Current Speculations 2001
Some years ago, I had the idea that perhaps we were looking at a "variable charge". Thus, the track in a bubble chamber might be shaped by composite changes in the electric field of the particle along with a different mass ... perhaps we weren't looking at a smaller mass - just a larger charge. However, I could never get past this fact ... that the thickness of the track in a bubble or cloud chamber is related to the charge strength. After all it's the charge that ionizes the atoms in the medium ... not the neutral mass. I gave up this approach.
You see what lengths I will go to to obtain an idea consistent within a "one universe" theory of everything.
In November of 2000 I had a "new brainstorm"
I rarely have any idea at all to work with in this area. The parameters are constrictive in the extreme. Let's name some of them.
The Quantization of Probablilty
Here is a normal Maxwellian type distribution.
It is well known that such a graph is an idealization. It is a "limit" curve representing a continuous spectrum of possibilities. But there can be no such continuous spectrum in reality for if it were so, the graph would collapse to a flat line.
Let us suppose that the x coordinate can take any value ...
Then, no two randomly selected x values could be the same because it is infinitely improbable that such would be the case.
In fact, the number of x values between any two randomly selected x values is infinitely greater than infinity by Cantor's diagonal proof.Thus, because relative probability is dependent on "stacking" one incidence on top of another, no probablistic calculation is possible.
What we do is define a finite interval and count the number of instances in that interval. This is the "probability score" for that interval as compared with all other intervals of the same size.
Now, we can draw a graph but it is not a continuous graph. It is a bar chart ... the smaller the bars ... the more closely the chart comes to resemble a continuous graph. But ... this is the important point ... The limit of the bar charting is not the continuous graph because that graph collapses to a straight line ... in principle.
We are therefore left with the inescapable conclusion that probability is fundamentally quantized in a strictly logical sense ... and ... because my interpretation of existence is that of the universe as the geometric embodiment of logic itself, this fact should find its expression in the physical world.
Subatomic particle masses must then represent the "smallest intervals" in any such interpretation.
The Basic Idea :
The distribution of masses discovered by experiment give no indication of a "standard" form of quantization ... so ... instead of cutting up the x axis in quantized units ... cut the y axis.
Like this ...
First, "zero" mass is recalibrated as the present electron mass. This prevents any mass from being lower than the electron's. The top of the curve is defined as the proton mass.
Now ... cut the graph with horizontal lines which section the length from electron to proton on the y axis in integral pieces 1/2, 1/3, 1/5 ... mainly the prime numbers and whole number ratios.
By this method we can achieve several solutions to the above "problems and expectations".
1) There won't be a mass lower than the electron.
There in no present reason for this ...
Other than the fact that it would appear to solve many diverse problems with the required simplicity. Basically, we take a simple curve (not necessarily this one ... maybe Gaussian would lead to something interesting), cut it up on the y axis with whole number ratios ... and ... Voila! a pile of quantized, inscrutable trash for output via a stupidly simple mechanism.
When I disprove or give up on this idea, I'll post the result right ... \/ here \/