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Is the Proton Mass just its Radius Squared
and if so, why?

by Miles Mathis

In my first paper on the universal gravitational constant G, I showed that according to Newton's own equations, the mass of any spherical particle could be written as an acceleration of its radius. Then, in my second paper on Bohr (concerning the magneton), I showed that by correcting the angular momentum equations, we could correct both the Bohr radius and the proton radius. I found a proton radius of about 4.09 x 10-14m. Of course that is very close to the square root of the mass, so we must now ask if that is a coincidence. Is the proton mass just its radius squared, and if so, why?

To answer this, we return to the first paper on G. One of my readers suggested that the mass was the radius squared because the radius squared gave us a sort of area. The area of a circle is πr2, so perhaps mass is a two-dimensional entity. We must shoot this down for several reasons. One, my quantum equations can't include π, so it is unlikely we are dealing with area. Two, this would create a scaling problem, since mass would be less than radius for all particles less than 1m and more than radius for particles more than 1m. An area is normally greater than its own radius, but here we find the opposite. The mass is much less, as a number, than the radius. That is counterintuitive as well as paradoxical. Three, I have shown that mass acts like a 3-dimensional motion, not a 2-dimensional motion. Using Newton's equations, mass reduces to three lengths over two times, and three lengths implies three dimensions. For this reason, mass should be analogous to volume, if anything. It shouldn't be the same as area, it should be the same as volume. But if we start talking about volume, we have r cubed, not r squared.

It turns out that the square doesn't come from area, it comes from acceleration. As I already said, the mass of any spherical particle can be written as the acceleration of the radius. In other words, it is the time squared in the denominator that is important here, not anything in the numerator. A gravitational acceleration is always written with a time squared in the denominator, and that is what we should be studying.

If, as Maxwell showed, mass can be written as length cubed over time squared, then with a spherical particle, mass is the acceleration of the radius. By this analysis, mass is not operationally a measure of ponderability, it is a measure of motion. It is the motion of the proton shell over a given time. This being the case, we just have to ask how this affects the math and the definitions. To answer this, we have to ask why the mass isn't the same number as the radius. Why can't all the radius express itself as mass over the time period? Why only the square root?

Well, it is because Newton's equations, as written, define mass as the motion of the radius, not as the radius. That is, mass is a change in the radius, not the radius itself. And not just as a velocity, but as an acceleration, as we have seen. Velocity is a simple change, and acceleration is a change of a change. A second order change. In this way, we see that it is a matter of exponents. Mass is tied not to the radius or the velocity of the radius, it is tied to the acceleration of the radius. Since acceleration is a squared change, mass must be a function of that exponent of 2. Logically, mass cannot be greater than the radius, because that would imply a change that was greater than what was changing. Therefore, mass must be smaller than the radius, and that means that the exponent of 2 must be working as a square here, rather than a square root. A square root would give us a mass greater than the original radius, since we are working below the number 1 here.

In other words, the square comes from the exponent of 2, and the exponent of 2 comes straight out of the definition of acceleration. In this way, we have unified mass and gravity at the foundational level. It is thought that Newton defined gravity as a function of mass, or that he defined mass as a function of gravity. But that is not the whole story. When we look really closely, we find that neither is a function of the other, since they aren't mechanically separable. As with time and distance, gravity and mass are two names for the same thing. In my paper on time, I showed that time is really a measure of distance. We simply relabel it to suit ourselves. It is a second measure of distance, so that we can compare the two distances in a ratio, obtaining a velocity. Operationally, it turns out that the same is true of gravity and mass. Both are defined and determined by the acceleration of the radius, but we give that measurement two different names in order to calculate force. Or, I should say that Newton did it, and we do as he did.

All this also applies to the electron. The mass of the electron is 9.109 x 10-31kg. The square root of that is 9.544 x 10-16kg. The only problem there is that I have already calculated the radius of the electron to be 2.24 x 10-17m. I am off by a factor of 42.6. Fortunately, 42.6 is roughly the square root of the Dalton, 1822. So that we get this equation:

me = Dre2

But that begs the question, “Why can we go from proton mass to radius with no transform, but not do so with the electron? Why the transform D?” The reason is that I have shown that the Dalton is basically an outcome of spin. The electron is four spin levels below the proton. Mechanically, the Dalton is not really an expression of the atomic mass unit or anything abstract like that, it is the number relation between the velocity on the shell of the spinning electron and the velocity on the shell of the spinning proton.

D = me /re2 = rp /re
me = re rp

As you can see, I have expressed mass once again as distance. Mass is not a function of distance, mass is distance. That last equation is amazing not only because it expresses mass as distance, but because it defines the electron mass in terms of the proton radius. Because the proton mass is the straight square of its radius, the proton must be more primary in this math. The electron mass is derived, and depends on the presence of the proton. But again, why? It turns out to be another instance of a sort of relativity. The proton is primary here because matter is composed of protons. It is the same reason that protons are given the plus sign in E/M and electrons are given the minus sign. I have shown that mechanically this is because protons act as the baseline and electrons are measured relative to that baseline. In other words, electrons are not attracted to protons, they are repulsed less than the baseline repulsion of proton/proton. Which makes them negative in the math. They are mathematically negative, not mechanically negative. Another way to see this is to remember that the proton creates the bulk of the charge field, by recycling and emitting far more photons than the electron. This is why the proton is the defining particle in the E/M field. For the same reason, the proton is again the baseline in this study of mass and radius, simply because protons are the primary constituent of matter. Electrons are a secondary constituent. Mass, as we measure it, is a unifed field number, so it is never beside the point that the proton emits and defines the E/M field. Beyond that, due to the spins, we cannot define both the electron and the proton as primary. For reasons of relativity, we have to pick a point of view. Because matter is composed of protons, we naturally and inevitably measure from the point of view of the proton. The actual material structure we measure in is composed of protons, and the charge field we exist in is emitted mainly by protons. We live and measure in the proton field.

We can see this just by looking at motion. We are not living primarily in the photon field, because photons are moving c relative to us. We are not living in the electron field, because electrons are either moving very fast or are orbiting relative to us. But nearby protons are nearly at rest, as an average, relative to us, since our “at rest” is determined by their “at rest.” This is why the proton is the defining particle in both the E/M field and the gravity field. This is why we require no transform, just a square, when we go from proton mass to radius, and why we require the transform D in going from electron mass to radius.

But let us return to that last equation, for a bit more analysis. I have just shown you why the electron's numbers are dependent on the proton's numbers. It is because for us the proton is the baseline. That being so, we see that the mass of the electron is determined by the motion of the electron's shell in the field of the proton. We monitor the expansion of the electron relative to the expansion of the proton. That is what the multiplication is about. We have two simultaneous motions, so we integrate or multiply them. The two motions give us an acceleration over some interval, and that acceleration is what we call mass. In that sense, we could write the last equation more rigorously as

me = Δre Δrp

It takes two expansions to give us a mass, since mass is meaningless except as a relationship. A single particle in the void has no mass, strictly speaking, since I have shown that mass is motion, not ponderability. But motion is relative. Therefore mass is relative. A lone particle has only a size. It has a potential mass. Of course we must postulate that our particle is not penetrable, which gives it a structure, which structure might be called ponderability or mass. But if we can and do write mass as motion, as in L/T, then strictly speaking mass must be relative, like motion.

Conclusion: I have shown that mass is really a function of motion, like everything else. My analysis implies that we must give the shell of the proton an impenetrability, yes, but other than that mass is just motion. Mathematically, mass can be calculated straight from rectilinear motion. This is a great improvement on current theory, since it reduces the mass variable to distance and time. It is also much preferable to all the talk we hear of bosons. We don't need a reductio like the boson to explain mass, we just need a bit of clear thinking.

[Thanks to my reader David Heron for his suggestions.]

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