Miles Mathis: G is the Key to the Secret of Gravity

Please note that this paper is a simplification by me of a paper or papers written and copyrighted by Miles Mathis on his site. I have replaced "I" and "my" with "MM" to show that he is talking. All links within the papers, not yet simplified, are linked directly to the Miles Mathis site and will appear in another tab. (It will be clear which of these are Miles Mathis originals because they will be still contain "I" and "my".) The original papers on his site are the ultimate and correct source. All contributions to his papers and ordering of his books should be made on his site. (This paper incorporates Miles Mathis' ug paper, g paper and quantumg paper).

 
Maxwell             Newton

First written January 2005 Abstract: In this paper MM will break open the universal gravitational constant G, showing the hidden information inside. G is not and has never been just a constant. It is the carrier of hidden motions and hidden theory, uncovered by neither Newton nor Einstein. In discovering what G contains, MM will be able to show that the current value of gamma (in Relativity) and the current estimate for the age of the universe are incommensurate. That is, they are in serious mathematical conflict. How MM pulls this information out of G is a fascinating journey, covered quickly here with only a few novel but logical postulates and some very simple math. By the end, MM will be able to show precisely why the proton has a speed and mass limit in accelerators. This limit has so far been a mystery for the standard model, as they admit.

In 1954, Erwin Schrodinger said in his book Nature and the Greeks [p. 6],

In an honest search for knowledge you quite often have to abide by ignorance for an indefinite period. Instead of filling a gap by guesswork, genuine science prefers to put up with it; and this, not so much from conscientious scruples about telling lies, as from the consideration that, however irksome the gap may be, its obliteration by a fake removes the urge to seek after a tenable answer. So efficiently may attention be diverted that the answer is missed even when, by good luck, it comes close at hand.

Background

Contemporary science is stung by this quote in a thousand places, but perhaps in no place is the sting as large a lump as in the constant G. Constants by their very nature act as gap fillers, and although we wouldn't call them guesswork, they hide even better than guesses. Because a constant comes from neither data nor theory, it hides better than either one. No one tries to correct it, because it is correct, as a number, almost by definition. Only new data can correct it, and new data tends to change the number only. New data rarely reminds anyone to put some mechanics under the constant. The constant is a fake that obliterates future science in a nearly perfect manner. G is the ultimate proof of this, since it has stood in for mechanics, and prevented mechanics, for over three centuries. It has become so invisible now that no one even thinks to look at it anymore.

It occurred to me some time ago that the Universal Gravitational Constant G might be the key to unlocking the secret to gravity, among other things. It has always seemed puzzling that a constant should have so many unexplained dimensions. A complex constant like that is normally a sign of incomplete theory. All the known concepts are assigned variables and the unknowns are lumped together in a constant. The numerical value is not such a puzzle, since it may just be an expression of incommensurate initial definitions. For instance, we chose the length of the meter and the second and so on pretty much arbitrarily, so it shouldn't be a surprise when all our numbers don't match up at first. But G is not just a number. It has lots of dimensions, L³/MT². Could there be a secret locked up in those dimensions?

MM is not the first to ask that question, but no one has yet presented us with any major secrets. Historically, the door for serious questioning was not open that long. Newton's theory became dogma so quickly that very few scientists had the gumption to look hard at it. The ones who did found it mostly convincing or mostly opaque. Since the time of Einstein, no one has taken the constant seriously. It is a piece of discarded and superceded math. To the contemporary physicist, G is about as interesting as the constants of Archimedes or Toltec hieroglyphics. Einstein gave us a new math to express the gravitational field, leaving the mysteries of Newton behind. But Einstein's new math and theory did not dispense with the old mysteries. In many ways it simply changed the text of the mystery. It substituted a new problem for an old one.

This paper is not concerned with critiquing the math of General Relativity. Here it is enough to point out that the mechanism of gravity is admitted to remain a mystery to this day. Relativity describes the gravitational field in ways that are mathematically superior to Newton. It cannot be denied that Einstein at the very least updated the math to include the finite speed of light c—a constant that was unknown in the time of Newton. The finite speed of light implied a difference in measurement of variables between an object and its observer, as well as a difference among various observers, so that even Newton would have admitted the necessity of a mathematical update. By returning to Newton's equations MM is in no way questioning the truth or usefulness of Relativity as a whole. MM is convinced beyond any doubt of time dilation, length contraction and mass increase; MM will say it again here. MM is returning to Newton's gravitational math not to argue for its historical superiority, but only to answer questions that have remained even after Einstein. No one denies that these questions remain; no one denies that gravity remains mysterious in many ways. Nor will anyone deny that gravity has resisted being incorporated into QED or unification theories.

In this paper MM will show that by studying the foundational theory of gravity a bit more closely we can arrive at a better understanding of both mass and gravity. By doing simple algebraic operations on Newton's equations we can derive new knowledge. This knowledge will allow us to discover many things that have so far been hidden. The most important of these is tying the classical equations of Newton to unexplained numbers coming out of particle accelerators. In this paper MM will provide the mathematical link between Newton's classical equations of gravity and the equations of mass increase of Einstein. In doing this MM will mathematically derive the limit for mass increase for the proton. Until now, this experimental limit has been a mystery. Neither Relativity nor QED has been able to explain the number 108 for the ratio of moving mass to rest mass for the proton. MM will derive it with simple high-school algebra and a few simple theoretical postulates.

To begin our inquiries, it is best to start with a new thought problem. In Newton's original problem there were several unclear points in the definitions or postulates. One of these was whether the distance r included the radius of the large mass. The variable r is supposed to be the distance between two masses, but if the larger mass is very large, its radius comes into question. Another unclear point concerned the smaller mass. In many calculations it is ignored because it is insignificant compared to the larger mass; but you cannot allow it to be zero, for obvious reasons. To avoid getting into the historical discussion of these points, MM will offer a thought problem that gets around them completely. In doing so, the thought problem will also bring other things to light.

Thought Problem

Let there be two equal spheres of radius r touching at a point. We know that according to the theories of Newton and Einstein there must be a gravitational force at that point, but neither math allows us to calculate it. Newton's math cannot apply since there is no distance between the objects; Einstein's math cannot apply because there is no field at a point. Both theories solve this problem in their own ways, it is true. They add further theory that allows them to calculate in this predicament. In a nutshell they both propose a field centered about a point or a singularity. This causes further problems due to the fact that the objects' gravitational strengths are determined by their masses, and all mass cannot be found at a point. By current theory, mass resides in matter, and matter is made up of atoms. These atoms have real positions: they are found throughout the object—at its outer shell just as at its core. If the mass is a summation of atomic masses, then the force must be a summation of atomic forces. It is difficult to see how the center of force can be behind (in a directional sense) half the mass that causes the force.

We can bypass these further theoretical questions by continuing to propose simple new theory. To do this, let us move our twin spheres s distance apart for a moment. If there is a gravitational force, then after a time interval Δt, this distance will diminish by Δs. Why has the distance diminished? Because a force between the two spheres pulled them closer—this is the classical and current interpretation given to the situation. But can we give it another interpretation? Yes, we can say that both spheres are expanding and that they moved into the distance between them. By the classical interpretation, the centers of the spheres moved toward each other. By MM's interpretation, they did not.

With MM's change in theory, you can see that we no longer have to assign Δs to the diminishing distance between the spheres. We can assign it to a change in the radii of the spheres. This being so, we can move the spheres back together, touching at a point. After a time Δt, the radius of each sphere will have changed Δs/2.

We have changed the idea of gravitational distance in our theory; now let us look at the idea of mass. In article 5 [chapter 1] of Maxwell's Treatise on Electricity and Magnetism, he tells us that mass may be expressed in terms of length and time, in this way: M = L³/T². He derives these dimensions from a simple substitution into two classical equations.

(1) a = m/r2 (2) s = at2/2 Substituting for (1) a in (2): m = 2r2s/t2

Notice that L³/T² may be thought of as the acceleration of a volume, or a three-dimensional acceleration. This is very suggestive.

This passing idea of Maxwell caused me to reconsider the concept of mass. His math is true, except for one thing. His first equation is not really correct. As written it should be a proportionality. To be an equation requires the constant G.

  a = Gm/r²
The dimensions of G are L³/MT², which gives the mass and acceleration the correct current dimensions. But what if G is a sort of mirage or misdirection? To pursue this further, MM went to Newton's gravity equation, like Maxwell had.

(1) F = Gmm/r2 (Newton's gravity) (2) F = ma  (Newton's 2nd law) Substituting for F: ma = 2Gmm/r2  transposed for a: a = 2Gm/r2

(We must have a 2 on the right side, since the force equation for gravity is the force between two masses, but the force that causes an acceleration on the other side of the equality applies to only one of the masses. It is customary to give all the acceleration to one of the masses, but in MM's thought problem the two equal spheres both accelerate.)

Now let us apply this equation to our twin spheres touching at a point. There is no distance between the spheres, so r would normally apply to the distance from center to center. But since the spheres are the same size, let us re-assign r to the radius of each sphere. The distance from center to center is then 2r. We have assigned Δs to a change in the radius instead of a change in the distance between the spheres, and this allows us to calculate even when the spheres are touching. For clarity let us make Δs into Δr.

(1) a = 2Gm/r2  transposed:  a/2 = Gm/r2 (2) s = at2/2  transposed with substitution of Δr for s; Δt for t:   a/2 = Δr/Δt2 Substituting for a/2: Δr/Δt2 = Gm/r2

The only remaining problem is the variable r. If the spheres are expanding, then r must be expanding. After time Δt, the radius will be r + Δr. After any appreciable amount of time, r will be negligible in relation to Δr, so that Δr ≈ r + Δr. Therefore we may simply drop the r variable as a variable that approaches zero.

Δr/Δt2 = Gm/Δr2 transposed for m: m = Δr3/GΔt2

Now all we have to do is reassign the dimensions of L³/T² to the mass, as Maxwell implicitly suggested. We will drop the dimension M altogether. This gives G no dimensions at all. It is just a number. This is actually much more sensible, since constants with dimensions are a sign of incomplete theory. That is what drew me to this solution in the first place. Newton had to give the dimensions L³/MT² to G only because he had mistakenly assigned mass a new dimension. Mass is not a new dimension. It is reducible to the old fundamental dimensions of length and time.

Our last problem is plugging known values into this new equation. At first it looks like the mass should be changing over time, since the radius is changing. But no. The mass is dependent on Δr/Δt², and that is not changing over time. As the radius gets larger, so does the change in time, so that the ratio is constant. It is a constant acceleration. A constant acceleration gives us a constant mass. Therefore we can plug known values for m into this equation.

(1) m = Δr3/GΔt2  transposed: Δt2 = Δr3/Gm (2) a = 2Δr/Δt2 Substituting (1) Δt2 into (2) a = 2mG/Δr2

That is the acceleration of each of two equal masses in a gravitational situation. But if we want to give all the acceleration to one of them, holding the other one steady for experimental purposes, then we simply double the value.

a = 4mG /Δr2 If the proton has a radius of 3.173 x 10-13m, this yields a = 4.425 x 10-12m/s2

(In the paper The Atomic World is 100 Times Larger Than We Thought, MM has found the current estimate of 10-15 too low, so it is not used here. The number used here is about 8 times the number from MM's paper: Bohr's Three Mistakes. The smaller number is the proton proper, the larger is the z-spin of the proton.)

It took me several years to notice it, but this number is ε₀/2, where ε₀ is the permittivity of free space. Yes, ε₀ is normally written as 8.85 x 10^-12C²/Jm, but that can also be written as 8.85 x 10^-12kg/m³ or 8.85 x 10^-12/s². (See charge discussion in Coulomb's equation is a Unified Field equation in disguise where MM shows that the permittivity of free space is a misdefined constant that has nothing to do with free space and is actually gravity at the quantum level.)

We are now in a position to use our new number for acceleration to explain a current experimental mystery. Using the new number to do this will also act as proof of MM's theory, since it gives us a sort of experimental confirmation.

  If the proton has a fundamental spherical acceleration, then in any one direction it will have a velocity at any given time. If we suppose that the age of the proton is on the order of the age of the universe, then we can estimate the current velocity of the shell of the proton. "Velocity relative to what?" you may ask. "If everything is expanding, then what is our background?" The velocity we will find must be relative to two things. It is relative to the velocity of the radius at t₀, which we define as zero. And, it is relative to the speed of light, c. Einstein defined the speed of light as the universal background, and MM continues to accept that definition.

  If we accept (one of) the current estimates for the age of the universe as around 15 billion years, then the current velocity of the proton's shell would be 2.1 x 10⁶m/s.
v = at = (4.44 x 10^-12m/s² )(4.73 x 10¹⁷s) = 2.1 x 10⁶m/s

(This is actually a Unified Field velocity caused by both acceleration due to gravity/mass and the E/M field. However, this is indeed the velocity we want here, since both fields will affect the limit in an accelerator, and the number 108.)

That seems ridiculously large at first, except that we have experimental confirmation of that number from accelerators. As MM has shown in his paper on accelerators, there is a limit to the speed achieved by the proton. This limit is a final energy of about 108 times the rest energy. Using gamma, this translates to a velocity of .999957c, which is 1.2 x 10⁴m/s short of c. If we theorize that the gap between c and the limit in velocity is caused by a residual velocity or velocity equivalent that the proton already has, then the limit is explained. (See E ≠ mc2 (Gamma is Kappa) Einstein's famous 1905 paper: The Accelerator Problem - (Why 108?).)

But there is more. My correction to gamma and to the mass increase equations predicts a limit in velocity for the proton of .9930474c, which is 2.1 x 10⁶m/s short of c. This is an exact match, as you see. If we plug the current form of gamma into MM's acceleration equation above, we get an age of the universe of only 85 million years. But MM's correction to gamma gives us an age of 15 billion years. We know that protons must be older than 85 million years. The earth is almost 60 times older than that itself.

Now let me address the first outcries. Some will say that MM's equations above give us a current radius for the proton of 5 x 10²³ meters, assuming the proton was at zero to start with (using d = at²/2). But all such calculations are pointless. Any distance some point on the surface of the proton may have traveled in an absolute sense will not tell us a current radius, since that is not what we mean by current radius. The current radius of the proton is measured relative to other radii of other things existing now, and current equations such as d = at²/2 are used for that. You cannot use these equations to claim that the proton radius is now 5 x 10²³ meters, since that would imply the original radius was 1, not zero. Or, you can use the equation if you like, but you have to use the number as a proportionality. Meaning, if the current radius is 3.17 x 10^-13m, then the original radius was 2 x 10^-49m. That may be interesting to some people, but since everything was smaller back then, the proton was NOT relatively smaller than it is now. To some god existing outside the universe, yes, the universe and the proton might look much smaller 15 billion years ago; but to everything inside the universe, both the proton and the universe would not have changed in size (due to gravity, anyway).

The next problem concerns MM's claim that velocity is constant. A velocity, such as the speed of light, will remain constant in an expanding universe simply because time is a function of distance. This means is that we define time in relation to distance. If this definitional distance increases, as everything expands, then the definitional period of time will increase proportionally. Distance gets larger, time gets "larger". So the ratio of the two stays the same. Which means that all relative velocities will stay the same.

As an example, we now use the cesium atom to define time. The baseline data in the cesium atom is an oscillation from one energy level to the other, or an atomic wobble. This oscillation is a motion, and all motion implies a distance. If the cesium atom gets bigger, then the distance increases, and the time period increases. Time is dependent on distance. This is even clearer with a pendulum clock. If all material lengths increase, then the length of the pendulum will of course increase, which will increase the length of the second. Time is connected definitionally and operationally to distance, therefore any increase in universal length will cause a proportional increase in universal time. Since velocity is defined as one over the other, velocity will not change. The numerator and denominator both get bigger at the same rate.

Of course there are many other questions that have to be answered, but MM has answered them in another place and will not repeat myself here. The purpose of this paper was to connect MM's use of Maxwell's hint and Newton's constant G to the number 108 in the particle accelerator.

(For a different derivation of the number 108, see Redefining the Proton.)

Explaining not the dimensions, but the number
shows that the number of G is actually a field transform.

Abstract: In this paper it will be shown that G acts as a transform between the two separate fields that compose the uber-field of Newton's gravitational equation. First MM will write each mass as density times volume and then give V to one field and D to the other field. This makes gravity, taken singly, dependent on volume or radius alone. Density then becomes a consideration of the foundational E/M field. That is, density is important only in that field. This density must apply to the density of the so-called "messenger photons" which mediate the foundational E/M field. But we cannot apply the density directly to this field. We require a transform. The reason we require the transform is that gravity is now dependent on radius, in the re-expanded equation. This means that forces and accelerations are not directly comparable to different-sized objects without a transform. Accelerations are comparable only when velocities are equal, but velocities at the surfaces of "gravitating" objects are not equal. Therefore, in order to put both fields in the same equation, we must transform one size to the other, or one velocity to the other. This is what G does. And because velocity is proportional to radius, the radius of the messenger photon must be 6.67 x 10^-11 times less than the radius of the hydrogen atom (or average particle of the physical field). This also explains the variation in G, since not all macro-objects are composed of hydrogen atoms.

Previously MM has unraveled the dimensions of the universal gravitational constant and shown its place in Newton's law is a Unified Field of Gravity and E/M by expanding Newton’s equation. In this paper it will be shown what the number in the constant refers to. Never before in history has anyone attempted to explain why G is the number it is, instead of some other number, or applied it to the mechanical relationship between real particles or fields. This has always been seen as akin to discovering why pi is 3.14 instead of 3.5, say, or why a cow has four legs instead of five. It has been thought that that is just the way things are. Up till now, G has maintained a heuristic presence only, known from experiment but otherwise unknown. Even in experiment, G has remained mysterious and ephemeral up to the present time. As proof of this assertion, see Gillies well-known review from IOP:George T Gillies 1997 Rep. Prog. Phys. 60 151-225

Abstract: Improvements in our knowledge of the absolute value of the Newtonian gravitational constant, G, have come very slowly over the years. Most other constants of nature are known (and some even predictable) to parts per billion, or parts per million at worst. However, G stands mysteriously alone, its history being that of a quantity which is extremely difficult to measure and which remains virtually isolated from the theoretical structure of the rest of physics. Several attempts aimed at changing this situation are now underway, but the most recent experimental results have once again produced conflicting values of G and, in spite of some progress and much interest, there remains to date no universally accepted way of predicting its absolute value. The review will assess the role of G in physics, examine the status of attempts to derive its value and provide an overview of the experimental efforts that are directed at increasing the accuracy of its determination. Regarding the latter, emphasis will be placed on describing the instrumentational aspects of the experimental work. Related topics that are also discussed include the search for temporal variation of G and recent investigations of possible anomalous gravitational effects that lie outside of presently accepted theories.¹

When MM started his search for G five years ago, he could not see why the number was so small. In his unified field paper, MM made great progress in unraveling Newton’s famous equation, showing that F = Gmm/R² must be a compound equation. That is, it is a distillation of two field equations, simplifying them into one uber-field. Newton interpreted terrestrial attractions and astronomical attractions as being caused by a single field, which has become known as the gravitational field. From experiment, he distilled an equation that successfully explained both local and orbital phenomena in a very compelling manner.

In re-interpreting Newton’s equation, MM has not brought into question the heuristic success of the equation. MM accepts that Newton’s equation is correct as written (minus Relativity). But MM has shown that Newton’s force F is a compound of two fields working simultaneously, and that the right side of the equation must now be understood as a distillation or simplification of more extensive equations. Because Newton was only looking at final motions, and not at fields, he arrived at what we would called an over-simplified equation. And because he was not able to show the full derivation of the equation from the existing fields, he was not able to show all the mechanics involved.

In the centuries since then, no one has been able to re-expand the equation, to show how it expresses mechanical fields in a logical and seamless manner. The equation has remained in its compressed state, keeping it mysterious. Even Einstein was not able to tease any more information out of it. Einstein’s additions are all external to Newton’s equation, and they add nothing to our knowledge of Newtonian mechanics.

The key to unlocking the Newton's equation was partly due to Maxwell’s suggestion that mass could be written as L³/T² (length cubed over time squared). This made it simple to rewrite the equation, returning all of G’s dimensions to the existing variables. Once this was done, G was no longer a constant with lots of dimensions; it is a constant with no dimensions. That is to say, a naked number. This allowed MM to ignore the current misdirection of linking the dimensions of G to the Planck length and time and so on. To re-expand Newton’s equation, we don’t have to get into Planck units or any other of the mysteries of QED.

The other thing that Maxwell’s dimensions did is allow me to express all force in terms of length and time. MM could dispense with any idea of mass. The idea of acceleration already includes the idea of impermeability, so that we do not need a dimension like mass that restates it. The mass dimension only mucks up our equations, making them harder to decipher.

Acceleration already includes the idea of impermeability, since you have to have something to accelerate. If all things were inter-penetrable, then acceleration would have no physical or mechanical meaning. Everything would then be just a ghost, and we would have no forces by contact. The fact that we have forces and accelerations means that we must have impermeability. If we have impermeability, we don’t need to talk of mass or of things being “ponderable”. Mechanically, all we need is the shells of our quantum spheres to be impenetrable to some degree, and the very existence of the variables a and F gives us that. We do not need mass or the idea of mass.

The second key to unlocking Newton’s equation was my discovery that the foundational E/M field must have mass equivalence. Having just ditched mass, speaking of mass equivalence must appear perverse. So instead of continuing to use old terms for the sake of convenience, MM will say that the foundational E/M field must have energy, which, by Einstein’s equation E=mc^<2, must give that field a degree of impermeability, and therefore what we have always called material characteristics.

Up to now, this foundational E/M field has only been represented in the standard model by the messenger photon. The foundational E/M field is the field that mediates the force or the “charge” between the proton and the electron. QED has been very un-mechanical from the beginning, with no apology, in fact with much bragging; but the fact remains that beneath their probabilities, there must be a field creating both the forces and the probabilities. This field is what MM is calling the foundational E/M field, since it exists as the sub-field underneath both electricity and magnetism.

If this field creates real motion, it must have energy. If it has energy, it must have materiality. Those messenger photons must have what is now called mass equivalence. If they have mass equivalence, they must be included in Newton’s equation. And this was done, Newton’s equation becomes a compound equation, distilling two fields, thus uncovering the root of the second field in Newton’s equation.

Even after finding that root, it was still a very long way from being able to separate Newton’s equation into its constituent parts. If Newton’s equation is a compound, that means that gravity, by itself, must be expressed in some other way. If Newton’s equation is not gravity alone, how do we express gravity alone?

See Newton's law is a Unified Field of Gravity and E/M for the full derivation of the separated equations. Suffice it to say, here, that gravity is expressed only by acceleration. Gravity is the acceleration of a length or a differential. This means that the gravitational “pull” of a body is determined only by its radius. Density, and therefore “mass”, is only a concern of the foundational E/M field. Which is to say that density considerations enter Newton’s equation only through the E/M field. Two spheres that are the same size have the same gravitational field, by definition. If they have different total fields according to Newton’s equation, it is because their densities are different; and their total fields are different only because one has more constituent quantum particles, and therefore more photon radiation.

This means that if the Earth were denser, you would weigh less, not more. You weigh less on the Moon not because it is less dense, or because it has less mass, but because its foundational E/M field is stronger. And its foundational E/M field is stronger because the Moon’s radius is smaller than the Earth’s. Although the Moon’s body is less dense, as a whole, its E/M field is more dense, on the surface. And this is simply because it has so much less surface area than the Earth (13 times less). You can’t just look at mass or density, you have to look at field lines; and the density of those field lines at the surface determines the strength of the foundational E/M field. This is an important point and it relates to why the Moon is stronger than the Sun in causing tides. (See Tides are caused by E/M field not Gravity)

But now to tell you what G is. The current number for G is 6.67 x 10^-11. That number is indeed a transform, and what it does is transform the size of one field to the size of the other, so that they can be compared directly. Remember that we have two fields in Newton’s equation, not one. The gravitational field, separated out from the compound field, is just the acceleration of a length. Therefore it has no mediating particle. It is not even really a field, in that sense. There is no graviton or any other radiated particle. Therefore, when MM speaks of the gravitational field, he is talking about the field of atoms and free electrons and so on. The field of “material particles:” particles that make up or constitute physical objects.

The second field comprising Newton’s equation is the foundational E/M field, and this field does not constitute material physical objects. This field is radiated by protons and nuclei and electrons, and mediates basic forces, but it does not physically constitute macro-objects in the same way. Certainly it exists in all the regions of all material objects.

Since this foundational E/M field has energy, it must have materiality. By jettisoning the idea of mass, materiality is now represented only by length and more specifically, materiality is represented by radius, in all the equations. In all gravitational or force equations, we have an accelerating radius of some sphere or spheres.

In Newton’s equation we don’t have a direct representation of the radius of the messenger photon, of course. We don’t even have a representation of the photon, or of the field. What we have is the masses of our objects and G. But from only the masses and G, we can find the radius of the messenger photon.

To do this, we first write the mass as a density and a volume.

M = DV

Since the gravitational field is proportional to radius only, and nothing else, the V variable applies to the gravitational field. But we give the D variable to the E/M field. The density part of both masses in Newton’s equation does not apply to gravity, it applies to the foundational E/M field.

But we cannot directly assign that density to the density of the photon field. Why? Because that density is not measured at the level of size of the photon. Let me put it another way. In that last equation, D and V are sitting right next to each other. That means that if we achieve a number for M from observation or experiment, D is attached experimentally to V. We have measured a density at that volume. But all volumes are no longer equivalent in a gravitational sense. As shown in Newton's law is a Unified Field of Gravity and E/M velocities are not equivalent, therefore accelerations cannot be compared directly.

To quickly gloss the argument in the UFT paper above: If we take Einstein’s equivalence postulate literally and simultaneously reverse all the gravitational acceleration vectors in the universe, we imply that all objects, macro and micro, are now expanding. In one sense they must be expanding at the same rate, since they all stay the same size relative to each other. We don’t see objects changing size relative to us, therefore they must be expanding at the same rate relative to us and to each other. But to achieve this, the surface of larger macro-objects must be moving faster during each dt than smaller objects. This is what is meant by dv in my UFT paper. The dv at the surface of large spheres must be much greater than at the surface of small spheres. This difference in dv’s must throw off the accelerations, too. The accelerations have to be measured in these dt’s, and if the dv’s in these intervals are not equal, then the accelerations cannot be compared directly. If the accelerations cannot be compared directly, the forces cannot be compared directly.

Let me simplify the idea even further. Let us say that someone tells you that the acceleration of one body is x and the acceleration of a second body is 2x. Does that tell you anything about their velocities over a given interval? No. Accelerations don’t give you lengths, or real motions over given times, unless you know an initial state. The velocities of the two bodies could be equal at the interval of measurement, even with totally different accelerations. By the same token, the two bodies could have the same acceleration and completely different velocities. Accelerations and forces are comparable only when dv’s are equal.

Now let us take that knowledge into our analysis of our two fields. Let say that one field is made up of hydrogen atoms, on average. The hydrogen atom is the average size of each particle in the field. The other field is made up of radiated photons. Like all other bodies, these bodies have to remain the same size relative to each other while time passes. If they didn’t, we would see effects that we do not see. But if we have reversed all our gravitational acceleration vectors, in order to see more clearly how our fields work mechanically, then if planets and stars expand, hydrogen atoms must also expand, and photons must also expand. In this case, the dv on the surface of the photon must be much smaller than the dv on the surface of the hydrogen atom. Which means we require a transform in order to compare any accelerations or forces mediated by any of these particles.

If we want to combine forces caused by gravity and forces caused by the foundational E/M field, we must transform the accelerations of the two fields during the same dt. We must transform the dv of one field to the dv of the other field. Once we do that we can compare the accelerations directly. We can put both fields in the same equation, compress them, and get a simplified final equation.

That is what Newton’s equation is. And G is the transform from one dv to the other. Since dv is directly proportional to the radius, we may deduce that the radius of the messenger photon is 6.67 x 10^-11 smaller than the radius of the hydrogen atom This gives us the unified field.

This also explains variations in G. G is dependent on the make-up of the bodies in question. The Earth is not made up of hydrogen atoms only. G is the transform between the average size of the atoms present in the field being calculated and the size of the radiated photons. Therefore G is not really a constant. As the average atoms vary, G varies.

Gravity at the Quantum Level

First posted January 22, 2009

Abstract: Using the unified field equations from Newton's law is a Unified Field of Gravity and E/M, MM will calculate the E/M field force, the force of gravity, and the unified force at the quantum level using only the numbers from the Earth and Moon, and MM's new size estimates for quanta. The standard model masses or charges will not be used. In doing this, the large and pandemic historical error in scaling accelerations and acceleration fields can be shown and that acceleration fields obey a new sort of relativity: not a relativity of distance or speed, but a relativity of size.

The standard model tells us that gravity is on the order of 10³⁶ - 10³⁹ weaker than E/M at the quantum level. To find this number, they scale the forces they find at the macrolevel to the forces they find at the quantum level. Seems pretty straightforward, but it turns out to be spectacularly wrong. The problem is that the standard model is scaling force numbers, but gravity is not a force, it is an acceleration. Gravity can cause a force, but as a defined variable it is an acceleration. The standard model knows this, but it tends to forget it at crucial times. They "forget it" on purpose in this case, simply because they can't figure out how to scale accelerations. You can't really scale accelerations, since accelerations don't tell us velocities or distances or times over a single interval, an infinitesimal interval, or what is now called an instant, unless we have an initial state. When comparing quantum particles to planets and moons, it is not clear what these initial velocities might represent; nor is it clear how to find them. Given an acceleration of gravity, how do you develop a velocity or distance that you can compare? The only velocity belongs to an object in the field, not to the large central object. So you see the problem: given an acceleration of gravity, you need a velocity or distance that belongs to the quanta or planet, so that you can then compare those velocities—in order to scale them. But there doesn't seem to be any way to develop those distances or velocities, since the quanta and planets aren't moving to create the accelerations. This is why the standard model chooses to scale the forces instead of the accelerations. Unfortunately, forces don't scale like accelerations. In fact, the two diverge very quickly, as we will see below. The only way to scale properly between the quantum level and the macro-level is to scale distances or velocities. The simple way to do that will now be shown.

It was in The Secrets of the E/M field are revealed at the Moon's surface paper that MM first discovered a simple method of separating the E/M field from the gravity field, and finding the sizes of each field. MM assumed that gravity was dependent on radius only, then ran the equations using the current numbers of the Earth and Moon. MM discovered that, according to this analysis, the Earth must have an E/M field acceleration of .009545m/s², and that the Moon must have one of 1.051m/s².

This final section on Quantum gravity builds from the following four papers: The Unification of the Proton and Electron, A Reworking of Quantum Chromodynamics and dismissal of the Quark, Explaining Mesons without Quarks, and Coulomb's equation is a Unified Field equation in disguise. It is time to do the full calculations such as MM's paper at his site of The Cavendish Experiment where MM used his unified field equations to find the separated forces of E/M and gravity on Cavendish’s balls.

First we need the radius for the proton using the precise radius for the proton of 4.09 x 10^-14 m from Bohr's Three Mistakes. That is about a hundred times larger than the current estimate (See The Atomic World is 100 Times Larger Than We Thought ). We know that the Earth’s gravitational acceleration is 9.809545m/s², and that its radius is 6,378,100 m. That is all we need for the gravitational part of this unified field equation. We just make a proportionality equation:

9.809545/6,378,100 = g_P/4.09 x 10^-14

g_P = 6.29 x 10^-20 m/s²that is the gravitational acceleration of the proton.

In Coulomb's equation is a Unified Field equation in disguise, MM show that the permittivity of free space ε₀ actually stands for gravity at the quantum level. The value found there: 2.95 x 10^-20 m/s² differs from the number here only because the gravity at the quantum level is also caused by the electron and neutron. The neutron, being nearly the same size as the proton, will not affect the number much, but since the electron is smaller, it must pull the total number down by a fraction.

The gravity of the electron is 3.43 x 10^-23 m/s², but, being smaller, the electron is a lesser partner in the total field. If we add the two fields and divide by two, we get 3.147 x 10^-20 m/s². That is still above my number for ε₀. This is probably telling us how many electrons we have relative to nucleons, but that calculation is for another paper.

However that may turn out, we must remember that acceleration is always a relative term. It is not like velocity, which can be compared across any equations. An acceleration is a rather tricky thing, since if you have twice my acceleration, that does not mean you are moving twice as fast or twice as far as me during any defined interval. Given an acceleration, your velocity and distance traveled during any interval can be anything. Without an initial velocity, an acceleration tells us nothing. We cannot compare accelerations, unless we have more information.

The acceleration we just found is an acceleration relative to the acceleration of the Earth. The form of the equation alone tells us that, since we are comparing the proton to the Earth. This means that we have found an acceleration for the proton as measured from the size of the Earth.

(Please note that earlier in this paper a different number for the gravitational acceleration of the proton was computed showing an acceleration about 7 exponents greater than this acceleration. It was greater because it was an acceleration relative to the meter itself, not to the radius of the Earth. The radius of the Earth is almost 7 exponents higher than 1 meter, hence the difference.)

This number just found here is an interesting number, but it is not really the number we want here, in this paper. We want to know how the proton would measure its own acceleration. Forces are transmitted and felt locally, and the relative field strengths must be calculated locally. To do this, we must compare velocities instead of accelerations. Velocities are always comparable, because they happen over one time interval. To get a velocity from this acceleration, we just use my trick from many other papers: we reverse the gravity vector, a la Einstein’s equivalence principle. We let it point out, and we let the surface of our object move with it. We look at how far the surface of the proton moves over one time interval, say one second. At that acceleration above, it moves:

x = at²/2 = 3.145 x 10^-20 m

The Earth moves 4.91 m during the same second. If we compare these velocities to the radii, we find something very interesting.

3.145 x 10^-20/4.09 x 10^-14 = 4.905/6,378,100

You will say that is just doing math in circles, and in a way it is. But MM has done it this way to show that the speed of the proton’s surface relative to its radius is the same as the speed of the Earth’s surface relative to its radius, at any given time. And this means that the speed of the proton’s surface relative to its SIZE is the same as the Earth. And this means that if the proton measures it’s own acceleration due to gravity, it will find the number 9.81 m/s²! It would have to, wouldn’t it, or the proton would be getting larger or smaller relative to the Earth.

To see the reasons for making the gravity field a function of radius, see MM's paper: Newton's law is a Unified Field of Gravity and E/M.

Once we apply the acceleration of gravity to a real motion, by reversing the vector like this, we see things we never could see before. We see that the acceleration of gravity is itself a relative number. It is relative not in an Einsteinian way, but in a completely new way. Acceleration depends on size, and who is measuring it. Einstein’s relativity was due to speed or distance. This relativity is due to size.

So, we have found two new gravitational fields for the proton, one as measured from the size of the Earth and one as measured by the proton itself. Now let us look at the E/M field.

The E/M or charge part of the equation is only slightly more difficult. As MM showed in my paper on the Moon, the E/M field is proportional to 1/r⁴. This is because the E/M field dissipates as it moves out from the surface, so we get one inverse square law right out of the surface area equation. But the E/M field also dissipates within the gravity field, so it picks up that inverse square law as well, just from the acceleration field. The radius of the Earth is 1.55 x 10²⁰ greater than the radius of the proton, so,

E_E /E_P = 1/(1.55 x 10²⁰)⁴ = 1.73 x 10^-81

E_P = 5.52 x 10⁷⁸m/s²

But we must make the same corrections to that number that we did to the gravity number. The E/M field is an emission field, so those photons will be traveling inside the gravity field. Which is to say, if we let the gravity vector point out, the photons will be emitted while the surface of our object is moving. The E/M field is a velocity inside a velocity, so anything that is happening to gravity will also be happening to E/M. As it turns out, we can represent all this by simply squaring our gravity correction. We have the fourth power here, which is square the power of the gravity field. Another way to look at it is that the size differential applies here twice, since we have two fields that are both smaller: one field inside the other. MM has already found a size differential between the Earth and proton of 1.55 x 10²⁰, so we just square that, to get 2.4 x 10⁴⁰.

E_P = 5.52 x 10⁷⁸/2.4 x 10⁴⁰ = 2.3 x 10³⁸ m/s²

That is the number the standard model is finding for the strength of the E/M field in quantum interactions. 9.8 is 4.26 x 10^-38 weaker than that, so that is where the numbers you read about in textbooks are coming from. Problem is, the standard model has only done the first part of the math. Let us complete it now.

At the size of the Earth we ignore the size or energy of the E/M field itself. We measure the results of the field, not the field itself. In other words, the photons that are emitted have no presence in the equations. They are invisible to the math, since they can be ignored. As a matter of size, they are inconsequential. But this is no longer true at the size of the proton. We are not only 1.55 x 10²⁰ smaller, we are 1.55 x 10²⁰ times closer to the photon. Compared to the proton, the photon is that many times bigger, as a field particle. This means that its size can no longer be ignored. The field has begun to take up measurable space, relative to the particle that is emitting it. This means we have to divide by 1.55 x 10²⁰ a third time.

E_P = 2.3 x 10³⁸/1.55 x 10²⁰ = 1.48 x 10¹⁸ m/s²

Now, MM could have ignored all the mechanics and just told you to divide once by 1.55 x 10²⁰, instead of going to the fourth power and then dividing by a cube. But although that would have gotten the right answer in much less time, in this case efficiency is not MM'a primary concern. The primary concern is uncovering the mechanics, and showing them in a transparent manner.

Let us look at one more outcome of our new numbers. MM went to an inverse fourth power and then cubed to get the number 1.48 x 10¹⁸, as you have seen. MM might just as easily have started with the proposal that the E/M field at the quantum level acts like the gravity field at the quantum level: that is, it is the same number as the Earth. If we can propose that the proton would get 9.81 for its own gravity, why not propose that the proton would get .009545 for its own charge field, just like the Earth? Well, actually, we could, and we would get the right answer, provided we made the right corrections. All we have to do is scale down using the radius differential again. In this case, the radius differential is representing the fact that the photon is that much larger relative to the proton. We have scaled the momentum of the photon up, relative to the proton, so that it has the right energy in the field.

1.55 x 10²⁰ (.009545) = 1.48 x 10¹⁸

The photon is going c whether it is taking part in quantum charge interaction or taking part in the E/M field of the Earth. But the photon will seem much bigger and more powerful to the proton.

Let us see what the current unified field acceleration of the proton is, using Coulomb’s equation. In Newton's law is a Unified Field of Gravity and E/M MM shows that Coulomb's equation, like Newton's equation, is already a Unified Field Equation. We can compare it to the acceleration above if we use the current charge on the proton and the current quantum force, but apply them to a motion of the proton instead of to the field.

a = F/m = 8.2 x 10^-8 N/1.67 x 10^-27 kg = 4.9 x 10¹⁹ m/s²

MM's acceleration is about 33 times less than that of the standard model. That makes sense, since my quanta are larger than standard model quanta. Being larger, they don’t need as much acceleration to cause the same field effects.

And we can find a force using this new acceleration:

F = ma = 1.48 x 10¹⁸ m/s² (1.67 x 10^-27 kg) = 2 x 10^-9 N

So you can see that this force computed here is not far off the proposed standard model force, despite all the corrections to the math whihc MM did. According to textbooks, using the Coulomb equation, the force between the hydrogen nucleus and the orbiting electron is 8.2 x 10^-8 N. This means that the Coulomb equation is not hopelessly off course, in the first instance. At this point it is less than 100x wrong, and most of that is because the Bohr radius is wrong (See Bohr's Three Mistakes). However, there are more corrections to be done. We have a very important step outstanding.

Before we do that, let us look at our new fields. MM has shown that the local charge field at the quantum level is E_P = 1.48 x 10¹⁸ m/s² . The local gravity field is g_P = 9.81 m/s². From this we see that the gravity field is still negligible, but not nearly as negligible as QED thinks. It is about 10²² times more powerful than we are told. We are told it is about 10³⁹ times weaker than E/M, but, from the point of view of the proton, it is only 10¹⁷ weaker. MM has been able to strengthen the gravity field by a large margin, but it still appears to be negligible. If it is still about 10¹⁷ smaller than the E/M field, it is difficult to see how it will involve itself in quantum interactions. In various papers MM has used gravity to explain the quantum orbit, one of the quantum waves, the apparent attraction of the electron (instead of its real attraction), and the margin of error in my meson states. None of these things can be explained with a gravity field that is still so weak.

That would be true if my math and theory stopped here, but we still have to consider the drop off of charge due to the spherical shape of the field.

This problem has already been encountered by QED in (one of) the famous zero-charge paradoxes. Although the measured charge is now said to be 1.6 x 10^-19 C, according to the original math of QED the effective charge at any distance from the electron or proton would seem to be zero but it is true that the charge would be expected to drop off quickly. This problem is at the root of renormalization, as MM showed in his paper on his site: The Disproof of Asymptotic Freedom, as most involved in QED know. In the equations above, MM developed an acceleration due to charge, but this acceleration was and is an analog of the charge field of the Earth. My charge field of the Earth is the charge field measured right at the surface. So the charge field MM calculated for the proton must also be right at the surface. This would apply only to protons at impact, but that is not what we normally mean by the charge strength at the quantum level. What we mean is the charge strength at an the radius of an orbiting electron is actually the radius of capture of the electron, not its orbit. (See How Elements are Built - A Mechanical Explanation of the Periodic Table.)

How far are the quanta apart given this situation? MM has recently developed a corrected number for the Bohr radius, which is 9 x 10^-9 m. MM has already given a number for the proton radius of 4.09 x 10^-14 m. That is a difference of about 100,000x [using the standard model we get the same factor]. So, using my 1/r⁴ equation, we get a drop off of charge of 10²¹. If the local charge is 1.48 x 10¹⁸m/s², then the effective charge at the orbital radius is about .00064 m/s² .

This means—according to the proton’s own measurements—that the surface of the proton is moving toward the electron at 9.81 m/s², and that the electron is being driven off at .00064 m/s². This is why we have an apparent attraction.

So let us use those new numbers to find a unified field force between the proton and electron in orbit.

a = 9.80 m/s² - .00064 m/s² = 9.80 m/s²

But we must ask if we want the force on the electron or the force on the proton. There is no such thing as a generalized force, since the equation must have a mass in it. Let us find the force upon the electron:

F = ma = (9.11 x 10^-31 kg) 9.80 m/s² = 8.93 x 10^-30 N

On the proton we get:

F = ma = (1.67 x 10^-27 kg) 9.80 m/s² = 1.64 x 10^-26 N

And now we see that the textbook use of Coulomb’s equation was a catastrophe. We are told that the force between the proton and electron is 8.2 x 10^-8 N, which you can see is off by a factor of 10²². Notice that this is also the factor that the standard model is off with the strength of gravity at the quantum level: 10²². Next time someone tells you that QED is so fabulously exact and precise, send them to this paper and tell them that you know that QED is wrong by 10²² on one of the fundamental questions of the atomic world.

How does the current number compare to my number? That is, how is the mistake made, precisely? Watch this: If we take the constant out of Coulomb's equation (when we apply it to quanta) and sum the charges, we get very near my number. MM has found separate forces for the proton and electron, but we can find the total force by adding them together and dividing by two. That gives us a sort of average force of 8.2 x 10^-27 N.

Coulomb's equation squares the charge, but you don't need to square the charge. The forces and charges don't square, since they are field charges and forces. They shouldn't multiply, they should add. If we were being rigorous, we would have to add them as density fields, so they don't even obey a straight addition, but since the electron force is so much less, we can just divide by two and get the right answer, as you see. Now, since the current equation multiplies both charges by the constant, we have to un-multiply twice to make the correction in the field. In other words, we have to divide by the square of the constant. We are going smaller, so we use the inverse of the constant, which is 1/k = 1.11 x 10^-10. Squaring that is 1.23 x 10^-20. So we multiply that by the current figure, to make the correction.

(1/k)²(8.2 x 10^-8 N) = (1.23 x 10^-20)(8.2 x 10^-8 N) = 1.01 x 10^-27 N

If we take the constant out of Coulomb's equation when we apply it to quanta, then when we seek the force between the electron and proton, we get 1.01 x 10^-27 N. If we use my new math, which gives an acceleration of 9.80 m/s² to both the electron and proton, we get an averaged field force of 8.2 x 10^-27 N. This is astonishing, no matter how you look at. The standard model will try to write it off as some sort of mathematical coincidence, but this paper shows that it is not a coincidence. The standard model has vastly overrated the forces between quanta, and it has done so because it doesn't understand how the constant is working in Coulomb's equation. It also doesn't understand how the charge field works mechanically, how the charge field interacts with gravity, or how to scale accelerations. All these mistakes have snowballed on them, creating a fundamental field error of 10²².

MM can even explain the apparent error between my number and theirs. MM found 8.2 and they found 1.01. Turns out we are both right, since one number is about 8 times the other. My number is the field average of the force applied to both proton and electron. Their number is the field applied to the motion of the electron (since the proton is not moving in the field). MM has shown elsewhere that the proton has four stacked spins to the electron's one, and the 4th or z-spin has 8 times the energy of the 1st or a-spin. So only 1/8th of the energy of the field goes to moving the electron. Hence, their number is 1/8th of mine. The fact that our differential is so near to 8 is another confirmation of theory, not a error.

We can also now see that the force between the proton and electron—the fundamental charge—is numerically almost precisely equal to the mass of the proton. Remember that the mass of the proton is 1.67 x 10^-27 kg. If we take the constant out of Coulomb's equation when we apply it to quanta, then when we seek the force between the electron and proton, we get 1.01 x 10^-27 N. Wow. Another coincidence, right? No. The numbers are nearly the same because one is measured in kilograms and the other is measured in Newtons, but the Newton is based on the kilogram. 1 N = 1 kg m/s². So this is what we should have expected from the beginning, if we had understood our equations. It makes no sense for the masses of the quanta to be at a scale of 10^-27 and the forces to be at a scale of 10^-8. Since accelerations scale with the radius, as MM just showed, the force must scale with the mass.

MM has simultaneously shown a very strong repulsion between protons at close range and an attraction between the proton and electron in orbit. This was done this without having an attractive field of any kind. The charge is always repulsive, and gravity is represented by a real motion, as you see.)

Of course, by this logic, protons would also be attracted to each other, up to a point. And it explains why free protons are excluded at greater radii than electrons.

Free protons would indeed attract each other, but any kind of proton/proton orbit would be well outside the electron orbits. Electrons, being smaller, can get closer to the proton. They encounter a smaller cross section of the charge wind.

It may be that electron orbits nullify any possible proton orbits, by making the atom neutral. But it is much more likely that the tendency of matter to form liquids and solids is due to this attraction between distant protons that has just been shown. Liquids and solids do form, and they form very near the quantum level. If protons are so exclusionary, to a power of 38 over gravity at the quantum level, it is not clear that liquids and solids could ever congeal. Even though solids are solid at a molecular level, not an atomic one, the molecular level is not far above the atomic level. Given the current quantum model, it is not at all clear how chemical bonds form, much less solid structures. “Sharing of electrons” and other similar statements have always been long on mystery and short on mechanics.

A charge or E/M field that is so gigantically overwhelming at the quantum level can hardly have evaporated at the molecular level, only a few factors of ten above the Bohr radius. And a gravity field that is so attenuated at the quantum level can hardly have become a major player again at the molecular level. Without these two fields acting in normal ways, the standard model is forced to explain molecular bonds and liquid and solid structures in very strange ways. But my theory begins to make some mechanical sense of it. You see that my charge field, though very strong as a bare charge, is weak enough to evaporate beyond the Bohr radius. And my gravity field is always at your service.

Conclusion

One very large scaling error has jeopardized the entire standard model explanation of forces at the quantum level. The standard model has historically treated the gravity field as a force field instead of an acceleration field. They have thought that forces could be scaled by a straight comparison of numbers, whereas MM has shown that it is the acceleration numbers that must be scaled, not the force numbers. And the acceleration numbers cannot be scaled in a straightforward manner.

To scale acceleration fields, you must develop a velocity over one interval, and scale the velocities. MM's method is sort of relativity, based on size and shows a very powerful gravity field at the quantum level. In fact, it is precisely the same gravity field we have at our level, and at all levels. Gravity is a constant, at all scales. But it is a constant only if it is a local measurement. If you measure gravity at one scale from another scale, you have to do a transform. MM has shown that very simple transform: the radius differential.

Of interest is The Vacuum Catastrophe where MM's solution also solves the "greatest predictive failure in the history of physics."

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