Is the Higgs Field a Positive and Negative Mass Planckion Condensate, and Does the LHC Produce Extreme Dark Energy?

Assuming a two-component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of, an undisturbed (unperturbed) vacuum. Thus we assume a lattice structure for space, made up of overlapping positive and negative mass wave functions, ψ + , and, ψ − , which together bind to form the Higgs field, giving it its rest mass of 125.35 Gev/c 2 with a coherence length equal to its Compton wavelength. If the vacuum experiences an extreme disturbance, such as in a LHC pp collision, it is conjectured that severe dark energy results, on a localized level, with a partial disintegration of the Higgs force field in the surrounding space. The Higgs boson as a quantum excitation in this field results when the vacuum reestablishes itself, within 10 −22 seconds, with positive and negative planckion mass number densities equalizing in the disturbed region. Using our fundamental equation relating the Higgs field, ϕ , to the planckion ψ + and ψ − wave functions, we calculate the overall vacuum pressure (equal to vacuum energy density), as well as typical ψ + and ψ − displacements from equilibrium within the vacuum.

cuum. Thus we assume a lattice structure for space, made up of overlapping positive and negative mass wave functions, ψ + , and, ψ − , which together bind to form the Higgs field, giving it its rest mass of 125.35 Gev/c 2 with a coherence length equal to its Compton wavelength. If the vacuum experiences an extreme disturbance, such as in a LHC pp collision, it is conjectured that severe dark energy results, on a localized level, with a partial disintegration of the Higgs force field in the surrounding space. The Higgs boson as a quantum excitation in this field results when the vacuum reestablishes itself, within 10 −22 seconds, with positive and negative planckion mass number densities equalizing in the disturbed region. Using our fundamental equation relating passing, and very mechanistic, theory. The fundamental symmetry of nature, he claims, is not relativistic, SO(1,3) Lorentz invariance, or extensions thereof, but rather the simpler, non-relativistic, SO(3)~SU (2), which our three dimensional space reflects. Lorentz invariance in his model is a dynamical symmetry, which nature mimics. His theory was presented as an alternative to string theory.
Finally, if we go back even further, Heisenberg, in his non-linear spinor theory [19]- [27], attempted nothing less, starting already back in the 1930's, and continuing on into the 1950's and 1960's. He introduced a fundamental length scale for space itself, and even proposed, initially, a lattice like structure for the vacuum, which was estimated to lie somewhere beyond, 10 −15 meters. Below this distance scale, it was argued that there is a veritable "explosion" in the production of all types of "elementary particles", few of which are now regarded as "elementary". His work was largely ignored and sidelined. Only, recently, in string theory and quantum loop gravity, have some of his ideas been partially resurrected, albeit in a much different guise. Some excellent review articles are given in references [28] [29].
In this work, we will attempt to make sense of, and connect all of these seemingly disparate ideas. Our contention is that Heisenberg, and Winterberg, are fundamentally correct in their interpretation of the vacuum having an intrinsic length scale, for the renormalizability of quantum field theories, to avoid singularities, and to prevent the divergences associated with the zero-point vacuum energy [15]. Interestingly, Winterberg studied under Heisenberg, and earned his PhD under his guidance. It is therefore perhaps no accident that they thought similarly in many respects. We believe that space has a lattice like structure, and moreover, that it is responsible for dark matter and dark energy [16] [17] [18], as well as ultimately, quantum mechanical entanglement (to be proven). Winterberg believes that the length scale for the vacuum is of the order of the Planck length, about, 10 −35 meters. Heisenberg, and others, believed it was much, much greater, about, 10 −15 meters, or smaller. We conjecture, based on previous work [18], that it lies in the neighborhood of about, 5.032E−19 meters, and will make heavy use of this result in this paper.
Extended gravity models are, of course, not new. While Einstein's general theory of relativity has been remarkably successful in predicting gravitational phenomena, finding a quantum theory of gravity has eluded many researchers.
Most tests of the general theory of relativity (GTR), and extensions thereof, have focused on studying astrophysical phenomena, and looking for deviations from the GTR. These would include gravitational wave phenomena, as detailed, for example, in reference [30]. This work is somewhat unique is that we are looking for microscopic, i.e., subatomic tests (signatures), to prove, or disprove the general theory of relativity.
The goal of the present work is to establish a connection between the planckions of Winterberg, and the Higgs field in the standard model of high energy physics, and show that the Higgs field really represents the vacuum made up of positive and negative mass planckion pairs. Our ansatz, or working assumption, is that one Higgs field is the equivalent of one positive and one negative mass, planckion pair, bound together through lattice like forces acting on the separate species individually. Because of these fluid forces, the positive mass planckions are forced to rub shoulders, spatially, with the negative mass planckions, and form a quasi, semi-bound state. Disrupting the vacuum means disturbing the Higgs fields. We also wish to make credible the idea that the LHC is really producing extreme dark energy, and disrupting some of these, ψ ± , bound states, temporarily, destroying the super-lattice structure for a small subset of the excited Higgs fields. When the vacuum re-establishes itself, within 10 −22 seconds, the Higgs boson is being produced. With the LHC, we may actually be probing and exploring the granular, lattice-like structure of space itself. This is our thought.
The outline of the paper is as follows. In section II we consider the Higgs sector. We believe it to be a phenomenological artifact of space, displaying ( ) 1,3 SO invariance as a dynamical, but not as a fundamental, symmetry of nature. In section III we posit the fundamental relation relating the Higgs field, ϕ , to a ψ + and ψ − , planckion pair. We show that, with this particular identification or assignment, the equations of motion for both the positive mass planckion, ψ + , the negative mass planckion, ψ − , and the Higgs field, ϕ , are satisfied. We also derive the continuity equations, connecting the two theories. In section IV, we use our, ϕ , and ψ + with ψ − , connecting ansatz, to explain what transpires in a LHC, pp collision from the viewpoint of the vacuum. This will be highly speculative interpretation, but numerical results are calculated, including increased vacuum pressure, and average, root mean square, planckion displacements from equilibrium within the vacuum. Finally, in section V, we summarize our results and present our conclusions.

The Higgs Sector
We start with the nonlinear, relativistic Higgs field equation, In this equation, the Higgs self-coupling strength, 0 λ > , and µ is defined as, m c ϕ µ ≡ , with m ϕ equal to the mass of the Higgs boson. To make a connection to the standard model in particle physics, ϕ , is, in reality, a SU (2) complex, doublet of the form, Upon symmetry breaking (electro-weak → electromagnetism + weak interaction), this reduces to, We will ignore the complexities associated with the complex, doublet structure as this will not be relevant for our discussion. Nor will we consider the specifics of spontaneous symmetry breaking, per se.
Experimentally, the self-coupling strength has been determined to equal, 0.260 λ = , and the mass of the Higgs is found to equal, 2 25 125. 35  174 GeV, is known as the electro-weak symmetry breaking scale. In actual, non-reduced units, The, µ , in Equation (2-1), can be evaluated; its value is The coherence length, ξ , for the Higgs field is its Compton wavelength, and represents the scattering size of the Higgs boson, given a Yukawa like potential. It is equal to, 1 µ − , and numerically, The numerical values are given to establish a connection with the standard model of particle physics.
The Winterberg model assumes that, ϕ , is, in reality, exactly nonrelativistic.
Making the transition to the non-relativistic limit, we must set [15], Then Equation ( We emphasize that Equation ( is the potential energy term. All are operators, which act on, ϕ . The relativistic theory, given by Equation , is assumed to be an asymptotic, phenomenological limit, derivable from the non-relativistic version, Equation (2)(3)(4)(5)(6)(7)(8). Lorentz invariance is assumed to be a dynamical, and not fundamental symmetry of nature. Equation (2-10), will be important when we make the identification of, ϕ , with a planckion positive mass wave function, ψ + , coupled with a planckion negative mass wave function, ψ − . The pair will form a quasi-bound state which we identify with a Higgs field.

Planckion Wave Functions and a Possible Connection with the Higgs Field
Planckion wave functions permeate all of space, and, in fact, our contention is that they make up a superfluid/supersolid lattice we call space. The vacuum as exemplified by the Higgs fields, we believe, is really made up of disguised, ψ + , and, ψ − condensate, planckion pairs. In this section, we discuss planckion wave functions, their equations of motion, SU(2) symmetry, and the lattice structure of space. We also relate the Higgs field, ϕ , to, ψ + , and, ψ − , by positing a very specific relation between them. According to Winterberg, the positive and negative mass, planckion, wave functions, obey the following operator equations [15], In this equation, , is the Planck mass, and, , is the Planck length. The potential energy operator in Equation , is given by, The potential energy, ( ) U ψ ± , acts on the positive and negative mass wave functions, ψ ± , respectively. The individual wave functions obey the canonical commutation relations Equation (3-1), can be derived from a non-relativistic Lagrange density of the form, The dot over the, ψ ± , signifies a derivative with respect to time. It will be noticed that Equation , has the form of a non-relativistic version of Heisenberg's non-linear spinor field theory equation [19]- [27], one of the earliest attempts at a "theory of everything". The interaction term, Uψ ± , the second term on the right hand side in Equation , involves an inherent length scale, PL l , a kind of coupling constant having inherent dimension. In contrast to Heisenberg's relativistic spinor theory, however, Equation (3-1), is non-relativistic. As pointed out by Winterberg, the Hilbert space derived by Equation (3-1), is therefore always positive definite. We believe that the length scale, Then, by adding the potential energy of, ψ + with that of, ψ − , we obtain, versus two times the right hand side if we were to use Equation . This seems much cleaner and less redundant. It was argued extensively in previous work by Winterberg that, ψ + , and, ψ − , do not interact directly, but rather indirectly, through fluid forces acting on each species separately. Equations (3)(4)(5) and (3)(4)(5)(6), fit that state of affairs precisely whereas Equation (3-1), does not. Notice that, ( ) 2 0 l ± , has replaced, 2 PL l , in both Equations (3)(4)(5) and (3)(4)(5)(6). Moreover, the right hand of Equation (3)(4)(5)(6) , represents the probability of finding the planckion fields, ψ ± , within volume 3 d x . Both ψ ± have canonical dimension, 3 2 L − , where, L, stands for length (or inverse momentum). Moreover, the respective, positive and negative mass, planckion number densities are defined by, These quantities tell us how many positive and negative mass planckions are contained within one cubic meter, centered around space-time point, ( ) , x t . Unless otherwise stated, MKS units are utilized throughout the paper.
The continuity equation reads, In this equation, v ± , is the velocity of, n ± , respectively. Equation (3)(4)(5)(6)(7)(8), is sa-C. Pilot Journal of High Energy Physics, Gravitation and Cosmology tisfied, provided the ψ ± planckion currents are defined as, We note that the particle number operator, satisfies the commutation relation, where, H, is the Hamiltonian operator. Also, The dot over a variable denotes a derivative with respect to time, i.e., Finally, Equation (3-1), and the simplified version, Equation (3)(4)(5), when both the positive and the negative mass planckions are included as a pair, are invariant under the following Invariance under the Lorentz group has to be derived dynamically, and is not an inherent symmetry of either Equation (3)(4)(5) or (3)(4)(5)(6).
This gives, Using Equations (2-8), (3-1), and , this simplifies. After some remarkable cancellations, we obtain, where the connecting length scale, Λ , between, ϕ , and, ψ ± , is defined as, This length scale connects the Higgs mass, with the nearest neighbor distance of separation, between either positive mass, or negative mass, planckions, within C. Pilot the lattice.
We next implement the mathematical identity, on both the left and right hand side of Equation . This renders, Now, using Equation (3)(4)(5)(6)(7)(8)(9), the right hand side reduces to, Notice that the mass, PL m , has factored out. Similarly, the left hand side, becomes, The Higgs current, j , has been defined as, where, † n ϕ ϕ ϕ ≡ , is the Higgs number density. The mass, m ϕ , also factors out in deriving expression, . We therefore obtain for Equation , after substitution of expressions , for the right hand side, and , for the left hand side, Or, using the continuity equation for, ϕ , as well as for, ψ + , and, We close this section with the following very important observation. If space has a natural cutoff in length, as indicated by, ( ) 0 l ± , then the Planck mass, the Planck energy, the Planck temperature, etc. all have to be modified in value. Take the Planck mass for example. We know that, by definition, PL m c G ≡ , and, , is the modified Planck length. This is precisely the term that sits in front of the second term in Equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22), and is our version of the Planck mass in Equations (3-1) and (3)(4)(5). The, MPL m , should also be substituted in place of, PL m , in Equations, (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) To take this a step further, for elementary particles to form in the Winterberg model, we need vortices set up within the vacuum. An elementary particle is just that, a stable vortex, where the kinetic energy of this excitation gives the elementary particle its mass, and the direction of motion, its spin. An unstable vortex reflects an unstable particle. At energies approaching Equation (3-38a), the vacuum loses its superfluid properties and the vortices can no longer sustain themselves. In other words, we enter another phase for the vacuum, where super-solidity is completely lost. Perhaps we have indeed reached an energetic limit for the production of elementary particles at a scale approaching approximately, 392.9 GeV. This is an interesting prediction of the model we are presenting. Perhaps there is no desert region in particle physics between roughly,

Application
In this section, we consider a specific application of our fundamental Equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), or equivalently, Equation . We consider the case of a pp collision such as is found in the LHC experiments at CERN. What happens within the vacuum, and what physical quantities can be determined? These results are highly speculative. Nevertheless, specific values for measurable quantities can be determined.
It has been estimated [35] [36] that the energy density reached in the latest series of LHC collider experiments, where pp annihilation takes place, is of the order of, The analysis presented here in this section, can be carried over into those realms as well.
We use Equation , to simplify Equation , and obtain, ( ) This small, but not insignificant fraction, tells us that only a tiny portion of the Higgs fields are actually excited, or activated, within volume, V ∆ .
We know the value for, 0 N N ∆ , as it is specified by Equation (4-6). Therefore we can find numerical values for the vacuum mass density, gg ρ′ , and the vacuum pressure, gg Using Equations (4-7) and (4-8), we find that, These values come as no surprise, as they reinforce our original assumption. They also hold only within the excited volume, V ∆ , and, moreover, they represent dark energy, according to previous work [16] [18]. We next want to find, V ∆ , the impacted volume. To determine, V ∆ , we first need the total number of collisions per second. According to the CERN documents, there are about 10 9 pp collisions per second, at the 6.5 TeV energy level [37]. And so, per second, we have an energy release of, 13E9 TeV. This energy is either given up in the production of new particles, or transmitted to the vacuum. Let's assume that all gets dissipated first within the vacuum, and from there, the production of elementary particles can occur. Then we can set, using Equations (4-9) and (4-10), and (4-15), we find that, 3 2.031E 32 m V ∆ = − (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) This is equivalent to a ball of radius, 1.693E−11 meters, being produced each and every second. The state of matter in that ball is, of course, in a state of a quark-gluon plasma. Alternatively, we could just as well have taken the total amount of energy being produced per second, which is, 13 E9 TeV, and divide that by 0.640 GeV/fm 3 , to obtain the same result.
We next want to calculate planckion displacements. For that, we will need some additional relations. From previous work [18], we have derived the equations, In Equation (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), the variable, y, is defined as, . It is the ratio of planckion elastic potential energy, to planckion rest mass energy. To be correct, we will replace the, 2 PL m c , above, by the modified Planck rest mass energy, indicated by Equation (3-38a). We modeled planckion displacements as a harmonic oscillator with spring constant, κ κ κ + − = = . When a positive mass, or a negative mass, planckion, is displaced a distance, from equilibrium, 0 x = , there are elastic restoring forces working to bring the planckion back to equilibrium position. The spring constant, κ , is assumed to be the same for both the positive, and the negative mass, planckion. The fluid forces of Winterberg are ultimately responsible for these restoring forces. We have to be careful with the, 2 PL m c , term; as, mentioned, it has to be replaced with the modified version, 2 MPL m c , Equation (3-38a), which we will do henceforth.
Another important note is the following. Many individual Higgs fields, or equivalently, positive and negative mass, planckion pairs are excited. The, 2 x , above, is some sort of root mean square average, i.e., ( ) We can substitute Equation (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17), into Equation . Doing this, we find that,   (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) This is a small fraction of the nearest neighbor distance of separation between either the positive mass, or, the negative mass, planckions, within the super-lattice in the undisturbed state. According to Equation (3-18a), that distance was estimated to equal, Again, in reality, a whole spectrum of individual displacements, { } i x , are possible for the individual, ψ ± , pairs, up to and even approaching the 13 TeV collision energy. However, the average root mean square displacement, rms x , is much, much less than that calculated if we had a single, 13 TeV exchange, as many, many planckion pairs are necessarily involved in displacements. The exact number is, 5.135E16 per second N ∆ = , as indicated by Equation (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15). We now wish to make a few important remarks. First, the 6.5 -6.5 TeV proton-antiproton collision produces a positive energy density in the amount of, 0.640 GeV/fm 3 . This will produce an excess of positive mass planckions, and a deficit of negative mass planckions, at the point of impact, x , as shown in reference [18]. The vacuum fluid thus acquires dark energy in the amount given above, at, and immediately surrounding, point x . In this region, which we can call region, A, we have, n n + − > , and, 2 0 n ∆ > . The positive mass planckions, which are drawn in, and the negative mass planckions, which are pushed out, must produce in the neighboring region, region, , a negative vacuum pressure hole. In the surrounding region, B, we must therefore have, n n + − < , and, 2 0 n ∆ < , forming a negative vacuum energy halo centered around the point of impact. The energy produced by the collision will quickly dissipate through the production of elementary particles, or through the vacuum wave propagating outwards. In other words, the vacuum will quickly reestablish itself to normal conditions where, n n + − = , and, 2 0 n ∆ =, in all regions. This, we believe, happens almost instantaneously, within about, 10 −22 seconds. It is within this time frame that the Higgs boson is thought to appear, when the vacuum reasserts itself, and falls back into its equilibrium position. This is the picture we imagine. The positive and negative, three-dimensional, vacuum energy density wavelet, produced by the collision quickly dissipates, and flattens out the vacuum to normal equilibrium conditions within short order.
Second, in the case of a LHC collision, extreme dark energy in region, A, and extreme light energy in region, B, is produced by the collision. As mentioned, this quickly dissipates. See Equation (4)(5)(6)(7)(8)(9)(10)(11)(12)(13), which holds for region, A. In region, B, we expect negative this amount within the vacuum. In region, B, we have extreme net negative vacuum pressure.
Third, in a previous paper [18], we conjectured that the vacuum has a maximum resilience of about, 1E34 J/m 3 . If the vacuum energy density exceeds this amount, then space itself may suffer "gravitic breakdown", the gravitational version of dielectric breakdown. There is now non-localized conduction of planckion currents, and space loses its lattice superstructure. We consider this next. Interestingly, for a 13 TeV pp collision, an energy density in the amount, 3 3 0.640 GeV fm 1.024E35 J m = , is being produced, and this pushes us beyond this limit. We will interpret this as a subset of the excited Higgs fields breaking their, ψ + , with ψ − , bond. Let, , refer to the number of excited Higgs fields, whose bonds remain intact, and let, , designate those excited Higgs fields where the ψ + , with ψ − , bond has been broken, within volume, V ∆ . Then, or, what is equivalent, It is specifically the, If condition (4-22a), is satisfied, then there is sufficient vacuum pressure such that the Higgs field has an effective mass greater than zero. In other words, there C. Pilot is effective binding. But if condition (4-22b), holds, then there is sufficient net negative vacuum pressure, in region, B, such that the Higgs field disintegrates, i.e., we have an effective mass less than zero. In other words, the ψ + wave function dissociates itself from the ψ − wave function, spatially. If any dissociation occurs, it is conjectured that the vacuum will reestablish itself very quickly, within the lifetime of the Higgs boson, about 10 −22 seconds.
As mentioned previously, we believe that the collection of individual vacuum activation variables, { } i y , may actually follow a Planck blackbody distribution function. When we have a severe proton-antiproton collision, the individual,
The Higgs particle is treated as a composite particle. Thus, it is a phenomenological construct, and one that can be shown to display symmetry is a dynamical, and not fundamental symmetry of nature. In the Winterberg model, the special theory of relativity, together with its generalization, the general theory of relativity, and quantum mechanics are two, separate, asymptotic limits C. Pilot of a more underlying theory, the planckion model. Because they are two separate branches, they can never be unified directly, but rather indirectly, through SO (3) symmetry, the symmetry of space and the vacuum.
An interesting consequence of introducing a fundamental length scale for space, is that the Planck mass, the Planck energy, the Planck temperature, etc. all assume new values. We called these values, the modified Planck values. Given the nearest neighbor distance of separation for an undisturbed vacuum, we estimated the new values are those given in Equations  and . The Planck scale is that scale where presumably, quantum mechanics, and gravity merge. So too is the case with the modified Planck scale. However, the modified value is much, much less, energy-wise, than the traditionally accepted Planck energy, 1 . See Equation . Within the Winterberg model, for the formation of elementary particles, stable vortices have to be set up within the vacuum. This is not possible above this cutoff energy level, 392.9 GeV MPL E = . See the discussion following Equation .
It was conjectured that if extreme negative vacuum pressure exists, then the Higgs field could disintegrate. In other words, the, ψ + no longer binds to the, ψ − . For that to happen, condition, , or equivalently, condition, (4-22b), has to be satisfied. For such instances where we have extreme net negative vacuum pressure, the Higgs loses its ability to maintain a mass, and hence, no spatial binding between the, ψ + , and the, ψ − , is feasible. It is thought that such conditions can actually occur in the vicinity surrounding a 13 TeV collision, in region, B, causing a temporary and highly localized subset of the excited Higgs fields to disintegrate. See the discussion surrounding Equations (4-21a,b) and (4-22a,b). The Higgs boson is thought to occur when the vacuum reestablishes itself, within a time frame of approximately, 10 −22 seconds. Any imbalance in positive and negative mass planckion number densities quickly rectifies itself.
We conclude that a 13 TeV pp collision may be strong enough to cause a subset of the excited Higgs particles to momentarily lose their binding energy. This paper is highly speculative, and much work remains to be done to prove our contention that a fundamental relationship exists between the Higgs particle, and the planckion, ψ + , with ψ − , wave functions. Higher accelerator energies would obviously lead to more excited Higgs fields, more partial Higgs field disintegrations within the vacuum, and a greater number of Higgs bosons being produced. Considering various energy level collisions might enable us to select the proper distribution function for, { } i y . The standard model of particle physics could be looked at from the perspective of replacing the Higgs particle with a positive, and a negative mass, planckion wave function. What, if anything, would change? How would the Yukawa coupling between the, ψ ± pair, and the fermionic matter fields play out? We could also look at replacing the 1 L − canonical Higgs field, with a 3 2 L − Higgs version, to make a connection with the Landau-Ginzburg theory in condensed matter physics. What would that imply?
How would things change continuity equation wise? Finally, we might consider what happens when an elementary particle such as an electron passes through the vacuum? How would the vacuum respond, and how specifically, is the mass for that particle created through its vortex structure. Can we establish a pattern between the different generations of elementary fermionic matter fields? These and other further questions will have to be addressed in future work.