Neuroquantology, the Ultimate Quest - Brain Theory from a Circuits and Systems Perspective - page 149

other important biological interfaces. Electrons are inherently quantum mechanical.
The question of the moment is: Does quantum mechanics affect biology in any
direct way? Or is it just about larger classical molecules?

Tunneling

A clear separation between quantum physics and classical physics is in our under-
standing of where small particles are located. For example, in the everyday world
an object is either inside a bottle or not. But for particles such as electrons that are
very small (rest mass or weight is 9.11 10 31 kg), they may have a high

probability of being inside their bottle, but a significant chance they are found
outside their bottle. Quantum mechanically, a small object can appear outside its
bottle without removing the top, breaking the bottle, and without punching a hole
through it, or squeezing past its cork. This unfamiliar behavior is known as
tunneling.
Tunneling, as predicted by quantum theory, is commonplace in the atomic
world. Solid-state devices depend on it, for example, tunnel diodes. Alpha particles
of radioactive decay are another common example; they suddenly pop out of a
nucleus even though nuclear forces hold the nucleus together, and even though they
do not have enough energy to get out. They tunnel out anyway. Small particles
behave in a nonlocal manner, appearing where they are not supposed to be.

Copenhagen Interpretation

An accord reached in Copenhagen and promoted by Neils Bohr, a pioneer of
quantum mechanics, is that humans know only what they can observe. This accord,
the Copenhagen interpretation, is mainstream today and implies that physicists do
not and cannot know the true nature of small particles. Quantum mechanics under
this accord is a system of rules, no more, no less, amazingly successful rules based
on observation, to predict what particles do.
In contrast, Heisenberg, another pioneer, proposed that waves of quantum
probability really exist in nature, and that they evolve, adjust, and resolve (or
collapse) to cause the events we observe in nature. This may be termed the
Heisenberg interpretation under which probability waves as determined by
Schr¨dinger's equation 2 are taken to be physical. Note, however, that such waves

2

Schr¨dinger, a pioneer of quantummechanics, contributed an equation which in one dimension is

2
2μ

2

η @ψ

@t ¼ η

@ ψ

@x 2 þ

i V ð x Þψ;

where (x, t) is a probability wave function that depends on time t; V(x) is a potential field; and all

else are given constants [ 11 ].

ψ