Fractal Physics Theory Success Summary and Proposed Experiments

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Scalativity LLC, Article 2, November 2012Published online at http://www.Scalativity.com/

© 2012 Scalativity LLC, all rights reserved

Fractal Physics Theory – Success Summary and Proposed Experiments

Leonard J. Malinowski [email protected]

Abstract

This article summarizes important results from six Fractal Physics Theory articles and proposes many experiments thatwill either support or refute the theory. Fractal Physics Theory is a scientific paradigm that claims the entire Universeand its composite quantum scale pieces such as nuclei, electrons, photons, neutrinos, and electric field lines are allfractals. For instance a pure neutron is composed of 1.2 x 1057 subquantum scale Hydrogen atoms. An electron iscomposed of 1.2 x 1052 subquantum scale Iron atoms with an excess of 2.1 x 1040 subquantum scale electrons. A

photon is composed of 4.5 x 1080 subquantum scale photons. The Fractal Universe also contains cosmic scale piecesself-similar to quantum scale pieces such as cosmic scale nuclei, cosmic scale electrons, cosmic scale photons, cosmicscale neutrinos, and cosmic scale electric field lines that are all fractals. For instance, ten billion years ago, the pre-solar system was a cosmic scale neutron. Our visible Universe is a cosmic scale ~ 1 Megaton fission explosion thatdetonated ~ 1 titanic scale second ago, relative to the human scale. All the electromagnetic radiation and neutrinosemitted by a star during its fusion burning cycle is one cosmic scale antineutrino.

1. Introduction

The current scientific paradigm, Modern Physics, stands on the pillars of Quantum Mechanics and Relativity, whichwere erected early in the 20th century prior to space-flight, computers, even the Great Depression. Quantum Mechanicsintroduced deviations from Euclidean geometry and typical human scale observations in order to understand atomicscale data. Continuous properties of space, matter, energy, charge, etc, are replaced by quantized properties of space,matter, energy, charge, etc. The certainty of an object’s trajectory is replaced with trajectory probabilities. QuantumMechanics also eliminates the ability to simultaneously measure the precision of select property pairs such as positionand momentum. Relativity also introduced deviations from Euclidean geometry and typical human scale observationsin order to understand an object’s properties when velocities approach the speed of light and properties of cosmic scalematter (gravity). Space and time are combined into space-time. Matter is equated to energy. Properties such as length,time and mass are linked to the relative velocity of an observer. Gravity becomes the curvature of space-time.

Modern Physics prefers to unify Quantum Mechanics and Relativity, but complete unification has not been achieved.

The author was born into this Modern Physics dichotomy paradigm while harboring an almost instinctual faith in theinfinite, rejecting a beginning or ending of time, or a limit to scale, whether minimum (subquantum) or maximum(supercosmic). As the years continue to pass and experimental data amasses knowledge, the world has witnessedanother non-Euclidean geometry, Fractal Geometry [1], exponentially increase in its applicability to understand diverse

phenomena of the Universe. A truly Fractal Universe must incorporate infinity completely into Physics as well as scalerelativity [2], with the understanding that there must exist a self-similarity between scales. Quantum Mechanics andRelativity have repeatedly been confirmed through experiment therefore these Modern Physics concepts must be validas a subset in a Fractal Universe. General Relativity does not address the ubiquity of cosmic scale charged objects so itfails to describe galactic structure (missing mass and massive black holes) and larger stellar masses (neutron stars andstellar mass black holes). Quantum Mechanics does not address nuclei and electron substructure, which containubiquitous subquantum scale charged objects, so it fails to describe internal binding of nuclei (strong nuclear force andweak nuclear force) and nuclei and electron lilliputian scale phase transitions (wave form and particle form).

2. Fractal Physics Theory – Foundation & Cosmic Scale Nuclear Explosion Cosmology

2.1. Postulates [3]

Fractal Physics Theory (FPT) is based on extending the two Special Relativity postulates to scale.

I. Scale Relativity – absolute uniform scale cannot be detected.

Scientists (human observers) exist at the human scale whereby all measured properties of the Universe can becompared relative to the scientist’s approximate mass, size, and awareness of time passage. FPT insists our humanscale is arbitrary.




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II. The speed (c) of electromagnetic radiation in vacuum is independent of scale.

Based on these two postulates, it is possible to reorganize the vast quantity of experimental data amassed by scienceinto a much simpler, more symmetric, and more predictive framework. Many facets of Fractal Physics Theory alreadymatch experimental data, but more importantly, many experiments can be conducted that could refute FPT.

How can the human scale be relative? Stars and galaxies appear to dominate the “large” scale, while atoms, photons,

and neutrinos appear to dominate the “small” scale. The ubiquity of Fractal Geometry provides the answer. The sum iscomposed of self-similar parts and infinite magnification reveals infinite resolution.

2.2. Neutrinos and Stars [4]

Consider stars: have mass and radiate energy; undergo fusion which alters their chemical composition; have masses ranging over two orders of magnitude; exist individually, in binary and more complex systems; can explode with tremendous energy as nova and supernova; are found in galaxies.

Consider nuclei that are in the process of the beta decay moment: have mass and radiate energy;

undergo a change which alters their composition; have masses ranging over two orders of magnitude; exist individually, in binary systems when capturing neutrons; can suddenly release beta particles with very high kinetic energy; are found in radioactive materials.

The vast majority of stars are fractally self-similar to nuclei in the process of beta decay. Stars are cosmic scale nucleiin the process of cosmic scale beta decay. The sum of electromagnetic and neutrino radiation emitted by a star over itslife time is one cosmic scale antineutrino. An observer existing at the lilliputian scale (with mass ~ 7 x 10-56 kilograms,and height ~ 5 x 10-24 meters) literally “sees” via neutrino energy. Likewise, by self-similarity, an observer at thehuman scale literally “sees” via cosmic scale neutrino energy. Billions of years perceived at the human scale is

perceived at the titanic scale as ~ one microsecond. From self-similarity, 1 μs perceived at the human scale is perceived as billions of years at the lilliputian scale. It is fact that time, length, and mass are all relative to referenceframe motion. Fractal Physics Theory proposes that time, length, mass, etc., are relative to reference frame scale.

2.3. Definitions

A curious observation provides a convenient way to define a set of scales. A familiar human scale mass 57.768 kgdivided by the quantum scale neutron mass 1.675 x 10-27 kg equals 3.449 x 1028. Multiplying 57.768 kg by 3.449 x1028 equals the cosmic scale solar system mass 1.992 x 1030 kg.

Object – any system of mass and/or energy that exists in the universe, symbolized by O. Examples of objects: electron, proton, neutron, atom, molecule, photon, person, car, house, planet, star, and galaxy.

Observable – the measurement of a property of an object, symbolized by f (O). Examples of observables: an electron’scharge, a person’s height, a planet’s mass, and a star’s luminosity. For convenience, consider an observer always

present to witness the observable.

Scale – a reference frame for establishing measurement units and defining their relationships

Fractal Universe – the infinite set of scales, the scale contents, and the relationships between the scales, whichcomprise physical reality.

Human Scale – a reference frame scaled to the mass range of humans. The human observer is an object in a scale. Theobserver is part of their scale. The units meter, kilogram, and second are relative to a human’s scale of size, mass, andawareness of time passage. Let an object located in the human scale be denoted by m = 0. Let an observation made inthe human scale be denoted by n = 0.





Cosmic Scale – a reference frame scaled to the mass range of stars. Let an object located in the cosmic scale bedenoted by m = 1. Let an observation made in the cosmic scale be denoted by n = 1.

Quantum Scale – a reference frame scaled to the mass range of atomic nuclei. Let an object located in the quantumscale be denoted m = -1. Let an observation made in the quantum scale be denoted by n = -1.

Titanic Scale – a reference frame more massive than but self-similar to the human scale. A reference frame scaled to

the mass range of humans multiplied by the factor ¥M = (1.992 x 1030

kg)/(1.675 x 10-27

kg) ~ 1.19 x 1057

. Let anobject located in the titanic scale be denoted by m = 2. Let an observation made in the titanic scale be denoted byn = 2.

Lilliputian Scale – a reference frame less massive than but self-similar to the human scale. A reference frame scaled tothe mass range of humans divided by the factor ¥M ~ 1.19 x 1057. Let an object located in the lilliputian scale bedenoted by m = -2. Let an observation made in the lilliputian scale be denoted by n = -2.

Supercosmic Scale – a reference frame more massive than but self-similar to the cosmic scale. A reference framescaled to the mass range of stars multiplied by the factor ¥M ~ 1.19 x 1057. Let an object located in the supercosmicscale be denoted by m = 3. Let an observation made in the supercosmic scale be denoted by n = 3.

Subquantum Scale – a reference frame less massive than but self-similar to the quantum scale. A reference framescaled to the mass range of atomic nuclei divided by the factor ¥M ~ 1.19 x 1057. Let an object located in thesubquantum scale be denoted by m = -3. Let an observation made in the subquantum scale be denoted by n = -3.

Scale Relativity – the relativity of scale. The laws of physics are scale invariant. That is, the laws of physics are thesame in every scale as viewed from that scale. The laws of physics in scale m as observed in scale n = m are equivalent

to the laws of physics in scale m + x as observed in scale n = m + x. Where m, n, and x are defined by the set { – ,…,

– 2, – 1, 0, 1, 2,…, + }. Every object exists within all the infinite scales simultaneously. Therefore, the measurementof any observable of an object requires the specification of two scales, the object’s scale and the observer’s scale.

Scaling Fractal – represented by the symbol ¥, is a unit less number that relates properties of self-similar objectsthrough simple division. Tables 1a, 1b list the SI units for seven defined scales.

Table 1a, International System of Units (SI) at Several Scales

Scale Mass Luminous Intensity Length or Time

m Name Unit (kg) Log(unit) Unit (cd) Log(unit) Unit (m or s) Log(unit)

3 Supercosmic4.10 x 1085 85.61 1.76 x 1050 50.25 2.33 x 1035 35.37

2 Titanic 1.19 x 1057 57.08 3.14 x 1033 33.50 3.79 x 1023 23.58

1 Cosmic 3.45 x 1028 28.54 5.60 x 1016 16.75 6.16 x 1011 11.79

0 Human 1.00 0.00 1.00 0.00 1.00 0.00

-1 Quantum 2.90 x 10-29 -28.54 1.78 x 10-17 -16.75 1.62 x 10-12 -11.79

-2 Lilliputian 8.41 x 10-58 -57.08 3.18 x 10-34 -33.50 2.64 x 10-24 -23.58

-3 Subquantum 2.44 x 10-86 -85.61 5.68 x 10-51 -50.25 4.29 x 10-36 -35.37

ΔLog(unit)/Δm = 28.538 16.748 11.789

Table 1b, International System of Units (SI) at Several Scales

Scale Current Mole Temperature

m Name Unit (A) Log(unit) Unit (mol) Log(unit) Unit (K) Log(unit)

3 Supercosmic 1.33 x 1025

25.12 1.00 0.00 3.24 x 10-21

-20.492 Titanic 5.60 x 1016 16.75 1.00 0.00 2.19 x 10-14 -13.66

1 Cosmic 2.37 x 108 8.37 1.00 0.00 1.48 x 10-7 -6.83

0 Human 1.00 0.00 1.00 0.00 1.00 0.00

-1 Quantum 4.22 x 10-9 -8.37 1.00 0.00 6.76 x 106 6.83

-2 Lilliputian 1.78 x 10-17 -16.75 1.00 0.00 4.57 x 1013 13.66

-3 Subquantum 7.54 x 10-26 -25.12 1.00 0.00 3.09 x 1020 20.49

ΔLog(unit)/Δm = 8.374 0.000 -6.830




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2.4. The Big Bang is a cosmic scale nuclear fission explosion

The Big Bang is a cosmic scale nuclear fission explosion about 1 titanic scale second into the fireball. The Big Bang’s

energy came from cosmic scale fission reactions:

Uranium 235 nucleus + 1 neutron→ larger fission product + smaller fission product + few neutrons

The fission products peak around 95 solar masses and 135 solar masses. Newly formed fission products, on any scale,are neutron rich and undergo a series of beta decays (appear as stars relative to some scale). A large percentage of anuclear fission explosion’s Uranium 235 and 238 do not take part in the fission. This provides much of the Universe’smissing mass (radiating at 2.7 K in some scale). Combining data for the following: fission product yields, fission

product decay rates, neutron cross sections, an estimate of the pre-explosion Universe cosmic scale chemicalcomposition and the time since the Big Bang, allows the mass of essentially every star in the Universe to be determined(not included in this series of articles).

Many free cosmic scale neutrons are still colliding with cosmic scale nuclei and scattering (gamma bursts) or are beingabsorbed (binary star systems) while some are undergoing beta decay (the solar system).

2.5. Calculation of cosmic scale cation charge at or near Sagittarius A (Sgr A*) [5]

Reference [5] scales observational data of “S-stars” that move in elliptical orbits within the central arcsecond of theMilky Way Galaxy. Table 2 lists the gravitational potential energy between a massive black hole (MBH) at one foci

and the cosmic scale electron rest mass for S-stars at pericenter. This article considers a Coulombic potential energy between a net positive charged object at one foci and a negative charged S-star at pericenter. A small adjustment ismade to the gravitational potential energy in Eq. (1) by using the relative cosmic scale electron mass. The gravitational

potential energy, EP(g), is equated to the Coulombic potential energy, EP(C). The distances drop from the calculation andEq. (1) is solved for the net positive charge (Z) at the position of Sgr A*:

- GMm2/R = - k(Zq)q/R, and solve for Z:

Z = GMm2/(kq2) = 6.0 (1)

G = 6.6742 x 10-11 Nm2/kg2 M = MBH, see reference [5]m2 = relative cosmic scale electron mass (for an S-star)k = 8.987551788 x 109 Nm2/C2 q = 3.40123 x 1021 C

R = distance from S-star to Sgr A*

Fractal Physics Theory demonstrates that a cosmic scale cation of cosmic scale +6 charge can account for an attractive potential energy at the Galactic Center near Sgr A*. Consider the fact that out of the infinite values of Z possible, onlyintegers from 1 to 92 are possible, and only integers from 1 to 22 are probable in Fractal Physics Theory. Equation 1and Table 2 data convincingly supports Fractal Physics Theory!

Table 2, Net Charge at the Galactic Center Near Sgr A*

Star M (kg)(1) Cs-e- mass(v) (kg)(2) Z (Coulomb) (3)

S1 8.6477 x 1036 1.08361 x 1027 6.02

S2 8.5683 x 1036 1.08394 x 1027 5.96

S8 8.6406 x 1036 1.08366 x 1027 6.01

S12 8.5965 x 1036 1.08376 x 1027 5.98

S13 8.5922 x 1036

1.08362 x 1027

5.98S14 8.6184 x 1036 1.08417 x 1027 6.00

(1)MBH, see reference [5](2)Relative cosmic scale electron mass at Pericenter(3)Z = Net positive charge near Sgr A* using Eq. (1)

The physics of our Universe does not allow black holes to form. Cosmic scale charged masses fill the Universe andconsequently electromagnetic forces dominate both stellar and galactic structure. The orbital data carefully measuredfor S-stars in the Galactic Center, when scaled using Fractal Physics Theory, yield data remarkably close to atomic datafound in authoritative texts such as the CRC Handbook of Chemistry and Physics. A cosmic scale +6 cation resides at





the Galactic Center, guiding its formation and structure. It is likely that similar cosmic scale cations reside at thecenters of many spiral galaxies, guiding their formation and structure. The Milky Way Galaxy may have a “partner”spiral galaxy forming around the “partner” to Sgr A* cosmic scale fission fragment. The majority of spiral galaxiesmay be similarly paired.

2.6. Scaling Fractals (¥)

The mass scaling fractal is determined by dividing the mass of a cosmic scale neutron (1.9928 x 1030

kg, identified asthe pre-solar system mass) by the mass of the quantum scale neutron (1.6749 x 10-27 Kg):

¥Mass = ¥M = 1.190 x 1057

By postulate 2, the speed of light scaling fractal is unity (¥c = c/c = 1). Therefore, ¥Energy = ¥Mass¥c¥c = ¥Mass;energy and mass scale at the same rate.

The length scaling fractal is determined by dividing the estimated radius of a cosmic scale proton (3.789 x 108 m) bythe radius of the quantum scale proton (1.0 x 10-15 m):

¥Length = ¥L = 3.789 x 1023

By postulate 2, ¥c = 1, therefore ¥time = ¥Length/¥c = ¥Length; time and length scale at the same rate.

It follows that: 1 nanosecond to the human scale is 12 million years to the lilliputian scale 12 billion years to the human scale is 1 microsecond to the titanic scale 1 angstrom to the human scale is 253 Astronomical Units to the lilliputian scale 12 billion light years to the human scale is 300 meters to the titanic scale.

Scaling Fractals are determined for many physical observables such as length, mass, time, current, charge, magneticfields, forces, constants, etc., all of which reduce to:

¥observable = (¥length j/2)(¥Massk/2) (2)

j, k = {−∞, …, − 2, − 1, 0, 1, 2, …, ∞}

2.7. Strings are subquantum scale atomic orbitals

In string theory particles are perceived as highly localized vibration of Planck length strings:

l p = (ħ-1,0G1,0c-3)1/2 (3)

= [(1.054 5717 x 10-34 Js)(6.6742 x 10-11 Nm2/kg2)(299 792 458 m/s)-3]1/2 = 1.62 x 10-35 m

From the Bohr model of the Hydrogen atom and in particular quantized angular momentum: mvnr n = nħ

Combined with the de Broglie relation: λ = h/p

The relation has long been known: 2πr n = nh/pn = nλ

The smallest atomic orbital circumferences are the ground state Helium shells (1s2 orbital) of the heaviest atoms. Thediameter of the helium shell for Radon (z = 86) ~ 0.02 Å. This shell has an average circumference = 2π(1 x 10-12 m) =

6.28 x 10

-12

m, which is also the smallest ground state wavelength of an atomic orbital in the quantum scale.Fractal Physics Theory length scaling fractal: ¥L = 3.789 x 1023

A self-similar Radon atom existing at the subquantum scale will have a self-similar subquantum scale 1s2 orbitalcircumference measured relative to the human scale:

[Radon, 1s2 circumference]-3,0 = 6.28 x 10-12 m/3.789 x 1023 = 1.66 x 10-35 meters

Vibrating string particles correspond to subquantum scale atoms. Strings are subquantum scale atomic oscillators.





2.8. Fractal certainty principle

Planck’s constant is not scale invariant. Measuring an electron’s position with subquantum scale electromagneticradiation (a small percent of a single neutrino) will not significantly alter the electron’s momentum. The position andmomentum of an electron can be determined, for practical purposes, simultaneously.

The fractal certainty principle:

[Δx]m,n[Δ p]m,n ≥ [0.5ħ]m,n [Δt]m,n[ΔE]m, n ≥ [0.5ħ]m,n (4)

m (object scale location), n (observable scale location)n, m = {-∞ … -2, -1, 0, 1, 2 … +∞}

The Fractal certainty principle embodies a paradigm shift for scientific inquiry. Fractal Physics Theory proposes it isalways possible to draw a picture of physical phenomena which can accurately describe the reality of the phenomena.

2.9. Experiment 1. Construct a Quantum Camera

FPT predicts that neutrino/antineutrino energy is mainly composed of subquantum scale electromagnetic radiation(emr) emitted from quantum scale stars. Quantum cameras placed near concentrations of beta decaying matter cancapture images that when scaled-up, will resemble images of stars and galaxies. This subquantum scale emr can beimaged, perhaps from bits of nuclear material, since nuclear material is composed of many different lilliputian scale

elements. Exposure times of 1 femtosecond will image subquantum scale emr for 12 lilliputian scale years. Aperturesizes of 1 femtometer correspond to 379,000 subquantum scale kilometers. The Quantum camera must collect,channel, and amplify subquantum scale photons until one quantum scale photon can be effected. The process continuesuntil an image is formed.

2.10. Solar system is a cosmic scale neutron midway through cosmic scale beta decay – FPT matches

experimental data

Our solar system is one cosmic scale neutron midway through the process of cosmic scale Beta decay. The sum total ofall the electromagnetic radiation and neutrino radiation emitted by the Sun in ~ 9 billion years is one cosmic scaleantineutrino.

Consider neutron Beta decay: n → p + e- + antiνe (5)

The mass of the neutron (1.6749 x 10-27 kg) before the decay exceeds the masses of the proton (1.6726 x 10-27 kg) andelectron (9.1094 x 10-31 kg) after the decay. The missing mass (1.39 x 10-30 kg) is converted to energy (1.25 x 10-13 J),the kinetic energy of the proton and the electron and creates the antineutrino. The energy liberated during cosmic scaleneutron beta decay (1.25 x 10 -13 J) x (¥Energy = 1.190 x 1057) = 1.49 x 1044 J.

The current solar luminosity (3.8515 x 1026 W) radiating for 9 billion years equals 1.09 x 1044 J.

2.11. Pre-Solar system mass was a cosmic scale neutron – FPT matches experimental data

The neutron mass (1.6749 x 10-27 kg) divided by the electron mass (9.1094 x 10-31 kg) equals 1839.The pre-solar system mass (1.9928 x 1030 kg) divided by 1839 equals the cosmic scale electron mass (1.084 x 10

27 kg).

Planetary masses sum to 2.67 x 1027

kg. Therefore the Iron-Nickel cores of the planets could be the seeds of oneforming cosmic scale electron.

2.12. The Big Bang looks like a Cosmic Scale 1 Megaton fission explosion – FPT matches experimental data

Galactic spectra increase in redshifts as the estimated distances to these galaxies increase. Only a nuclear explosion,about 1 second into the fireball, if viewed from the lilliputian scale, would have properties self-similar to human scaleobservations of a Big Bang with all galaxies hurdling away from each other. The tremendous energy released that

powers a 1 Megaton nuclear explosion takes place in 0.60 μs, which the lilliputian scale perceives as 7 billion years.From self-similarity, FPT proposes that the energy that powered the Big Bang explosion was generated in 7 billionyears. Most of this energy, 99.9%, is released in the last 7 generations of fission. Therefore most of the Big Bangenergy was generated in the 840 million years immediately preceding the Big Bang. After 1.8 seconds, a 1 Megatonnuclear explosion has a fireball radius of 960 meters. If our visible universe is 13.6 billion years old, then it couldhave a radius = ct = 1.3 x 1026 meters. This corresponds to a titanic scale radius of 340 meters.





2.13. Missing Mass in Cosmology – FPT matches experimental data

The dynamics of galaxies and other cosmic structures require far more matter to exist in their vicinity than the matterestimated present from observed stars. FPT considers the vast majority of “visible” stars to be cosmic scale neutronrich cosmic scale fission fragments undergoing cosmic scale beta decay, the result of a cosmic scale fission explosion.The amount of stable, non-decaying nuclei in a fission nuclear explosion far exceeds the amount of nuclei decaying.Consequently, FPT predicts the “missing mass” to be a multitude of cosmic scale nuclei (from 1 to 240 solar masses)

with surface temperatures ~ 2.7 K distributed within and around galaxies. A significant percent of galactic dynamicscan be attributed to cosmic scale molecular bonds; electrostatic attractions of positively charged cosmic scale nuclei fornegatively charged cosmic scale electrons.

2.14. Largest Stellar masses are ~ 150 solar masses – FPT matches experimental data

Modern Physics estimates the largest stellar masses to be about 150 solar masses. FPT estimates the Sun’s mass to beabout 1 cosmic scale atomic mass unit (amu). The largest fission product masses, from either controlled fission ornuclear explosions are about 150 amu. Newly formed fission products undergo a series of beta decays until stablenuclei are formed. Each beta decay process radiates antineutrino energy from the nucleus. The final stable nuclearmass is only slightly less than its parent fission product.

2.15. WMAP 30 μKelvin anisotropies – FPT matches experimental data

Anisotropies in the cosmic microwave background (CMB) radiation have been detected by WMAP at 30 μK.

Applying the Doppler formula to the FPT predicted ambient flux of cosmic scale neutrons emitting radiation at T =2.725 K but measured at T = 2.725 K ± 30 μK indicate an ambient flux of cosmic scale neutrons moving at 3.3 km/s.

Nuclear explosion debris contains thermal neutrons with velocities as low as 2.2 km/s, and velocity is scale invariant.

2.16. High energy cosmic ray acceleration – FPT matches experimental data

Fissioning nuclei almost always split into two large fragments of unequal mass plus a few neutrons. Once formed, thefission fragments rip through the electron cloud of the original fission nucleus as they pass into the surroundingmedium. The new born fission fragments appear as highly energetic and highly ionized (+20 to +22) ions. Anyquantum scale atoms in the path of newly formed cosmic scale ions will have their positive nuclei blasted away. TheGreisen-Zatsepin-Kuz’min (GZK) cut off process applies to the highest energy cosmic rays interacting with the 2.7 KCMB radiation through photoproduction or photodisintegration. Cosmic ray energies greater than 5 x 1019 eV thattravel over 150 million light years will have their flux noticeably reduced due to these interactions. Therefore thehighest energy cosmic rays must be accelerated by cosmologically local sources. The cosmic scale proton charge is3.40 x 1021 C. A quantum scale proton and cosmic scale proton separated by Neptune’s orbital radius experiences

Coulomb potential energy:

(8.99 x 109 Nm2/C2)(1.60 x 10-19 C)(22)(3.40 x 1021 C)/30 AU = 24.0 J = 1.5 x 1020 eV

This energy is the same order of magnitude measured for very high energy cosmic rays! Furthermore, due to theinteraction of cosmic rays with CMB photons, the requirement of a cosmologically local accelerator is met. With theenormous abundances of highly charged, spinning, spherically distributed cosmic scale electrons, it is readily apparentwhy cosmic rays are observed to arrive at earth from all directions.

2.17. Solar cycle of 22.2 years – FPT matches experimental data

Unfissioned cosmic scale Uranium has combined with cosmic scale Oxygen to crystallize into cosmic scale UO2 crystals forming the core of the Milky Way galaxy. The UO2 crystal system is cubic; the structure type is fluorite. Thequantum scale length of the cell’s edge at room temperature = 5.47 x 10-10 m which is fractally self-similar to thecosmic scale UO2 crystal cell’s edge length = 2.07 x 1014 m = 1385 AU. The solar cycle is about 22.2 years long. Thesolar system has a velocity of 368 km/s ± 2 km/s calculated from WMAP data. The solar system travels 1723 AUs during one solar cycle. If the solar system travels at a 30° angle to a cell’s edge through a cosmic scale UraniumDioxide crystal, it will pass through 1 cosmic scale UO2 crystal in 22.2 years. Therefore regular periodicity observed inthe solar system can be correlated to points of gravitational and electric potential maxima and minima of cosmic scalemolten UO2.

2.18. CMBR Temperature is 2.725 K – FPT matches experimental data

Radiation emitted from the Sun is close to a black body curve; it is reasonable to expect radiation emitted at 2.725 K would fit a black body curve. Stellar spectra reveal a majority of Hydrogen and Helium is present in hot stars. In Earth





labs, with surface gravity = 9.81 m/s2, Helium has a normal boiling point 4.222 K with atmospheric pressure 101325Pa, and a superfluid transition temperature 2.1768 K with saturated vapor pressure 3130 Pa. FPT predicts local “dark” cosmic scale solar mass neutrons, with surface gravity = 926 m/s2, are relatively near the solar system. FPT predictssome cosmic scale neutrons have pure Helium atmospheres radiating at 2.725 K.

2.19. Experiment 2. Echo Radar off nearby cosmic scale nuclei

If radar focused at anisotropies in the CMBR is reflected back within weeks then the current Big Bang model isincorrect. Local cosmic scale nuclei and their cosmic scale electrons can be mapped by radar echo.

2.20. Gamma-ray bursts are cosmic scale neutron collisions – FPT matches experimental data

FPT proposes that gamma ray bursts arise from cosmic scale neutrons colliding with cosmic scale nuclei. Gamma-ray bursts are currently detected by orbiting satellites ~ 1/day or 1/86400 seconds. Therefore the cosmic scale neutroncollision rate = 1.16 x 10-5 collisions/second measured relative to the human scale. This corresponds to a cosmic scale

neutron collision rate = 4.38 x 1018 collisions/second relative to the cosmic scale. This rate is self-similar to quantum

scale neutron collision rates in solid fissioning material just prior to explosion time.

2.21. Supernovae and Nova are cosmic scale beta decay explosion moments – FPT matches experimental data

One second into a 1 Megaton fission bomb explosion will have particles of radioactive and stable matter coalescing.Many of the radioactive nuclei will be experiencing beta decay. At the end of beta decay an explosion occurs typically

hurtling the newly formed beta particle off at great velocities with the newly formed nuclei recoiling in the oppositedirection at a lower but high velocity.

2.22. Galaxies are cosmic scale radioactive particles – FPT matches experimental data

One second into a 1 Megaton fission bomb explosion will have particles of radioactive and stable matter coalescing.Many of the radioactive nuclei will be experiencing beta decay.

2.23. Binary stars are cosmic scale neutron absorption by cosmic scale nuclei – FPT matches experimental data

One second into a 1 Megaton fission bomb explosion will have many nuclei in the process of absorbing free neutrons.When this neutron capture process involves both the host nucleus and the captured orbiting neutron decaying, the pairwill appear as quantum scale binary stars.

3. Fractal Physics Theory – Electrons, Photons, Wave-Particles, and Atomic Capacitors

3.1. Fractal electron [6]

Modern Physics does not theoretically determine the electron’s mass, electric charge, magnetic dipole moment, andspin. These values can only be determined by measurement. The magnetic dipole moment is due to the spin. ModernPhysics considers the electron spin to be a Quantum Mechanical property that can not be visualized.

Fractal Physics Theory calculates the electron’s mass, electric charge, magnetic dipole moment, and spin from the properties of subquantum scale atoms. The electron’s mass is composed of 1.2 x 1052 of the most energetically stablesubquantum scale nuclei such as subquantum scale Iron and subquantum scale Nickel. Iron, Nickel, and to a lesserextent Cobalt all have the unique duel distinction of being both stellar thermonuclear endpoints and when cool enough,ferromagnets. The electron’s charge is due to an excess of 2.1 x 1040 subquantum scale electrons on its surface.Conducting metals contain a “gas” of mobile electrons that flow about the relatively stationary positive matrix. Theelectron has a reservoir of 1.2 x 1052 subquantum scale conduction electrons available to provide surface currentgenerating the electron’s magnetic dipole moment.

3.2. Experiment 3. El ectron li ll ipu tian scale phase energy predictions

Fractal Physics Theory calculates the energies required to heat, melt, boil, disperse and completely ionize thesubquantum scale iron atoms of an electron (Table 3). For a given object, such as an electron, FPT predicts its waveform to contain slightly higher mass-energy content than its particle form.





Table 3, Electron phase energies relative to the Human scalePhase # Electron Phase Energy (eV)

1 Heating Solid 5.46 x 10- 2 Melting Solid 1.41 x 10- 3 Heating Liquid 4.32 x 10- 4 Boiling Liquid 3.57 x 10-6 5 Work against qs-gravity

to disperse gas

0.015

6 Ionizing Iron 0.400

3.3. Wave/particle duality

Each subquantum scale atom composing an electron shares the same translational velocity as the electron. Encounterswith external fields of ambient objects can stimulate conversion of some of the electron’s translational kinetic energyinto increasing the internal kinetic energy of the electron’s subquantum scale atoms; the parallel subquantum scaleatoms’ translational velocities become randomized. The electron becomes “hotter” in the lilliputian scale and changes

phases. The quantum scale gaseous phase electron is now spreading out in space, delocalizing. Classical objects emitradiation from their surface according to the Stefan-Boltzmann equation:

P = εσ(surface area)T4 (6)

For a constant mass and size, a 10-fold increase in temperature results in a 10,000-fold increase in energy radiated per

unit time. According to the Viral Theorem, as a cloud expands, half of the gravitational potential energy gained comesfrom the kinetic energy of the cloud. As a gas expands it cools. Self-similar lilliputian scale equations are predicted byFPT to apply to objects such as electrons. For a given particle, a higher particle momentum has the potential togenerate a higher lilliputian scale internal temperature, leading to quantum scale phase changes, and emittingsubquantum scale radiation rapidly, thus limiting the delocalized size of the wave form (Figure 1).

3.4. Fractal Atomic Absorption and Emission – FPT matches experimental data

A capacitor is a device that stores energy in an electrostatic field. A capacitor is charged if its plates carry equal andopposite charges +q and – q. Charge is directly proportionally to the potential difference between the plates, q = CV. Acharged capacitor has stored in it an electric potential energy U equal to the work done by an external agent as thecapacitor is charged. This energy can be recovered if the capacitor is allowed to discharge. FPT proposes that the 1.2 x1052 subquantum scale atoms of the electron, in the ground state Hydrogen atom, disperses to occupy space within avolume of radius b = a0. The 2 x 1040 excess subquantum scale electrons distribute themselves evenly across thesurface area of this volume. The ground state of this H-atom is now a spherical capacitor with capacitance:

_+

Electron particle,Qs-solid sphere

Screen

-V

Electron waveform,

Qs-gaseous disk

+V

Figure 2, Electron dual slit experimentFigure 1, Electron dual slit experiment





C = (4πε0ab)/(b – a) (7)

ε0 = permittivity constanta = the proton’s radius ~ 1fm

b = a0

Using r n = n2r, spherical capacitor energy levels are calculated and Δn transitions between these energy levels

exactly reproduces the Bohr atom transition energies.

3.5.

Experiment 4. Measur e the radiu s of the soli d phase quantum scale electron

Fractal Physics Theory calculates the solid phase of the quantum scale electron to have a radius = 7.2 x 10 -17 m.

3.6. Origin of equal & opposite charges

Modern Physics does not explain why the proton charge is exactly equal and opposite the electron charge. FPT proposes that during neutron beta decay 2.1 x 1040 subquantum scale electrons are ionized from the forming proton andadhere to the forming electron. Exactly equal and opposite charges arise on the proton and electron.

3.7. Experiment 5. FPT predicts the electron’s mass slightly exceeds the positron’s mass

If the subquantum scale Iron/Nickel main body of the electron includes 2.1 x 1040 excess subquantum scale electrons,

then it seems reasonable to suspect the main body of the positron is also subquantum scale Iron/Nickel with 2.1 x 1040

missing subquantum scale electrons. The electron mass is predicted to exceed the positron mass by:

2(2.123 x 1040)(9.109 3826 x 10-31 kg)/(1.189 533 x 1057) = 3.25 x 10-47 kg

3.8. Fractal photon

Fractal Physics Theory proposes that a photon is the result of an enormous collection of subquantum scale photons.These subquantum scale photons all travel together in the same direction, are the same frequency, and are in phase. A

photon is the result of an enormous amplification of coherent subquantum scale photons. A photon is a subquantumscale LASER pulse. Regardless of its frequency, a single photon has angular momentum spin S = ħ = 1.054 572 x 10-34 Js. Using the scaling fractal ¥ħ = 4.506 624 x 1080, yields the cosmic scale value [ħ]1,0 = 4.752 559 x 1046 Js. A cosmicscale photon’s spin angular moment of 4.752 559 x 1046 Js is due to the sum of the spin angular moment of 4.506 624 x1080 photons. It is proposed that a photon is composed of 4.506 624 x 1080 subquantum scale photons. Each of the4.506 624 x 1080 subquantum scale photons composing a single photon all have the same wavelength and frequency as

the parent photon. These subquantum scale photons all have the same energy equal to 1/4.506 624 x 1080 of the parent photon’s energy.

3.9. Fractal Beta Decay

Subquantum scale cosmic rays are proposed to exist flowing randomly amongst nuclei and electrons. Thesesubquantum scale cosmic rays will impinge upon the surfaces of nuclei and electrons if not deflected by protectiveelectric and magnetic fields. Protons and electrons are naturally protected from subquantum scale cosmic rays by theirinherent force fields. Free neutrons and neutrons bound in nuclei have various amounts of their surface areasunprotected (exposed to bombarding subquantum scale cosmic rays). Various amounts of subquantum scale Helium isavailable on free neutrons and nuclei to act as subquantum scale thermonuclear engine coolant, boiling away excessheat which results from subquantum scale cosmic rays penetrating the nuclear surface.

3.10. Experiment 6. Lower Beta-decay activit y rates using subquan tum scale li quid Helium

3.11.

Experiment 7. Predict when specif ic fr ee neutrons will beta decay

The probabilistic nature of Beta decay can be improved upon. Detailed knowledge of the subquantum scale chemicalcomposition of free neutrons or nuclei and their neutron “surface area exposure level” will provide more accurate

predictions of specific nuclear lifetimes.

3.12. Experiment 8. Raise Beta-decay activit y rates by increasing fl ux of subquan tum scale cosmic ray parti cles





4. Fractal Physics Theory - Nucleons and the Strong Nuclear Force

4.1. Fractal Strong Nuclear Force [7]

The binding energy of a nucleus is the energy released when individual protons and neutrons are brought together toform a nucleus. The strong nuclear force is claimed to be a combination of inter-nucleon interactions and intra-nucleoninteractions (Figure 2). The inter-nucleon interactions involve quantum scale (qs) gravitational attraction, the reducing

effects of the intervening neutron’s lilliputian scale (ls) dielectric on proton-proton Coulomb repulsion and a variety oflilliputian scale electromagnetic attractions induced by a proton on adjacent neutrons. The intra-nucleon interactionsinvolve subquantum scale (sqs) fusion of the nucleon’s composite subquantum scale atoms, which results in increasingthe subquantum scale nuclear bonds of the subquantum scale atomic nuclei composing the nucleons.

4.2. Fractal nucleon quantum scale chemical compositions – FPT matches experimental data

With just two postulates, that the pre-solar system mass is the mass of a cosmic scale neutron and that a cosmic scaleneutron is composed of 100% Hydrogen atoms, FPT can calculate the fractal chemical compositions and bindingenergies of all nuclei (Z = 1 to 92+), refer to Tables 4, 5. It seems miraculous that the only way to obtain the mass ofthe most stable nuclei such as Iron 56 by this FPT method, is to completely fuse all the subquantum scale Hydrogenand subquantum scale Helium available in 56 separate protons and neutrons all the way to 100% subquantum scale Iron56. No further subquantum scale fusion is possible. The Iron 56 nucleus is one of the most stable nuclei precisely

because it is composed entirely of subquantum scale Iron 56 atoms.

4.3. Quantum scale gravity

Modern Physics Theory and Fractal Physics Theory diverge significantly on this point. FPT proposes that thegravitational constant, G, is not scale invariant. The gravitational constant scaling fractal:

¥G = ¥Length/¥Mass = 3.185 x 10-34 = [G]1,0/[G]-1,0

[G]1,0 = 6.6742 x 10-11 m3/(s2kg) gravitational constant at cosmic scale, measured relative to human scale[G]-1,0 = 2.0956 x 1023 m3/(s2kg) gravitational constant at quantum scale, measured relative to human scale

4.4. Experiments 9.a, 9.b, 9.c, etc., Many experiments wil l be able to distinguish between Modern Physics

Theor y’ s gravitation constant and Fractal Physics Theory’s quantum scale gravitati on constant.

Figure 2, Diagram of the fractal strong nuclear forceStrong Nuclear Force

Figure 2, Fractal Strong Nuclear Force Diagram

Proton-neutronPolarized sqs-atoms

U = -μE

Proton-neutron-protonls-Dielectric

U = +pp/(4πεr)

Inter-nucleon Forces Intra-nucleon Forces

Proton-neutronConduction sqs-electrons

U = -pnq/(4πε0r)

Sqs-FusionQs-Gravity Ls-Coulombic





4.5. Proposed origin of the Muon – FPT matches experimental data

Cosmic scale beta decay of a cosmic scale neutron ends with mostly Helium formed in the core of the cosmic scale proton. When cosmic rays (~ 90% protons) strike Earth’s upper atmosphere (mainly Nitrogen and Oxygen nuclei)many pions are released that quickly decay into muons. The muon’s mass is 1.883 531 x 10-28 kg, which is 11.261 %of the proton mass. The 1.900 826 x 10-28 kg of subquantum scale Helium roughly calculated to exist in a proton isextremely close, 100.9 %, to the muon’s mass. It is proposed that the collision of a high energy proton and a Nitrogen

or Oxygen nucleus are releasing coated subquantum scale Helium cores from protons, the pions. The charged pionthen sheds its subquantum scale coated layer and the subquantum scale Helium fuses to subquantum scale Iron, themuon. Helium 4 has zero spin and pions have zero spin. This mass of fused Iron equals 100.6% of the cs-muon’smass.

Table 4, Idealized subquantum scale chemical compositions

Particle*[Hydrogen]-3,0

(% Mass)[Helium]-3,0 (% Mass)

[Carbon]-3,0 (% Mass)

[Magnesium]-3,0 (% Mass)

[Iron]-3,0 (% Mass)

n 100.00 --- --- --- ---

p+ 88.64 11.36 --- --- ---

e− --- --- --- --- 100.00

d+ 83.45 16.55 --- --- ---

t+ 61.99 38.01 --- --- ---3He2+ 60.67 39.33 --- --- ---

4He2+ --- 80.96 19.04 --- ---12C6+ 8.84 5.72 75.44 10.00 ---

56Fe26+ --- --- --- --- 100.00*[O]-3,0 refers to an object located in the subquantum scale as observed from the human scale

Table 5, Fractal strong nuclear force

ParticleQuantum Scale

% GravityLilliputian Scale

% CoulombicSubquantum Scale

% Fusiond+ 0.08 33.18 66.74

t+ 0.05 17.41 82.543He2+ 0.06 15.80 84.144He2+ 0.04 7.78 92.1812C6+ 0.16 16.81 83.03

56

Fe26+

0.46 7.13 92.41

5. Fractal Physics Theory – Neutrinos and stars

5.1. The sum total of electromagnetic radiation and neutrinos emitted during a star’s life time is one antineutrino

relative to the cosmic scale [8]

Neutrinos and antineutrinos both arise during subquantum scale nuclear fusion and as such are considered to be similar.The totality of a star’s radiated energy (electromagnetic radiation plus neutrinos) over its nuclear burning lifetimecomprises one cosmic scale antineutrino. The Sun’s energy that constantly bathes the Earth is part of a single cosmicscale antineutrino (Table 6). Likewise, an antineutrino is the result of an ever spreading sphere of subquantum scale

photons, which are not in phase, and include a wide range of subquantum scale frequencies. Fractal antineutrinoscontinuously delocalize as they propagate; this differs markedly from Modern Physics antineutrinos.

Table 6, Solar Cosmic Scale Antineutrino Energy Over 9 Billion YearsSolar Radiation Power (Watts) Energy (Joules) % Energy

Photons 3.8418 x 10 1.0911 x 10 97.60 Neutrinos 9.4394 x 10 2.6810 x 10 2.40

Total 3.9362 x 10 1.1179 x 10 100.00

Fractal Physics Theory claims solar neutrinos do not “oscillate” but have their energies transformed by interactionswith stable atomic surfaces, the lilliputian scale “2.7 K cold” nuclear and electron surfaces. The neutrino’s initial rangeof subquantum scale photon energies are lowered to 1.570 x 10-79 Joules from absorption/radiation by the nuclear andelectron surfaces. This absorption/radiation of initial neutrino energy also increases the initial number of subquantum





scale photons by a factor = [fusing nuclei, surface temperature]-2,0/[1.246 x 1014 K]. The Sun emits electromagneticradiation approximately as Planck’s radiation law; therefore the majority component of neutrino energy is modeledwith a scaled version of Planck’s radiation law. Several radiation equations are generalized to scale; scaled radiationequations are used to model neutrino emission.

5.2.

Experiments 10.a, 10.b, 10.c, etc., Many experiments wil l be able to distingui sh between M odern Physics

Theory neutri nos and Fr actal Physics Theory neutri nos.

6. Conclusion

Fractal Physics Theory is a scientific paradigm that incorporates Fractal Geometry concepts of infinity, scale relativity,and self-similarity between scales, into the Universe and all its component pieces. This article summarized successesof six Fractal Physics Theory articles currently available. Dozens of facets of this theory already match experimentaldata, but far more important, many experiments are proposed that can refute Fractal Physics Theory. One group ofexperiments can explore fractal neutrinos, while another can explore the fractal electron, and a third set of experimentscan probe radioactivity. There are two sets of experiments that should be fairly easy to perform, one probing quantumscale gravity, and the other detecting nearby “dark stars”. This is the dawning of the age of Scalativity, when humanityembraces infinity, through Fractal Physics.

References

[1] B. Mandelbrot, Fractal Geometry of Nature, W. H. Freeman & Company, New York, 1983.

[2] L. Nottale, Fractal Space-time and Microphysics, Towards a Theory of Scale Relativity, World Scientific,Singapore, 1993.

[3] L. J. Malinowski, Fractal Physics Theory – Foundation, Fundamental J. Modern Physics 1(2) (2011), 133-168.

[4] L. J. Malinowski, Fractal Physics Theory – Cosmic Scale Nuclear Explosion Cosmology, Fundamental J. ModernPhysics 1(2) (2011), 169-195.

[5] L. J. Malinowski, Fractal Physics Theory – Cosmic Scale Cation (Sgr +6) at the Galactic Center, Scalativity LLC,Article 1 (2012), 1-9.

[6] L. J. Malinowski, Fractal Physics Theory – Electrons, Photons, Wave-Particles, and Atomic Capacitors,Fundamental J. Modern Physics 2(1) (2011), 73-88.

[7] L. J. Malinowski, Fractal Physics Theory – Nucleons and the Strong Force, Fundamental J. Modern Physics 2(1)(2011), 23-72.

[8] L. J. Malinowski, Fractal Physics Theory –– Neutrinos and Stars, Fundamental J. Modern Physics 1(2) (2011),197-221.

Fractal Physics Theory Success Summary and Proposed Experiments

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