Both Newton’s and Coulomb’s famous equations are unified field equations in disguise. This was not understood until I pulled them apart, showing what the constant is in each equation and how it works mechanically.

A unified field equation does not need to unify all four of the presently postulated fields. To qualify for unification, it only has to unify two of them. The unified field equations that will be unmasked in this paper both unify the gravitational field with the electromagnetic field. This unification of gravity and E/M was the great project of Einstein and is now the great project of string theory. But neither Einstein nor string theory has presented a simple unified field equation. As time has passed this has seemed more and more difficult to achieve, and more and more difficult math has been brought in to attack the problem. But it turns out the answer was always out of reach because the question was wrong. We were seeking to unify fields when we should have been seeking to un-unify them. We already had two unified field equations: which is why they couldn’t be unified. We were trying to rejoin a couple that was already happily married.

Yes, both Newton and Coulomb discovered unified field equations. That is why their two equations look so much alike. But the two equations unify in different ways. Newton was unaware of the E/M field, as we know it now, so he did not realize that his heuristic equation contained both fields. And Coulomb was working on electrostatics, and likewise did not realize that his equation included gravity. So the E/M field is hidden inside Newton’s equation, and the gravitational field is hidden inside Coulomb’s equation.

Let’s look at Newton’s equation first.

F = GMm/r²

We have had this lovely unified field equation since 1687. But how can we get two fields when we only have mass involved? Well, we remember that Newton invented the modern idea of mass with this equation. That is to say, he pretty much invented that variable on his own. He let that variable stand for what we now call mass, but it turns out he compressed the equation a bit too much. He wanted the simplest equation possible, but in this form it is so simple it hides the mechanics of the field. It would have been better if Newton had written the equation like this:

F= G(DV)(dv)/r²

He should have written each mass as a density and a volume. Mass is not a fundamental characteristic, like density or volume is. To know a mass, you have to know both a density and a volume. But to know a volume, you only need to know lengths. Likewise with density. Density, like volume, can be measured only with a yardstick. You will say that if density and volume can be measured with a yardstick, so can mass, since mass is defined by density and volume. True. But mass is a step more abstract, since it requires both measurements. Mass requires density and volume. But density and volume do not require mass.

Once we have density and volume in Newton’s equation, we can assign density to one field and volume to the other. We let volume define the gravitational field and we let density define the E/M field. Both fields then fall off with the square of the radius, simply because each field is spherical. There is nothing mysterious about a spherical field diminishing by the inverse square law: just look at the equation for the surface area of the sphere:

S = 4πr²

Double the radius, quadruple the surface area. Or, to say the same thing, double the radius, divide the field density by 4. If a field is caused by spherical emission, then it will diminish by the inverse square law. Quite simple.

The biggest pill to swallow is the necessary implication that gravity is now dependent only on radius. If gravity is a function of volume, and no longer of density, then gravity is not a function of mass. We have separated the variables and given density to the E/M field, so gravity is no longer a function of density. If gravity is a function of volume alone, then with a sphere gravity is a function of radius, and nothing else.

It is only the compound or unified field that is a function of mass. Yes, Newton’s equation still works like it always did, and in that equation the total force field is a function of mass. But in my separated field, gravity is not a function of mass. It is a function of radius and radius alone.

Now we only need to assign density mechanically. I have given it to E/M, but what part of the E/M field does it apply to? Well, it must apply to the emission. Newton’s equation is not telling us the density of the bodies in the field, it is telling us the density of the emitted field. Of course one is a function of the other. If you have a denser moon, it will emit a denser E/M field. But, as a matter of mechanics, the variable D applies to the density of the emitted field. It is the density of photons emitted by the matter creating the unified field.

Finally, what is G, in this analysis? G is the transform between the two fields. It is a sort of scaling constant. As we have seen, one field--gravity--is determined by the radius of a macro-object, like a moon or planet or a marble. The other field is determined by the density of emitted photons. But these two fields are not operating on the same scale. To put both fields into the same equation, we must scale one field to the other. We are using both fields to find a unified force, so we must discover how force is transmitted in each field. In the E/M field, force is transmitted by the direct contact of the photons. That is, the force is felt at that level. It can be measured from any level of size, but it is being transmitted at the level of the photon. But since gravity is now a function of volume alone, it is not a function of photon size or energy. It is a function of matter itself, that is, of the atoms that make up matter. Therefore, G is a scaling constant between atoms and photons. To say it another way, G is taking the volume down to the level of size of the density, so that they may be multiplied together to find a force. Without that scaling constant, the volume would be way too large to combine directly to the density, and we would get the wrong force. By this analysis, we may assume that the photon involved in E/M transmission is about G times the atom, in size.

Now we continue on to Coulomb’s equation:

F = kq₁q₂/r²

One hundred years after Newton, we got another unified field equation. Here we have charges instead of masses, and the constant is different, but otherwise the equation looks the same as Newton’s. Physicists have always wondered why the equations are so similar, but until now, no one really knew. No one understood that they are both the same equation, in a different disguise.

I unveiled this equation using a different trick. With Newton’s equation, I pulled the veil off by writing the masses as densities and volumes. With Coulomb’s equation, it was the constant that got me in. In fact, if it weren’t for Bohr, I would never have unveiled Coulomb’s equation.

It happened like this: I noticed that the angular velocity equation in textbooks didn’t make any sense, so I went back to Newton to see how it was derived. I discovered that Newton had given us different values for tangential velocity and orbital velocity, but that the two numbers had gotten conflated since then. Meaning, the two numbers had become one. Modern physicists now think tangential velocity and orbital velocity are the same thing, but they aren’t. In correcting this muddle, I found that the angular momentum equation had to change. By my analysis, L = rmv was no longer true. After I corrected it, I went to Bohr’s equations for hydrogen, finding that they had to be redone. Once I fixed them, it turned out that the value for the Bohr radius was exactly the same as Coulomb’s constant (in reverse). The new Bohr radius is 9 x 10^-9 meters. Coulomb’s constant is 9 x 10⁹.

I could immediately see that Coulomb’s constant is another scaling constant, like G. Instead of scaling smaller, like G, k scales larger. Coulomb’s constant takes us up from the Bohr radius to the radius of macro-objects like Coulomb’s spheres. It turns the single electron charge into a field charge.

But where is the gravitational field in Coulomb’s equation? If we study charge, we find that it has the same fundamental dimensions as mass. The statcoulomb has dimensions of M ^1/2 L^3/2 T ^-1. This gives the total charge of two particles the cgs dimension ML³/T² . But mass has the dimensions L³ /T², which makes the total charge M². So we can treat Coulomb’s charges just like Newton’s masses.

We write the equation like this:

F = k(DV)(dv)/r²

Once again, the volume is the gravitational field and the density is the E/M field. The single electron is in the emitted field of the nucleus, and D gives us the density of that field. But this time the expressed field is the E/M field and the hidden field is gravity. So we have to scale the electromagnetic field UP to the unified field we are measuring with our instruments.

If k and G had been the same number, all this would have been seen earlier. It would have then been easy to see that Coulomb’s equation was just the inverse of Newton’s equation. But because the constants were not the same number, the problem was hidden.

In scaling up and scaling down, we don’t simply reverse the scale. It is a bit more complex than that, as you have seen. In scaling down, we go from atomic size to photon size. In scaling up, we go from atomic size to our own size.

Unifying the two major fields of physics like this must have huge mathematical and theoretical consequences. Because Coulomb’s equation is a unified field equation, gravity must have a much larger part to play in quantum mechanics and quantum electrodynamics. Gravity must also move into the field of the strong force, and require a complete overhaul there.

By the same token, the E/M field must invade general relativity, requiring a complete reassessment of the compound forces. At all levels of size, we will find both fields at work, creating a compound field in which each field is in opposition to the other.

Yes, according to my new equations, the two fields are always in vector opposition. And since gravity, by itself, is a function of radius alone, it must be much larger at small scales than we thought--and somewhat smaller at large scales.

Update, 2011: I have now shown that the Lagrangian is another unified field equation in disguise.

Update, 2013: I have now shown that Maxwell's Equations are another unified field in disguise.

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