Crouching Tigers: New Physics on the Road to Unification by Mr. Anonymous, a Physicist & Friend

Crouching Tigers: New Physics on the Road to Unification

by

Mr. Anonymous, a Physicist & Friend of FREE

Abstract

In recent years a number of theories have emerged suggesting that large scale and small scale structures in our universe share a common organizational pattern. Two of these theories are directly complimentary, each resulting in a range of similar predictions, each advancing purported solutions to long-standing problems in physics and cosmology. This article compares the two bodies of work and identifies those issues addressed in common. Both theories propose that a logarithmic fractal scaling rule underlies and constrains fundamental physical processes, and that a wide range of observed phenomena can be explained and accounted for by the application of a mathematical schema compatible with both formulations. Each theory advances a novel approach to unification in physics, asserting that the properties of space-time from the relativistic to the Planck scales are essentially holographic in nature.

The Schism

For the better part of a century physicists and cosmologists have grappled with the problem of trying to unify the observed forces of nature. The physical world described by scientists today is governed by four fundamental forces: Strong, Weak, Electromagnetic, and Gravitation. Each appears to dominate the behavior of matter within specified regions of scale. Gravity primarily affects the behavior of very large assemblages of matter — planets, stars, black holes, quasars,
galaxies, meta-galactic clusters, and thus, deeply influences the evolutionary progression of the universe as a whole. Electromagnetism seems to predominate at the scale of atomic and molecular interactions. The Strong and Weak forces appear to predominate within the subatomic arena where they govern the behavior of particles that constitute the atomic nucleus. Correspondingly, our discourse about the nature of matter, energy, motion, time and space is moderated by two highly successful yet mutually exclusive predictive theories: Relativity and Quantum Mechanics. Each theory yields precise predictions within specified regions of scale, but fundamental questions remain as to the origin and disposition of the four elemental forces. It appears that any further understanding about the birth, evolution and fate of the universe as we observe it may depend upon answering the following questions: How did these elemental forces come into existence?; and: Were they ever united? Ongoing attempts at achieving such a broad and applicable synthesis within physics fall under the rubric of Grand Unification Theories, GUTs, otherwise known as “theories of everything”. Such was the holy grail of Albert Einstein, who initially embarked upon his quest to unite Gravity with Electromagnetism in the early 20th Century. He failed to achieve this grand synthesis, but today there are a number of credible and provocative forays that could yield tangible fruit.

The introduction of Einstein’s relativity theories recast our cosmological debate by removing gravity from the realm of Newton’s mechanical forces and replacing it with a radical new geometric interpretation. Space was redefined as “space-time”, and the world was introduced to the notion of time as a “fourth dimension”. Space, we were told, is “curved” in the presence of matter, and the attractive effect of gravity that governs the behavior of massive objects is the result of that curvature. So accurate were Einstein’s geometric formulations, his General Relativity Theory has replaced Newton’s formulations for predicting how bodies should behave under the influence of gravitational fields.

In the same fashion, the introduction of the Quantum Theory in the 1920s made it possible to describe with precision the behavior of atoms and their constituents. This led to the emergence of Feynman’s Quantum Field Theory (1), which gave birth to the “Standard Model” that appears to accurately describe the behavior of subatomic particles. A problem arises at this magnitude of scale because Einstein’s gravitational formulations either break down or become irrelevant when quantum interactions and statistically-governed fluctuations predominate. At what point does Gravity interact with the other three elemental forces, and how can we account for its presence or seeming lack thereof at the level of the quantum? Gravity as we understand it appears to drive much of the behavior of the universe at large. Gravitational field strength is a function of mass concentration per unit of space-time. Compared in magnitude at the subatomic scale to the other three forces that closely bind the atom, Gravity is weak. How then, does it fit in? The overall coherency of physics may thus rest upon our comprehending Gravity’s connection to the other three forces that we observe. At this point, our basic understanding of nature is woefully incomplete.

Today’s physics literature is peppered with proclaimed “theories of everything”. Various contending quantum gravity theories, in addition to variations on the theme of multidimensional superstring theories, all vie for adoption. A number of these theories purport to resolve contradictions and omissions within Relativity and the Standard Model by adding additional hidden dimensions in order to confer the needed “degrees of freedom” required to solve perplexing differential equations, and to resolve paradoxes exhibited by extreme concentrations of mass, as in the formation of predicted singularities, such as black holes. Absurd valuations of Schrödinger’s wave equation that yield infinite energy values for hypothetical “point particles” at resolutions approaching and possibly exceeding the Planck interval are another bone of contention facing hopeful GUT proponents. A workable GUT must resolve such implicit paradoxes, while providing a street map for unifying the four fundamental forces backwards in time to a point where the hot infant universe first emerged out of the Big Bang. At that point in the thermodynamic history of the universe, the Standard Model tells us the four forces were united. Theories that aspire to unite Gravity with the other three fundamental forces are referred to as “super unified theories”, and a successful version would effectively fulfill Einstein’s quest.

Outlying Pioneers to Center Stage

Enrique Álvarez Vita is a Peruvian mathematician and theoretical physicist. He studied physics and mathematics at the Pontificia Universidad Católica del Peru, and at the Instituto de Biociencias, Letras y Ciencias Exactas in Sao Paulo, Brazil. He was a member of the Sociedade Brasileira Para o Progresso da Ciência. Mr. Vita is founder and director of the philosophy and science forum “La Serpiente de Oro.”; founder and current President of Centro de Estudios Aeroespaciales y Ciencias del Espacio. He is an advisor to the Science and Technology Department and to the Departamento de Investigación de Fenómenos Aéreos Anómalos of the Dirección de Intereses Aeroespaciales of the Peruvian Air Force. He is a member of the Asociación Peruana de Historia de la Ciencia and Vice President of the Academia Peruana de Filosofía y Ciencia. Mr. Vita is Vice Director of the philosophy circle “Yachaywiñay”, and member of the Ricardo Palma Foundation. Enrique Álvarez Vita promotes cultural, philosophic and scientific activities in Brazil and Perú, and is the author of several essays, articles and monographs. Due to his permanent institutional support he was awarded the Diploma and Medal of Honor by the Congress of the Republic of Peru and by the Peruvian Institute of Astronomy.

In 2014, Mr. Vita published a lecture (3) outlining a unique approach to the problems of unification in physics. He tackled long standing paradoxes head-on, arriving at a model that purportedly allows for predictions at resolutions up to and even exceeding the seemingly impenetrable Planck scale intervals. He did this by applying classical formulations that historically helped to lay the foundation for complex vector field analysis, the very same formalism that undergirds Einstein’s vector-tensor formulations for the gravitational field. If his model holds up, it would represent a heuristic synthesis within physics as well, because it purports to demonstrate that one can indeed apply non-statistical methodologies at scale resolutions largely thought to be barred by quantum-statistical uncertainty. In essence, his theory proposes a holographic “as above, so below” unified mathematical schema that re-formulates space-time into a nested infinite fractal series of bounded zones, where fundamental internal ratios and proportions are repeated and thus conserved. Placing Gravity within such a scaling framework radically adjusts the context of our enquiry, presumably allowing us to then ask the proper questions concerning the identity of this “force”.

The Problem of Renormalization

Perhaps one of the most persistent and long-standing difficulties encountered within quantum field theory is the issue of renormalization. Under complex path or extreme value circumstances, the cumulative sums, or integrals of possible states describing the likely energy values of say, an electron, can assume infinite magnitudes, making it nearly impossible to solve equations that should otherwise accurately predict particle behavior. Such paradoxes first cropped up in the 1930s when physicists were laying the foundation for quantum electrodynamics. Theoretically, such calculations should be straightforward if one knows the mass of a particle, it’s momentum, it’s electric charge mass value equivalent, and the values for the electromagnetic field in which it is moving. But nature is far more complex and interactive. Space-time at the quantum scale resolves into a froth of virtual particles and antiparticles that spontaneously emerge out of the “vacuum” of potential energy, colliding and annihilating one another. These hidden zero sum “virtual” interactions are always taking place, and yet they convey real energy to the particles whose behaviors we are attempting to describe and predict. These all-pervasive interactions should confer infinite energy to particles of small radius, a condition that is clearly not observed. Physicists learned to defuse the paradox of absurd infinite values for mass, energy and inertia by essentially fudging their calculations, thus preserving the usability of their equations. They adjusted the assumed magnitudes for mass, energy, momentum and field strength to agree with measured observation, thus ignoring or sidestepping the absurdities of predicted infinite values. Strictly speaking, they have created a tautology. This widely accepted method, which some would argue still represents a fundamental conundrum, has become standard practice: Renormalization. It has never been resolved. As such, it represents a dangling conceptual thorn at the very heart of quantum physics: The equations work fine if we “fix” some of the values going into them; but what do the, predicted infinities actually mean? Or do they represent a fundamental flaw in our model?

Enrique Álvarez Vita decided to tackle this one undeterred, and to apply a time-honored standard of classical scaler-vector field analysis to the conundrum. The result, he claims, was surprising:

“In this paper, we propose a physical model where the particles and antiparticles of the quantum vacuum, which in turn contains sub-levels of quantum vacuum, polarize electrical charges and the color of leptons and quarks in an infinite convergent sequence that includes gravity, which facilitates its incorporation with the other fundamental forces of nature.” …

For the sake of argument and exposition, Mr. Vita begins by calculating the electro and gravitational field potentials for an electron as if it were a classical particle of radius r:

“Let us first consider the gravitational and electrostatic fields of the electron. According to classical physics, the forces of gravitational attraction and electrical repulsion, which the electron exerts over itself (considering a spherical shell with a radium of r) is given as:

where G is the universal gravitational constant, is the electron mass, k is the Coulomb’s electrostatic constant and is the charge of the electron. The resulting force between both forces is expressed as:

The potential energy between the distances of a and b of the electron is expressed as:

Multiplying and dividing by (a length constant associated with the electron which for now is undetermined) we have:

where:

This change of variable is essential to the development of the model proposed. The expression is a potential electro-gravitational energy associated with the electron and is invariable with regard to the distance r. The integral pertaining to the function in the equation defines the potential electro-gravitational potential energy between two points situated at distances a and b from the particle.”

Thus, in rather straightforward classical reasoning, Mr. Vita employs standard field strength calculations to define a function relationship in potential energy between the gravitational and electrostatic fields for an electron. The same would apply to its antiparticle, the positron. Given that electrons and positrons each repel their like, while attracting their antiparticles, the quantum vacuum, with its fluctuating virtual particle-antiparticle pairs, argues Mr. Vita, naturally “polarizes” the concentration and distribution of charge and mass by repeating the above described dynamic for all the other particle–antiparticle pairs, which in turn affects over-all mass concentrations and the resulting cumulative gravitational field potential accordingly:

“At the experimental level, it has been proven that the electron attracts virtual positrons and repels virtual electrons present in the quantum vacuum, which diminish the intensity of the electrostatic field and produce quantum shielding or polarization. The opposite occurs with the gravitational force as a consequence of the repulsion between matter and anti-matter, an effect that later on attracts virtual electrons and repels virtual positrons, reinforcing the intensity of the
gravitational field. Still, given that the electrostatic force is much more intense than the gravitational force, the virtual positrons will be attracted and the virtual electrons will be repelled and this will produce an electro-gravitational shielding.”

He contends that such a dynamic is repeated in the next smaller region of scale by the interactions between quarks that are tightly bound within larger hadrons, the protons and neutrons. The color values or charges of the quarks, Mr. Vita asserts, are likewise “polarized”, impacting the resultant concentrations of mass, which ultimately determines the cumulative gravitational field strength for larger stable particle ensembles. In the general case, these would be the hadrons comprising densely packed atomic nuclei. The universe at this scale then begins to become recognizable, and it is at this scale level where the detectable effects of gravitation begin to emerge. At this point, Einstein’s field equations describing space-time
curvature begin to yield relevant predictions.

This repeating “polarizing” structural dynamic, according to Enrique Álvarez Vita, is the reason why we do not observe the infinite values for mass, energy or inertia that are predicted by quantum field equations prior to “renormalization”. The quantum universe has a built-in limiting factor that prevents runaway values. The excess energy is absorbed by virtual interactions, and values remain finite. Mr. Vita identifies this condition as an “energy drain”, and it appears to manifest a self-sealing property within each bounded region of scale where the appropriate fundamental forces tend to predominate. The overarching pattern is repeated within each scale zone, conserving ratios and proportions, while generating a nested infinite series of scale zones–a fractal pattern.

“This result leads us to a finite value for the potential at a null distance from the electron unlike the scenario in classical physics, which produces an infinite value. The potential energy leads us to a finite value for the potential at a zero distance from the electron unlike classical physics, which produces an infinite value. Potential energy is the very energy that, through successive integrations, generates the net potential electro-gravitational energy of the electron, and of the positrons and virtual electrons, invariant of the distance r.…”

… “As mentioned, in the case of the latter, the color charges attract their respective virtual anticolor particles which also polarizes gravity. The strong force is cancelled out at the level of the atomic nucleus while the electromagnetic forces are cancelled out at the atomic and molecular level due to the neutralization of the charges of protons and electrons, with the exception of some materials and massive bodies with weak electromagnetic fields. Unlike other forces, the weak gravitational forces do not cancel each other out and their cumulative effect transforms them into a dominant force on a cosmic level. Our calculations show that gravitational shielding can be generalized to any mass; gravity polarizes under the quantum fractal effects of virtual anti-particles; the infinite remains trapped and gravity is captured. At large distances, the potential gravitational energy is negative but a Planck scales, where nuclear and electric forcesbecome relevant, it polarizes and converges with others forces in the intrinsic energy of mass E = mc2, which would be the origin of all interactions, including gravity, which is in line with the fact that forces are the gradient or derivative of energy. This constitutes a step toward unifying the fundamental forces of nature.”!

Mr. Vita develops his representation of opposing electrostatic charges, opposing color charges associated with quarks, and gravitational field potential also described as a polarized charge, by evoking complex vector field dynamics. The use of complex numbers and polar coordinates provide the combinatoric latitude whereby he is able to derive a meta-structural geometry that is consistent for all of the binding or repulsive charge quantities under consideration. CPT symmetry would also be conserved within each bounded scale region:

“According to the model presented, the quantum vacuum appears to be formed by different sublevels in which the virtual particles and antiparticles would exert a polarizing action on the charge of real particles, which can be electrons or positrons. This process would continue indefinitely to the infinite. The total energy of the system is null. Given that the positron’s time flows from the past to the future but in an opposite direction to the electron’s, the sum total of time also is null as is the sum total of space, preserving CPT symmetry. This property would apply to all the fundamental particles of nature, meaning to the leptons and quarks, along with
their respective antiparticles. We can represent this process in the following diagram:

“We have seen that a real elemental particle such as the electron is polarized by the action of virtual particles from different energy levels in the quantum vacuum. These virtual particles should also polarize in the same manner as real particles in order to avoid generating infinite energies or exploding due to their own repulsive charge. Consequently, each virtual particle of the different sub-levels of the quantum vacuum follows the same laws as the real particles and are determined by the same equations. Keeping in mind this particularity and given that these sub-levels are an infinite sequence, it is relevant to question whether it is possible for a real particle to also be a virtual particle located on the first level of the quantum vacuum of another real particle. This model would be similar to that of a holographic universe, which is a virtual particle of another real particle and so on towards infinity; a model in which we can visualize a diagram included in another larger diagram and so on successively.

“From the proposed model, it is possible to infer the potential existence of a universe of antimatter and universes of matter and anti-matter within the other universes in an infinite sequence in which our universe would be merely a link in a chain of multiverses. For example, in the diagram, our universe would be represented by one of the areas that would in turn contain a micro-universe of matter and anti-matter. In the same way, our universe, along with the antimatter
universe, would be contained in a macro-universe of matter and antimatter.”

Summary and Implications

Due to spatial constraint, this paper can only review and summarize the core concepts articulated within Mr. Vita’s theory. For a full articulation, I refer the reader to: New Model of the Universe, by Enrique Álvarez Vita; English translation by Giorgio Piacenza. The manuscript is available at: (Giorgio: a download URL for the Spanish original and your translation is needed)

In summary, Mr. Vita’s theory proposes a unification schema whereby charged virtual particle interactions at the Planck scale actively influence and determine gravitational mass concentrations at larger scales, which in turn determines very large scale patterns and dynamics within our universe. A nested infinite series of quantum vacuum energy sub-levels is proposed in which fundamental ratios, proportions and symmetries are conserved. This could potentially make it possible to predict behaviors at scales hitherto considered inaccessible due to quantum-statistical uncertainty. The theory should therefore be testable in several domains:

• In the domain of cosmology, modified gravitational tensor and quantum field equations can be implemented that dispose of the infinite values predicted by current theory. Singularities predicted by Schwarzschild’s 1916 solutions to Einstein’s field equations would not occur. The massive objects that have been identified as black holes could then be reinterpreted based upon formulations that preclude infinite values. The properties of these objects may consequently differ from the classic interpretation of black holes.

• The asymmetry between matter and antimatter within our universe is potentially resolved by the erection of a multiverse schema that predicts adjacent antimatter and matter universes that share information in a manner consistent with quantum uncertainty fluctuations via membranes. Although anisotropic values exist within a given universe, overall symmetry would be conserved on the scale of a multiverse wherein the cumulative sum of all charges and energy gradients would be null.

• In the domain of quantum field theory, modified vectorial formulations utilizing complex numbers can be implemented to represent charge quantities that moderate particle behavior at various levels of scale. The sums and products of these complex vectors would yield real numbers which can be used to specifically predict attractive and repulsive particle behaviors and energy levels without requiring renormalization. The implementation of polar coordinates to create a complex vector space provides the degrees of freedom needed to account for and predict phenomena, which includes the strong force that binds hadrons within the atomic nucleus. Thus, a unified mathematical schema whereby the four primary forces are interoperable and can be co-derived is proposed that does not require additional dimensions:

“It is interesting to note that the unitary charges of nature’s fundamental forces can be represented in a complex vector field of four dimensions, as illustrated in the figure below, in which the color charges of the quarks are represented on a plane determined by the directional vectors i, j; the electrostatic charge by k and the gravitational charge by li. Gravity, the only force that has not been unified until today, would possess an imaginary charge and a gravitational field and gravitational mass mi, differing from the inertial mass m, which would be real. This concept is not contemplated in current physics. In this case, the directional vectors form an angle of 90° whose cosign is 0, meaning that there is neither attraction nor repulsion, corresponding with the fact that these forces do not interact.

For example, the electro-gravitational force between two electrons separated by a distance r would be expressed as the scalar product of two complex vectors:”

The use of complex numbers in a vector space of four dimensions suggests that the model of a fluctuating virtual quantum vacuum as delineated in Mr. Vita’s theory would allow phase-conjugate interactions supportive of a quantum hologram operating at the Planck scales.

Global Scaling Theory

In 1982, a young German mathematician working on sensitive and restricted projects at the old Soviet Academy of Sciences published an extraordinarily comprehensive body of work.

Dr. Hartmut Müller was born in 1954 in Hildburghausen, Thuringia, Germany. He studied mathematics, physics and philosophy at Leningrad (St. Petersburg) University in the USSR, and in 1979 was promoted to a full Professorship in Applied Mathematics at the prestigious Soviet/Russian Academy of Sciences. There he was employed until 1991 as a professor and research scientist. During his time in the Soviet Union and Russia, Dr. Müller conducted extensive research into the fundamental patterns that underlie observable natural phenomena. He made
significant contributions to the Soviet Space Program. In 1982 he developed a pan-disciplinary systems theory that could be applied to nearly all fields of scientific enquiry. His “Global Scaling Theory” is today regarded by many as a highly significant and important contribution to the natural sciences.

Due to the potential technological ramifications of the theory, most of his work was deposited into the information archives of the Russian Academy of Sciences and secretly secured with limited access. Unfortunately, therefore, this important research and theory, although confirmed by numerous well known Russian and other international scientists, was unavailable to the larger scientific community until 2001. This was due to a confidentiality agreement between Dr. Müller and the government of the Russian Federation stipulating that he not publish anything about his research results for ten years after his return to Germany in 1991. The world at large did not find out about Global Scaling Theory until the first decade of this century. To this day, there is still a dearth of familiarity with this body of work.

Global Scaling Theory (GST) asserts that all observable natural processes conform to a logarithmic rather than linear numerical progression. This runs contrary to many systems of scientific measurement in use today, which presume linearity in numerical standards. In addition, Dr. Müller has determined that this logarithmic pattern is “fractal and hyperbolic” in form, which provides a universal ordering principle that can be identified and quantized in virtually all natural phenomena.

One of the theory’s greatest and most fundamental achievements is in mathematics, and it is this contribution that sets the stage for possible wide-spread application of GST across disciplines. Dr. Müller has purportedly solved the mystery of predicting the occurrence of prime numbers. Primes, natural numbers greater than 1 having no other divisors other than 1 and themselves, are sprinkled seemingly at random throughout the number line. For centuries, mathematicians have attempted to articulate a reliable rule that could predict their occurrence.

This has never been achieved. The pattern remains inscrutable until one counts out successive groups of numbers that are logarithmically greater by volume than previous groups. At that point, the primes always occur within the same position on the number line as in the smaller number groups, rendering their frequency of occurrence entirely predictable. The over-arching pattern is logarithmic and recurring, whereby the distribution of primes becomes scale-invariant.
This establishes the repeating pattern as fractal.

The repeating distribution of prime numbers plotted on a fractal logarithmic scale.

“If one compares the distribution, for example the lighter marked areas, one can recognize a repeat of the example, from right to left, so to speak, with decreasing resolution. The further one moves along the number line from right to left, the more the logarithmic fractal unfolds to reveal the set of prime-factors.”

“The logarithmic scale-invariance of the distribution of the prime numbers is a fundamental property of the continuum of numbers. Moreover, this is the only non-trivial statement that holds true for all prime numbers.”

“Logarithmic scale-invariance of the prime-factor density distribution means that one can speak about a standing density-wave in the number continuum. The prime factors, 2 and 3 produce the base-oscillation, and early prime factors produce the spectrum of overtones.”

“We live in a logarithmic world”…, writes Dr. Müller. “…Scaling means logarithmic scale-invariance. Scaling is a basic quality of fractal structures and processes. The Global Scaling Theory explains why structures and processes of nature are fractal and the cause of logarithmic scale-invariance.”

At the heart of GST is a recognition that the very structure of space-time conforms to a logarithmic fractal pattern. The pattern is one that was established by the dynamic event that birthed our universe nearly 14 billion years ago, a cataclysmic occurrence that we term the “Big Bang”. The rapid inflationary expansion of space acted as a shockwave under confinement. The result was an echo slightly out of phase with the primary concussion, which then logarithmically fractured due to cumulative phase interference. The trigonometric functions established by this phasing imbued the universe with a resultant rotational coefficient. As space expanded outward and the universe cooled and coalesced, this “gravitational standing wave” continued to pervade the space-time continuum, maintaining its fundamental phase relationship to the initial concussion that sent matter hurling outward. This manifestation can be viewed as an initial parameter of the universe from its inception. Harmonic iterations of the gravitational standing wave can be found within the quantum resonance spectrums of fundamental subatomic particles. (6) Consequently, all of physics, and by extension, all of chemistry, eventually planetary geologies and biological evolution, were constrained and modulated by this fundamental “pressure wave” pattern. This is a holographic “as above, so below” construct.

According to Dr. Müller, the implicit embedded fractal pattern profoundly affects the distribution and clustering of information and entropy throughout the cosmos. It permeates down to subatomic scales, repeating itself ad infinitum. The same patterning can presumably be used to decipher and predict the gravitational clustering of the very largest of astronomical structures7, as well as the distribution of charge, spin and mass at Planck scale intervals. If the theory can be repeatedly tested and corroborated, its applicability appears to be universal.

What is a standing wave? Tie one end of a string onto a doorknob. Stand some distance away, and jiggle the other end of the string up and down at regular intervals. Observe the recurring stable transverse waveform that appears to fill the space between the doorknob and your hand. The stationary form of the wave remains stable as long as your hand remains in motion. Only the number of crests and valleys change in proportion to the frequency of your hand oscillations.

Dr. Müller:

“A standing wave in a homogenous space arises only if in the direction of the wave penetration the space is finite and if the half wave length is equal to an integer part of the medium size…”(4) (in this case, the spatial distance between the doorknob and your hand)

According to Dr. Müller, the existence of all standing waves, by definition, is directly dependent upon to the existence of prime numbers:

“As a consequence we can find for any low enough resonant oscillation mode frequency, f0 a higher mode frequency f1 with an integer relationship n = f1/f0. The frequencies of such resonant oscillation modes generate exponential series:

“The next figure shows the situation with n = 3 and k = 0, 1, 2, … for transversal oscillations:

“Therefore, the compete resonant oscillation frequency spectrum can be represented as a set of logarithmic fractal spectra with natural n = 1, 2, 3,… In this representation the generation of the complete resonant oscillation frequency spectrum can be understood as an arithmetical task, what can be reduced to the fundamental theorem of arithmetic, that every natural number greater than 1 can be written as a unique product of prime numbers.” (4)

The formula stated above is a preliminary iteration of the Müller Fractal Equation whereby GST is able to calculate optimal harmonic resonance frequencies operating within energetic and informational systems at various levels of scale. This has enabled Dr. Müller and his colleagues to identify and predict the best operating conditions for phenomena observed throughout the natural world. It has enabled them to predict the taxonomy and distribution of known and hypothesized subatomic particles; the mass and charge distribution for hadrons bound and clustered within the atomic nucleus, and hence, the optimal morphology of the Periodic Table. It has enabled them to calculate the optimal distribution for ecological niches and species within the earth’s biosphere given the spectral, thermodynamic and gravimetric parameters of our solar system and planet.

“Oscillations are the most energetically efficient kind of movement. For this reason, all matter, not only each atom, but also the planetary system and our galaxy, oscillate, and light is unfolding oscillation and, naturally, the cells and organs of our bodies also oscillate.” (4)

“Based on their energy efficiency, oscillatory processes determine the organization of matter at all levels — from atoms to galaxies.” … (4)

“Scaling arises very simply — as a consequence of natural oscillation processes. Natural oscillations are oscillations of matter that already exist at very low energy levels. Therefore they lose few energy, and likewise fulfill the conservation law of energy.” (4)

“The energy of an oscillation is dependent on its amplitude as well as on its frequency (events per time unit). … (4)

“Natural oscillations of matter produce logarithmic, fractal spectrums of the frequencies, wavelengths, amplitudes and a logarithmic fractal network of oscillating nodes in space.” (4)

Thus, Dr. Müller outlines a unitary mathematical schema that describes an interactive and embedded organizing principle operant at all levels of scale. This principle is one that conserves fundamental ratios, proportions and symmetries irrespective of the level of scale under consideration, rendering these values scale-invariant. This schema also establishes the interconnecting principle of harmonic oscillation as fundamental to the processes and organizational structures found throughout the physical world.

“In physical mediums, base-tones, upper- or undertones are produced simultaneously, and in this there arise consonances and dissonances. Not only our hearing can distinguish consonance from dissonance; this capability extends to all matter, and has to do with the energy expenditure necessary to produce an overtone. A musical ‘Fifth’ arises most easily (the least expense of energy per oscillation period), because merely a frequency doubling and trebling is
necessary in order to produce an overtone in interval of 3/2 of the base frequency. Somewhat more energy is necessary to produce a musical ‘Fourth’, 4/3, while this additionally requires a quadrupling of the base frequency; and even more energy is necessary for the production of the larger musical ‘Third’, 6/5, of the same amplitude, and so forth.

Natural oscillations of matter are probably the most important structure-forming factor in the universe. For this reason one finds fractal proportions everywhere in nature. The logarithmic fractal distribution of matter in the universe is a consequence of natural oscillation processes in cosmic, space and time measurement scales. In this connection, one speaks of the “Melody of Creation” (4)

GST also asserts that matter resonates harmonically at the lowest levels of energy. These harmonic vibratory patterns correspond to quantum fluctuations at the Planck scales; the so-called zero-point oscillations of virtual particles in the vacuum:

“The Spectrum of Vacuum Resonances (4)

The physical vacuum represents the possible energetically-lowest state of matter. This means, however, that in the vacuum only natural oscillations are possible:!

The Planck Formula:

(h is the Planck Constant) gives the impression that the energy of the natural oscillation of a vacuum-oscillator is frequency-dependent and quantized. Consequently, energy can only be absorbed or emitted in determined portions. That also means that blue light is more energetic than red light.)

Based on the continued fraction method we search the natural oscillation frequencies of a chain system of many similar harmonic oscillators in this form:

ƒ is a natural frequency of a chain system of similar harmonic oscillators, ƒ0 is the natural frequency of one isolated harmonic oscillator, S is a continued fraction with integer elements:

Dr. Müller and associates have determined that the oldest, most energy efficient, stable, compact and all-pervasive structure in the known universe should constitute the baseline standard for anchoring their logarithmic fractal formulations. It is a structure that was created in vast abundance at the very beginning of the universe, and it forms the basis for all subsequent iterations of matter and complex evolving systems. Once this primary reference standard is identified and calibrated, all other forthcoming structures and processes can then be subjected to analysis and comparison. That stable and compact structure is the proton. (13)

“The Proton Resonance Spectrum

Whether atom, planetary system, or Milky Way — over 99 percent of the volume of normal matter consists of vacuum (particle-free physical fields). Elementary particles, from which matter consists, are vacuum-resonances, and consequently oscillation-nodes, attractors, and singularities of the vacuum. Vacuum-resonance is one of the most important mechanism, which regulates the harmonic organization of matter at all levels (scales) — from the subatomic particles to the galaxies. And this is a matter of harmonic oscillations, one speaks of the ‘Melody of Creation.’

The proton is, by far, the most stable vacuum-resonance. Its life-span exceeds everything imaginable, exceeding minimum one-hundred-thousand billion billion billion years. No one knows the actual life-span of the Proton. No scientist could ever witness the decay of a proton. The unusually high life-span of the Proton is the reason why over 99 percent of matter’s mass consists of nucleons — protons and proton resonances. This is why proton resonances determine the course of all processes and the composition of all structures in the universe.

The objective of the Global Scaling Theory is the spectrum of proton resonances. As spectrum of natural oscillation processes, it is fractal, that means fragmentary, similarly which is itself and logarithmically scale-invariant. The Global Scaling Theory sees in logarithmic scale-invariance of the spectrum of proton resonances the origin of the Global Scaling phenomenon — the logarithmic scale-invariance in the composition of matter.

Based on the logarithmic spectrum of the proton, resonances can be described by the following continued fraction:

“… The physical properties of the proton define the calibration units of the Global Scaling Theory, which are used in the Global Scaling analysis of measurement data.” (4)

Using a detailed breakdown of the proton’s physical parameters, Dr. Müller and colleagues have been able to identify “harmonic resonance frequencies” based upon those parameters that can be scaled up logarithmically for analysis and application within larger regions of scale. Those harmonics of the proton resonance spectrum are then utilized to define optimal energetic levels and morphological patterns within a wide range of observable natural systems. (5)

The following argument excerpted from Dr. Müller’s Global Scaling Theory Compendium (4) illustrates the origination of the Müller Fractal based upon data derived from analysis of the proton’s quantum resonance spectrum.

“Global Scaling Analysis

Global Scaling Analysis begins with the localization of reproducible measure values in the correspondingly calibrated proton resonance spectrum. Mathematically, this first stage in Global Scaling Analysis consists of the following steps:

1. One divides the measure value by the corresponding proton calibration unit.

Example: GS Analysis of the wavelength

2. The logarithm of the result based on e = 2,71828… is calculated:

ln(2,56765… •109 ) 21,666…

3. The logarithm is decomposed into a Global Scaling continued fraction:

21,666… = 0 + 21 + 2/3 = [21 + 0;3]

Thus GST establishes a fulcrum point whereby analysts are purportedly able to leverage a predictive algorithm operating across multiple domains. This has resulted in a realignment in measurement standards producing a logarithmic scale that identifies regions or nodes of high information density alternating with regions of high entropy and thermal equilibrium. These regions are symmetrically distributed and scale-invariant. Where regions of high information density occur, they appear to coincide with resonance nodes that are harmonics of the proton spectrum. Where regions of low information and high entropy occur, they appear to coincide with resonance patterns that are chaotic or discordant with respect to the proton spectrum. (9, 10)

This has enabled Dr. Müller and colleagues to identify key optimization parameters driving the structures and processes evidenced within specified regions of scale. This rule purportedly applies at the Planck scales as well as at the cosmological Schwarzschild intervals. (15) The optimization rule also applies to regions of scale where biological evolution is likely to occur in planetary systems, yielding a set of energetic values most conducive for the emergence of life.

Summary and Implications

Global Scaling Theory represents a comprehensive multidisciplinary synthesis that has been under development for more than three decades.

Again, space in this article does not permit a full exposition of this provocative and complex work. Links for additional reading will be provided in the reference section at the end.

The theory has wide-ranging applicability. It should therefore be testable in several domains:

• In the domain of cosmology, GST provides algorithms that can be used to recalibrate the rate of the universe’s continued and accelerating expansion. It provides a scaffold for predicting the distribution of gravitational mass concentration (6,7), and the frequency of occurrence for such objects as black holes and the clustering of galaxies. At the cosmological scale, GST asserts that the physical parameters of our universe are consistent with those predicted for the interior of a rotating black hole. (10,16) Such parameters would also apply to the interior of the proton, suggesting that the ensemble of three quarks forming these highly stable and durable structures are themselves rotating black hole-like manifestations. (13) This places gravity within a scaling framework that can be adjusted to a fractal logarithmic pattern anchored to the proton resonance spectrum, which may form the basis for a “super unified theory”.

• In the domain of quantum field theory, GST predicts a specific means whereby quantum information can be conveyed at trans-luminal speed by tapping into harmonic vibratory nodes identified within the proton frequency spectrum. Dr. Müller claims to have achieved reliable quantum teleportation to facilitate such instantaneous data transfers. (8) Prototype devices have been constructed. GST asserts that such information transfers continually occur in nature via zero-point vacuum fluctuations. (5) Such manifestations would potentially support the operating of a quantum hologram at the Planck scale intervals.

• In the domain of evolutionary biology, GST predicts optimal thermal and spectral parameters for the creation of life, and provides a basis for predicting the frequency distribution of solar systems and planets that are likely to support such manifestations. (4) It can also be used to calibrate and analyze information gleaned from earth’s fossil record.

• In the domain of environmental science, GST predicts optimal energetic and thermal conditions for maintaining a healthy and diverse biosphere. It provides quantitative guidelines for establishing the boundaries of stability for the planet’s thermal equilibrium. (4)

• In the domain of information science, GST establishes a means whereby it is possible to transmit, store and retrieve data directly from the quantum vacuum, taking “cloud computing” to an exponentially higher level. This would be a quantum equivalent to the “Akashic Records”. Recent experiments have demonstrated that such data transfers can occur at trans-luminal speed, with no need for protective encryption. (12)

• In the domain of public infrastructure, GST purportedly provides the parameters for achieving highly energy-efficient non-polluting transportation via anti-gravity technology. The proton resonance spectrum also provides a quantum means for wireless telecommunication that eliminates the electromagnetic “smog” associated with today’s cell phone technology, thus ameliorating the potential negative health effects of the current system. (8,11)

• In the domain of medicine and healing, GST supports audio, visual and electromagnetic vibratory modalities that may be able to optimize growth and repair in living tissue. Such frequencies can be rigorously identified and applied through appropriate technologies. (4)

• In the domain of urban design, social organization, planning and esthetics, GST can provide guidance for architects, engineers, political and corporate innovators to enable the creation of vibrant, healthy and accessible human-scale community environments. (4, 11)

The system optimization protocols that have been derived from the proton resonance spectrum and the gravitational standing wave can be implemented to design new, sustainable, environmentally benign technologies. (17)

Dr. Müller has conducted a number of experiments to illustrate those potentials, and a number of prototypes have allegedly been constructed. An R&D company has been set up, Global Scaling Applications, to explore, prototype and bring such innovations to market. (17)

Conclusions

Both the “New Universe” theory of Enrique Álvarez Vita, and the Global Scaling Theory of Dr. Hartmut Müller hold promise for resolving a number of long-lived problems within physics and cosmology. Both theories support a holographic model of space-time based upon a logarithmic fractal structure. Independent of one another, each theory clearly articulates a mathematical framework for addressing the issues associated with Grand Unification, which includes redefining the relationship of gravitation to the other three fundamental forces identified by the Standard Model. Both theories make specific and complimentary predictions about fluctuating energy densities at the Planck scale. The framework of both theories can support the existence of a quantum hologram based upon virtual particle fluctuations in the vacuum.
References

1. Feynman, R.P., Leighton, R.B, Sands, M; The Feynman Lectures on Physics, Vol. III: The New Millennium Edition: Quantum Mechanics (Volume 2) © 1965, 2006, 2010 by California Institute of Technology; published by Basic Books

2. The Schrödinger Equation: Erwin Schrödinger 1887–1961 Nobel Prize in Physics 1933 http://inside.mines.edu/~fsarazin/phgn310/PDFs/QuantumLect4.pdf

3. New Model of the Universe, © 2014 by Enrique Álvarez Vita; English translation by Giorgio Piacenza. (PDF download URL to be established)

4. Müller H. and Müller E, Global Scaling Theory Compendium; © 2008 Global Scaling Research Institute, Munich, Germany
http://www.anr-institute.com/wp-content/uploads/2011/09/gscompv18_en.pdf

5. Müller H. Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators; Progress in Physics, Vol 2, April, 2009
http://www.ptep-online.com/index_files/2009/PP-17-13.PDF

6. Müller H. Fractal Scaling Models of Natural Oscillations in Chain Systems and the Mass Distribution of Particles; Progress in Physics, Vol 3, July, 2010
http://www.ptep-online.com/index_files/2010/PP-22-10.PDF

7. Müller H. Fractal Scaling Models of Natural Oscillations in Chain Systems and the Mass Distribution of the Celestial Bodies in the Solar System; Progress in Physics, Vol 1, January 2010
http://www.ptep-online.com/index_files/2010/PP-20-10.PDF

8. Dr. H. Müller, Quantum Teleportation demonstration: Wolfratshausen to Krems, Germany, 2003 (German language page): http://web.petabox.bibalex.org/web/20050306171535/
www.donau-uni.ac.at/de/studium/fachabteilungen/tim/zentren/timlab/news/archiv/02475/
index.php

9. Belyakov A. V. Is the Field of Numbers a Real Physical Field? On the Frequent Distribution and Masses of the Elementary Particles; Progress in Physics, Vol 3, July, 2010
http://www.ptep-online.com/index_files/2010/PP-22-09.PDF

10. A. Ries, M.V. L. Fook. Fractal Structure of Nature’s Preferred Masses: Application of the Model of Oscillations in a Chain System; Progress in Physics, Vol 4, October, 2010

11. Prof. Alfred Evert on Global Scaling Theory:
http://www.evert.de/ap0207e.htm

12. Universe as Internet Provider?: Global Scaling Theory and telecommunications (German language page)
http://www.nachrichten.ch/detail/168756.htm

13. Tatischeff B. Fractals and log- periodic corrections applied to masses and energy levels of several nuclei; arXiv: 1107.1976v1 [Physics.gen-phh] 11, July, 2011 http://arxiv.org/pdf/1107.1976v1.pdf

14. A. Ries, M.V. L. Fook. Application of the Model of Oscillations in a Chain System to the Solar System; Progress in Physics, Vol 1, January, 2011
http://www.ptep-online.com/index_files/2011/PP-24-18.PDF

15. Simon E. Shnoll. Changes in the fine structure of stochastic distributions as a consequence of space- time fluctuations; http://arxiv.org/pdf/physics/0602017.pdf

16. V.A. Panchelyuga, S.E. Shnoll. Experimental investigation of spinning massive body influence on fine structure of distribution functions of alpha- decay rate fluctuations; http://arxiv.org/pdf/physics/0606173.pdf

17. Global Scaling Theory: What is it? http://globalscalingtheory.com