Particle Masses
Current Speculations 2001

he one constant in my search for a comprehensive theory of existence is to explain the mass values of elementary particles. I consider this the lynchpin for anyone's theory. Here is the "hard thing" ... what one must do to cement one's speculations into a unified whole. Without this ... one might just as well start a new religion.

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.

    My personal restriction:

  1. The truth must be very simple and all-encompassing
    There is only one possible universe therefore one rule covers all masses at the fundamental level

    Experimentally known restrictions:

  2. There are no masses smaller than the electron and none as massive as your house.
    In fact there are no known rest masses even approaching that of a grain of sand.
  3. The masses, as a category, exhibit no specific order.
    They have the appearance of being "picked out of a hat" ... anathema to my sensibilities.
  4. Some 'resonance' masses are evenly spaced a few electron masses apart in good order like a dozen well-behaved soldiers.
  5. There are no particle masses extremely close to that of the proton or the electron.
    Except the neutron which is considered fundamentally a proton (baryon) without its charge. There are numerous cases of a neutral particle paired with a charged one. So much so that this fact is part of general classification schemes.

    Some Expectations:

  6. The masses of all elementary particles are "keyed" to the electron-proton mass ratio.
    Since there is only one possible universe, and the e/P mass ratio changes with time (as shown previously), the masses of all elementary particles must also change in concert with the e/P ratio because all are subsumed by the same rules.
  7. Despite appearances to the contrary, the masses of all particles should obey some variant quantization procedure.
    We should find simplicity of form as in integral and half-integral spins ... or, as in integral charges.
  8. I expect particle masses to be governed to a large extent by known or "new" rules of probablility.
    Particle decay branching ratios comply fully with a simple, off-the-shelf, probablistic interpretation (experimentally verified). My explanation of the e/P mass ratio is that of "most probable ratio" given the mathematical form of their interaction in the hydrogen ground state. Therefore, I expect other masses to follow suit.

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.
2) There won't be a mass higher than some particle well above the proton mass ... but not grossly above it.
3) If we consider that lower numbered quantization is more common ... 1/3 more common that 8/41 for instance ... then ... a particle mass very close to the proton (heavier or lighter than) is unlikely to be found.
4) The masses of particles will appear to be "picked out of a hat" since the quantization procedure is not orderly and ... the graph over which it is drawn is non-linear. Disorder from simplicity.
5) If the quantization were tight enough ... like 48/1836, 49/1836. 50/1836 ... the graph would be relatively straight in that short interval generating orderly resonances.
6) There is some possibility for paired production of seemingly unrelated particles because a horizontal line through the graph will cut it at two places ... one lesser and one greater than the mass of the proton.
7) One can "reflect" the graph to the negative x axis to get anti-particles, etc.
8) Particle masses will change with time in lockstep with the electron-proton mass ratio as my "one possible universe theory" necessitates.
9) One tends to think in terms of decay difficulties when the ratio is "prime" like say, 1/3 ... what would it decay to? ... if 2/3 maybe two 1/3's ... see? There are many possible variations here ... all simple ... all mathematical.

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 \/

"It can't be right ... therefore, it isn't"

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