return to homepage The Electron Radius
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as a Function of c
by Miles Mathis
Abstract: I show that the current equation for the classical electron radius is off by 252x due to ignoring a necessary scaling constant. Once this simple correction is made, the electron radius is simply 1/c2.
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I discovered something astonishing today. I was re-reading my paper on angular velocity, checking for errors, when I began reconsidering my main equation, and what it might mean beyond what I had already written about it. Remember that I had shown that the old angular velocity equation v = ωr was wrong. Due to an error of Newton, or an error interpreting Newton, the equation had gotten skewed. Instead of v = ωr, the equation should be v = ω/r.* This allows us to get rid of the moment of inertia, which I showed is just a fudge factor. It also corrects the Bohr radius and a thousand other things. But what I hadn't yet done is actually insert some numbers into the equation. This is always a big eye-opener.
In a different paper on the Bohr Magneton, I had calculated the radius of the electron by other (but related) means, finding 2.244 x 10-17m. And in still another paper, I had proposed that c2 in the famous equation E = mc2 was another scaling constant, taking us from the size of the photon up to a larger field size. I explained that we were scaling a local wave—local at the photon level—up to our own level, where we were measuring it. The scaler was c2 because the linear motion stretched out the local wave. If the linear speed is c and the spin speed is 1/c, then the difference between them is c2. That is where the number comes from. But I implied or perhaps even stated in that paper that we are scaling the photon when we do this.
It turns out that is not quite right. It turns out that we are actually scaling the electron up when we do that, and that the spin speed 1/c applies to the electron, not the photon. How do I know that? Watch this:
If we take the equation v = ω/r and insert c for v and 1/c for ω, we get r = 1.11 x 10-17m. Look familiar? That is almost exactly half my electron radius. We can confirm this method by instead using c for v and 1/c2 for ω. In that case, we get r = 3.7 x 10-26m, which I have shown is about the radius of a photon (photons come in a variety of sizes, depending on many spins they have).
This is important because it tells us more about the equation E = mc2. I had shown where the c2 came from, but only in part. I had not seen that it could also be assigned to a radius. With this new information, we can rewrite Einstein's equation like this
E= mc2 = m/re
This tells us that the energy of any given mass is always a function of that mass relative to the electron radius. Or we can rewrite the equation like this
m = Ere
That tells us that any mass is some number times the radius of the electron. By that way of looking at it, energy itself becomes a scaler. Energy is not really energy, it is just the number of electron radii involved in the event. Or, we can continue to calculate. Since I have just shown that mass and radius are a function of one another, with the proton mass just the square of its radius, we can rewrite the last equation like this
m = Ere
me = Dre2
re = √(me/D)/2
m = E√(me/D)/2
The constant D is the Dalton, which is just the number 1821. I use this number as a scaler between the electron and proton, for reasons I explain in that other paper. This last equation allows us to express the mass of any object as a number of electron masses involved.
E = 85.336m/√me
This allows us to calculate the energy of any mass as a multiple of electron masses.
It also allows us to see where the Dalton comes from.
D = mec4/4
Physicists have never understood where these numbers come from, but the Dalton, also called the atomic mass unit, comes from this equation.
If you go to the standard model, you find that the “classical electron radius” is calculated from this equation:
re = e2/4πε0mec2
But I have shown how and why that is about 102 too large. It turns out the equation is too complex. The radius of the electron is just one over c squared. I have also shown that the permittivity constant is mis-assigned to space. The constant is not an attribute of space, since space has no attributes; it is the gravity field of the proton. Since the equation contains both the gravity field and the charge field, it is another unified field equation. And since charge is dimensionally the same as mass, we can reduce:
e2/ε0me = 1
You will say that in the current equation, that fraction is about 252. Am I saying that one of these constants is wrong? No, I am saying the current equation is wrong. They have left out a constant, and so they have the wrong number for r. The equation should look like this
re = e2/a4πε0mec2
where a is the number 252. You see, they forgot to scale the electron to the proton. Since ε0 applies to the proton, they have both the proton and the electron in the same equation. So they need to scale one to the other with the Dalton, 1821. But if we put that number into the equation, we are still off by 7.22. Well, that number 7.22 comes right out of another paper of mine, since it is the difference between a moving electron and an electron at rest. The electron in this equation is moving relative to the proton, therefore we have to use the moving electron. The full equation is
re = e2/(1821/7.22)4πε0mec2
And that reduces to 1/c2.
What I have just shown is that the current equation is wrong. A field scaling constant has been left out, which makes the equation misfire. Since both the proton and electron are in the equation, we have to scale one to the other. This explains directly why the current equation gets an electron radius that is 252 times too large. The scaling constant is a = 1821/7.222. Once we correct the equation by adding the scaling constant, the equation reduces to 1/c2.
Still, this begs other questions, like why is the spin speed of the electron 1/c? Is that really what the equation v = ω/r is telling us? It can't be, because the electron can't even go c. So why is the electron radius 1/c2?
*For those who think this can't work due to units, you should know that my variables are a bit different than current variables. My v is the tangential velocity. The current v is defined as the tangential velocity, but it isn't. It is the orbital velocity, v = 2πr/t. Since that is a curve, it can't be a linear velocity. My ω is also different. Although it is an angular "velocity", I don't measure it in radians. An angular motion is a curve, therefore it is an acceleration. And so my units do resolve. You may have to take the link to the other paper to understand this fully.
To answer this, we have to go back to my unification of all quanta. I have shown that the proton and electron and all the mesons are really the same particle, just with a different number of spins. If you take a moving electron and give it one more spin, it becomes a meson; two more spins, it becomes a proton or anti-proton. By the same token, if you take an electron and subtract several spins, you can turn it into a high-energy photon. So the electron is just a common spin level. We could call an electron a very big photon, if we like. Which means that it is almost quibbling when I say the particle we are dealing with is an electron instead of a photon. Rigorously, ALL particle are photons.
The only difference is, at the size of the electron, the particle becomes large enough to begin “eating” smaller particles. The big outer spins are large enough to trap and intake smaller photons, recyling them. These recycled photons then become the charge field.
You will say, “Aren't these photons the charge field both before and after they are recycled?” That's a good question, one I am only now getting close to being able to answer. If larger particles are indeed recyling the charge field, we may ask why. Is it just by accident, as it were, the smaller particles getting trapped only as matter of statistics; or are the larger particles actually feeding off the smaller ones, taking energy from them in some way, and subsisting on them in some way? It is difficult to say. I certainly don't wish to propose that electrons have intention, and it is not even necessary I do so to continue my theory. Even if the trapping of photons by large spins is just an accident, caused by no intention of any electron, the trapping could still function to keep the electron viable. We do not need to say that the electron “lives” on this trapping. We only need to say that the various motions of the electron are maintained by this trapping. Physically, all spins must come from field collisions, and the field collisions of larger particles are simply more complex than those of smaller particles. At a certain level of size, these field collisions create greater vortices, ones that are able to funnel smaller particles through intakes and exhausts. We have such engines at our level of size, and we do not assign intention to them. Gas maintains an engine, or keeps it running, but the engine is not thereby alive. If you wish to assign life to engines or electrons, you won't offend me, but as a matter of physics, it is an external question. Not uninteresting, but external. Physics, as I define it, is mechanics. Such questions are not mechanical.
At any rate, if the larger particles are getting their energy from the smaller ones, then the smaller ones must be losing energy. Which means the photons coming out of the engine must be changed in some way. They must have lost some energy. We may propose that the engine strips the outermost spins of the photon, using it to maintain its own spin. But this means charge emitted is less energetic than charge taken in. Particles aren't emitting a charge field, they are taking the ambient charge field and weakening it in the near vicinity. Therefore, what we call charge is actually a charge LOSS. The charge wind is WEAKER (in some way) near particles than everywhere else. This would create the appearance of an attraction.
Well, you will say, if that is so, can we apply this new attraction to gravity, getting rid of both it and expansion? I don't think so, though it is initially a good proposal. The first reason we can't is that the variance in a primary field can't be larger than the field itself. At the level of the Earth, we know that gravity is much larger than E/M, and that can't be explained if gravity is just a variance in E/M.
It turns out that this energy loss near matter is only a magnetic energy loss. The emitted photons lose spin but not linear velocity, therefore the field is weakened only as a matter of magnetism or spin. The photon density is still higher near matter, and the total linear energy is still higher near matter. Only the spin energy is weakened. Which means we still require a second fundamental motion or field to explain all interactions. We cannot explain everything with E/M any more than we could explain everything with gravity. The unified field must still be dual at all levels, quantum and macro. We require two fundamental fields or forces in opposition to explain the universe.
However, this new finding concerning magnetism may come in useful in later papers. If spins are being stripped to act as fuel for larger quanta, then this may explain other phenomena or data we have not yet addressed. It also may better explain old data, or lack of data. For instance, although I have said that the entire E/M spectrum is probably acting as the charge field, many have complained that my charge field is a poor hypothesis in that we haven't detected it directly. Especially problematic is my calculation that the field should peak in the infrared. I have been told that we don't measure a ubiquitous field at the infrared level. Well, we do, both in heat and in cosmic background radiation (which peaks in about the right place). Black body radiation also confirms my hypothesis. I have shown that many photons assigned to other causes or functions are probably acting as the charge. We had long recognized their existence, we just hadn't found a basic function for them. But if that is not satisfying to some of you, I propose that by this mechanism I have uncovered in this paper charge photons are being partially de-magnetized and de-spun by matter. Since most of our experiments are on the surface of the Earth, this would explain a lack of detection. Our detectors commonly use magnetic fields for detection, and temporary charge loss near matter would explain many things, including energy deficits and inability to “see” the charge field.
In this case, space would have a higher magnetic charge than matter (this charge being the spin of the photons). You will say that if that is so, we would know it, but that is not necessarily so. Since space has little or no matter in it (no ions), there is nothing for this charge field to work upon. Our machines currenty detect magnetic fields by detecting the presence of ions. Our machines cannot detect the fundamental E/M field or charge field, except in the presence of ions, since it is the ions they are calibrated to detect. A magnetic field without ions would be undetectable. Which is another way of saying we currently have no way to measure the inherent or photonic magnetism of space. Our machines could hardly be calibrated to detect the spin of small photons, when the standard model does not even know or admit that photons have real spin.
But let us return to the original question. Why does the spin speed tend to be the inverse of the linear speed? I have not answered that in other papers or here. Well, notice that according to the equation v = ω/r, we are not being told that the spin speed of the electron is 1/c or that the linear speed is c. We are told that a spin speed of 1/c is equivalent to a linear speed of c, given that radius. We aren't being told anything about the actual linear velocity of the particle, we are being told the tangential velocity of a point on the surface of the spin. In other words, the velocity v is not the linear velocity of the electron, it is the linear velocity of a point on the spin tangent. At that radius r, an angular velocity of ω will give us a linear velocity at the tangent of v. We can interpret that to mean that a particle of radius r and angular velocity 1/c will cast off or emit a particle from its outer spin at a velocity of c. And we can interpret that to mean that since we see photons travelling at c, and since we propose they are emitted by electrons (as well as protons and other quanta), the electron must be spinning at 1/c. This tells us nothing about the linear velocity of the electron, it only tells us that if the electron is emitting, it is emitting at that radius and that spin velocity.
Fair enough. If that is true, then we should be able to calculate a spin velocity for the proton, by the same equation:
v = ω/r
cr = ω
ω = 1.23 x 10-5m/s
The angular speed of larger particles is greater than the angular speed of smaller particles, which is precisely why they have more energy.
Still, why is the electron special? Why is it's spin speed 1/c? We can't just accidentally have a fundamental particle with a spin speed of 1/c. No, all our fundamental particles have spin speeds that are simple fractions of c. Just look at the spin speed of the proton I just calculated, ω = 1.23 x 10-5m/s. That is also not an accident:
ω = 1.23 x 10-5m/s = 2D/c = mec3/2
This takes us back to my spin quantum equation, whereby all spins are multiples of 2, based on gyroscopic rules. Because all larger quanta are built on photons, they must be multiples of the photon. So we can use c and simple equations like this to build any particle, showing both its size and its spin.
But again, why does the electron happen to have a spin speed of 1/c? Because it is one level up from the photon in mass. It is several levels of spin up, but only one level of mass up. What I mean by that is that to find the photon mass, we can divide the electron mass by c, giving us 3 x 10-39kg. True, in another paper I calculated the photon mass as 92 times larger than that, but photons come in different sizes, as I have said.
Even G is a multiple of c.
G = 1/50c
That is not a mathematical coincidence. Simple fractions like 1/50 or 2/100 tell us that our numbers are closely related, and G is simply a function of c, as I have shown elsewhere. Just as D is the scaler between electron and proton, G is the scaler between photon and proton. And, as you have seen here, they can both be written in terms of c.