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SCALE UNIFICATION – A UNIVERSAL

SCALING LAW FOR ORGANIZED MATTER

Nassim Haramein, † Michael Hyson, ‡ E. A. Rauscher §

Abstract. From observational data and our theoretical analysis, we demonstrate that a scaling law can be written for

all organized matter utilizing the Schwarzschild condition, describing cosmological to sub-atomic structures. Of

interest are solutions involving torque and Coriolis effects in the field equations. Significant observations have led

to theoretical and experimental advancement describing systems undergoing gravitational collapse, including

vacuum interactions. The universality of this scaling law suggests an underlying polarizable structured vacuum of

mini white holes/black holes. We briefly discuss the manner in which this structured vacuum can be described in

terms of resolution of scale analogous to a fractal-like scaling as a means of renormalization at the Planck distance.

Finally, we describe a new horizon we term the “spin horizon” which is defined as a result of a spacetime torque

producing boundary conditions in a magnetohydrodynamic structure.

INTRODUCTION

In astrophysics, black holes have been ubiquitously confirmed from large scale super-giants such as quasars and

galactic centers to smaller stellar size black hole systems. These new discoveries represent a long term progress to

confirm the 1916 Schwarzschild solution to Einstein’s field equations. The observed black hole at the center of the

Milky Way galaxy was first discovered by its gravitational influence on nearby stars. So far, black holes seem to

have been found at the center of all galaxies that have been carefully examined [1]. Now, quasars and globular

clusters, have been found to host large black holes and stellar black holes are well documented [1].

In this paper we develop a scaling law utilizing the Schwarzschild condition as well as discuss charge and

rotation within a modified Kerr-Newman metric (the Haramein-Rauscher solution involving torque and Coriolis

effects in the field equations [2]) for cosmological, galactic, stellar and micro physical black holes. It is important to

note that all observed objects, from macro to micro, are predominantly x-ray emitters, which is typical of black hole

horizons. At the horizon the gravitational force balances the electromagnetic radiation, a state previously thought to

be only present at cosmogenesis, which implies a continuous creation model. This is based on the topology of

“Schwarzschild’s zones” generating cells depicting a dynamic expanding and contracting universe first described by

Wheeler and Lindquist [3]. Thermodynamic and acoustic processes occupy an important role in energy transfer

between gravitational attraction, magnetohydrodynamic (MHD) and electrodynamic repulsion [4]. Solving the

collective and coherent behavior of plasma MHD soliton structures, their thermo and acouston dynamics, results in a

good description of the processes occurring externally, near and at the horizons of black holes [4]. A dual brane

torus model of a U group and the cuboctahedral cover group is utilized (see Appendix A). This approach leads to a

polarized structured vacuum and an extended unified model. This model is a central feature of the Harameinian

topological picture [4, 5, 6].

At the cosmological resolution, plasma dynamics surrounding the event horizon give us a good indication

of the fundamental structure underlying the dynamical vacuum state polarization, its relationship to the event

horizon [4, 7] and the topology of the spacetime manifold. Some recent observations by the Wide Field Planetary

Camera 2 of the Hubble Space Telescope of Supernova SN1987A and Nebula MyCn18 (so-called Hourglass

Nebula) and large galactic superstructures display certain qualities that relate to the plasma state field and its

interaction with the vacuum structure producing double torus-like dynamics [8, 9, 10].

In this paper, we have developed a scaling law for the universal, galactic, stellar– solar and atomic scale

frequencies vs. radius of the system, with the consideration of a fundamental response of these systems within the

surrounding structured vacuum polarization, and we briefly discuss a new approach to renormalization. In this

paper, we will touch on the details of the field topology and its intera ction with the vacuum structure, and focus

mostly on describing our scaling law where we compare our scaling rotation to the standard atomic model in which

1A~10 -8 cm. By way of comparison, we find the Big Bang cosmogenic parameters, R~10 -33 cm and  ~2 x 10 43 Hz

and the current universe at R ~ 10 28 cm. We derive a scaling law and discuss possible explanations of the missing

†

Director of Research, The Resonance Project Foundation, haramein@theresonanceproject.org

‡ Research Director, Sirius Institute, michaelhyson@yahoo.com

Tecnic Research Laboratory, 3500 S. Tomahawk Road, Bldg. 188, Apache Junction, AZ 85219

Preprint: N. Haramein, M. Hyson, E. A. Rauscher, Proceedings of The Unified Theories Conference (2008), Scale

Unification: A Universal Scaling Law for Organized Matter, in Cs Varga, I. Dienes & R.L. Amoroso (eds.)

mass of the Universe in terms of vacuum state, polarizable and nonlinear structures which includes a new

description of solar dynamics to generate the physics of a unified view [2, 4].

1. THE SCALING EQUATION FROM MACRO TO MICRO COSMOS IN TERMS OF FREQUENCY,

 VS. RADIUS, R

The primary constraint on the conditions relatin g the frequency of a system to its radius is through the

Schwarzschild condition. Schwarzschild’s 1916 solution is an extension solution to Einstein’s gravitational field

equations, which were published in 1915. The Schwarzschild solution is the most simple and elegant solution to the

field equations for a spherical system. [11] This solution represents a space-time curvature structure produced by

the presence of matter-energy. The field equations represent the universality of the gravitational f orce as

represented by a spin 2 tensor gravitation, expressed as the curvature of four space or space-time. The

Schwarzschild condition is given for the Schwarzschild radius, R s and mass m s as

(1)

2 G

for the constant

where G is the gravitational constant and c is the velocity of light. This term is



 cm/gm,

1.48

(2)

2 G







which we term

, so that

J. A. Wheeler used the Schwarzschild solution as the solution for a black hole, a system in which gravity is

so strong that light, once absorbed, cannot be reemitted. This led to the search for astrophysical black holes. He

attempted to apply this description of the structure of space-time in order to explain the generation of the

electromagnetic forces in terms of the micro “quantum” structure described by mini Planck black holes [12, 13, 14].

R.W. Lindquist and Wheeler also published work depicting a “dynamic lattice universe” based on the topology of

Schwarzschild membrane zones arranged to generate cells [3] (See Fig. 1a).

This topological approach results in a dynamic expanding and contracting universe, where a test particle is

found to rise and fall against the gravitational attraction. This author expresses a concentric black hole/white hole

theorem by combining a Kerr-Newman charge and rotation metric of the Haramein-Rauscher solution [2] with the

concept of an expanding and contracting Schwarzschild cell.

E.A. Rauscher [13], and more recently Haramein and Rauscher [2, 4, 14], developed a scaling law for

physical variables as a function of the radius of the expanding universe. This cosmogenic model depends on the

approximation that the universe obeys the Schwarzschild condition given by R s ~ 10 -28 cm/gm  M u yielding R u = R s

~ 10 28 cm with the current universe radius at R u ~ 10 28 cm and a mass of M u ~ 10 56 gm. The early Big Bang

conditions, as conceived of, yields R s ~ 10 -28 cm/gm  m pl where m pl is the mass of the initial Planck black hole of

m pl ~ 10 -5 gm giving R s ~  ~ 10 -33 cm, the Planck length.

Haramein [5] and Rauscher [13] have developed a detailed scaling law for the characteristic frequency of a

system and its radius [4]. This unique scaling law treats cosmological and micro systems in terms of black hole

physics, under the Schwarzschild condition, for various systems, which are also ubiquitous x-ray emitters. This

approach will be expanded to include the nature of a variety of black hole conditions. These conditions will not

describe the detailed, more complex dynamics of each specific black hole system, but will, in general form, obey the

first order Schwarzschild condition. Some of the more complex dynamics include x-ray emissions due to energy

exchange of rotating and rotating-charged black holes [15, 16]. More appropriate descriptions of the origin of spin

and its implications to the Field equations will yield new physics, such as the Haramein-Rauscher solution with

torque and Coriolis forces [2]. Of particular interest is the description of local plasma and thermodynamic

properties described by the Kerr and Kerr-Newman solutions for black holes, and the application of this

understanding to micro-physics [4].

We can categorize the types of black hole solutions in the following manner. In general, a collapsing black hole

system preserves its mass, electric charge and angular momentum or rotation. There are five general categories of

black hole solutions. They are: (1) an uncharged, non-rotating black hole which is described by the Schwarzschild

solution field equations, (2) a charged, non-rotating black hole which is described by the Reisner-Nordstrom

solution, (3) an uncharged but rotating black hole which is described by the Kerr solution, (4) a rotating, charged

black hole which is described by the Kerr-Newman solution and 5) the Haramein-Rauscher solution with the

inclusion of torque and Coriolis forces to define the origin of spin. [2] Returning to our Schwarzschild condition,

we have calculated the conditions for micro to macro cosmological black holes [16]. Consider the usual

Schwarzschild condition given above. Haramein, [5, 6] Rauscher [13, 17] and others have noted that at the universal

scale for R u = 10 28 cm and M u = 10 56 gm and where







1.48



cm/gm,

(3)

we find a set of conditions for the entire universe as a black hole, i.e., the mass of our universe exceeds the mass of a

system needed to overcome the escape velocity of light [12].

Figure 1(a)

Figure1(b)

Figure 1(c)

Figure 1. The Lattice Universe, Kerr-Newman and Haramein Topologies

a) Lindquist and Wheeler dynamic universe utilizing a Schwarzschild-cell method [3] (from Lindquist and Wheeler Fig.

27.3) Many Schwarzschild zones are fitted together to make a closed universe. This universe is dynamic because a test

particle at the interface between two zones rises up against the gravitational attraction of each and falls back under the

gravitational attraction of each. Therefore the two centers themselves have to move apart and move back together again.

The same being true for all other pairs of centers, it follows that the lattice universe itself expands and recontracts even

though each Schwarzschild is viewed individually as static. This diagram taken from Lindquist and Wheeler (1957). b)

Typical representation of a Kerr-Newman black hole (C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, Freeman

and Co. (1973), p. 880). c) A schematic model of the N. Haramein toroidal topological membrane of a dual

manifold and its singularity in a cuboctahedral field [2] (See Appendix A).



2. A SCALING LAW OF FREQUENCY VS RADIUS FOR BLACK HOLES

There appear to be different mass groupings of black holes. These categories of black holes fit well with the scaling

model of Haramein [5, 6] and Rauscher [2, 4, 17]. The three main categories that astrophysicists have identified are,

(1) “stellar” black holes, having a few times the Sun’s mass, (2) a mid-size black hole of perhaps 200 to

500 (3) “supermassive” black holes having a range of masses from 10 6 to 10 9 M , at the center of

galaxies and including quasars which are currently considered to be such black holes. However, the manner in

which these systems, from supermassive to stellar black holes relate to each other, and certainly the manner in which

micro physics relates is currently theoretically unclear. It may be that by describing all organized matter as various

stages of evolution of black hole dynamics, and through the Haramein [5, 6] and Rauscher scaling law [2, 4, 13, 14],

that these various systems can be related and understood to include microphysics as well. This will be discussed

later in this paper.

We hypothesize that the characteristic frequency for the super giant black holes are of the order of, or less

than, the characteristic frequency of the mid-size or intermediate black holes. We denote the mid-size black holes as

G 1 and the super massive black holes as G 2 in our scaling law (See Figure 2a). Note that these systems are also x-

ray emitters due to the plasma envelope surrounding them. We have developed a scaling law for the universal,

galactic, stellar – solar and atomic scale frequencies with the consideration of a fundamental dynamical form of

these systems within the Schwarzschild model. We plot fundamental associated frequencies,  , vs. radius R of

each of the systems (See Table 1. and Figure 2a).

In Figure 2a, we give the characteristic frequency and radius for each system derived from the

Schwarzschild condition. We also give the mass for each system as well as the associated velocity, for verification

of the model, which is approximately the velocity of light. In the figure we display an approximate plot of the

various black hole systems. A more detailed analysis is currently in progress [14].

We find the scaling law fits the data on a linear-linear scale factor, which is significant. We start with the

 as a first order approximation. For the R intercept at R = 10 then  ~ 8. If  ~ 0 which can

also be considered as 10 –17 Hz, then for R = 28, we have b/a ~ -1. Thus we have the  or Y intercept as (0, 8) and

the R or X intercept as (8, 0) to a good approximation so that  = -R + 8. This law is derived from our graph

utilizing dimensionless quantities for c = 1 from the relation

aR 

form

 , c = R/t so that R  = c giving

units  = c/R and R = c/  . These are the dimensional conversion factors. Then  = -R+8. In our graph we are

using powers to the base 10 or plotting base 10 exponent factors. Hence we have 10

 

 R

10 8



 

10 8



10 8



so that 10



. In this form we can take the log to the base 10 of both sides and return

to our original equation  + R = 8 or    

 R 8 .

E. A. Rauscher calculates the evolution of physical parameters from a big bang universe, comprising a

scaling law, which is consistent with the evolution under the constraints of a Schwarzschild universe [18]. Under the

initial conditions of the big bang (as described by current theory),

10   yields a frequency

of rotation of 10 43 Hz. Under the constraints of self consistency for its Schwarzschild condition, we have a rotational

frequency of 10 -17 Hz for the present universe.

In Figure 2a, we should mention that the form 10

10 





and



10 8



is an approximation because of the variation

in specific galactic and stellar systems. Also, we utilize the unit conversion of  to R using c=1. We show this in

Figure 2a. We can also write 10



10 8



using dimensional analysis in terms of a new vector quantity   and

 

  1



introducing a unit vector velocity as  c . Then we can write

where  c = 10 8 to also preserve proper

dimensionality of our  and R variables. We observe an approximate linear relation between R s and M s and also

 and R which is derived from fitting current astrophysical data. These fits utilize the first order Schwarzschild

condition on astrophysical and cosmological systems as well as for atomic systems. In this approach we will

analyze in detail the event horizon and ergospheric dynamics that will give us a more complete model of galactic

and stellar formation and structure. Note that the expression which we derive here is a good first order

approximation. Refinements, which include a more detailed formulation of black hole dynamics and other

cosmological factors from general relativity, will include higher order effects in our scaling law.

Figure 2a. A scaling law for organized matter of frequency vs. radiu s. The black hole system is presented in this figure.

Plotted from the top left is the mini black hole at the Planck distance of

10  through to the stellar-sized black holes,

larger black holes, galactic center black holes and at the lower right is a Universe-sized black hole. Note that in between

the stellar size and the Planck distance mini black hole we have included a data point for the atomic size which we as well

calculate a new value for its mass that includes the energy availabl e in the vacuum space of a nuclei and yields the correct

radius to describe an atomic resolution as mini black holes (see equation (5) to (18)) It is of interest that the microtubules

of eukaryotic cells, which have a typical length of





and an estimated vibrational frequency of

lie

quite close to the line specified by the scaling law and intermediate between the stellar and atomic scales [19].

Table 1. We list the associated radius, frequency, mass and velocity with various relevant systems. Plots of these values

are given in Fig. 2(a) and 2(b). Note that the mass of the atomic resolution is given as the standard value (see the

calculated value in equation (5) to (18)).

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