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, <i>q<...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, <i>q<sub>pl</sub></i>, 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, <img src="Edit_770c2a48-039c-4cc9-8f66-406c0cfc565c.png" width="90" height="15" alt="" />, where <i>ζ</i>(3) equals Apery’s constant, 1.202 …, and, <i>n</i><sub>+</sub>(0)=<i>n</i>_(0), is the relaxed, <i>i.e.</i>, <img src="Edit_813d5a6f-b79a-49ba-bdf7-5042541b58a0.png" width="25" height="12" alt="" />, number density of the positive and negative mass planckions. In the present epoch, we estimate that, <i>n</i><sub>+</sub>(0) equals, 7.848E54 m<sup>-3</sup>, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, <i>l</i><sub>+</sub>(0)=<i>l</i><sub>_</sub>(0)=5.032E-19 meters. 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, <img src="Edit_efc8003d-5297-4345-adac-4ac95536934d.png" width="80" height="15" alt="" />, 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, <i>g</i>=9.81m/s<sup>2</sup>, 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.展开更多
A model is presented where the quintessence parameter, w, is related to a time-varying gravitational constant. Assuming a present value of w = -0.98 , we predict a current variation of ?/G = -0.06H0, a value within cu...A model is presented where the quintessence parameter, w, is related to a time-varying gravitational constant. Assuming a present value of w = -0.98 , we predict a current variation of ?/G = -0.06H0, a value within current observational bounds. H0 is Hubble’s parameter, G is Newton’s constant and ? is the derivative of G with respect to time. Thus, G has a cosmic origin, is decreasing with respect to cosmological time, and is proportional to H0, as originally proposed by the Dirac-Jordan hypothesis, albeit at a much slower rate. Within our model, we can explain the cosmological constant fine-tuning problem, the discrepancy between the present very weak value of the cosmological constant, and the much greater vacuum energy found in earlier epochs (we assume a connection exists). To formalize and solidify our model, we give two distinct parametrizations of G with respect to “a”, the cosmic scale parameter. We treat G-1 as an order parameter, which vanishes at high energies;at low temperatures, it reaches a saturation value, a value we are close to today. Our first parametrization for G-1 is motivated by a charging capacitor;the second treats G-1(a) by analogy to a magnetic response, i.e., as a Langevin function. Both parametrizations, even though very distinct, give a remarkably similar tracking behavior for w(a) , but not of the conventional form, w(a) = w0 + wa(1-a) , which can be thought of as only holding over a limited range in “a”. Interestingly, both parametrizations indicate the onset of G formation at a temperature of approximately 7×1021 degrees Kelvin, in contrast to the ΛCDM model where G is taken as a constant all the way back to the Planck temperature, 1.42×1032 degrees Kelvin. At the temperature of formation, we find that G has increased to roughly 4×1020 times its current value. For most of cosmic evolution, however, our variable G model gives results similar to the predictions of the ΛCDM model, except in the very early universe, as we shall demonstrate. In fact, in the limit where w approaches -1, the expression, ?/G , vanishes, and we are left with the concordance model. Within our framework, the emergence of dark energy over matter at a scale of a ≈ 0.5 is that point where G-1 increases noticeably to its current value, G0-1 . This weakening of G to its current value G0 is speculated as the true cause for the observed unanticipated acceleration of the universe.展开更多
This is the first paper in a two part series on black holes. In this work, we concern ourselves with the event horizon. A second follow-up paper will deal with its internal structure. We hypothesize that black holes a...This is the first paper in a two part series on black holes. In this work, we concern ourselves with the event horizon. A second follow-up paper will deal with its internal structure. We hypothesize that black holes are 4-dimensional spatial, steady state, self-contained spheres filled with black-body radiation. As such, the event horizon marks the boundary between two adjacent spaces, 4-D and 3-D, and there, we consider the radiative transfers involving black- body photons. We generalize the Stefan-Boltzmann law assuming that photons can transition between different dimensional spaces, and we can show how for a 3-D/4-D interface, one can only have zero, or net positive, transfer of radiative energy into the black hole. We find that we can predict the temperature just inside the event horizon, on the 4-D side, given the mass, or radius, of the black hole. For an isolated black hole with no radiative heat inflow, we will assume that the temperature, on the outside, is the CMB temperature, T2 = 2.725 K. We take into account the full complement of radiative energy, which for a black body will consist of internal energy density, radiative pressure, and entropy density. It is specifically the entropy density which is responsible for the heat flowing in. We also generalize the Young- Laplace equation for a 4-D/3-D interface. We derive an expression for the surface tension, and prove that it is necessarily positive, and finite, for a 4-D/3-D membrane. This is important as it will lead to an inherently positively curved object, which a black hole is. With this surface tension, we can determine the work needed to expand the black hole. We give two formulations, one involving the surface tension directly, and the other involving the coefficient of surface tension. Because two surfaces are expanding, the 4-D and the 3-D surfaces, there are two radiative contributions to the work done, one positive, which assists expansion. The other is negative, which will resist an increase in volume. The 4-D side promotes expansion whereas the 3-D side hinders it. At the surface itself, we also have gravity, which is the major contribution to the finite surface tension in almost all situations, which we calculate in the second paper. The surface tension depends not only on the size, or mass, of the black hole, but also on the outside surface temperature, quantities which are accessible observationally. Outside surface temperature will also determine inflow. Finally, we develop a “waterfall model” for a black hole, based on what happens at the event horizon. There we find a sharp discontinuity in temperature upon entering the event horizon, from the 3-D side. This is due to the increased surface area in 4-D space, AR(4) = 2π2R3, versus the 3-D surface area, AR(3) = 4πR2. This leads to much reduced radiative pressures, internal energy densities, and total energy densities just inside the event horizon. All quantities are explicitly calculated in terms of the outside surface temperature, and size of a black hole. Any net radiative heat inflow into the black hole, if it is non-zero, is restricted by the condition that, 0cdQ/dt FR(3), where, FR(3), is the 3-D radiative force applied to the event horizon, pushing it in. We argue throughout this paper that a 3-D/3-D interface would not have the same desirable characteristics as a 4-D/3-D interface. This includes allowing for only zero or net positive heat inflow into the black hole, an inherently positive finite radiative surface tension, much reduced temperatures just inside the event horizon, and limits on inflow.展开更多
A black hole is treated as a self-contained, steady state, spherically symmetric, 4-dimensional spatial ball filled with blackbody radiation, which is embedded in 3-D space. To model the interior distribution of radia...A black hole is treated as a self-contained, steady state, spherically symmetric, 4-dimensional spatial ball filled with blackbody radiation, which is embedded in 3-D space. To model the interior distribution of radiation, we invoke two stellar-like equations, generalized to 4-D space, and a probability distribution function (pdf) for the actual radiative mass distribution within its interior. For our purposes, we choose a truncated Gaussian distribution, although other pdf’s with support, r ∈[0, R], are possible. The variable, r = r(4), refers to the 4-D radius within the black hole. To fix the coefficients, (μ,σ), associated with this distribution, we choose the mode to equal zero, which will give maximum energy density at the center of the black hole. This fixes the parameter, μ = 0. Our black hole does not have a singularity at the center, and, moreover, it is well-behaved within its volume. The rip or tear in the space-time continuum occurs at the event horizon, as shown in a previous work, because it is there that we transition from 3-D space to 4-D space. For the shape parameter, σ , we make use of the temperature just inside the event horizon, which is determined by the mass, or radius, of the black hole. The amount of radiative heat inflow depends on mass, or radius, and temperature, T2 ≥ 2.275K , where, T2, is the temperature just outside the event horizon. Among the interesting consequences of this model is that the entropy, S(4), can be calculated as an extrinsic, versus intrinsic, variable, albeit in 4-D space. It is found that S(4) is much less than the comparable Bekenstein result. It also scales not as, R2 , where R is the radius of the black hole. Rather, it is given by an expression involving the lower incomplete gamma function, γ(s,x), and interestingly, scales with a more complicated function of radius. Thus, within our framework, the black hole is a highly-ordered state, in sharp contrast to current consensus. Moreover, the model-dependent gravitational “constant” in 4-D space, Gr(4), can be determined, and this will depend on radius. For the specific pdf chosen, Gr(4)Mr = 0.1c2(r4/σ2), where Mr is the enclosed radiative mass of the black hole, up to, and including, radius r. At the event horizon, where, r = R, this reduces to GR(4) = 0.2GR3/σ2, due to the Schwarzschild relation between mass and radius. The quantity, G, is Newton’s constant. There is a sharp discontinuity in gravitational strength at the 3-D/4-D interface, identified as the event horizon, which we show. The 3-D and 4-D gravitational potentials, however, can be made to match at the interface. This lines up with previous work done by the author where a discontinuity between 3-D and 4-D quantities is required in order to properly define a positive-definite radiative surface tension at the event horizon. We generalize Gauss’ law in 4-D space as this will enable us to find the strength of gravity at any radius within the spherically symmetric, 4-D black hole. For the pdf chosen, gr(4) = Gr(4)Mr/r3 = 0.1c2r/σ2, a remarkably simple and elegant result. Finally, we show that the work required to assemble the black hole against radiative pressure, which pushes out, is equal to, 0.1MRc2. This factor of 0.1 is specific to 4-D space.展开更多
This is a second follow up paper on a model, which treats the black hole as a 4-D spatial ball filled with blackbody radiation. For the interior radiative mass distribution, we employ a new type of truncated probabili...This is a second follow up paper on a model, which treats the black hole as a 4-D spatial ball filled with blackbody radiation. For the interior radiative mass distribution, we employ a new type of truncated probability distribution function, the exponential distribution. We find that this distribution comes closest to reproducing a singularity at the center, and yet it is finite at 4-D radius, . This distribution will give a constant gravitational acceleration for a test particle throughout the black hole, irrespective of radius. The 4-D gravitational acceleration is given by the expression, , where R is the radius of the black hole, MR is its mass, and is the exponential shape parameter, which depends only on the mass, or radius, of the black hole. We calculate the gravitational force, and the entropy within the black hole interior, as well as on its surface, identified as the event horizon, which separates 3-D from 4-D space. Similar to a truncated Gaussian distribution, the gravitational force increases discontinuously, and dramatically, upon entry into the 4-D black hole from the 3-D side. It is also radius dependent within the 4-D black hole. Moreover, the total entropy is shown to be much less than the Bekenstein result, similar to the truncated Gaussian. For the gravitational force, we obtain, , where Mr is the radiative mass enclosed within a 4-D volume of radius r. This unusual force law indicates that the gravitational force acting upon a layer of blackbody photons at radius r is strictly proportional to the enclosed radiative energy, MrC2, contained within that radius, with 0.1λ being the constant of proportionality. For the entropy at radius, r, and on the surface, we obtain an expression which is order of magnitude comparable to the truncated Normal distribution. Tables are presented for three black holes, one having a mass equal to that of the sun. The other two have masses, which are ten times that of the sun, and 106 solar masses. The corresponding parameters are found to equal, , respectively. We compare these results to the truncated Gaussian distribution, which were worked out in another paper.展开更多
Based on the latest Planck surveys, the universe is close to being remarkably flat, and yet, within observational error, there is still room for a slight curvature. If the curvature is positive, then this would lead t...Based on the latest Planck surveys, the universe is close to being remarkably flat, and yet, within observational error, there is still room for a slight curvature. If the curvature is positive, then this would lead to a closed universe, as well as allow for a big bounce scenario. Working within these assumptions, and using a simple model, we predict that the cosmos may have a positive curvature in the amount, <span style="white-space:nowrap;"><span style="white-space:nowrap;">Ω<sub>0</sub>=1.001802</span></span>, a value within current observational bounds. For the scaling laws associated with the density parameters in Friedmann’s equations, we will assume a susceptibility model for space, where, <img src="Edit_18751d6f-dbfa-47ba-be7c-8298073a34fd.png" alt="" style="white-space:normal;" />, equals the smeared cosmic susceptibility. If we allow the <img src="Edit_18751d6f-dbfa-47ba-be7c-8298073a34fd.png" alt="" /> to <em>decrease with increasing</em> cosmic scale parameter, “<em>a</em>”, then we can predict a maximum Hubble volume, with minimum CMB temperature for the voids, before contraction begins, as well as a minimum volume, with maximum CMB temperature, when expansion starts. A specific heat engine model for the cosmos is also entertained for this model of a closed universe.展开更多
We propose a model for gravity based on the gravitational polarization of space. With this model, we can relate the density parameters within the Friedmann model, and show that dark matter is bound mass formed from ma...We propose a model for gravity based on the gravitational polarization of space. With this model, we can relate the density parameters within the Friedmann model, and show that dark matter is bound mass formed from massive dipoles set up within the vacuum surrounding ordinary matter. Aggregate matter induces a gravitational field within the surrounding space, which reinforces the original field. Dark energy, on the other hand, is the energy density associated with gravitational fields both for ordinary matter, and bound, or induced dipole matter. At high CBR temperatures, the cosmic susceptibility, induced by ordinary matter vanishes, as it is a smeared or average value for the cosmos as a whole. Even though gravitational dipoles do exist, no large-scale alignment or ordering is possible. Our model assumes that space, <i>i.e.</i>, the vacuum, is filled with a vast assembly (sea) of positive and negative mass particles having Planck mass, called planckions, which is based on extensive work by Winterberg. These original particles form a very stiff two-component superfluid, where positive and negative mass species neutralize one another already at the submicroscopic level, leading to zero net mass, zero net gravitational pressure, and zero net entropy, for the undisturbed medium. It is theorized that the gravitational dipoles form from such material positive and negative particles, and moreover, this causes an intrinsic polarization of the vacuum for the universe as a whole. We calculate that in the present epoch, the smeared or average susceptibility of the cosmos equals, <img src="Edit_77cbbf8c-0bcc-4957-92c7-34c999644348.png" width="15" height="20" alt="" />, and the overall resulting polarization equals, <img src="Edit_5fc44cb3-277a-4743-bfce-23e07f968d92.png" width="15" height="20" alt="" />=2.396kg/m<sup>2</sup>. Moreover, due to all the ordinary mass in the universe, made up of quarks and leptons, we calculate a net gravitational field having magnitude, <img src="Edit_c6fd9499-fe39-4d15-bc1c-0fdf1427dfd8.png" width="20" height="20" alt="" />=3.771E-10m/s<sup>2</sup>. This smeared or average value permeates all of space, and can be deduced by any observer, irrespective of location within the universe. This net gravitational field is forced upon us by Gauss’s law, and although technically a surface gravitational field, it is argued that this surface, smeared value holds point for point in the observable universe. A complete theory of gravitational polarization is presented. In contrast to electrostatics, gravistatics leads to anti-screening of the original source field, increasing the original value, <img src="Edit_a56ffe5e-10b9-4d3f-bf1e-bb52816fd07c.png" width="20" height="20" alt="" />, to, <img src="Edit_a6ac691a-342e-4ad4-9be0-808583f9f324.png" width="90" height="20" alt="" />, where <img src="Edit_69c6f874-5a3d-4d4a-84f7-819e06c09a83.png" width="20" height="20" alt="" style="white-space:normal;" /> is the induced or polarized field. In the present epoch, this leads to a bound mass, <img src="Edit_24ed50ca-84c2-4d3a-a018-957f7d0f964a.png" width="140" height="20" alt="" />, where <i>M<sub>F</sub></i> is the sum of all ordinary source matter in the universe, and <img src="Edit_5156dc24-3701-4491-9d10-58321e7d2d85.png" width="20" height="20" alt="" /> equals the relative permittivity. A new radius, and new mass, for the observable universe is dictated by the density parameters in Friedmann’s equation, and Gauss’s law. These lead to the very precise values, R<sub>0</sub>=3.217E27 meters, and, <i>M<sub>F</sub></i>=5.847E55kg, respectively, somewhat larger than current less accurate estimates.展开更多
Using the two-component superfluid model of Winterberg for space, two models for the susceptibility of the cosmic vacuum as a function of the cosmic scale parameter, a, are presented. We also consider the possibility ...Using the two-component superfluid model of Winterberg for space, two models for the susceptibility of the cosmic vacuum as a function of the cosmic scale parameter, a, are presented. We also consider the possibility that Newton’s constant can scale,<em> i.e.</em>, <span style="white-space:nowrap;"><em>G</em><sup>-1</sup>=<em>G</em><sup>-1</sup>(<em>a</em>)</span>, to form the most general scaling laws for polarization of the vacuum. The positive and negative values for the Planckion mass, which form the basis of the Winterberg model, are inextricably linked to the value of G, and as such, both G and Planck mass are intrinsic properties of the vacuum. Scaling laws for the non-local, smeared, cosmic susceptibility, <img src="Edit_bd58a08a-5d33-4e33-b5c0-62650c0b1918.bmp" alt="" />, the cosmic polarization, <img src="Edit_56bd1950-09ae-49fa-bd34-e4ff13b30c56.bmp" alt="" />, the cosmic macroscopic gravitational field, <img src="Edit_1e22ee4f-7755-4b29-8f8d-66f20f98aaa7.bmp" alt="" />, and the cosmic gravitational field mass density, <img src="Edit_aabb0cf4-080e-4452-ba73-8f3d50e95363.bmp" alt="" />, are worked out, with specific examples. At the end of recombination,<em> i.e.</em>, the era of last scattering, using the polarization to explain dark matter, and the gravitational field mass density to explain dark energy, we find that, <img src="Edit_b4b9804e-a8db-4c86-a1ad-1bc5f8ec72fa.bmp" alt="" />. While this is an unconventional assignment, differing from the ΛCDM model, we believe this is correct, as localized dark matter (LDM) contributions can be much higher in this epoch than cosmic smeared values for susceptibility. All density parameter assignments in Friedmanns’ equation are cosmic averages, valid for distance scales in excess of 100 Mpc in the current epoch. We also evaluate the transition from ordinary matter dominance, to dark matter dominance, for the cosmos as a whole. We obtain for the transition points, <em>z</em>=1.66, for susceptibility model I, and, <em style="white-space:normal;">z</em><span style="white-space:normal;">=2.53</span> , for susceptibility model II.展开更多
Using a space filled with black-body radiation, we derive a generalization for the Clausius-Clapeyron relation to account for a phase transition, which in-volves a change in spatial dimension. We consider phase transi...Using a space filled with black-body radiation, we derive a generalization for the Clausius-Clapeyron relation to account for a phase transition, which in-volves a change in spatial dimension. We consider phase transitions from dimension of space, n, to dimension of space, (n - 1), and vice versa, from (n - 1) to n -dimensional space. For the former we can calculate a specific release of latent heat, a decrease in entropy, and a change in volume. For the latter, we derive an expression for the absorption of heat, the increase in entropy, and the difference in volume. Total energy is conserved in this transformation process. We apply this model to black-body radiation in the early universe and find that for a transition from n = 4 to (n - 1) = 3, there is an immense decrease in entropy accompanied by a tremendous change in volume, much like condensation. However, unlike condensation, the volume change is not three-dimensional. The volume changes from V4, a four-dimensional construct, to V3, a three-dimensional entity, which can be considered a subspace of V4. As a specific example of how the equation works, we consider a transition temperature of 3 × 1027 Kelvin, and assume, furthermore, that the latent heat release in three-dimensional space is 1.8 × 1094 Joules. We find that for this transition, the internal energy densities, the entropy densities, and the volumes assume the following values (photons only). In four-dimensional space, we obtain, u4 = 1.15×10125 J? m-4, s4 = 4.81×1097 J? m-4? K-1, and V4 = 2.14×10-31 m4. In three-dimensional space, we have u3 = 6.13×1094 J? m-3, s3 = 2.72×1067 J? m-3? K-1, and V3 = 0.267 m3. The subscripts 3 and 4 refer to three-dimensional and four-dimensional quantities, respectively. We speculate, based on the tremendous change in volume, the explosive release of latent heat, and the magnitudes of the other quantities calculated, that this type of transition might have a connection to inflation. With this work, we prove that space, in and of itself, has an inherent energy content. This is so because giving up space releases latent heat, and buying space costs latent heat, which we can quantify. This is in addition to the energy contained within that space due to radiation. We can determine the specific amount of heat exchanged in transitioning between different spatial dimensions with our generalized Clausius-Clapeyron equation.展开更多
Based on previous work, it is shown how a time varying gravitational constant can account for the apparent tension between Hubble’s constant and a newly predicted age of the universe. The rate of expansion, about nin...Based on previous work, it is shown how a time varying gravitational constant can account for the apparent tension between Hubble’s constant and a newly predicted age of the universe. The rate of expansion, about nine percent greater than previously estimated, can be accommodated by two specific models, treating the gravitational constant as an order parameter. The deviations from ∧CDM are slight except in the very early universe, and the two time varying parametrizations for G lead to precisely the standard cosmological model in the limit where, , as well as offering a possible explanation for the observed tension. It is estimated that in the current epoch, , where H0 is Hubble’s parameter, a value within current observational bounds.展开更多
Cosmic inflation is considered assuming a cosmologically varying Newtonian gravitational constant, <em>G.</em> Utilizing two specific models for, <em>G</em><sup>-1</sup>(a), where, ...Cosmic inflation is considered assuming a cosmologically varying Newtonian gravitational constant, <em>G.</em> Utilizing two specific models for, <em>G</em><sup>-1</sup>(a), where, a, is the cosmic scale parameter, we find that the Hubble parameter, <em>H</em>, at inception of <em style="white-space:normal;">G</em><sup style="white-space:normal;">-1</sup>, may be as high as 7.56 E53 km/(s Mpc) for model A, or, 8.55 E53 km/(s Mpc) for model B, making these good candidates for inflation. The Hubble parameter is inextricably linked to <em>G</em> by Friedmanns’ equation, and if <em>G</em> did not exist prior to an inception temperature, then neither did expansion. The CBR temperatures at inception of <em style="white-space:normal;">G</em><sup style="white-space:normal;">-1</sup> are estimated to equal, 6.20 E21 Kelvin for model A, and 7.01 E21 for model B, somewhat lower than CBR temperatures usually associated with inflation. These temperatures would fix the size of Lemaitre universe in the vicinity of 3% of the Earths’ radius at the beginning of expansion, thus avoiding a singularity, as is the case in the ΛCDM model. In the later universe, a variable<em> G </em>model cannot be dismissed based on SNIa events. In fact, there is now some compelling astronomical evidence, using rise times and luminosity, which we discuss, where it could be argued that SNIa events can only be used as good standard candles if a variation in <em>G</em> is taken into account. Dark energy may have more to do with a weakening <em>G</em> with increasing cosmological time, versus an unanticipated acceleration of the universe, in the late stage of cosmic evolution.展开更多
Using simple box quantization, we demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy. Increasi...Using simple box quantization, we demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy. Increasing spatial dimension for a given number of particles costs energy while decreasing dimensions supplies energy, which can be quantified, using a generalized version of the Clausius-Clapyeron relation. We show this explicitly for massive particles trapped in a box. Compactification from N -dimensional space to (N - 1) spatial dimensions is also simply demonstrated and the correct limit to achieve a lower energy result is to take the limit, Lw → 0, where Lw is the compactification length parameter. Higher dimensional space has more energy and more entropy, all other things being equal, for a given cutoff in energy.展开更多
We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckion...We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G<sup>-1</sup>, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.展开更多
We present a new interpretation of the Higgs field as a composite particle made up of a positive, with, a negative mass Planck particle. According to the Winterberg hypothesis, space, i.e., the vacuum, consists of bot...We present a new interpretation of the Higgs field as a composite particle made up of a positive, with, a negative mass Planck particle. According to the Winterberg hypothesis, space, i.e., the vacuum, consists of both positive and negative physical massive particles, which he called planckions, interacting through strong superfluid forces. In our composite model for the Higgs boson, there is an intrinsic length scale associated with the vacuum, different from the one introduced by Winterberg, where, when the vacuum is in a perfectly balanced state, the number density of positive Planck particles equals the number density of negative Planck particles. Due to the mass compensating effect, the vacuum thus appears massless, chargeless, without pressure, energy density, or entropy. However, a situation can arise where there is an effective mass density imbalance due to the two species of Planck particle not matching in terms of populations, within their respective excited energy states. This does not require the physical addition or removal of either positive or negative Planck particles, within a given region of space, as originally thought. Ordinary matter, dark matter, and dark energy can thus be given a new interpretation as residual vacuum energies within the context of a greater vacuum, where the populations of the positive and negative energy states exactly balance. In the present epoch, it is estimated that the dark energy number density imbalance amounts to, , per cubic meter, when cosmic distance scales in excess of, 100 Mpc, are considered. Compared to a strictly balanced vacuum, where we estimate that the positive, and the negative Planck number density, is of the order, 7.85E54 particles per cubic meter, the above is a very small perturbation. This slight imbalance, we argue, would dramatically alleviate, if not altogether eliminate, the long standing cosmological constant problem.展开更多
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 con...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, l<sub>+</sub> (0) = l<sub>-</sub> (0) = 5.032E-19 meters, for an undisturbed (unperturbed) vacuum. Thus we assume a lattice structure for space, made up of overlapping positive and negative mass wave functions, ψ<sub>+</sub>, and, ψ<sub>-</sub>, which together bind to form the Higgs field, giving it its rest mass of 125.35 Gev/c<sup>2</sup> 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<sup>-22</sup> 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<sub>+</sub> and ψ<sub>-</sub> wave functions, we calculate the overall vacuum pressure (equal to vacuum energy density), as well as typical ψ<sub>+</sub> and ψ<sub>-</sub> displacements from equilibrium within the vacuum.展开更多
文摘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, <i>q<sub>pl</sub></i>, 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, <img src="Edit_770c2a48-039c-4cc9-8f66-406c0cfc565c.png" width="90" height="15" alt="" />, where <i>ζ</i>(3) equals Apery’s constant, 1.202 …, and, <i>n</i><sub>+</sub>(0)=<i>n</i>_(0), is the relaxed, <i>i.e.</i>, <img src="Edit_813d5a6f-b79a-49ba-bdf7-5042541b58a0.png" width="25" height="12" alt="" />, number density of the positive and negative mass planckions. In the present epoch, we estimate that, <i>n</i><sub>+</sub>(0) equals, 7.848E54 m<sup>-3</sup>, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, <i>l</i><sub>+</sub>(0)=<i>l</i><sub>_</sub>(0)=5.032E-19 meters. 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, <img src="Edit_efc8003d-5297-4345-adac-4ac95536934d.png" width="80" height="15" alt="" />, 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, <i>g</i>=9.81m/s<sup>2</sup>, 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.
文摘A model is presented where the quintessence parameter, w, is related to a time-varying gravitational constant. Assuming a present value of w = -0.98 , we predict a current variation of ?/G = -0.06H0, a value within current observational bounds. H0 is Hubble’s parameter, G is Newton’s constant and ? is the derivative of G with respect to time. Thus, G has a cosmic origin, is decreasing with respect to cosmological time, and is proportional to H0, as originally proposed by the Dirac-Jordan hypothesis, albeit at a much slower rate. Within our model, we can explain the cosmological constant fine-tuning problem, the discrepancy between the present very weak value of the cosmological constant, and the much greater vacuum energy found in earlier epochs (we assume a connection exists). To formalize and solidify our model, we give two distinct parametrizations of G with respect to “a”, the cosmic scale parameter. We treat G-1 as an order parameter, which vanishes at high energies;at low temperatures, it reaches a saturation value, a value we are close to today. Our first parametrization for G-1 is motivated by a charging capacitor;the second treats G-1(a) by analogy to a magnetic response, i.e., as a Langevin function. Both parametrizations, even though very distinct, give a remarkably similar tracking behavior for w(a) , but not of the conventional form, w(a) = w0 + wa(1-a) , which can be thought of as only holding over a limited range in “a”. Interestingly, both parametrizations indicate the onset of G formation at a temperature of approximately 7×1021 degrees Kelvin, in contrast to the ΛCDM model where G is taken as a constant all the way back to the Planck temperature, 1.42×1032 degrees Kelvin. At the temperature of formation, we find that G has increased to roughly 4×1020 times its current value. For most of cosmic evolution, however, our variable G model gives results similar to the predictions of the ΛCDM model, except in the very early universe, as we shall demonstrate. In fact, in the limit where w approaches -1, the expression, ?/G , vanishes, and we are left with the concordance model. Within our framework, the emergence of dark energy over matter at a scale of a ≈ 0.5 is that point where G-1 increases noticeably to its current value, G0-1 . This weakening of G to its current value G0 is speculated as the true cause for the observed unanticipated acceleration of the universe.
文摘This is the first paper in a two part series on black holes. In this work, we concern ourselves with the event horizon. A second follow-up paper will deal with its internal structure. We hypothesize that black holes are 4-dimensional spatial, steady state, self-contained spheres filled with black-body radiation. As such, the event horizon marks the boundary between two adjacent spaces, 4-D and 3-D, and there, we consider the radiative transfers involving black- body photons. We generalize the Stefan-Boltzmann law assuming that photons can transition between different dimensional spaces, and we can show how for a 3-D/4-D interface, one can only have zero, or net positive, transfer of radiative energy into the black hole. We find that we can predict the temperature just inside the event horizon, on the 4-D side, given the mass, or radius, of the black hole. For an isolated black hole with no radiative heat inflow, we will assume that the temperature, on the outside, is the CMB temperature, T2 = 2.725 K. We take into account the full complement of radiative energy, which for a black body will consist of internal energy density, radiative pressure, and entropy density. It is specifically the entropy density which is responsible for the heat flowing in. We also generalize the Young- Laplace equation for a 4-D/3-D interface. We derive an expression for the surface tension, and prove that it is necessarily positive, and finite, for a 4-D/3-D membrane. This is important as it will lead to an inherently positively curved object, which a black hole is. With this surface tension, we can determine the work needed to expand the black hole. We give two formulations, one involving the surface tension directly, and the other involving the coefficient of surface tension. Because two surfaces are expanding, the 4-D and the 3-D surfaces, there are two radiative contributions to the work done, one positive, which assists expansion. The other is negative, which will resist an increase in volume. The 4-D side promotes expansion whereas the 3-D side hinders it. At the surface itself, we also have gravity, which is the major contribution to the finite surface tension in almost all situations, which we calculate in the second paper. The surface tension depends not only on the size, or mass, of the black hole, but also on the outside surface temperature, quantities which are accessible observationally. Outside surface temperature will also determine inflow. Finally, we develop a “waterfall model” for a black hole, based on what happens at the event horizon. There we find a sharp discontinuity in temperature upon entering the event horizon, from the 3-D side. This is due to the increased surface area in 4-D space, AR(4) = 2π2R3, versus the 3-D surface area, AR(3) = 4πR2. This leads to much reduced radiative pressures, internal energy densities, and total energy densities just inside the event horizon. All quantities are explicitly calculated in terms of the outside surface temperature, and size of a black hole. Any net radiative heat inflow into the black hole, if it is non-zero, is restricted by the condition that, 0cdQ/dt FR(3), where, FR(3), is the 3-D radiative force applied to the event horizon, pushing it in. We argue throughout this paper that a 3-D/3-D interface would not have the same desirable characteristics as a 4-D/3-D interface. This includes allowing for only zero or net positive heat inflow into the black hole, an inherently positive finite radiative surface tension, much reduced temperatures just inside the event horizon, and limits on inflow.
文摘A black hole is treated as a self-contained, steady state, spherically symmetric, 4-dimensional spatial ball filled with blackbody radiation, which is embedded in 3-D space. To model the interior distribution of radiation, we invoke two stellar-like equations, generalized to 4-D space, and a probability distribution function (pdf) for the actual radiative mass distribution within its interior. For our purposes, we choose a truncated Gaussian distribution, although other pdf’s with support, r ∈[0, R], are possible. The variable, r = r(4), refers to the 4-D radius within the black hole. To fix the coefficients, (μ,σ), associated with this distribution, we choose the mode to equal zero, which will give maximum energy density at the center of the black hole. This fixes the parameter, μ = 0. Our black hole does not have a singularity at the center, and, moreover, it is well-behaved within its volume. The rip or tear in the space-time continuum occurs at the event horizon, as shown in a previous work, because it is there that we transition from 3-D space to 4-D space. For the shape parameter, σ , we make use of the temperature just inside the event horizon, which is determined by the mass, or radius, of the black hole. The amount of radiative heat inflow depends on mass, or radius, and temperature, T2 ≥ 2.275K , where, T2, is the temperature just outside the event horizon. Among the interesting consequences of this model is that the entropy, S(4), can be calculated as an extrinsic, versus intrinsic, variable, albeit in 4-D space. It is found that S(4) is much less than the comparable Bekenstein result. It also scales not as, R2 , where R is the radius of the black hole. Rather, it is given by an expression involving the lower incomplete gamma function, γ(s,x), and interestingly, scales with a more complicated function of radius. Thus, within our framework, the black hole is a highly-ordered state, in sharp contrast to current consensus. Moreover, the model-dependent gravitational “constant” in 4-D space, Gr(4), can be determined, and this will depend on radius. For the specific pdf chosen, Gr(4)Mr = 0.1c2(r4/σ2), where Mr is the enclosed radiative mass of the black hole, up to, and including, radius r. At the event horizon, where, r = R, this reduces to GR(4) = 0.2GR3/σ2, due to the Schwarzschild relation between mass and radius. The quantity, G, is Newton’s constant. There is a sharp discontinuity in gravitational strength at the 3-D/4-D interface, identified as the event horizon, which we show. The 3-D and 4-D gravitational potentials, however, can be made to match at the interface. This lines up with previous work done by the author where a discontinuity between 3-D and 4-D quantities is required in order to properly define a positive-definite radiative surface tension at the event horizon. We generalize Gauss’ law in 4-D space as this will enable us to find the strength of gravity at any radius within the spherically symmetric, 4-D black hole. For the pdf chosen, gr(4) = Gr(4)Mr/r3 = 0.1c2r/σ2, a remarkably simple and elegant result. Finally, we show that the work required to assemble the black hole against radiative pressure, which pushes out, is equal to, 0.1MRc2. This factor of 0.1 is specific to 4-D space.
文摘This is a second follow up paper on a model, which treats the black hole as a 4-D spatial ball filled with blackbody radiation. For the interior radiative mass distribution, we employ a new type of truncated probability distribution function, the exponential distribution. We find that this distribution comes closest to reproducing a singularity at the center, and yet it is finite at 4-D radius, . This distribution will give a constant gravitational acceleration for a test particle throughout the black hole, irrespective of radius. The 4-D gravitational acceleration is given by the expression, , where R is the radius of the black hole, MR is its mass, and is the exponential shape parameter, which depends only on the mass, or radius, of the black hole. We calculate the gravitational force, and the entropy within the black hole interior, as well as on its surface, identified as the event horizon, which separates 3-D from 4-D space. Similar to a truncated Gaussian distribution, the gravitational force increases discontinuously, and dramatically, upon entry into the 4-D black hole from the 3-D side. It is also radius dependent within the 4-D black hole. Moreover, the total entropy is shown to be much less than the Bekenstein result, similar to the truncated Gaussian. For the gravitational force, we obtain, , where Mr is the radiative mass enclosed within a 4-D volume of radius r. This unusual force law indicates that the gravitational force acting upon a layer of blackbody photons at radius r is strictly proportional to the enclosed radiative energy, MrC2, contained within that radius, with 0.1λ being the constant of proportionality. For the entropy at radius, r, and on the surface, we obtain an expression which is order of magnitude comparable to the truncated Normal distribution. Tables are presented for three black holes, one having a mass equal to that of the sun. The other two have masses, which are ten times that of the sun, and 106 solar masses. The corresponding parameters are found to equal, , respectively. We compare these results to the truncated Gaussian distribution, which were worked out in another paper.
文摘Based on the latest Planck surveys, the universe is close to being remarkably flat, and yet, within observational error, there is still room for a slight curvature. If the curvature is positive, then this would lead to a closed universe, as well as allow for a big bounce scenario. Working within these assumptions, and using a simple model, we predict that the cosmos may have a positive curvature in the amount, <span style="white-space:nowrap;"><span style="white-space:nowrap;">Ω<sub>0</sub>=1.001802</span></span>, a value within current observational bounds. For the scaling laws associated with the density parameters in Friedmann’s equations, we will assume a susceptibility model for space, where, <img src="Edit_18751d6f-dbfa-47ba-be7c-8298073a34fd.png" alt="" style="white-space:normal;" />, equals the smeared cosmic susceptibility. If we allow the <img src="Edit_18751d6f-dbfa-47ba-be7c-8298073a34fd.png" alt="" /> to <em>decrease with increasing</em> cosmic scale parameter, “<em>a</em>”, then we can predict a maximum Hubble volume, with minimum CMB temperature for the voids, before contraction begins, as well as a minimum volume, with maximum CMB temperature, when expansion starts. A specific heat engine model for the cosmos is also entertained for this model of a closed universe.
文摘We propose a model for gravity based on the gravitational polarization of space. With this model, we can relate the density parameters within the Friedmann model, and show that dark matter is bound mass formed from massive dipoles set up within the vacuum surrounding ordinary matter. Aggregate matter induces a gravitational field within the surrounding space, which reinforces the original field. Dark energy, on the other hand, is the energy density associated with gravitational fields both for ordinary matter, and bound, or induced dipole matter. At high CBR temperatures, the cosmic susceptibility, induced by ordinary matter vanishes, as it is a smeared or average value for the cosmos as a whole. Even though gravitational dipoles do exist, no large-scale alignment or ordering is possible. Our model assumes that space, <i>i.e.</i>, the vacuum, is filled with a vast assembly (sea) of positive and negative mass particles having Planck mass, called planckions, which is based on extensive work by Winterberg. These original particles form a very stiff two-component superfluid, where positive and negative mass species neutralize one another already at the submicroscopic level, leading to zero net mass, zero net gravitational pressure, and zero net entropy, for the undisturbed medium. It is theorized that the gravitational dipoles form from such material positive and negative particles, and moreover, this causes an intrinsic polarization of the vacuum for the universe as a whole. We calculate that in the present epoch, the smeared or average susceptibility of the cosmos equals, <img src="Edit_77cbbf8c-0bcc-4957-92c7-34c999644348.png" width="15" height="20" alt="" />, and the overall resulting polarization equals, <img src="Edit_5fc44cb3-277a-4743-bfce-23e07f968d92.png" width="15" height="20" alt="" />=2.396kg/m<sup>2</sup>. Moreover, due to all the ordinary mass in the universe, made up of quarks and leptons, we calculate a net gravitational field having magnitude, <img src="Edit_c6fd9499-fe39-4d15-bc1c-0fdf1427dfd8.png" width="20" height="20" alt="" />=3.771E-10m/s<sup>2</sup>. This smeared or average value permeates all of space, and can be deduced by any observer, irrespective of location within the universe. This net gravitational field is forced upon us by Gauss’s law, and although technically a surface gravitational field, it is argued that this surface, smeared value holds point for point in the observable universe. A complete theory of gravitational polarization is presented. In contrast to electrostatics, gravistatics leads to anti-screening of the original source field, increasing the original value, <img src="Edit_a56ffe5e-10b9-4d3f-bf1e-bb52816fd07c.png" width="20" height="20" alt="" />, to, <img src="Edit_a6ac691a-342e-4ad4-9be0-808583f9f324.png" width="90" height="20" alt="" />, where <img src="Edit_69c6f874-5a3d-4d4a-84f7-819e06c09a83.png" width="20" height="20" alt="" style="white-space:normal;" /> is the induced or polarized field. In the present epoch, this leads to a bound mass, <img src="Edit_24ed50ca-84c2-4d3a-a018-957f7d0f964a.png" width="140" height="20" alt="" />, where <i>M<sub>F</sub></i> is the sum of all ordinary source matter in the universe, and <img src="Edit_5156dc24-3701-4491-9d10-58321e7d2d85.png" width="20" height="20" alt="" /> equals the relative permittivity. A new radius, and new mass, for the observable universe is dictated by the density parameters in Friedmann’s equation, and Gauss’s law. These lead to the very precise values, R<sub>0</sub>=3.217E27 meters, and, <i>M<sub>F</sub></i>=5.847E55kg, respectively, somewhat larger than current less accurate estimates.
文摘Using the two-component superfluid model of Winterberg for space, two models for the susceptibility of the cosmic vacuum as a function of the cosmic scale parameter, a, are presented. We also consider the possibility that Newton’s constant can scale,<em> i.e.</em>, <span style="white-space:nowrap;"><em>G</em><sup>-1</sup>=<em>G</em><sup>-1</sup>(<em>a</em>)</span>, to form the most general scaling laws for polarization of the vacuum. The positive and negative values for the Planckion mass, which form the basis of the Winterberg model, are inextricably linked to the value of G, and as such, both G and Planck mass are intrinsic properties of the vacuum. Scaling laws for the non-local, smeared, cosmic susceptibility, <img src="Edit_bd58a08a-5d33-4e33-b5c0-62650c0b1918.bmp" alt="" />, the cosmic polarization, <img src="Edit_56bd1950-09ae-49fa-bd34-e4ff13b30c56.bmp" alt="" />, the cosmic macroscopic gravitational field, <img src="Edit_1e22ee4f-7755-4b29-8f8d-66f20f98aaa7.bmp" alt="" />, and the cosmic gravitational field mass density, <img src="Edit_aabb0cf4-080e-4452-ba73-8f3d50e95363.bmp" alt="" />, are worked out, with specific examples. At the end of recombination,<em> i.e.</em>, the era of last scattering, using the polarization to explain dark matter, and the gravitational field mass density to explain dark energy, we find that, <img src="Edit_b4b9804e-a8db-4c86-a1ad-1bc5f8ec72fa.bmp" alt="" />. While this is an unconventional assignment, differing from the ΛCDM model, we believe this is correct, as localized dark matter (LDM) contributions can be much higher in this epoch than cosmic smeared values for susceptibility. All density parameter assignments in Friedmanns’ equation are cosmic averages, valid for distance scales in excess of 100 Mpc in the current epoch. We also evaluate the transition from ordinary matter dominance, to dark matter dominance, for the cosmos as a whole. We obtain for the transition points, <em>z</em>=1.66, for susceptibility model I, and, <em style="white-space:normal;">z</em><span style="white-space:normal;">=2.53</span> , for susceptibility model II.
文摘Using a space filled with black-body radiation, we derive a generalization for the Clausius-Clapeyron relation to account for a phase transition, which in-volves a change in spatial dimension. We consider phase transitions from dimension of space, n, to dimension of space, (n - 1), and vice versa, from (n - 1) to n -dimensional space. For the former we can calculate a specific release of latent heat, a decrease in entropy, and a change in volume. For the latter, we derive an expression for the absorption of heat, the increase in entropy, and the difference in volume. Total energy is conserved in this transformation process. We apply this model to black-body radiation in the early universe and find that for a transition from n = 4 to (n - 1) = 3, there is an immense decrease in entropy accompanied by a tremendous change in volume, much like condensation. However, unlike condensation, the volume change is not three-dimensional. The volume changes from V4, a four-dimensional construct, to V3, a three-dimensional entity, which can be considered a subspace of V4. As a specific example of how the equation works, we consider a transition temperature of 3 × 1027 Kelvin, and assume, furthermore, that the latent heat release in three-dimensional space is 1.8 × 1094 Joules. We find that for this transition, the internal energy densities, the entropy densities, and the volumes assume the following values (photons only). In four-dimensional space, we obtain, u4 = 1.15×10125 J? m-4, s4 = 4.81×1097 J? m-4? K-1, and V4 = 2.14×10-31 m4. In three-dimensional space, we have u3 = 6.13×1094 J? m-3, s3 = 2.72×1067 J? m-3? K-1, and V3 = 0.267 m3. The subscripts 3 and 4 refer to three-dimensional and four-dimensional quantities, respectively. We speculate, based on the tremendous change in volume, the explosive release of latent heat, and the magnitudes of the other quantities calculated, that this type of transition might have a connection to inflation. With this work, we prove that space, in and of itself, has an inherent energy content. This is so because giving up space releases latent heat, and buying space costs latent heat, which we can quantify. This is in addition to the energy contained within that space due to radiation. We can determine the specific amount of heat exchanged in transitioning between different spatial dimensions with our generalized Clausius-Clapeyron equation.
文摘Based on previous work, it is shown how a time varying gravitational constant can account for the apparent tension between Hubble’s constant and a newly predicted age of the universe. The rate of expansion, about nine percent greater than previously estimated, can be accommodated by two specific models, treating the gravitational constant as an order parameter. The deviations from ∧CDM are slight except in the very early universe, and the two time varying parametrizations for G lead to precisely the standard cosmological model in the limit where, , as well as offering a possible explanation for the observed tension. It is estimated that in the current epoch, , where H0 is Hubble’s parameter, a value within current observational bounds.
文摘Cosmic inflation is considered assuming a cosmologically varying Newtonian gravitational constant, <em>G.</em> Utilizing two specific models for, <em>G</em><sup>-1</sup>(a), where, a, is the cosmic scale parameter, we find that the Hubble parameter, <em>H</em>, at inception of <em style="white-space:normal;">G</em><sup style="white-space:normal;">-1</sup>, may be as high as 7.56 E53 km/(s Mpc) for model A, or, 8.55 E53 km/(s Mpc) for model B, making these good candidates for inflation. The Hubble parameter is inextricably linked to <em>G</em> by Friedmanns’ equation, and if <em>G</em> did not exist prior to an inception temperature, then neither did expansion. The CBR temperatures at inception of <em style="white-space:normal;">G</em><sup style="white-space:normal;">-1</sup> are estimated to equal, 6.20 E21 Kelvin for model A, and 7.01 E21 for model B, somewhat lower than CBR temperatures usually associated with inflation. These temperatures would fix the size of Lemaitre universe in the vicinity of 3% of the Earths’ radius at the beginning of expansion, thus avoiding a singularity, as is the case in the ΛCDM model. In the later universe, a variable<em> G </em>model cannot be dismissed based on SNIa events. In fact, there is now some compelling astronomical evidence, using rise times and luminosity, which we discuss, where it could be argued that SNIa events can only be used as good standard candles if a variation in <em>G</em> is taken into account. Dark energy may have more to do with a weakening <em>G</em> with increasing cosmological time, versus an unanticipated acceleration of the universe, in the late stage of cosmic evolution.
文摘Using simple box quantization, we demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy. Increasing spatial dimension for a given number of particles costs energy while decreasing dimensions supplies energy, which can be quantified, using a generalized version of the Clausius-Clapyeron relation. We show this explicitly for massive particles trapped in a box. Compactification from N -dimensional space to (N - 1) spatial dimensions is also simply demonstrated and the correct limit to achieve a lower energy result is to take the limit, Lw → 0, where Lw is the compactification length parameter. Higher dimensional space has more energy and more entropy, all other things being equal, for a given cutoff in energy.
文摘We work within a Winterberg framework where space, i.e., the vacuum, consists of a two component superfluid/super-solid made up of a vast assembly (sea) of positive and negative mass Planck particles, called planckions. These material particles interact indirectly, and have very strong restoring forces keeping them a finite distance apart from each other within their respective species. Because of their mass compensating effect, the vacuum appears massless, charge-less, without pressure, net energy density or entropy. In addition, we consider two varying G models, where G, is Newton’s constant, and G<sup>-1</sup>, increases with an increase in cosmological time. We argue that there are at least two competing models for the quantum vacuum within such a framework. The first follows a strict extension of Winterberg’s model. This leads to nonsensible results, if G increases, going back in cosmological time, as the length scale inherent in such a model will not scale properly. The second model introduces a different length scale, which does scale properly, but keeps the mass of the Planck particle as, ± the Planck mass. Moreover we establish a connection between ordinary matter, dark matter, and dark energy, where all three mass densities within the Friedman equation must be interpreted as residual vacuum energies, which only surface, once aggregate matter has formed, at relatively low CMB temperatures. The symmetry of the vacuum will be shown to be broken, because of the different scaling laws, beginning with the formation of elementary particles. Much like waves on an ocean where positive and negative planckion mass densities effectively cancel each other out and form a zero vacuum energy density/zero vacuum pressure surface, these positive mass densities are very small perturbations (anomalies) about the mean. This greatly alleviates, i.e., minimizes the cosmological constant problem, a long standing problem associated with the vacuum.
文摘We present a new interpretation of the Higgs field as a composite particle made up of a positive, with, a negative mass Planck particle. According to the Winterberg hypothesis, space, i.e., the vacuum, consists of both positive and negative physical massive particles, which he called planckions, interacting through strong superfluid forces. In our composite model for the Higgs boson, there is an intrinsic length scale associated with the vacuum, different from the one introduced by Winterberg, where, when the vacuum is in a perfectly balanced state, the number density of positive Planck particles equals the number density of negative Planck particles. Due to the mass compensating effect, the vacuum thus appears massless, chargeless, without pressure, energy density, or entropy. However, a situation can arise where there is an effective mass density imbalance due to the two species of Planck particle not matching in terms of populations, within their respective excited energy states. This does not require the physical addition or removal of either positive or negative Planck particles, within a given region of space, as originally thought. Ordinary matter, dark matter, and dark energy can thus be given a new interpretation as residual vacuum energies within the context of a greater vacuum, where the populations of the positive and negative energy states exactly balance. In the present epoch, it is estimated that the dark energy number density imbalance amounts to, , per cubic meter, when cosmic distance scales in excess of, 100 Mpc, are considered. Compared to a strictly balanced vacuum, where we estimate that the positive, and the negative Planck number density, is of the order, 7.85E54 particles per cubic meter, the above is a very small perturbation. This slight imbalance, we argue, would dramatically alleviate, if not altogether eliminate, the long standing cosmological constant problem.
文摘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, l<sub>+</sub> (0) = l<sub>-</sub> (0) = 5.032E-19 meters, for an undisturbed (unperturbed) vacuum. Thus we assume a lattice structure for space, made up of overlapping positive and negative mass wave functions, ψ<sub>+</sub>, and, ψ<sub>-</sub>, which together bind to form the Higgs field, giving it its rest mass of 125.35 Gev/c<sup>2</sup> 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<sup>-22</sup> 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<sub>+</sub> and ψ<sub>-</sub> wave functions, we calculate the overall vacuum pressure (equal to vacuum energy density), as well as typical ψ<sub>+</sub> and ψ<sub>-</sub> displacements from equilibrium within the vacuum.
