Q-Theory: A Connection between Newton’s Law and Coulomb’s Law?

Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, Pl q , was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, , where equals Apery’s constant, 1.202 …, and, , is the relaxed, i.e., g =  , number density of the positive and negative mass planckions. In the present epoch, we estimate that, equals, 7.848E54 m −3 , and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, . These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, 0 2.387E 9 g = − , due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E−48 meters, within the vacuum made up of these particles. On the surface of the earth, where, 2 9.81 m s g = , the displacement amounts to, 7.824E−38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.

. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, 0 2.387E 9 g = − , due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E−48 meters, within the vacuum made up of these particles. On the surface of the earth, where,

Introduction
Students of physics I and II, as well as professional physicists, have long been intrigued by a possible connection between Newton's law and Coulomb's law. Some similarities are that they are both inverse square laws, they both depend on the product, (M 1 M 2 ) or (Q 1 Q 2 ), and they both involve coupling constants, G for , for Coulomb's law. Some notable differences are that the gravitational force is only attractive, whereas the electrostatic force is both attractive and repulsive. Second, only positive mass exists whereas two species of charge exist, positive and negative. Third, positive masses attract, but like charges repel, and unlike charges attract. Fourth, and perhaps most mysterious, is the strength of these forces. The k value in electrostatics is so much larger than G in gravistatics, in reduced units where factors such as, ħ and c are set equal to one.
The fact that Newton's constant, G, is so weak, has impressed many notable physicists, including Dirac and Jordan. Dirac [1] [2] [3], already in 1936, in his large number hypothesis (LNH), forwarded the notion that G is not really a true constant of nature, but actually varies with cosmological time. Jordan [4] [5] [6]  , refers to the cosmic scale parameter. The, R, is the Hubble radius, the, T, the CBR temperature, and the, z, stands for the redshift.
All the variables with a subscript, "0", refer to the present epoch, and we are using the convention where, 0 1 a = . All the variables, without a subscript, refer to a different cosmological era. Coming back to Jordan, he claimed that, ' G G H = − .
He further recognized that G must now be related to a scalar field, ϕ , within a year of Dirac's LNH. We claim that if G does vary cosmologically, then, . We identify Jordan's scalar field with the, ϕ , in the above equation [8] [9]. The, CBR temperature equals, 0 2.725 Kelvin T = . The idea was to help explain the discrepancy between the cosmological constant, 2 8 G c ρ Λ Λ = π , in past epochs, versus today. There was also the issue of renormalizing gravity. If gravity effectively disappears at extremely high temperatures, then there is no theory to renormalize at high momentum exchanges. We believe that gravity is an order parameter, which vanishes at very high temperatures, much like magnetization.
In order to fix the parameters for the two models for, , we demanded that, w, the quintessence parameter, equal exactly, . In the ΛCDM model this parameter is assumed to equal exactly negative one. But this is not what is observed after over a decade of observations and measurements [10]. Although the negative one can easily be accommodated within observational error, perhaps this is not its true value. By setting, 0.98 w = − , we were able to fix the parameters in our two models. Moreover, we were able to prove that, 0.06 , in the current epoch. This is a variation within observational bounds. Jordan's original thesis, that, ' G G H = − , seems to be unsupportable given current observations and measurements.
The challenge was, of course, to show that in virtually all other aspects, the deviation from the ΛCDM model was not great. The ΛCDM model has proven to be very successful and robust. It is only in the very early universe that marked deviations occurred between our models, which were called models, A and B, and the ΛCDM model. In fact both functions for, mimic order parameter behavior. Before approximately, E22 Kelvin, it is conjectured that Newton's constant, as we know it, did not exist.
In another series of papers [11] [12], we developed a gravitational polarization model for the vacuum. Based on previous work of Hajdukovic [13] [14] [15] [16], and Winterberg [17]- [23], it was realized that polarization might offer the key towards a fuller understanding of dark matter, and dark energy. If the ambient temperature is low enough, ordinary matter, made up of quarks and leptons, can polarize the surrounding space forming a polarization cloud or halo. In gravistatics, this leads to anti-screening versus screening in electrostatics. The gravitational dipoles formed in gravistatics, add to the source field, ( ) 0 g  , making the macroscopic field, , larger than the original applied field, , is an induced field set up within the dielectric due to net charge dipole ordering. For dark matter, we need extra mass, in order to explain the halo effect surrounding galaxies, rotation curves, virial motion of galaxies within superclusters, gravitational lensing, etc. There will be bound mass due to the massive dipoles produced within the vacuum, or gravitic, which is our gravitational version of a dielectric. This bound mass trapped within mass dipole formation in the vacuum, and macroscopic ordering, seems to us a perfect candidate for dark matter [11].
Dark energy, on the other hand, was identified [11] as the gravitational field mass density, produced by both source matter, and bound, polarized matter.
According to Gauss's law, if the universe contains net source matter, which it does, and bound, polarized mass, which is an assumption, then there must be gravitational fields associated with each. We identify the dark energy density with, In this equation, K is the relative gravitational permittivity, and, ( ) then, the gravitational permittivity, ( ) a ε ε = , is also an intrinsic property of the vacuum. We will work with this assumption in this paper. The, is the smeared, cosmic gravitational field obtained from Gauss's law. This gravitational field is associated with the universe as a whole, once all source, and bound, matter is taken into account. Winterberg [17]- [23], in particular, developed a model of space made up of positive and negative mass particles called planckions. These particles are assumed to be real particles, versus virtual, and have positive and negative the Planck mass. We believe that the magnitude of these masses changes cosmologically, whereas he claims they are constant. According to Winterberg, the planckions form a very rigid two-component superfluid (we prefer supersolid), where disturbances move at the speed of light. The positive and negative mass species interact amongst themselves, and maintain a fixed distance of separation C. Pilot from other neighboring particles of the same species. Unlike mass planckion particles do not interact directly [23], but indirectly. Because positive and negative planckion particles occupy the same space, and are spread evenly, the positive and the negative masses are invariably drawn next to one another. They are forced to rub shoulders with one another, so to speak, and also maintain a fixed distance of separation from each other.
Winterberg developed an extensive and elaborate theory along this idea, and we will use it here, to establish an intimate connection between electrostatics, and gravistatics. We believe that the two-component superfluid is the key towards understanding the connection between gravity and electrostatics.
In the Winterberg model, fluid forces are responsible for keeping the planckions a fixed distance apart. When planckions are displaced from their equilibrium positions, increased planckion pressure forces them back into position. We can think of them as restoring forces, and we have modeled them as such [11]. Winterberg assumed that two like planckions, whether they have positive or negative mass, repel each other much like charges in electrostatics. The question naturally arises … is the planckion force ultimately an electrostatic force?
The Q theory, we believe, provides the answer to this question. If like mass planckions are anchored in position, and keep a finite distance apart, then there must be two forces acting on the individual planckion, one attractive and one repulsive, along any given direction in space. The repulsive force is electrostatic, and the attractive force is also electrostatic. An electrostatic attractive force might simulate gravity, however. What if Planck charge and Planck mass were created at the same time, as two components of the same particle? Wouldn't they attract and repel simultaneously? Also, their creation need not be at the Planck temperature, ~E32 Kelvin. If G is varying with respect to cosmological time, then, , could have formed out of the vacuum at a reduced temperature of the order, ~E21 -E22 Kelvin. Irrespective of the temperature of formation, we would have a vacuum, which is not only electrically neutral, but also massively neutral in its very earliest stages. It is well known that all particles in the standard model, i.e., all quarks and leptons, started to freeze out later at reduced temperatures, well below, ~E16 Kelvin, or 1 TeV [24] [25] [26] [27]. According to the proposed model, the universe is born electrically and massively neutral because there are equal numbers of positive and negative masses, as well as positive and negative charges. In the Winterberg model, fermions, and interacting bosons are quasiparticles, i.e., collective excitations, which are stable and form within the two-component superfluid. See reference, [23], for specific details.
The outline of this paper is as follows. In section II, we formulate the Q theory, the assumption that Planck mass and Planck charge were created at the same time, as two components of the same particle. The temperature of formation could be at, ~E32 Kelvin, but also in the neighborhood of ~E21 -E22 Kelvin. Upon their creation, two force laws were formed simultaneously, and spontaneously, one electrostatic, and one seemingly gravistatic. In fact, both will be shown to be electrostatic in origin, in Section III.
In Section III, we show that the gravitational force is electrostatic in origin.
We derive an expression for the Planckion spring constant. Then we proceed to find the number density of planckions, and nearest neighbor distance of separation, using box quantization. In Section IV, we calculate individual displacements for various gravitational pressure fields. We show how gravitational potential, and gravitational pressure, within the vacuum are related. We also talk about latent gravitational field energy and vacuum resiliency. When the vacuum is mechanically stressed through very intense gravitational fields, it may have its limits. Gravitic breakdown is a possibility. The Winterberg vacuum is mechanistic in its very structure. In Section V, the present day imbalance in planckion number density is discussed. Because there is net mass in the universe, there is also, a net cosmic gravitational field mass density by Gauss's law. That will result in a net planckion mass density, which is unequal to zero. The reason why the planckion number densities are mismatched, n n + − > , in the current era is unknown, but we speculate it may have something to do with macroscopic mass formation. Our summary and conclusion are presented in Section VI.

The Q Theory
We start by noting that Planck mass, Pl m , is related to Planck charge, Pl q , by the following relation.  We next multiply Equation (2-1), by 1/r 2 . This, will stand for the distance of separation between two Planck mass particles, which is the same distance as between the two Planck charge particles. Because they are one and the same particle by our hypothesis, we have two separate forces coming into being at the same time, as two separate force magnitudes are formed.  Gm r , will be attractive, and the other, 2 2 Pl kq r , repulsive, when acting on an individual Planck particle, or planckion. From Equation , it follows namely that, The unit vector, î , points from one mass to the other. In Equation ( We interpret Pl q as the naked charge of an electron or a proton, whereas "e" is the dressed charge, which takes into account the electrostatic polarization of space surrounding the naked charge [28]. Due to the screening in electrostatics, the polarization cloud will lower the original naked charge by a factor, (1/137) 1/2 .
The elementary unit of charge is what is measured and not the naked charge. We expect the same in gravistatics. The, Pl m , will not be measured directly, but rather a dressed version, taking the gravistatic polarization cloud into account. In contrast to electrostatics where we have screening, in gravistatics, we have anti-screening. This should serve to enhance, i.e., increase the naked mass. The dressed mass will be heavier than the naked Planck mass, a prediction.
It was stated that positive and negative mass planckions want to maintain a fixed distance of separation from one another. When displaced from equilibrium, the planckions will experience a restoring force wanting to bring them back to their original configuration. For a positive and negative mass planckion, those forces are [11], respectively, The, κ κ κ + − = = , is the planckion spring constant, which is assumed the same for both positive and negative mass particle. The, +κ, on the right hand side of Equation (2-6b), is needed for a bounded solution. Choosing a negative spring constant on the right hand side would give us a hyperbolic sinusoidal solution, which is unbounded. The, x, here, refers to the displacement from equilibrium, either positive or negative, along a particular direction. If planckion particles get too close to other particles of the same species, then there will be repulsion. If they stray too from each other, then there will be attraction. In this way equilibrium is maintained within the fluid, where the individual planckions are, more or less, anchored in position.
As was demonstrated by Winterberg, the collective fluid force acting on a positive mass planckion is, This is due to the other positive mass planckion particles within the fluid. In Equation ( We notice that p − is inherently negative. The mass density, , is also inherently negative. Note that in Equation (2-10), the negative mass particle is taking the path of steepest ascent, because we are taking the positive gradient. Think of a negative mass particle in the earth's gravitational field… it would accelerate upwards when released. This is in contrast to Equation (2-7), where we are looking at the path of steepest descent, i.e., negative the gradient, for a positive mass particle.
In one dimension, Equation (2-10), reduces to ( ) See Equation (2-6b). We have set the left hand side equal to, x κ + , because this is a restoring force for the negative mass planckion. The solution to Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11), is found by integration. The result gives, This Gaussian looking function indicates a peak at, 0 x = , versus a trough, as in Equation (2-9). A peak for a negative mass particle is equivalent to a "hole", for a positive mass particle. In other words, a negative mass planckion will move in such a way, as to increase its planckion pressure. Think of a negative mass particle in the earth's gravitational field. When released it would accelerate upwards at, 9.81 m/s 2 , increasing its gravitational pressure. At, 0 x = , in Equation (2-12), we have maximum pressure for a negative mass planckion. Any positive or negative displacement from this equilibrium position, will lead to restoring forces tending to bring the negative mass particle back to, 0 x = .
The total planckion pressure, p, due to positive and negative Planck particles,  where, 1 w = + , in all instances. Therefore, by Equation (2-13), we may also write, In a gravitational field, the two component superfluid will no longer be undis-  , as will be shown shortly. Then we have a net planckion pressure, and a net planckion mass density, which is now unequal to zero. A net planckion mass density and pressure for the vacuum is a new prediction of Winterberg's theory.
In the present epoch, the gravitational permittivity, The relative permittivity, K, is a bit tricky.
It is determined from the gravitational susceptibility, through the relation, 1 K χ = − . The gravitational susceptibility has been found for the cosmos as a whole, as a smeared quantity [11]. However, its value locally depends on many factors such as the localized gravitational dipole moment, local gravitational field, and local ambient temperature [12]. It varies from place to place in the universe.

Determination of Planckion Number Density, Nearest Neighbor Distance of Separation, and Planckion Spring Constant
We next want to establish a connection between the planckion spring constant, κ, which holds for both species of Planck particle, and, , the undisturbed positive and negative mass planckion number density. As shown previously in section II, a positive mass planckion will simultaneously attract and repel another positive mass planckion through gravitational and electrostatic forces. The same will hold true for negative mass planckions. In short they strive to maintain a fixed distance of separation from one another. Unlike mass planckions really do not interact directly [11] [23]. Instead they interact indirectly by being forced close to one another by their respective fluid forces.
Consider a string of positively charged planckions, all in a row, along the x-axis, and label them, #1, #2, #3, etc. Due to the symmetry, forces in the, y, and, z, direction cancel, and we are concerned only with forces in the x-direction.
Focus on particle, #3, and sum up the forces acting on that particle, when that 3 rd C. Pilot Journal of High Energy Physics, Gravitation and Cosmology particle is displaced a distance, x, to the right. We claimed previously, that displacing this planckion will cause a restoring force in the amount, In the last line, we used Equation (2-1). The force that particle, #4, exerts on particle, #3, which is, 43x F , is pointing to the left, and hence the negative sign in Equation (3-1). The force that particle, #2, exerts on particle, #3, which is, 23x F , is pointing to the right, and hence the positive sign associated with this force in Next, we recognize that, for any arbitrary, "b", and, "β" values, the following identity holds, This can be proven algebraically. We set, In Equation (3)(4), we first factor out the, β − , term on both left and right hand sides. Then we bring the, l + , term from the left hand side over to the right hand side, and make use of Equation , to simplify. The result, after pulling out a factor of 4, is, Equation ( The infinite series within Equation (3)(4)(5)(6), is a known series, ( ) ( ) Here, ζ , is the Riemann Zeta function [29] [30], and ( ) , in Equation (3)(4)(5), the infinite series within that expression on the right hand side, must equal, ( ) 3 ζ . The arguments above for a positive mass/charge planckion particle also hold for a negative mass/charge planckion particle. Some of the signs change, but the outcome is the same. The negative mass planckions are also held in check by what are, essentially, electrostatic forces.
We still have to determine the planckion number density, spatially anchored or locked in position. Hence they are confined to a region of space where box quantization must apply. They are also oscillating, i.e., continuously accelerating, which produces gravitational radiation. Because they are "boxed in", and radiating, the energy of the radiation emitted must be related to the energy level jumps, or transitions, permissible within that box. Much like the Bohr atom for Hydrogen, energy level transitions account for the radiation frequency emitted. The situation here is totally analogous.
To see this more clearly, we consider the energy levels for a particle trapped in a 3-dimensional cubic box, having volume, L 3 . These are well known to be quan- The unprimed quantum numbers refer to the situation before, and the primed quantum numbers correspond to the situation after the transition. This is completely analogous to the situation in the Hydrogen atom, where we have the Lyman series, the Balmer series, the Paschen series, etc.

C. Pilot
The most probable transition is the most frequent one, and there, This is already obvious from the few examples of energy levels given. The energy being emitted is determined by the Planck radiator formula, Here, ν, is the frequency of the photon being emitted, and T is the blackbody CBR temperature. The, k B , is Boltzmann's constant. Nowhere in this formula, is mass, or charge, explicitly stated. We interpret this to mean that any quantum radiator will emit this amount of energy irrespective of whether it is mass or charge which is oscillating. In our case, it is both, due to the Q hypothesis. We will consider quantum radiators due to planckions at CBR temperature. In the present epoch, The oscillating and continuously accelerating positive mass/charge planckion acts as a radiator, and at a CBR temperature of 2.725 Kelvin emits this specific frequency as its peak frequency. In reality a whole spectrum of frequencies are being emitted as an infinite number of quantum transitions are possible. See Equation (3)(4)(5)(6)(7)(8)(9)(10)(11). We singled out one particular frequency, the most probable.
Equation (3)(4)(5)(6)(7)(8)(9), is explicitly mass dependent. If the mass of the positive mass planckion changes, due to a change in G value, this will affect the energy levels, and the transitions which are possible. Lower mass means higher energy levels for the same quantum numbers according to Equation (3)(4)(5)(6)(7)(8)(9). This means that, in general, larger frequencies will be emitted. But this is exactly what we expect at higher CBR temperature. The frequencies being emitted, in general, will also change as a consequence, being shifted towards higher values. They are still quantized, but will take on different values.
What about the negative mass planckions? For a negative mass, such as a negative mass planckion, the energy levels are inherently negative, by Equation (3-9), as measured from the top down. We have inverted box quantization, where instead of a potential energy square well, we have the mirror image, an upright potential energy square well. This upright well is populated with energy levels, according to Equation (3)(4)(5)(6)(7)(8)(9), taken from the top down. The largest energy level jumps are near the top. The highest level in this inverted potential energy well is the "ground state". And negative mass particles will want to transition to this highest energy level. Equation (3)(4)(5)(6)(7)(8)(9)(10)(11), is still valid. But instead of going from less negative energy to more negative energy, which is the case for a positive mass C. Pilot particle, we will be transitioning from positive energy levels to higher positive energy levels for a negative mass particle. By transitioning upwards, a negative mass planckion actually lowers its binding energy. Due to the symmetry of the energy levels between positive and negative planckions, the most probable transition here, also, releases, The dimensions of the cubic box, just so happen to equal the distance of separation between nearest neighbor positive, and negative, mass planckions. The only difference is that the geometric center of the box is centered around the positive or negative mass planckion.
One will notice that our nearest neighbor inter-planckion separation distance, within a specific species, is very close to the limits what modern day accelerators are able to probe. The diameter of a quark is about, 8.60E−19 meters, and Equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16), is just a hair below that. The LHC at CERN produces 7 TeV protons whose Compton wavelength is 1.78E−19 meters. All these distances are comparable to the nearest neighbor inter-planckion separation distance. If our estimates are correct, we may be on the verge of establishing an inherent "graininess" for the vacuum.
Having determined the nearest neighbor separation distance, we proceed to find the average number density for both the positive and the negative mass planckions, when the vacuum is in the undisturbed state. For this, we use Equations , and, (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16). Substituting Equation ( The number densities are, needless to say, very high. But now, we are attempting to find a graininess to the vacuum, or space, which many believe is smooth and continuous.
In this section, the spring constant was defined strictly in terms of electrostatic forces. See Equation , which is entirely electrostatic in origin. In the previous section, κ was associated with the restoring force if either the gravitational force or the electrostatic force got the upper hand. For equilibrium, the electrostatic force of repulsion counteracted the gravitational force of attraction between two like mass planckion particle. Realizing that we are dealing with the same κ, it should be recognized that the gravitational force is really electrostatic in nature.
We can look more carefully at the sum given in Equation . All the negative sign contributions pull the #3 particle to the left. All the positive sign contributions pull planckion particle #3 to the right. If, 0 x = , then there is no displacement and particle #3 is in equilibrium. In other words, both the individual forces pulling to the left and the individual forces pushing to the right add up to zero. We can identify the gravitational force with the sum of either one of these net forces, pushing or pulling. The electrostatic force would then be identified with the counteracting force. In short, the force of gravity is really electrostatic in origin within the Q theory. When the planckions were first created two force magnitudes were simultaneously created. But one counteracted the other, and being an attractive force between two masses was treated as a gravitational force.
The gravitational force has evolved with cosmological time through a varying G value, whereas the electrostatic force has not. That is our hypothesis.

7.566E 48 meters
This is an incredibly small displacement. However, we keep in mind that space is very, very dilute, only about 6 hydrogen atoms per cubic meter. Due to this dilution, there is hardly any displacement. In the true voids, where there is no source matter, we would expect zero gravitational field displacement. Also keep in mind that the maximum displacement seems to be in the neighborhood of about, 5E−19 meters, as is indicated by Equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16). Another example might be the gravitational field of the earth. On the surface of the earth, the source gravitational field is, 9.81 m/s 2 . The relative permittivity, K, is essentially one because, as far as we are able to determine, there is virtually no vacuum susceptibility on the surface of the earth, if we take this surface to equal our Gaussian surface. There is virtually no polarized mass enclosed within this surface. For that we have to have a substantial vacuum or "empty" space, which doesn't exist close to the earth. We calculate, gg ρ , using Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16), and find ( ) The gravitational permittivity equals, Following the same steps as before, but now using the new gravitational field mass density, indicated by Equation (4-8), we find for the new gravitational displacement, Compared to the value in Equation (2)(3)(4)(5)(6), this is about 10 orders of magnitude larger. However, it is still extremely small in value. We next look at the gravitational potential and its relation to the gravitational pressure. We designate the gravitational potential by, , because it is really a difference in gravitational voltage that we are considering. The subscripts indicate that this difference in voltage is due to gravitational fields.
Some numerical examples are as follows. For the cosmos as a whole, the average displacement of planckions within the vacuum, due to the presence of source and bound mass, is specified by Equation (4-7). Here, Equation (4-13), gives On the surface of the earth, we have a difference displacement, indicated by Equation (4)(5)(6)(7)(8)(9). This leads to a different gravitational potential in the amount, Note that the units for gravitational potential are the same units as, c 2 .
The general relation between gravitational pressure, and gravitational potential, is considered next. Start with Equations (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19), and, (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), and recognize that, Here, we see a direct proportion between gravitational pressure and gravitational potential. The mass of the planckion, and planckion number density are also important. Incidentally, planckion pressure and gravitational field energy density, gg u , are equal to one another, since We already identified, gg ρ , with dark energy [11]. See also Equations (2-16), C. Pilot Journal of High Energy Physics, Gravitation and Cosmology and, . Gravitational pressure, gravitational field mass density, which is the same as planckion mass density, and dark energy, are all synonymous with one another. Equations (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), and (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), are another way to find gravitational potential, . They will of course give the same results as before. We close this section with some thoughts on the magnitude of the gravitational pressure here on the surface of the earth. As we saw, the mass density equaled the value indicated by Equation (4-8), namely, 6.373E−7 (MKS). This is much, much, less than the lightest gases found here on the earth's surface. We can multiply this by c 2 to obtain the gravitational pressure, or gravitational field energy density. The result is, 2 3 5.736E10 N m or J m gg gg This is a comparatively large value for pressure, or energy density. Atmospheric pressure, for example, equals, 1.013E5 N/m 2 . Why don't we feel this gravitational pressure? Why can't the energy in one cubic meter be released? In cosmology, the energy densities can be related to the stress-energy tensor. To release the energy trapped in a box, means we would have to alter the stress energy tensor. For that to happen, it takes a certain violent gravitational reaction, such as a supernova explosion, or a black hole merger. These are not the conditions found here on earth. To give you an analogy, there is a lot of energy trapped within the nucleus. But only under certain circumstances can this be released, such as in a reactor, or in a bomb, or in a star. We believe something similar happens here. This is not energy trapped in matter, but energy stored, or trapped, within the vacuum, i.e., space itself. It cannot be released without altering the gravitational field itself. If there is no gravitational field, then there is no gravitational pressure, nor is there a gravitational field energy density. We would have to alter the, 9.81 m/s 2 , here on earth, in order to tap into this energy, or release the gravitational pressure associated with this slightly gravitationally stressed vacuum. If we could eliminate the 9.81 m/s 2 in a box, one cubic meter in size, here on earth, we would liberate, 5.736E10 Joules, according to Equation (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). We can refer to this energy as latent gravitational energy.
This brings us to mechanical resiliency. Wherever there is a gravitational field, the vacuum is stressed, i.e., the individual planckions making up the vacuum are displaced from equilibrium. Our vacuum is very much mechanical in origin. In material science, resilience is the ability of a material to absorb energy when it is deformed elastically. Once the stress is released, the elastic energy goes away upon unloading. This describes the vacuum particularly well to our thinking. Resilience, or mechanical energy storage capacity, can be defined for the vacuum, and is measured in units of, N/m 2 , or J/m 3 . The maximum resilience of space seems to be in the neighborhood of about, 8.66E33 J/m 3 , to about, 1.54E34 J/m 3 . The first value holds on the surface of a four solar mass black hole, where the gravitational field is particularly strong, about, 3.81E12 m/s 2 . The second value is the gravitational field energy density for a three solar mass black hole, where the gravitational field is even stronger, approximately, 5.08E12 m/s 2 . No black holes have been found in nature having a mass less than three solar masses. The cutoff between neutron stars and black holes seems to lie in the neighborhood between three to four solar masses. Neutron stars can have gravitational fields as high as roughly, ~2E12 m/s 2 , once newly formed. So the gravitational fields above seem to fit the scheme. Now it is known, that next to a black hole, three-dimensional space will develop a rip or a tear in the space-time continuum according to the general theory of relativity. In other words, three-dimensional space starts to break down. This would be our version of "gravitic breakdown". Just like there is dielectric breakdown when the electric fields get too strong for the medium, we can expect that gravitationally, something similar happens. The gravitational fields listed above must be close to those limits. It should have been mentioned that the smallest mass black holes have the largest gravitational fields, due to the Schwarzschild condition. So the above gravitational fields are probably the strongest macroscopic gravitational fields known to science.
For the earth, the numbers are drastically reduced because the surface gravitational field is so much less. We still use Equation , but now the mass density is given by Equation (4)(5)(6)(7)(8). Substituting this value into Equation , and carrying through the calculation, gives ( ) ( ) 3

m n x n x
This is a very interesting result. The imbalance only amounts to approximately 29 more positive mass planckions than negative mass planckions in one cubic meter.

C. Pilot
Next we look at the cosmos. There we also have a net macroscopic gravitational field due to the ordinary and polarized matter, which is contained within it. This gravitational field is a smeared average, valid only for distance scales in excess of about, 100 Mpc. Only then is the cosmos fairly homogeneous, and isotropic. The appropriate gravitational field mass density is specified by Equation (4-2). We substitute this value into Equation , and find, Why the universe has a net positive mass is unknown. The result in Equation (5)(6)(7)(8), may suggest that, when planckions were first formed, there was an excess of positive mass planckions over negative mass planckions. But this would go counter to the Q theory, because as planckion mass was created, so too was planckion charge. And, as far as we can tell, the universe has zero net charge.
Somehow between then, when planckions were first created, and now, the imbalance must have formed. And it probably had something to do with the formation of quarks and leptons. Why and how negative mass planckions were used up in this process is unclear.
We close with a quick calculation for the imbalance in terms of absolute planckion numbers. If the Hubble radius in the present epoch is, 0 R , then,  , we have used Equation (5)(6)(7)(8). And for the radius of the observable universe, 0 R , we took this to equal, 0 3.215E27 meters R = , a value found in reference, [11]. The, , is the present day difference in planckion numbers, with the positive mass planckions being more plentiful than negative mass planckions. This excess, while it appears large, is only an insignificant amount when compared to total planckion numbers. Using Equations (3-17a), or, (3-17b), and Equation (5-8), we see that ( ) 0 7.09E 74 n n n This fraction is very minute.

Summary and Conclusions
We introduced a model where Planck mass and Planck charge were frozen out of the vacuum simultaneously. We treated mass and charge as two components of a more fundamental particle, the planckion. Based on previous and extensive work by Winterberg, the vacuum is a vast assembly (sea) of positive and negative mass planckions, which form a two-component superfluid and fill all of space.
Finally, in section V, we considered the imbalance in planckion mass density between positive and negative mass planckions. Because there is ordinary mass in the universe, a given, and polarized mass in the cosmos, an assumption, we have a net smeared gravitational field which does not vanish for the cosmos as a whole. By Equations , and, (5)(6)(7)(8), this forces us to accept that, in the present epoch, the average positive planckion number density exceeds the average negative mass planckion number density, n n + − > . There are more positive mass planckions per unit volume than negative. The exact amount has been calculated in Equation (5)(6)(7)(8). The reason for this is unclear, although it may have something to do with ordinary matter, made up of quarks and leptons, being formed in the universe. When planckions were first created in the very early universe, there were equal numbers according to the Q-theory.
There is also the intriguing possibility, although not very likely, that there are regions in the universe where planckion mass density, or dark energy, is negative.
This would balance the total number densities between positive and negative mass planckions, then, in the early universe, as well as now, in the present epoch.
There is, however, no direct observational evidence for this, i.e., negative dark energy does not appear to exist. As such, we are left with Equation (5-8), which shows a net imbalance.
Q-theory explains charge and mass neutrality in the early universe, but it does not explain quasiparticle formation, collective excitations in the Winterberg model. Nor does it explain positive planckion density imbalance over negative planckion density, in the present epoch. Q theory can, however, provide a connection between gravistatic and electrostatic force laws. In the very early universe these were formed simultaneously. The gravistatic force of attraction, upon closer inspection, turned out to be electrostatic in origin.
Work is in progress on a microscopic theory of planckions, which would include scaling behavior upon expansion of the universe.