters allows to calculate a set of functions φ, from which an integral is then calculated. That seems quite similar to a neural network of neurons in the first row, n neurons in the second row, and one neuron in the third row. An example of a similar neural network applied to the calculation of chemical activities (figure 1) can be found in Nami and Deyhimi (2011).
This brings the
question of whether the calculation of energies for molecular
orbitals is really mechanistically based, or just a black box model.
We go back to Rosenblum and Kuttner (page 119): "

*Here’s something to ponder: Suppose the cat was placed in the box and the atom sent into the mirror system eight hours before you looked. The system evolves unobserved during those eight hours. If you find the cat alive, since it has gone eight hours without eating, you find a hungry cat. If you find a dead cat, an examination by a veterinary forensic pathologist would determine the cat to have died eight hours ago. Your observation not only creates a current reality, it also creates the history appropriate to that reality. You might consider all this absurd. Precisely Schrödinger’s point! He concocted his cat story to argue that, taken to its logical conclusion, quantum theory, at least its Copenhagen interpretation, was absurd. Therefore, he claimed, it must not be accepted as a description of what’s really going on.**"*
A
perverse hypothesis is proposed. Let us assume that electromagnetic
fields, as a consequence of the emissions of subatomic particles,
combine in an interference pattern instead of leading to homogenenous
potential barriers. Such pattern would create regions of maximum and
minimum field intensity, and regions of intermediate field intensity
in between. The juxtaposition of the individual fields is represented
pictorially in Figure 2(left) by means of cross sections of
concentric spheres centered on field generating particles. The
illustration does not intend to be rigorous (force lines of a
magnetic field have nothing to do with an spherical distribution
around the originating particle), but to show the complex patterns
resulting of the juxtaposition of individual particle-centered
patterns. The arrows try to show how a particle would try to
negotiate passage through the field through favorable field intensity
regions, which can obviously be regarded as a 3-D maze. Figure
2(right) represents even more schematically the now obvious
consequence of the hypothesis: random motion through a potential
barrier may result in the particle taking “the wrong turns” and
getting out the way it entered. Although not illustrated, a potential
well’s effect to reject particle may be the consequence of less
interference between particle fields at the boundary of said field
making it more “impermeable”. The conclusion would be that a wave
function Ψ does not describe a quantum behaviour as we think of it,
but is simply a function good at being fitted to give values between
0 and 1 within a certain interval, a probability generator.

A
final element of this “heretic” quantum model would be the
following: let us assume that considering electrons as basic
subatomic particles is flawed because the fact they cannot be broken
is due to their high mobility, which prevents the stress due to the
impacting energy to break up the assembly of sub-particles
constituting the electron, instead accelerating the electron and
changing the configuration of the particle. If so, then the
Hamiltonian of an electron:

HΨ
= EΨ

Would
be in fact

H

_{e-n}Ψ_{e-n}+ ΣH_{se-ec}Ψ_{se-ec}= Ψ_{e-n}E_{e-n}+ ΣΨ_{se-ec}E_{se-ec}
The subindex

_{e-n}would mean electron-nucleus interaction, and the subindex se-ec would refer to the interactions between the sub-electronic particles and the electronic virtual center. As a consequence, what we accept as wave function for an electron would be a combination:
Ψ
= (

_{ }Ψ_{e-n}E_{e-n}+ ΣΨ_{se-ec}E_{se-ec})/E
No
wonder the integral of the square of the wave function can assume
very intricate forms! And no wonder trying to make sense of any steps
of the calculation makes quantum theory “queerer than we can
suppose”, as Haldane puts it or that Einstein found its
implications “spooky” (Rosenblum and Kuttner, 2006, page 3). The
fact is that it may be a black box tool with no significant meaning
whatsoever: neural networks are precisely extremely good calculation
tools with no pretense of giving us an explanation of why.

REFERENCES

Levine,
I..N., Quantum Chemistry, (Sp. trans of the first edition) Editorial
AC (1977)

Nami, F., Deyhimi, F.; Prediction of activity coefficients at infinite dilution for organic solutes in ionic liquids by artificial neural network, J. Chem. Thermodynamics

**43**22–27 (2011)
Rosemblum,
B.; Kuttner, F.; Quantum Enigma, 112 Oxford University Press (2006)