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Go to Part I
The Third Wave
A Redefinition of Gravity
Part II
Preface
(or divertissiment?)
Newton's Tree
by Miles Mathis
[Preface added August 11, 2005] This week I became aware of the theories of Mark McCutcheon and his book The Final Theory. I haven't read it, but I have read all the material on his website and the long discussion he has with Dave Ruske that is (was) linked from Wikipedia. Readers of part 1 of my Third Wave paper who know of The Final Theory will no doubt immediately equate my theory with his. And I admit that it appears to be very similar at first. We are both hypothesizing universal expansion of matter as an explanation of mass. I therefore rush to explain the differences. McCutcheon has proposed his theory as a replacement not only for the current concepts of mass and gravity and inertia, but also for all other physical fields. The charge on the proton is explained by expansion, which also negates the electromagnetic field. In fact, McCutcheon summarily throws out all atomic forces, all Relativity, and all the findings of QED and QCD. This is why he calls his theory the final theory. He tells us that it explains everything.
My theory is very different. It is not a theory of everything, although it does resolve several physical concepts, giving us a partial simplification of theory. I would never call my theory a final theory, since I don't believe in final theories or theories of everything. We are so far from knowing how things work in the universe that any talk of a final theory or a unification theory is pure hubris, whether it comes from inside academia or outside. We don't have enough knowledge to unify, at this point. You cannot unify near chaos. You can only make your contribution to order.
Beyond that, I don't see that it is possible to explain everything by motion. I think that mass and gravity may be partially explained by motion, but we should still be able to use exclusionary fields in any future theories. What I mean by that is that we do not need to question the logic or the explanatory power of fields that may ultimately be expressed by the bombardment of subparticles. A repulsive force does not have to be explained by movement away. It can just as easily be explained by bombardment (by photons or neutrinos or Higgs bosons or whatever subparticle you can ultimately justify). The only reason I have theorized expansion is to bypass the need for attractive forces. Attractive forces cannot be expressed in mechanical ways, as I have explained in greater detail elsewhere. It is attractive forces that beg the question of force at a distance, even given curved space.1
All this just goes to say that I am not attempting to explain all physics by expansion. I am explaining only mass (and inertia). As you will see, gravity is also explained by expansion, but only if we keep some of the other "forces" of physics. Electromagnetism, for instance, cannot be explained by expansion. It will have to be explained by some other genesis of field, which I expect will be bombardment. At any rate, I do not have to concurrently explain the ultimate genesis of every field, and I don't claim to be able to any more than the Standard Model claims to be able to. All I claim here is that mass is reducible to motion.
It is also worth noting that my expansion theory never even confronts Relativity. I don't see that the two theories contradict eachother at all. McCutcheon is correct when he points to the mathematical errors of Einstein, but anyone who has looked at my website will see that I believe that these errors are correctable. I show conclusively that SR must stand—albeit with slightly different transforms. If SR must stand, then GR must stand in some form, since GR is just SR applied to acceleration and the spherical influence of this acceleration. Expansion explains the genesis of the acceleration, but it says nothing about transforming a measurement in one field to that in another, which transformation is Relativity.
Finally, I am not wholly opposed to Quantum Math. I think it is flawed in some ways (see "renormalization"), and I think that it requires a lot more foundational theory. Many mainstream physicists would agree with that assessment. String theory is the attempt to supply that theory, for instance. I am opposed to string theory, for the simple reason that it does not correctly predict the dimensions of the known universe—or predict anything. Once again it is too much math for the job. It is a cowardly hiding in esoterica. To answer one question, the theory makes two unprovable assumptions. To answer two questions, the theory makes eight unprovable assumptions. The theory is an exponential diversion of time and intelligence. The Standard Model folks have begun to quote Popper, telling us that theories must be judged on whether they are falsifiable or not (which is rich in itself, considering how Popper was treated by the status quo—see, for instance, Feynman's many comments on philosophers in science). But the premises of string theory are not in the least falsifiable. The conclusions are falsifiable, in that there are not ten or eleven or even five dimensions. But the status quo can't get enough of "extra dimensions curled up like pillbugs under a rock" and such things. Outside academia, anyone who proposes anything the least bit unconventional is immediately dismissed as a crank. Inside academia, you can propose the most outlandish things imaginable and the journals eat it up like cake. In fact, the more "paradoxical" it is the more they like it.
I am also opposed to the Copenhagen interpretation, which is idealism posing as science.2 But I am not opposed to many of the interesting findings and mathematics of Schrodinger and all the rest. Future theory will and must benefit from the work of many of the pioneers in the field of Quantum Mechanics.
McCutcheon's theory has been dismissed primarily due to his inability to explain orbits. I find it tragic that McCutcheon was not able to present a more convincing theory, since he must have known that much would depend on orbits. It is the first question that comes to mind whenever expansion theory is mentioned. That said, I find it equally tragic that the status quo would think his failure a sufficient reason for dismissing the theory in toto. As I have shown in my paper on Celestial Mechanics, the Standard Model cannot explain orbits either.3
McCutcheon is criticized for a lot of other things, but I cannot comment on those things since I have not read the book. I don't know how convincing his argument is in explaining the two-slit experiment or the charge on the proton, etc.4 But I do know that the Standard Model cannot explain any of these things rationally. McCutcheon is chided for just making up theory to fit fact, but this is precisely what physics has done for decades. Much of QED and especially QCD is just giving names to things without even trying to explain the mechanical genesis of interaction. If McCutcheon cannot explain every side-effect of his theory, this does not make him a sinner among saints. It makes him a sinner among sinners. At least he attempts to provide concepts beneath his math and his terminology; I can't see that most mainstream theoretical physicists even bother anymore with concepts—particularly mechanical concepts.
In my opinion, McCutcheon's greatest sin appears to be overreaching. This would make him like, not unlike, current theoretical physicists. The cardinal error was in calling the book The Final Theory. Everyone wants to tie up all loose ends before they have got to the ends.
The Explanation of Orbits
Now that I have cleared a bit of ground for my continued sowing of seeds, I will proceed to the first furrow. That, as I have said above, must be orbits. In my paper on the Universal Gravitational Constant, I gave a mathematical expression of the concepts I introduced in part 1 of this paper. To recap from the UGC paper, I used a hint of Maxwell to give the dimensions of G to the mass.
m = 4Δr3/GΔt2
where r is the radius of the sphere in question. G has no dimensions in this equation.
From this equation and Newton's gravity and force equations, I developed an equation for the acceleration due to mass.
a = 4mG /Δr2
I applied this equation to the proton, using the current number for mass and G and arrived at the number:
a = 4.44 x 10-12m/s2
I then proposed that the proton has been accelerating at this rate over its entire lifetime. Further, I proposed that the reason the proton could not reach c in the accelerator was due to this acceleration. Using my correction to gamma and the experimental number 108mrc2 for the maximum energy at acceleration, I found that the proton stopped 2 x 106m/s short of c. This fits my theory, provided we let the proton accelerate for 15 billion years. Using the equation above, this fits the gap perfectly, and also fits current estimates for the age of the universe. If we use gamma to fill the gap in this way, we get an estimate for the age of the universe that is way too low (about 600 million years). This stands as experimental proof of both my correction to gamma and my hypothesis about the cause of the number 108.
This means that the shell of the proton really does have a current velocity of 2 x 106m/s relative to its center, according to my theory. I do not claim that this velocity is only apparent. It must be real in order to prevent further mass and energy increase in the accelerator. Of course this implies that the shell of the proton will reach c at some point in the future, causing some as yet unknown tragedy or effect, but as that event would still be 15 trillion years in the future it is not a scientific emergency.
I also showed that although this implies a surprisingly large velocity for the shell of the proton, it does not imply an absurdly large current radius. It does imply an extremely small original radius for the proton 15 billion years ago: if the current radius is taken to be on the order of 10-13m, then the original radius must have been 10-26m.
Now, on to the orbit. We have explained the genesis of the acceleration. When we apply that to a gravitational situation, all we have to do is take the Newtonian or GR acceleration vector (or tensor or what have you) and reverse it. Instead of giving it to the orbiting body and making the vector point inward, we give it to the central body and make it point outward. This gives us the same math, except for one thing. The path of the orbiting body cannot be made to curve using expansion alone.
We solve this by remembering that, unlike McCutcheon, I have not discarded the electromagnetic field. All central bodies with orbiting satellites, whether planets or moons or electrons, are currently given electromagnetic fields. As I said before, I have no problem with electromagnetic fields. I believe they ultimately require a mechanical genesis, but I don't refute their existence or believe they can be explained away by the expansion of mass. It is quite easy for me to assign the centripetal acceleration to mass, and at the same time to keep electromagnetism. Since we have it to work with, all we have to do is make use of it now.
The only change I propose for the electromagnetic field is that we no longer need to give any body a negative charge. We can give all bodies a positive charge.6 Here is why. On the atomic level, given expansion, we no longer have to explain why the electron is attracted to the nucleus. We now have to explain why the electron is not immediately sucked into the nucleus. An electron wandering by a proton accelerating at 4.44 x 10-12m/s2 should be immediately gobbled up. That it isn't, must be due to charge. I propose that the electron and the proton both have a positive charge, just as if they both had iron cores (although, by my theory, the electron's charge is proportionally smaller than the proton's) and this keeps the electron at a distance. Notice that this allows me, in a pinch, to explain the repulsion without force at a distance. That is, the proton and electron may logically be exclusionary simply due to mutual bombardment of eachother with photons or other subparticles.
I have explained the orbiting distance by a combination of expansion and equal charge. But how do I explain the circling? Why doesn't the electron just sit on some level of the electromagnetic shell? At this point I bring in another classical and currently accepted force that I have not jettisoned: angular momentum and torque. I have never denied that the proton is spinning. I have ignored it to simplify initial equations, but I have not denied it. Now I re-introduce it to explain the orbit. A spinning object that has a charge will obviously transmit its spin to its E/M field. This field will act in many ways like a physical extension of its shell, since the field is in fact physical. If the field is made up of radiated photons, for instance, then these photons will carry angular momentum out from the mass itself. The best way to think of this tranferred momentum is to give it to the magnetic field. The E/M field is known to have two components, the magnetic component being orthogonal to the electric component. It is this magnetic component that carries the torque I am using to create tangential motion and thereby the orbit. In this way, a torque must be applied to any object that comes in contact with the E/M field. An electron impinging on the E/M will be given a tangential push and will achieve some initial velocity.
"Aha," you say, "but the electron will be given a tangential push. It must go off on a tangent! It doesn't curve." That's right. Directly after the tangential push, it starts off in a line, at a constant velocity, just as Newton would have it. If we imagine that the electron was at rest initially, then it will have only a small initial velocity relative to c. But since the proton and its E/M field are accelerating outward, they will soon catch the electron again. The electron will then impinge on the field once more and be given another torque. This continues to happen until the electron reaches its own velocity limit, a limit which can now be calculated due to my new equations above.
Notice that my theory also explains the wavelength of the electron, since this bouncing off the E/M field will continue indefinitely. The field must impart a tangential force to the electron each time, which sends it to a wave peak. The E/M then catches up to the electron, and we are at a trough.
So you can see that I am not contradicting QED, I am in fact bolstering it. My theory dovetails with the math of QED, but it simplifies the underlying conceptions. The main simplification here is that we don't need a negative charge on the electron.
Electric current doesn't require a negative charge on the electron either, since the so-called potentials will be set up just by the huge difference in electrons and nuclei. Nuclei have much greater positive E/M fields than electrons as well as much stronger acceleration "fields". These differences are enough by themselves to explain electric potential and electric current. What we lost in switching the electron from negative to positive, we gain by giving the proton an acceleration. Besides, neither classical theory nor quantum theory ever gave half the field, or even a proportional part of the field to the electron anyway. Quantum theory has not been much concerned with the genesis of the field, especially from the point of the electron. The negative charge on the electron has been little more than a place-filler. It was used to express a difference from the nucleus, but the nature of that difference was not known. I propose that it is only a difference of magnitude, and that the electron does contribute proportionally to the creation of the exclusionary field. But it does so with a positive charge. That is to say, if the electron is 1,800 times less massive than the proton, then it is produces 1/1,800 of the exclusionary force.7
In addition, giving the electron a small positive charge works as well as current theory in explaining why electrons don't bond in currents and elsewhere. Two negative electrons repel eachother, but so do two positive electrons. And the difference in positrons and electrons was never thought to be a difference of E/M charge anyway. The difference in positrons and electrons has been signified by charge signs, but it was known that this difference must be more than a charge difference, since charge differences do not normally cause annihilation. In a more recent paper, I show that the difference between particles and anti-particles is not a charge difference, it is a spin difference. So the positive sign on the positron should signify a spin opposite the electron, not an opposite charge. The charge is caused by the emission of B-photons, but these photons are also spinning. To simplify, they can be spinning CW or CCW. If they are spinning CW, then the particle is an electron; if they are spinning CCW, then the particle is a positron. So you see that even the charge has "charge." The each photon in the emission has spin.
[To see a fuller mathematical analysis of the unified field at the quantum level, including the relative size of the gravity field and the charge field at the Bohr radius, you may now go to my paper on Gravity at the Quantum Level.]
I must mention one other thing before I go on to explain orbits in the macro-world. I said above that the electron gained an initial trajectory from the spinning E/M field of the proton, and that this initial trajectory was a straight line. This does not mean that the wave must now be understood as a jagged progression of straight lines. Although the initial trajectory is a straight line, the trajectory must immediately begin curving according to the perspective of any observer at any level of size who either sees or assumes that the proton is staying the same size. This would be all observers, since my theory proposes that all observers are material objects and that all material objects see themselves as staying the same size unless their background tells them otherwise in no uncertain terms. They also see objects with accelerations proportional to their own as staying the same size. They therefore see this particular orbit as a sinusoidal wave.
Only if you take an observer who is not expanding and have him measure the wave orbit in relation to his own background, will you achieve an orbital shape that is not a curve. What you will achieve is a sort of ever-increasing polygon, one that never connects up to its starting point (see illustration). Since there is no possible observer of this sort—it being a contradiction to have mass or matter without expansion, according to my theory—this diagram is only a game. It has no possible existential or mathematical reality. 
Since the proton expands absolutely, but does not expand relative to us (we assume), we must diagram the orbit as a sinusoidal wave, just as we were taught in high school. Relative to us and our background, this is the correct shape, to a first approximation.
Now I will move from the orbit of the electron to the orbit of the Moon. Once again I propose the orbit is a balancing of forces. The Earth expands toward the Moon but cannot catch it due to the E/M field. In this case the two bodies really do have iron cores, which makes the conceptualization even easier. We know that the Earth and Moon both have strong E/M fields. In my theory all E/M fields are positive, so that an exclusionary force must be the result. The Earth is also spinning, and this spin transmits a sideways force to the Moon. Remember that we have the magnetic component of the field to work with here, not just the electric component. Magnetism is orthogonal to electricity, as a field, and this is what creates the tangential torque. And so once again we obtain a sinusoidal wavelength as an orbit. The only remaining question is why the Moon shows so little amplitude in its wavelength. The amplitude has been squashed to near zero. Why? I propose that is due to the braking effect of the Sun's E/M field (including the Solar Wind). The Moon is also feeling constant forces from the Sun, of course, and the total effect over billions of years is to dampen the wavelength of the Moon. This is also a partial explanation for why the Moon does not reach the orbital velocities of the electron. The Sun's E/M field acts as an atmosphere that eventually creates a sort of friction—a limit on the Moon's orbital velocity. The other major factor is of course the Moon's mass. The Moon receives a tangential force from the Earth's E/M field, but this is not an infinite force, even over near-infinite time. The Moon's resists this force with its own acceleration force, which we call mass. It is clear that at some rather low speed a limit in orbital velocity will be reached, with or without a braking effect by the Sun's E/M.
The first benefit we get by redefining the orbit in these terms is that we now have a correctible orbit. I showed in my paper on Celestial Mechanics that the current orbit as a balance between g and the velocity of the Moon was not correctible. Any perturbation should be fatal, since the forces are either balanced or not. Once they are unbalanced, the orbit is permanently lost and cannot be saved. This is due to the fact that the Moon is not self-propelled. It cannot speed up or slow down as a correction. Current theory does not explain why orbits are self-correcting. According to current theory, the Sun's gravitational (or E/M) field should be fatal to the Moon's orbit, since it immediately breaks the balance between g and the velocity of the Moon. But this is not what we see. We see great correctibility. My theory explains this correctibility. If the Moon is pushed too far away from the Earth for a few days as the Moon passes farthest from the Sun, then the Earth can catch up with it later. If the Moon is forced into the Earth's E/M field with a bit greater force by the Sun's field, then the Earth just resists it more, and it returns to its optimal distance.
[Update, Feb 2012: To see mainstream data in conspicuous agreement with my analysis here, you may go to Wikipedia and type in "Heliospheric Current Sheet". The field in the Solar System is very clearly unified and includes charge. The mainstream admits that. Why will it not update the field equations to include charge and E/M?]
I know that I have thousands of other things to explain, but first I must address the most important complaint at this stage, which is that the E/M field of the Earth is not strong enough to replace the gravitational field as we know it. This complaint, which is very common, overlooks the genesis of my gravitational field and the new orbit. I am not using the E/M field to replace the gravitational field. I am using the E/M field only to explain curvature and exclusion. The strength of the gravitational field is still explained in my theory by g, and g is caused completely by expansion. It is a real acceleration, and so it obviously still applies. I am not replacing it with the strength of the E/M field. I am keeping g, I am simply changing its genesis. I am using the E/M field only to give a tangential force to the Moon, which keeps it moving "sideways" all the time. And I am using it to keep the Earth from catching the Moon.
Using current theory, there is no way to mathematically explain the given radius. Yes, given the radius, you can calculate an orbital velocity using current theory; but you cannot explain why the current radius and velocity are what they are. Why is the Moon not further away and going slower or closer and going faster? My theory provides an answer, and that answer is based on the combined E/M fields, which cause the exclusionary distance in the first place.
The next complaint will then be that current theory can use the E/M field in the same way I have. We don't need expansion theory to get a better orbital theory. Why not just take my orbital theory above, concerning the E/M field, and ditch the expansion part of the theory? Then we have a perfected orbital theory without all this expansion nonsense.
The problem with that is that without expansion you can't explain why the orbit is correctable on the outside. There is containment of the orbit from the inside, since the Earth's E/M field is the constraint. But there is nothing to keep the Moon from flying off into space after it receives a tangential force from the field. You will say that gravity keeps it from flying off, but using current math and theory, gravity won't do the job. If the Moon is kicked into a slightly higher orbit either by a tangential force from the E/M field or by a nudge from the Sun, current theory cannot save it. It would have a greater energy than it had the moment before, and it would be in a higher orbit. It would have to escape.
Therefore my E/M field theory only works as a counterpart to expansion theory. If g is an actual expansion of the Earth, then the Earth will catch up with the Moon. The orbit is correctable both on the outside and on the inside.
Finally, my theory is confirmed by current empirical data that shows that all bodies in prograde orbit in the solar system gain angular momentum from their primaries, and that all bodies in retrograde orbit lose angular momentum and tend to decay. Orbiting bodies are in fact receiving torques. This has been known for decades. But torques cannot be explained by gravitational fields, whereas torques from E/M fields are quite easy to explain. The E/M field is an exclusionary field created by bombardment of photons. There is a ready mechanism for carrying angular momentum out from the primary, via the spin of the emission. There is no mechanism in the current gravitational field. [See part 4 for more on orbits and the E/M field].
[For a proof of the inverse square law using expansion theory, see Part 3 of the The Third Wave.]
1Mass curving space is just as much force at a distance as mass attracting other mass, since space is also at a distance from matter.
2See my paper on Quantum Mechanics.
3Orbits show great correctability but according to current theory should show none. link to paper on Celestial Mechanics
4I can comment on orbits since the conversations McCutcheon had with Ruske were very extensive. It was clear that orbits had not been explained to my satisfaction.
6The cause of this charge may be that all bodies are radiating photons. The question of cause is ultimately beyond the topic of this paper: the question is the same whether you accept expansion theory or not.
7Of course, this would depend on whether the field was proportional to the mass or the angular momentum or some other factor, which question this paper does not propose to address.
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