Jim,
Yes, this is fun!
The colloquial cloud image is intended to describe the electrons wave
function. Even at this point, the wave/particle duality has proponents
polarized. At one end, the wave function describes the particles
probability distribution in space - its actual location being unobservable
until measured. At the other end, the wave function describes the actual
electron distributed through space as a standing wave. In either case,
there is still a mixture of continuous and discrete models and tools to
explain/predict their behavior. For example, to calculate the energy of an
electron in an atom, the quantum mechanic calls upon the continuous
relationships of the attractive force between the nucleus and the electron
and the repulsive force of the electrons momentum driving it from a fixed
position. This results in a set continuous partial differential equations.
That is, the problem is set up in a continuous space. The solution(s) to
the problem are a set of wave equations whose parameters must be identified
through the problems boundary conditions. Application of the boundary
conditions produce the discrete result of quantized energy states.
So what do we have here? We have a set of relationships that are continuous
in nature and produce a result that are discrete. So is the system
continuous or discrete? It depends upon what system is being described.
The forces and masses are all continuous in an open system. As soon as
there is a physical constraint added (the electron bound to the neighborhood
of the nucleus), the behavior of the atomic system is discrete. Photon
studies produce similar results.
I would only have a little difficulty with Franco Modiglianis comment that
the world was neither continuous or discrete. But this is only due to
semantics. The world is both, depending upon how one looks at it.
Please let me apologize for my brash statement: "All physical processes are
discrete in nature."
My intent was to convey that in chemical reactions, each reaction is at the
atomic or molecular level and involve a small number of components -
discrete. Macroscopically, these produce a bulk product that may more
easily be viewed as continuous. As most all processes of interest (e.g.
people shuffling paper) involve some material, the laws of chemistry and
thus QM are thus involved.
Note 1: The discrete states of electrons in atomic orbital are steady state
values. The actual transitions from one state to the other may be described
through continuous dynamics.
Note 2: Although A. Einstein has been quoted to denying quantum mechanics
interpretation of the bound electrons wave function as a probability
distribution ("God doesnt roll dice"), he did understand the discrete
nature of QM solutions. Also, he pointed out (1950s) that he was
reconsidering his previous belief of natures fundamental continuity; he was
open to the possibilities that the substances of nature may have both
discrete and continuous properties.
Ray
From: "Raymond T. Joseph" <
rtjoseph@ev1.net>