So, why should there be a proton-proton repulsion, mechanically speaking? Both particles are considered to have wave functions that chop off at nuclear distances, so at long distance, their wave functions don’t interact. By what spooky “force at a distance” (historic paraphrase) could an electrostatic repulsion occur between them?
The key here is to look again at the premise. The proton wave function is not truly small, it is one part of a larger wave function, the other part of which is the electron. Let’s see if we can explain electrostatics based on action through the total wave function.
Positive and negative attract because the more the positive nucleus is separated, the higher the energy state. This is a fundamental property, based in the fact that we are stretching out the “excited neutron” like a rubber band.
The electrons repel each other because they are in a sense competing for the same space. Two electrons place spatial constraints on each other, limiting the basis-set waves available to them, and so distorting each other’s orbital shapes and raising their energy level. Since this is proportional to the original energy of those orbital states, this force will be proportional to the original proton-electron force. Not a big stretch.
Another effect we’ve not accounted for is, if the electron is constrained and can’t respond to background energy passing through, by skipping to certain orbitals and hence polarizing in response, this also limits the entropy of the universe. Not sure if this is truly an issue, or just another way of looking at the same thing.
Now, is it possible that the positions of the protons are creating a potential energy gradient because they are influencing each other’s electronic orbital energies? By bringing the protons together, you are forcing the two cloudy electron wave functions to be closer to each other. Are the two electrons really doing the pushing apart, and dragging their protons behind them?
Here is an example from classic physics. You have a metal conductive sphere and you place one electron of negative charge on it (it allegedlly spreads out evenly over the surface) and place one proton floating inside the sphere. Because of the geometry of the R-squared law, the tug from all the portions of the sphere cancel out, and the proton feels no force. Now you place a second electron on the surface and a second proton inside the sphere and what happens? Classical physics would say the electrons still spread out evenly but the protons repel each other. This alternative view suggests that the two electrons will stay away from each other, separating to opposite halves of the sphere, and the protons will tend to follow, such that each proton is more associated with its own electron, and the protons as a consequence speed apart. Of course these motions happen in concert.
Obviously I’m leaving a lot of detail “as an exercise for the student” here. Sorry, that’s as far as I’ve taken it to date. The point is, a better understanding of the wave nature of the electrons leads to an alternative perspective on the nature of electronic forces. Instead of having THREE different forces, seemingly between completely different combinations of quantum mechanical wave entities, all happening to have the exact same strength and form, this view suggests that only one is fundamental (p+/e-), one is directly derivative (e-/e-), and the third (p+/p+) is actually a book-keeping device because we have not fully accounted for all the consequences of the first two. Such a treatment would avoid this seeming three-way coincidence and be much more satisfying if we could work it out.
In even simpler terms, the total potential energy of a collection of excited neutrons is just a function of how much space they have to expand out their excitation energy, i.e., the secondary electron wave function that fills surrounding space and results from the thermodynamic drive to “perfect” the particle-like wave function in the nucleus. Because the electron wave function is just the “trash” left over from selection of basis-set sine waves to optimize the lump of mass that makes up the central massive particle, any limitations on those electron wave functions is actually acting by limiting the ability of the proton to achieve the lowest possible internal energy state. Or something like that. Give me another 30 years to chew on that, and I’ll either have all the details, or have forgotten them as I develop Alzeheimer’s.
Pretty different from the view of ping-pong balls and bowling balls, with inexplicably opposite “charges” on them, yes?
[© Copyright 2016 by Gerald Keep. All Rights Reserved.]