In the previous chapter we touched on the idea that mass is a vibration along the positive-negative charge dimension.
It is fun to speculate on just what the collapsed wave function of a neutron would look like that appears to have no outside charge, yet has angular momentum and mass. I admit that the details are beyond me, but I like to consider such things by starting to visualize a single stark blip going up, then down across the axis. One side tapers to infinity with positive charge, the other side tapers to infinity with negative charge. Now you spin the whole thing and at a distance, the tapered tails alternate so rapidly they effectively cancel out. The center would be a rotating figure eight, with the positive and negative portions spinning around each other tightly.
Let’s set aside the speculation about neutrons and focus on the wave function of the proton. Here we are trying to paint a spike, nearly a pure delta function, but really more of a narrow bell curve, using a sine-wave basis set. You start adding a little bit of this wave and a little bit of that wave, until eventually, with the humps lined up at zero, you eventually build up a picture of your bell curve – all nice and looking like a positive bump.
Now, the problem with the math in doing this is what engineers always have trouble with, which is truncating infinite series and ignoring what goes on in the wings.
Does a sine wave have more positive or negative amplitude? Cosine? These are all the same wave shape – just shifted in the x direction. I think you’ll have to agree, there is just as much “up” as “down” in a wave, unchanged by shifting it side to side. So how do we add up a bunch of these waves to get net positive area? Mathematically, you can’t. We got a positive bulge at the zero point by shifting them so they lined up – there has to be as much negative hidden out in the wings as there is positive in the middle. That is inherent in the basis set, and in the concept of a vibration.
So, if you “paint” the picture of a positively charged proton with sine waves, you have simultaneously created a diffuse cloud of negative “round-off-error” on the edges with exactly the opposite charge as what you’ve built up in the middle. Ever wonder why there are exactly as many protons as there are electrons in the universe? I would like to suggest they are two sides of the same coin. The existence of a wave function with a concentrated positive lump in the middle must by it’s nature have an exactly matching amount of negative in the wings. This is NOT true of building up a neutral particle like a neutron.
The take-home here is that the electron-neutron “pair” is actually a result of wave mechanics, and that there is a very intimate coupling in the basis set between these two supposedly separate particles. This is similar to the idea of the constraints that the existence of one wave packet has on another, but more. This implies not just that the very existence of the negatively charged electron is the direct result of the creation of a positively charged particle. The point is that they are actually two regions of the same wave function.
Apply this to the lesson of the previous chapter and you can see more clearly how the hydrogen atom wave function is just a higher energy state of the neutron.
[© Copyright 2016 by Gerald Keep. All Rights Reserved.]