Variable Planck Scale Model

8/14/2019 Variable Planck Scale Model

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VARIABLE PLANCK SCALE MODEL

By: Paul Hoiland

Special thanks to the online yahoo group Stardrive former known as ESAA, Fernando

Loup, and many others who have aided this creative research.

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ABSTRACT:

Cosmological theories and theories of fundamental physics must ultimately not onlyaccount for the structure and evolution of the universe, the physics of fundamental

interactions but also an understanding of why this particular universe follows the physics

that it does. Such theories must lead to an understanding of the values of the fundamental

constants themselves. Moreover, the understanding of universe has to utilizeexperimental data from the present to deduce the state of the universe in distant regions

of the past and also account for certain peculiarities or coincidences observed.

The prevalent view today in cosmology is the big bang, inflationary evolutionary model.

Although certain problems have remained, e.g. the need to postulate cold, dark matter in

amounts much larger than all the observable matter put together, dark matter not detectedso far in the laboratory or the recent need to re-introduce the cosmological constant, the

big bang cosmology has, nevertheless, achieved impressive results (Silk 1989). There

have also been recent observational evidence hinting at (Barrow and Magueijo 1998) hasrecently been found which seems to be consistent with a time-varying fine structure

constant = e

2

/(hc). A varying speed of light theory (with h c) has also been proposedby Albrecht and Magueijo(1998). Added to this we are confronted with a Pioneerslowdown that seems to require some modification to General Relativity and evidence of

higher amounts of certain elements than the standard model can account for. These

mixed messages could be found via one common model that stems from both the DutchEquation[1] and Fernando Loups model for hyperdrive[2] that was based upon that

equation.

BACKGROUND:

Fernando Loup has in several published articles offered a possible theoretical method of

star travel via hyperspace out of modern brane theory. Part of this model involves theusage and implications of a certain Dutch equation in which the Planck scale is seen as a

variable as far as size goes. A compact extra dimension has a completely different effect

on the Newtonian Force law. In a D-dimensional space with one dimension compactifiedon circle of Radius R with an angular coordinates that is periodic with period 2p, the line

Element becomes


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The force law derived from the potential that solves the Laplace equation

Becomes

noncompact space dimensions, then D=4, but D-2=2, so the force law is still an inverse

square law. The Newtonian force law only cares about the number of noncompactdimensions. At distances much larger than R, An extra compact dimension can't be

detected gravitationally by an altered force law.

But you might be asking how this extra space manages to act like its horizon is set at the

horizon of our universe? Part of the answer lies in its own local velocity of light. If thatvelocity crosses its own universe in 1 second then in essence as you shrink that universe

in volume size one still has a lightcone extending far further than our own. When you tryto compare both these frames even though C is a constant in any one frame the velocity

of C remains different from each other. The result is any information carried from our

space-time through it seems to transfer non-local due to differences in our measuring rod,while information transferred from hyperspace to here is forced to remain local so that we

only get a fraction of the total information.

This is where the difference between quantum derived expectation values for the ZPF and

observed values comes into play. Quantum Theory deals with the Planck scale. By nature

it measures value from this external frame of reference and derives answers that do not

equal those based upon observation. If one knows the actual velocity of C withinhyperspace one can reduce those answers back to our observed ones simply by division

of those answers by that value for C there. That leads one to assume that the local

velocity of C is some 120 powers higher in hyperspace than here. Such a large velocity asfar as localized lab experiments go would seem infinite. But if we could perform

quantum information transfer via entanglement over a very large distance then one could

detect that actual local value for C in hyperspace. Dirac waves transfer throughhyperspace the same as they do here using the model I have proposed. The difference is

in the wavelength spread due to the much faster local velocity of C. The energy spectrum

is simply spread out to the point that we can only measure a small fraction of its totalenergy per Planck unit here. Thats why we observe an energy for the vacuum some 120

powers smaller than theory predicts. Its actual energy is the higher value. But we only see

part of the picture due to the wave function spread. The only thing required to solve this

quantum problem is the acceptance of a two reference frame system instead of one.

The effect of adding an extra compact dimension is more subtle than that. It causes the

effective gravitational constant to change by a factor of the volume 2pR of the compact


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dimension. If R is very small, then gravity is going to be stronger in the lower

dimensional compactified theory than in the full higher dimensional theory.

So if this were our Universe, then Newton's constant that we measure in our noncompact

3 space dimensions would have a strength equal to the full Newton's constant of the total

4-dimensional space, divided by the volume of the compact dimension. The actualvolume internal for hyperspace is set by its lightcone horizon. In hyperspace all four

forces (strong, weak, EM, and Gravity) are equal. But their transfer into our noncompact

3 space dimensions alters these forces to all look different.

This leads then to the issue that quantum information is different from normal

information, yet, it in its own frame it is the same. In theory, normal information could be

sent through hyperspace. But to get the correct picture of that information so as to restoreit correctly wed have to measure the return over a far longer time period. What wed get

is just bits of the information that wed have to add together to get the whole message. In

essence every EM signal ever sent out has traveled through hyperspace. But we only get

the results back in a limited fashion here because of the frame difference. In essencethose signals traveled ahead in time all the way to their course end in a fraction of a

second there. But we only arrive at that point here in a much slower time rate.

Consider a 5-dimensional space-time with space coordinates x1,x2,x3,x4 and time

coordinate x0, where the x4 coordinate is rolled up into a circle of radius R so that x 4 is

the same as x4+2pR

Suppose the metric components are all independent of x4. The space-time metric can be

decomposed into components with indices in the three noncompact directions (signifiedby a,b below) or with indices in the x4 direction:

The four ga4 components of the metric look like the components of a space-time vector in

four space-time dimensions that could be identified with the vector potential of

electromagnetism with the usual field strength Fab

The field strength is invariant under a a reparametrization of the compact x4 dimensionvia


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which acts like a U(1) gauge transformation, as it should if this is to act like

electromagnetism. This field obeys the expected equations of motion for an

electromagnetic vector potential in four space-time dimensions. The g44 component of themetric acts like a scalar field and also has the appropriate equations of motion.

In this model a theory with a gravitational force in five space-time dimensions becomes atheory in four space-time dimensions with three forces: gravitational, electromagnetic,

and scalar. But the idea that Dirac waves can carry through in hyperspace also brings up

in itself that there is more than 1 extra dimension at play here.

The solution for the scalar field smoothly interpolates between the two attractor

solutions, the function A(r) is singular. It behaves as log |r| at |r| 0. Metric near the

domain wall is given by:

ds2 = r2dxdx+ dr2

This implies the existence of the curvature singularity at r = 0, which separates theuniverse into two parts corresponding to the two different attractors each with their own

respective space-time. The relevant equation of motion for the interpolating scalars in thebackground metric is:

+(4A+g,/g)()+6g -1 P,=0

where at the critical points P, is positive. If we assume that the solution of this

equation asymptotically approaches an attractor point cr at large |r| > 0, so that g and g,

are then constant, A becomes negative constant, and gradually vanishesat large |r|. Then the deviation gradually vanishes at large |r|. Then the deviation of

the field from its asymptotic value crat large |r| satisfies the following equation:

4|A|= 6|g1P, | ,

This is equation for a harmonic oscillator with a negative friction term |A| .Solutions of this equation describe oscillations of with amplitude blowing up at large |

r|. But I think the solution to this runaway inflation at large |r| is exactly that found with

the variable Planck scale where at large |r| the universe simply recycles finding itself back

in only the enlarged Planck scale state it started with because the far side of the harmonicoscillator at large |r| equals the initial stage of rebound in the first place.

As a further solution to the problems presented above we will first look at the Planckscale itself. The Planck scale can be written as a function of some very well known

constants for which its expression was obtained by a research group at the University of

Amsterdam Holland[1]. In the Dutch equation

R=4ie20Gh-cross2m0/e0


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G=6.67 * 10-11Nm2/Kg2, h-cross=6.626/2Pi * 10-34J s, e=1.6 * 10-19C, m0=4P * 10-7H/m,

and e0=8.854157817 * 10-12F/m to yield the known present vacuum state. Allow that the

value of e0 has varied higher over time during the history of the cosmos one finds that thePlanck scale would become larger as one went backwards in time, small at the BB stage,

increasing with time as the universe expands and local energy density begins to lower,

and eventually becoming large again to start the whole cycle over. At the BB stage theeffect here would be the same in a forward time fashion as the compacting process of

String Theory making the Planck scale itself equal to this hidden extra dimensional set.

An interesting comment can be made about the properties of the excitations around the

two gauged theory vacua. The gravitino mass near one critical point is positive M-

grav=Z> 0 and the one near the second critical point is negative M+grav = Z+ < 0 since

its value at each critical point is the value of the central charge. This would lead to anexplanation of the different values of C in hyperspace compared to our 3-brane. This

includes a change of matrices into , as well as of the representation of the little part

SO(4) of the Lorentz group. We need both versions of the theory to make acceptable not

only the vacuum state but also the excitations around each vacuum. We also need thatrebound energy state from out of LQFT to account for why inflation took place and why

there would never be a singularity in our model. Its the large |r| and the local 3-branedecrease in energy density that allows the Planck scale to increase in volume and force a

recycle stage prior to runaway inflation and deflation in either side of the oscillator. It is

also the divergence at large |r| that accounts for the accelerated expansion seen by

observation.

But the above also supplies a solution the Pioneer slowdown problem. If C can vary as

the Planck scale varies from region to region then it is not General Relativity that needsto be modified at all. It would also account for why this slowdown seems to be pointed

sunward since the Sun has the most mass density in our local area.

THE MODEL:

The Friedmann-Lematre-Robertson-Walker (FLRW) metric:

ds2FLRW=-dt2+a2(t)[(dr2/1-kr2)+r2(d2+sin2d2)]

describes a homogeneous and isotropic universe. Here is cosmological time, (r, , ) arecomoving coordinates, a is the scale factor and k = 0, 1 the curvature index. The proper

radial distance is defined as ar. FLRW branes with k = 0 and brane cosmological constant

, embedded symmetrically. The bulk is the Vaidya-anti de Sitter space-time with

cosmological constant , and it contains bulk black holes with masses m on both sides ofthe brane. The black hole masses can change if the brane radiates into the bulk. An ansatz

comparable with structure formation has been advanced for the Weyl fluid m/a4 for the

case when the brane radiates, m = m0a, where m0 is a constant and = 2, 3. For = 0the Weyl fluid is known as dark radiation and then the bulk space-time becomes

Schwarzschild-anti de Sitter. The brane tension and the two cosmological constants are

inter-related as


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2=K2+k2

The Friedmann equation gives the Hubble parameter to , m, the scale factor a and the

matter energy density on the brane:

H2=/3+(K2 /3)[1+(p/2)]+(2mo/a4-)

It is normally assumed that in the matter dominated era the brane is dominated by dust,obeying the continuity equation

+3H

which gives ~ a3.

But given the modification a variable Planck scale would add to such a model the brane

may be dominated by dust and vacuum pressure differences at the same time. With =0, the Weyl fluid is itself a variable and then the bulk space-time becomes a variable from

any of the Schwarzschild de Sitter types. In this case the universe is no longer ahomogeneous and isotropic universe. It in fact would be a composite whose general

global pattern tends to fit the homogeneous and isotropic universe type with

Schwarzschild-anti de Sitter the global normal on the bulk space-time. If you add in the

similar aspect from out of Loop Quantum Gravity of no singularity point and a recyclefrom this model then some matter may be present from other cycles which would tend

over several cycle histories to push the cosmos eventually towards a dust dominated

model which is either flat or collapsing due to a rise in matter/energy density over thathistory. At that future point given all the variables no one can predict with accuracy

which it will end up in even though I would tend to wager towards the latter.

Given all the above I would see our cosmos is somewhere in the early cycle succession

stage based upon aspects from observable cosmology at present.

REFERENCES:

1,) Stefan Kowalczyk, Quinten Krijger, Maarten Van Der Ment, Jorn Mossel,

Gerben Schoonveldt, Bart Verdoen, Contraints on Large Extra Dimensions(pp12 eq. 14)

2.) Fernando Loup , Paulo Alexandre Santos, and Dorabella Martins da Silva Santos:

Can Geodesics inExtra Dimensions Solve the Cosmic Light Speed Limit General Relativity and

Gravitation 35(10) p.1849-1855

October 2003

AUTHORS NOTES

:


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1.) This model I am using has similar properties to the one used under Double Special

Relativity (see: Jerzy Kowalski-Glikman, Sebastian Nowak, Noncommutative space-time

of Doubly Special Relativity theories, Int.J.Mod.Phys. D12 (2003) 299-316). But the twoframes system here is different from the one employed there owning to the PV nature of

this model. The actual model basis employed and its implications can be found at:

Hyperspace a Vanishing act, http://doc.cern.ch//archive/electronic/other/ext/ext-2004-109.pdf, Implication of the Dutch Equation Modified PV Model,

http://doc.cern.ch//archive/electronic/other/ext/ext-2004-115.pdf, and Why Quantum

Theory does not fit observational data,http://doc.cern.ch//archive/electronic/other/ext/ext-2004-116.pdf

2.) The strongest basis for assuming that C stays constant in hyperspace is from

observations of the CMB itself. However, it is possible that C may also vary inhyperspace. The implications of such have not been worked out in this model to date.

Also to be noted the K=0 in the original paper assumes that value for hyperspace itself

before inflation took place. The best fit currently with our space-time is that K would

equal 1. The usage of K=0 was to simplify the modeling. In reality I suspect that K=1 forboth space-time frames. At one time I had played with modeling K as a variable with

extra values to simulate a PV model where one can account for the Pioneer Problem andan older PV based problem where C ought to increase instead of observational evidence

that it either stays constant or slows with time.

3.) Aside from the variable planck scale idea one is left with these solutions:

1. The equation of state w may differ from -1 by an observable amount, or may

change rapidly with time.

2. The dark energy may be a scalar field, coupled to matter in such a way as to cause

time variations in fundamental constants, or to violate the gravitational equivalenceprinciple.

3. The cosmic acceleration may be caused by a deviation from general relativisticgravity on cosmological scales, rather than by a dark energy.

None of the above alternatives seems viable at this time.

4.) DIFFERENT BRANE MODELS:
http://doc.cern.ch//archive/electronic/other/ext/ext-2004-116.pdfhttp://doc.cern.ch//archive/electronic/other/ext/ext-2004-116.pdf


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This figure shows how different theories vary from each other as far as classification

goes. All modeling is

based upon the Friedmann-Lematre-Robertson-Walker (FLRW) metric later modified by

Loop QuantumGravity.

5.) Using =(/-3) 4G from a non-viscous model (Arbab 2002). This form isinteresting since it relates the vacuum energy directly to the matter content in theuniverse. Hence, any change in will immediately imply a change in . Thiswould apply both locally and globally which is also consistant with the variablePlanck scale model:

( Metric used here comes from Arbab I. Arbab The Universe With Bulk Viscosity, Chin.

J. Astron. Astrophys. Vol. 3 (2003), No. 2, 113118 ( http://www.chjaa.org or

http://chjaa.bao.ac.cn with a different equation of state)

In a flat Robertson Walker metric

ds2=dt2-R2(t)(dr2+r2d2+r2sin2d2)

Einsteins field equations with a time-dependent G and read (Weinberg 1971)


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R -1/2(gR)=8G(t)T+(t)g,

Now cosmologists believe that is not identically, but very close to zero. They relate thisconstant to the vacuum energy that firstinflated our universe, causing it to expand. From the point of view of particle physics, a

vacuum energy could correspond to a quantum field that is diluted to its present smallvalue. However, other cosmologists dictate a time variation of this constant in order toaccount for its present smallness. The variation of this constant could resolve some of thestandard model problems. Like G, the constant is a gravity coupling and both shouldtherefore be treated on an equal footing. A proper way in which G varies is incorporatedin the Brans-Dicke theory (Brans & Dicke 1961). In this theory G is related to a scalarfield that shares the long range interaction with gravity.

Considering the imperfect-fluid energy momentum tensor

T=(p+p)uu-pg,

this yields the two independent equations,

3(/R)=4G(3p+p)+,

and

3(/R)2=8Gp+(/8G)R,

Elimination of between the first and the second differentiated form of the equationgives

3(p+p)=-((/G)p+p+ /8G)R,

where a dot denotes differentiation with respect to time t and p=p-3H, being thecoefficient of bulk viscosity, H the Hubble constant. The equation of state relates thepressure (p) and the energy density (p) of the cosmic fluid:

p=1/((-1)p),

where =constant. Vanishing of the covariant divergence of the Einstein tensor and theusual energy-momentum conservation relation T=0 leads to

8Gp+=0

and

p+3(p++p)H=0


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One finds that the bulk viscosity appears as a source term in the energy conservationequation.

Now if we consider the very special form (Arbab 1997),

=3H2

, =constant,and

=opn , o0, n=constant.

This is equal to writing =(/-3)4Gp for a non-viscous model (Arbab 2002). Thisform relates the vacuum energy directly to the matter content in the universe or in anylocal region. Hence, any change in p will immediately imply a change in , i.e., if pvaries with the cosmic time then also varies with the cosmic time. If local mattercontent varies so will the vacuum energy density.

Now what makes the difference is weather we have a decaying mode of the energy densityor an increasing mode of energy density globally and locally. From an expansion of thecosmos perspective the mode is decaying while locally it will vary in mode. This yields astress energy tensor that also varies locally which leads to C being a variable itself whichindirectly implies that certain values of the Dutch Equation are a variable. Thattranslates to the Planck scale as a variable.

While the above equations are just one way we could express the general idea from acosmological perspective the example does point out that the general idea of expanding abubble of hyperspace around a craft is possible. I would also suggest this same modelingoffers a possible solution to some of our own sub-light methods of propulsion.

One other implication of this is the system has to always have some local energy densitypresent even at the start or one is left with a runway inflation of hyperspace. This issueis solved by the fact that at large expansion R the Planck scale has a near infiniteprobability of having virtual particles borrow enough energy to become real particleswhich starts the collapse of the planck scale towards a second rebound point guaranteedby aspects of Loup Quantum Gravity. This implies that not only may some mattertransfer over from other cycles accounting for more of certain elements than theStandard model can account for. It also implies some elementary particles have alwaysbeen present even if the rebound point during collapse tends towards a high enoughtemperature to wipe a lot of the entropy history clean.

The actual Dutch Equation is:

R=42oGh-cross2mo/eo

G=6.67 * 10-11Nm2/Kg2, h-cross=6.626/2Pi * 10-34J s, e=1.6 * 10-19C, m0=4P * 10-7H/m,

and e0=8.854157817 * 10-12F/m to yield the known present vacuum state.


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DISCUSSION AND CONCLUSIONS

The existence of horizons of knowledge in cosmology, indicate that as a horizon is

approached, ambiguity as to a unique view of the universe sets in. It was precisely these

circumstances that apply at the quantum level, requiring that complementary constructsbe employed (Bohr 1961). Today we stand on another horizon that seems to be

displaying ambiguity. This if forcing us as Scientists to rethink established dogma and

cosmological views. It has been my attempt here to offer just such a rework of an oldermodel into something that fits the observational evidence a bit closer. Further testing of

this idea could come via study of signals from more than one probe outside of our solar

system. It could come from experimenting with some of Fernando Loups ideas. It could

come from ways I have not even thought of at present.

At present the Universe is considered a general relativistic Friedmann space-time with

flat spatial sections, containing more than 70% dark energy and at about 25% of dark

matter. Dark energy could be simply a cosmological constant , or quintessence orsomething entirely different. There is no widely accepted explanation for the nature of

any of the dark matter or dark energy (even the existence of the cosmological constantremains unexplained). This has been my attempt to come up with a solution that fits the

observational mixed signals at present.

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Variable Planck Scale Model