Fractal String Theory

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Copyright © 2012 Anthony William Green

Hillside Quarry Road Clydach Abergavenny NP7 0RR

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Fractal String Theory the structure of dark matter and dark energy

Introduction

This paper offers an explanation for the physics of dark matter and dark

energy. Beginning with a structure for the smallest particle of matter,showing the way mass is distributive up to the level of the hydrogen atom.

Elementary Particles

Quantum fluctuations allow the creation of small packets of energy out of

empty space, assuming this energy appears at random through out space and

time, it is also reasonable to assume that it could also appear with random

values of energy and rotation. The rotation of the energy would create a

small amount of mass; for the purpose of this paper I have assumed the

mass would be in the order of 10-30

grams. This is the point where gravity is

first detected.

The universe has almost unlimited mass, but has zero energy. This is

explained by the elementary particle having equal amounts of positive and

negative energy. As shown in the equation E1 + (E2 x - 1) = MC2.

Fractal Strings

Most packets exist for very short periods of time, but energy with the outer

surface rotating above the speed of light would have a speed gradient

reducing to zero at the centre of rotation. A barrier would exist between the

energy rotating above and below the speed of light. This would form a

stable structure and persist.

The energy above the barrier would try to contract and the energy below the

barrier would try to expand, resulting in compressive forces at the barrier,

the energy would extrude along the barrier forming a tube.

Tours

The rate of extension would be moderated by the surface tension of the

energy. Any disturbance in the tube would cause the tube to bend into the

form of a circle; the joining of the ends would form a tour. The tour offers astructure that could form part of a fractal sequence.

The diameter of the tube would be fixed by the speed of light and the

diameter of the tour would be fixed by the mass. If the tour was subject to

acceleration the increased speed would increase the mass and increase the

diameter of the tour; for the purpose of this paper I have assumed the

diameter of the tube or the tour would be in the order of 10-30

centimetres.





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Fractal Tours

The tours would become the building blocks for larger structures as follows.

Tours moving at random would on occasion come into contact, as opposites

attract the inward rotating face of the tours would join together with the

outward rotating face of the adjacent tour. As there would be variations inthe diameters of the tours, tours with slight differences in diameter may

form stronger joints then tours of the same size. The result would be a string

of tours with 2 or more diameters growing in length, the different diameters

would allow some flexibility in the string and when the string has grown

past the point where the ends can join together a new larger tour can be

created. This represents the beginning of a fractal sequence building tours of

greater and greater magnitude until some change prevents the continuation.

One candidate for this change would be the mass reaching a point where

smaller tours could go into orbit around the mass preventing the addition of

further tours.

Another candidate for the change would be the relationship between the

diameters of the hole in the tour and the cross sectional diameter of the tour.

When strings or tours could pass through the hole in the tour and go into

orbit around the body of the tour the opportunity to disrupt the fractal

sequence would also be possible.

Space Time

This would be the point where electrical, nuclear and space time effects

would be seen in the macro world. When subjected to acceleration the

increase in the size of all the tours would increase the orbital period of the

tours and the time needed for all physical process to take place would

increase, space time would slow down.

Due to the range of particles forming each cycle of the sequence a large

number of different size tours could pass the cut off point, resulting in the

opportunity for complex structures to be created with different properties.

We would see more Helium than hydrogen atoms but we may see samples

of many of the atoms found in the periodic table.

Tour as shown could be seen at all scales.





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Conclusions

The continuous creation of new particles would create the mass we see as

dark matter and dark energy result in the expansion of the universe.

The existence of black holes offers a way of disrupting the fractal particlescausing the energy each side of the speed of light barrier to cancel each

other out, removing the fractal particle from the universe.

The universe could now be described as a self organized critical system, a

system that is not in equilibrium because there is a flow of energy passing

through it.

The current expansion of the local volume of the universe would suggest the

numbers of local black holes are currently removing less matter than is

being created. If the increase in matter is also increasing the number or size

of black holes it would be reasonable to expect that the removal of matterwill at some point exceed the creation of matter and a tipping point will be

passed, reversing the expansion until the black holes are reduced due to the

reduction in the material available for consumption. The local universe

would then be able to alternate between these two states. The change in the

ratio of dark energy and dark matter may be an indicator of this process, and

the need for a big bang would be removed.

The availability of such a large number of different fractal particles and

strings would also suggest that all energy fields may involve the interaction

of fractal particles.





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Notes

1/ After visualising that the fractal structure of dark matter would be in the

form of tours; I looked for supporting evidence of tours in existing

publications and found the picture detailed in the final page on Wikipedia.

This resulted in me revising my paper to reflect the final structure havingtours of different diameters joining together.

Acknowledgments

1/ The inspiration for this paper was found from reading selected

publications from the author, teacher and elementary particle theorist Lee

Smolin and the philosopher and mathematician G. W. Leibniz.

2/ Julian Barber was kind enough to read my notes and commented, the

concepts were far from standard and there were no definite equations. This

was a problem for me I thought I did not have the level of maths to create

the required equations. After weeks of thought I realised that a very small

change to a very well known equation would work.

With E1 being positive energy rotating below the speed of light, E2 being

negative energy rotating above the speed of light and mass always being

positive the equation E1 + (E2 x - 1) = MC2

was born.

3/ The following artwork is published under licence.



EN.WIKIPEDIA.org/wiki/file:hydrogen_eignstate_n4_l3_m1.png

Hydrogen eigenstate n4 l3 m1

English: Calculated 4f 1 orbital of an electron's eigenstate in the Coulomb-field of a hydrogen

nucleus. An eigenstate is a state which keeps it's shape except for a complex phase when the

Hamilton operator is applied, thus being invariant in time while obeying the Schrödinger equation.

The orbital is aligned around the z-axis, but remains an eigenfunction if rotated to any direction.

The wavefunction is:

The state is an eigenstate of H, L² and Lz, which constitute a complete set of commuting

observables. The quantum numbers mean that the following quantities have a sharp certain value:n = 4: Energy:

l = 3: Angular momentum:

m = 1: Angular momentum in z-direction:

Since l=3, this is called a f-orbital.

The depicted rigid body is where the probability density exceeds a certain value. The color shows

the complex phase of the wavefunction, where blue means real positive, red means imaginarypositive, yellow means real negative and green means imaginary negative. The image is raytraced

using modified phong shading.The fine structure is neglected.

Date August 2010

Source Own work; created with hydrogen 1.0

Author Geek3

I, the copyright holder of this work, hereby publish it under the following licenses:Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free

Documentation License, Version 1.2 or any later version published by the Free Software Foundation;

with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

A copy of the license can be found at

EN.WIKIPEDIA.org/wiki/file:hydrogen_eignstate_n4_l3_m1.png

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Fractal String Theory