Geometry of the quantum structure of spacetime

Alexander Esih Muvrin

INTRODUCTION

Werner Heisenberg in Physics and Philosophy, 1958

We offer evidence that our discoveries present a significant contribution towards resolving some of the current difficulties of grand unification research, such as the questions regarding the fundamental structure of our universe, its origin, evolution and its age; the reconciliation of the mathematical concept of continuum and limitless continuity with the concept of spacetime; the concept of an *acausal** connection *active in the spacetime continuum, where according to Carl Gustav Jung and Wolfgang Pauli, "our primary mathematical intuitions could be arranged before we become conscious of them" -- with the number being primordial, pre-existent to our consciousness (in quantum mechanics there are effects such as quantum tunneling, radioactive decay of an atom and the probability function collapse that might be considered acausal); the essence of the material body, that is extension itself and its universal non-local connections; the shortcoming of the Cartesian coordinate system with its patchwork of bounding surfaces and coordinates; the indeterminate notion of a point particle; the space composed of points; the relationship of space to matter and light to time; the *res** cogitans* and the *res** extensa*; the cosmological position of man and the inevitability of the *weak *anthropic principle, as demonstrated within an interval of 1-5-9-13 stem cells -- an *evolutionary cycle* that is an integral, coherent, *zusammenhangend** *part of the 27 stem cells of The Life Sequence.

When observed and studied in their geometrodynamic interaction and within the interval of 1-5-9-13 cells of references, we notice the importance of a *dynamic equilibrium *of the composite states of matter as experienced by us the* observers *and *participants*, the phenomena that emanate throughout the various scales of resolution of the cellular structure of spacetime. These evolutionary sequences of a threesmalized *** **and quantized system, elucidated as the ratio between space, time, energy, matter, length, volume, surfaces and distances among each and every physical phenomena in our universe are subsumed by our metric causal structure of spacetime and its intrinsically interdependent gravitational field (s) within its unique and comprehensive coordinate system of intervals -- all emanating from the coherence theory's ** sole criterion of truth, that is from the realm of universal quantum ħ=c=1. ***

When gravity is added at 1.22 ^{19 }GeV to a realm of the universal quantum and the world of Planck scale, Planck constants, units and Planck time -- the all of physics becomes one. As the widely used Mendeleev's Periodic Table of Elements arranged in order of increasing proton number describes the physical and chemical properties of elements, our system of 137 (141) stem cells, arranged in intervals of 1-5-9-13 proposes a model to describe the creation and the evolution of all forms of matter, energy states, fundamental forces, transitory astronomical events and the quntum structure of spacetime. By providing a new speculative insight into the pre-Big Bang unfolding of the Primordial energy fluctuation, the carriers of the information at - and before - the Planck time, we observe a strong complementarity between the sources of the Primordial gravitational waves, PGW and the Cosmic microwave background, CMB. A B

We recall that, as in quantum mechanics, our all embracing Theory is determined and governed by a single parameter ħ. As such it offers a new insight into dynamical structure, order and measure of the quantum world of the entire universe,* discrete and yet continuous on the global scale, *by identifying the universal gravitational field and the metric causal structure of spacetime to which all physical events are reducible. It is in accord with Einstein's theory of general relativity that is a field theory of gravitation that acts across large scales, quantum mechanics which describes electromagnetism and the strong and weak nuclear interactions, theory of quantum gravity that resembles general relativity at the microscopic scale, simplicity principle, Heisenberg's uncertainty principle... and our capacity to comprehend it in the first place.

The fact that, our Theory is in conformity with the proposition of Einstein's theory of relativity that the laws of nature and the geometry of spacetime are *interdependent*, also implies that the universality of length, distance and volume criterion *must *emerge as a simple, logical and rational, predictable, measurable and verifiable quantity, based on the simple order, ratio, measure, symmetry, structure and interval of its combinatorial geometrodynamic system of stem cells (space, time, energy and matter).

The geometry of our Grand Unified Theory, encoded in the metric causal structure of spacetime, connects us to here and there and now and then**.** It is a transeunt four plus seven-dimensional map of our rationally comprehended objective reality where the concept of extended matter is fully integrated with the concept of spacetime by eliminating the existence of a space composed of points. It allows us to intuit, imagine, discover, observe, predict and study all natural phenomena -- to visually, empirically and rationally explore their essence and existence.

The fundamental quantum structure of our universe emerges as a dynamic, fundamentally harmonic phenomenon with its "center" everywhere and its circumferences clearly definable by its intrinsic, unique and comprehensive coordinate system and by its intervals being our measuring rods -- whose metric value was deciphered by threesmalizing our currently used decimal system -- by reducing it to a system pertaining to thirds or to the number 3.

We are proposing that the Cartesian coordinate system, while still retaining its obvious usefulness in regard to its geometric and mathematical exactitude in describing the world of unrelated parts be superseded by our new coordinate system, an inevasible framework for predicting, measuring and verifying the geometry and the structure of spacetime from the outset, one that encompasses the totality of the unitary structure of the whole universe. The difficulties that a man has encountered in the search for truth, the real quality and the real relation, through the use of ratios, proportions, intervals and their relationships, particularly within the realm of infinitesimal and infinitival appear to vanish when each and every physical phenomenon attains its full and equal, intelligible, logical and rational, finite but without boundaries spacetime field of representation, thus, unifying the reality of our universe with the geometrical and mathematical exactitude.

We are witnessing the revolution in scalable high-performance modeling, simulation, visualization and computing that requires a novel conception of the structure of spacetime. Our Theory provides an inevitable spacetime coordinate system and a discrete yet continuous cosmological scale emanating as an exact threesmalized multiple of ħ=c=1. Its AUHCR -- Adaptive Universal Hierarchical Cell Refinement Algorithm (still to be developed) supersedes the obsolete decimalized single scale grid and the variant forms of AMR -- Adaptive Mesh Refinement. As such it can resolve features or physical phenomena within the real and physical scale and four-dimensional spacetime. It saves computer memory and CPU by concentrating on one of twenty-seven stem cells at one time -- where more precise resolution is required; it eliminates the need to arbitrarily repartition subdomain; it employs the same algorithms throughout the intervals of 1-5-9-13, as the hierarchically organized magnitude of each of the 137 stem cells is *a priory *predeterminated. F

TO DECIPHER, THAT IS TO UNDERSTAND THE FUNDAMENTAL LAWS OF OUR METRIC UNIVERSE, WE MUST FIRST

*"It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them, which gives us the key to the understanding of Nature... In a certain sense, therefore, I hold it true that pure thought can grasp reality as the ancients dreamed." *
**DISCRETE AND YET CONTINUOUS SPACETIME COORDINATE SYSTEM**
** SUMMARY**

A Creation, evolution, structure and age of our universe...

B Big Bang, Planck Constants...

C Sonoluminescence and The Life Sequence...

D Atoms - Atomic Radii of 71 Elements...

E Nuclei...

F Gravity as Geometry of the Structure of Spacetime, the Earth-Moon system ...

B Big Bang, Planck Constants...

C Sonoluminescence and The Life Sequence...

D Atoms - Atomic Radii of 71 Elements...

E Nuclei...

F Gravity as Geometry of the Structure of Spacetime, the Earth-Moon system ...

TO DECIPHER, THAT IS TO UNDERSTAND THE FUNDAMENTAL LAWS OF OUR METRIC UNIVERSE, WE MUST FIRST

"THREESMALIZE" OUR CURRENTLY USED DECIMAL SYSTEM

WE ARE PROPOSING:

1. The conceptual unification and reconciliation of the theory of relativity with quantum theory of gravity and the mathematical concept of continuum with the concept of spacetime. We are proposing to supersede the Cartesian coordinate system, which describes the world of unrelated parts, with a new coordinate system or structure, an inevasible framework for measuring, predicting and verifying the geometry encoded in the metric causal structure of spacetime from the outset, by connecting us to here and there and now and then**.** By providing a new insight in describing the nature of spacetime at the Planck length scale often described as *foamy*, Planck mass and Planck time through the primordial universal quantum ħ=c=1 we are clearly demonstrating the relationship between seven enfolded dimensions of our universe, unfolding of three space and one time dimension and its subsequent hierarchically organized evolutionary strata as manifested through its intervals of 1-5-9-13 stem cells.

2. That the physical reality of our universe's four plus seven spacetime dimensions emanate from the *geometrodynamic conservation principle* which includes the expansion of the whole universe, as well as its evolutionary processes that include expansion and recontraction, with degrees of freedom of a fluctuating quantum field of the multitude of *local *cells; that, "...gravitational collapse is in effect perpetually being done and undone...," ^{1} as presented through a system of 137 (141) finite but with no boundaries stem cells.

3. That the rate at which the velocity of the galaxies increases with distance is determined and manifested by the quantum* *structure of spacetime of our theory -- its *principle of continuity and extensity of the length, distance and volume criterion. *The Wilkinson Microwave Anisotropy Probe (WMAP) data shows that the rate of this expansion (Hubble constant) H _{0} = 71 (km/sec)/Mpc (+ - 5%). The recent discoveries by the Hubble Space Telescope (ACS - Press release of April 2003) seems to indicate that by measuring the changes in the faint glow of the two examples of type Ia supernovae, thus measuring their distance from Earth -- five and eight billion light years, respectively -- the rate of universe's expansion had somehow "switched from deceleration due to gravity to acceleration due to the repulsive force of the dark energy."

4. That our theory supports the proposition of Jean-Pierre Luminet ** ^{2}** that the diameter of Abell's superclusters is, "...of the order of 100 megaparsecs." And that, "the universe might be constituted of elementary cubes of side 100 megaparsecs. Inside such a cube, space would be practically empty, and the galaxies and clusters would be found on the walls." More recently, a paper on "A 120--MPC Periodicity in the Three-dimensional Distribution of Galaxy Superclusters" provided some evidence of such immense three-dimensional structures, rich superclusters and voids, that were based on observational measurements of the redshifts of the distant galaxy superclusters' apparent periodic configuration. (J. Einasto et al., Nature January 9. 1997.) A

Measuring redshifts in order to "determine distances of galaxies has been undertaken in three directions on the sky: towards the Coma Supercluster, towards the Perseus Supercluster, and towards the Hercules Supercluster... The results have been very surprising; the universe seems not only to contain large aggregates of matter in the form of superclusters of galaxies, but also to contain the opposite, with vast regions being practically empty of galaxies. It seems, moreover, that it would be possible for clusters and superclusters to be confined within the walls of gigantic blocks of emptiness 100 megaparsecs on a side. The theoretical and cosmological impact of such a discovery, if it is confirmed, is immense. Structures as vast as the superclusters and the voids are an accurate reflection of the original distribution of matter, as opposed to smaller scales which have been perturbed by mixing and subsequent interactions between galaxies, literally erasing the initial conditions." ** ^{3 }**(After S. A. Gregory and L. A. Thompson, 1982)

5. That the multitude of open clusters of stars could be categorized within the spacetime of five consecutive stem cells, with their respective radii of: 4.93^{16}1.48^{17}, 4.44^{17}, 1.33^{18}, and 3.99^{18 }meters, the interval of 1-5, or 1-531,441 units or cells. A

6. That our theory provides a comprehensive framework for study of stars in binary pairs or larger systems -- their evolutionary sequence, Roche lobes, Lagrangian points, equipotential surfaces and other physical phenomena. F

7. That J. Robert Oppenheimer's and George M. Volkoff's paper, On Massive Neutron Cores (Physical Review 55, 374-381, 1939) and subsequent revisions of equation of state of neutron stars, by incorporating nuclear interactions in their core and the lattice structure of the surface, lead us to believe that neutron stars can reach stable equilibrium "in a finite range of radii between 9 and 164 km." ** ^{4 }**A

In 2002, the scientists estimated that a star with mass of ~ 1.4 M

We are proposing that our theory's stem cell Neutron Star, with its minor radius of 6,282 meters, its major diameter of 15,579 meters, corresponds to often quoted neutron star's diameter of 10 miles = 16,093 meters) would be a better approximation of the lower range of radii of neutron stars. Its upper range of radius of 164,000 meters, or diameter of 328,000 meters would extend into a stem cell with minor radius of 169,609 meters, or minor diameter of 339,219 meters and its major radius of 210,315 meters. An interesting and significant observation is that the next larger stem cell, fifth in the sequence in range of neutron stars' radii is missing or enfolded stem cell. A

8. That the evolution of our sun and other stars with mass under Chandrasekhar limit of 1.4 M_{¤}, is being manifested and described within a sequence of 1-5-9-(13) stem cells of our solar system. A

9. That the cosmological position of man and the inevitability of the *weak* antropic principle, as demonstrated within a cycle or interval of 1-5-9-13 stem cells is an integral, indelible part of the 27 stem cells of The Life Sequence**. **A

10. That the sequence of the realm of *nuclei** *and *atoms* encompasses the spacetime of *thirteen *stem cells; that the nuclei and atoms, from smallest to largest, occupy the realm of three consecutive stem cells, respectively; E that each nucleus' stem cell is congruous to the appropriate scale of the respective atom; D that the scale ratio of most nuclei to their respective atom is within a ratio of 1**:**59,049 and that this ratio encompasses *eleven *stem cells, or** ***"eleven dimensions*." A

11. That the phenomenon of sonoluminescence C could be tested by using the real and physical spacetime of an interval of 1-5-9-13 stem cells -- each and every cell being an exact threesmalized multiple of ħ=c=1. We believe that such experiments, ideally in the condition of micro-gravity, would confirm that the size, evolution of the bubbles, their catastrophic collapse as well as their energy states are directly determined and correlated with the size and the interval of the relevant stem cells. Such research might advance possibility of comparison between the inertial confinement scheme where a pallet of solid deuterium and tritium is bombarded from all sides by intensive laser beams, cold fusion and other physical phenomena. Not surprisingly, the Sperm Stem Cell, with radius of 2.2352...^{- 6 }meters and diameter of 4.47...^{- 6} meters corresponds to experimentally confirmed diameter of 5 microns at which the bubble starts. "It starts at 5 microns in diameter, expands to 50 microns and then collapses to one micron." Matula and Crum ** ^{5}. **C

We may never be able to probe directly the enormous energies of 1.22 ^{19 }GeV of the Planck scale at the realm of seven *enfolded* dimensions. The Large Hadron Collider (LHC) and its detectors, due to start in spring of 2007, will study collisions among quarks at energies of hidden electroweak symmetry. Higgs boson, the carrier of Higgs field according to Peter Higgs, is a neutral particle with zero spin that gives the W and Z particles as well as quarks and leptons their masses. Being a proton - proton collider the LHC will achieve the energies of 14 TeV. It may discover the *unfolded large extra dimensions of spacetime*, *the huge virtual energy of quantum gravity and the correspanding hypothetical gravitons,* from within the energy scale of 6.561 TeV that is from stem cell with side of 1.57 ^{- 19 }meters to stem cell with side of 4.45 ^{- 8} meters, where the realm of quantum confinement begins. We are proposing that the threesmalized intervals of 1-5-9-13, *specifically within the realm of nuclei and atoms,* may represent a* schemata *or a concept at this time, that is similar to universal but limited to phenomenal knowledge of* gravity permeating into large extra dimensions as *a consequence of *hierarchical manifestation of the resonances* of the all-pervading seven-dimensional enfolded fundamental quantum structure of spacetime - the universal quantum ħ=c=1.

12. That the fundamental underlying principle governing the manifestation of the inverse-square law in physics, optics and in the law of gravitation, is to be found in *an eleven-dimensional quantum theory of gravity -- reconciled at the outset with a quantum theory of spacetime. *F

GRAND UNIFIED THEORY

We are proposing that our theory, with its universal quantum ħ=c=1 B which represents the fundamental conceptual and geometrodynamic reality and frame of reference elucidates the ultimate principle of Creation and emanant evolution of our universe including humankind. The universal quantum ħ=c=1 is analogous to the *first principle*, the cause of all causes, or to the *first cause*. Furthermore, it represents the universal length and the universal unit of volume -- a quantum of spacetime. It represents a permanent, true and whole order of reality, a fundamental building block inherently defined by its own essence in the theory from the outset and as such it reconciles the limitless continuity with the reality of spacetime. Moreover, the difficulties that a man has encountered in the search for truth, the *real quality* and the *real relation*, through the use of ratios, proportions, intervals and their relationships, particularly within the realm of infinitesimal and infinitival appear to vanish when each and every physical phenomenon attains its full and equal, intelligible, logical and rational, finite but without boundaries spacetime field of representation, thus, unifying the reality of our universe with the geometrical and mathematical exactitude. In terms of these proposals it follows that our theory, with its universal quantum ħ=c=1 unifies and reconciles the theory of relativity and quantum theory of gravity by providing the necessary link at the most fundamental level of the all encompassing, continuous and indivisible gravitational field -- whose structure, effect and manifestation emanate as stem cells, the curvature of spacetime. Evidently, this principle of gravity equals geometry is universal. It manifests itself in each and every local and global region of spacetime, in each and every stem cell where geometrodynamic and physical processes occur.

From a quantum of spacetime ħ, a sphere with a diameter of 1.054589 ^{-34 }meters and its equivalent cube/stem cell with side of 8.499943975 ^{-35 }meters -- to sub-nuclear, atomic, human, stellar, interstellar and intergalactic scale, and ultimately the scale of the whole universe, these cells or spaces of references contain structural multitude of gravitational, weak nuclear, strong nuclear and electromagnetic forces with their respective waves-particles rushing through the reality of spacetime at the speed of light -- exemplifying natural laws that were predeterminated by their primordial universal quantum ħ=c=1 and the antecedent realm of the primordial energy fluctuation at the instant of the Big Bang. A B Within a stem cell we can predict and observe, identify, measure and analyze the complex events and processes. Within a system of 137 (141) visualizible, pictorial and physical, fundamentally harmonic geometrodynamic cells of reference, we can describe the creation and subsequent evolution of our universe as the manifestation of the underlying ratio or interval:

A : B = B : C = C : D = D : E ...

By tripling each step outward, there is a corresponding reduction to one third of each of the steps inward, as in *geometric progression* where a sequence of terms in which the ratio between any two successive terms is the same, as the progression:

1 : 3 = 3 : 9 = 9 : 27 = 27 : 81 = 81 : 243 ...

By increasing each step outward by 26 cubic units, there is a corresponding decrease of 26/27 cubic units to each of the steps inward.Our theory proposes that all physical qualities do have the dimension of a power of length and volume, where,

ħ = sphere-stem cell with radius of 5.272944418^{-35} meters = c = 1

or:

ħ = cube-stem cell with side of 8.499943975^{-}^{35 }meters = c =1

or:

ħ = cube-stem cell with side of 8.499943975

Thus, just as in quantum mechanics our theory is determined and governed by a single parameter ħ. While the perspicuity of the intrinsic ratio and interval manifests itself throughout the interval of 137 (141) stem cells, from the quantum world of quantum gravity, Planck constants at the Planck scale represented by stem cell with side of 8.499943975^{-35 }meters, B to the scale of the whole universe represented by stem cell with side of 2.77 ^{26} meters, A there is one* partial break* in the interval between stem cell with side of 339,219 and 844,484 meters, that manifests itself as an *enfolded or missing *stem cell. A

We are proposing that the manifestation of this* enfolded* or missing stem cell may be the result of a relative expansion of the relatively brief history of about 4.5 billion year old our solar system within a scale of our Milky Way Galaxy's spacetime. This may have been perturbed by the complex evolutionary processes *which include expansion and recontraction of the multitude of local stem cells within the expanding structure of spacetime on the global scale. *A Please note that stem cells representing the largest structures, that is from the realm of *enfolded* stem cell upward are derived from the approximate size of our solar system, by applying its diameter of 81 Astronomical Units, or 1.21...^{13 }meters to the side of stem cell Our Solar System.

In the second version the enfolded stem cell is omitted. Here, the entire history of the universe, from Big Bang to stem cell with a side of 1.00^{ 27} meters, is depicted as a continuous expansion by an exact threesmalized multiple of ħ=c=1. The photons from the edge of the visible universe that is from the furthest and oldest transitory astronomical structures that are reaching us now have traveled for about 14.7 billion light years, not only in our direction, but in all directions as the universe continued to expand. Thus, the radius of the universe today may be at least 29.4, and the diameter 58.8 billion light years, respectively. Top of table A

The Lambda force might have taken control of the universe at the large scale from gravity. This period of transition has only recently became an area of more intensive research. Recent data from the observations since 1998 of the exploding stars or supernovae, by comparing their distances from us with their brightness, indicate that the universe's expansion is accelerating at an ever-increasing speed. This may be result of a *complex hierarchical, discrete and yet continuous on the global scale** quantum structure of spacetime *and our theory's *principle of continuity and extensity of the length, distance and volume criterion. *As the recent discoveries by the Hubble Space Telescope (ACS - Press release of April 2003), by measuring the changes in the faint glow of the two examples of the type Ia supernovae thus measuring their distance from Earth -- five and eight billion light years, respectively seems to indicate -- the rate of universe's expansion had somehow "switched from deceleration due to gravity to acceleration due to the repulsive force of the dark energy."

* *Albert Einstein, in his Herbert Spencer lecture in 1933

We believe that reality is knowable through the intuitive processes of pure thought that encompass our sensory and sensible experience of the world based on the universal order of mathematical, geometric, harmonic and physical concepts inevitably elucidated through the manifestation of the universal quantum ħ=c=1, and that human mind can reach and comprehend *truth *that is based on *the principle of universality of dynamic equilibrium* and *the necessity of matter to be identified with extension*.

When we observe a fundamental particle, object, mass or an energy event being represented in a spacetime of a stem cell, we know that object or entity -- and we know that we know it. The beautiful edifice, for example, of The Life Sequence where man's cosmological position and anthropic principle within our universe emerge as an intrinsic, predictable and determinated, full and equal act and fact of creation is analogous to the ultimate order, structure, measure, truth, beauty, justice and meaning of reality**. **A C Accordingly, we believe, to paraphrase George Orwell that, even though a*ll the forms of life are perfect, the man is more perfect than the others.* Our reality, communicated on the rational level as our oneness and exemplified in natural laws, is what it is, and it belongs to each and every thing or being, as represented in each and every stem cell. Or, to paraphrase Georg Cantor's definition of a set, *Universe is a Many that allows itself to be thought as a One.* The reality of the existence, and the reality of human existence became predictable through the act and the fact of creation, giving us the definitive reasons to believe that all events, including man's emotive and cognitive powers, his choices and decisions have sufficient causes.*"Man is,"* indeed, as Protagoras c. 480-410 b.c. stated,* "the measure of all things." *Now, we finally understand why are our fundamental principles validated by our discerning and rational conventions, harmonizing the reality of our ordinary experience to include the universal order, the four plus seven-dimensional geometry of the whole universe. The very essence and existence of our *objective reality *and of the i*mmeasurable primary reality* become determinately simple, compelling and inevitable to our minds, when the laws that govern our universe are demonstrated as universal, coherent, inferential and intelligible to all humankind, We are (at) the final, ultimate source, the manifestation and the harmony of the cosmic consciousness of the existence* - Nous*, the self-contemplating order of the universe.

*"It is a wonderful feeling to recognize the unifying features of a complex of phenomena which present themselves as quite unconnected to direct experience of the senses."*

Albert Einstein, 1909

From Pythagoras to Plato, Einstein's relativity to quantum theory the quest for such a master theory has slowly progressed. Pythagoras believed that primary reality, being a manifestation of connection between numbers, ratios and music is in the abstract realm of pure thought, and that the perfect reality should be knowable to man though the propositions of mathematics and geometry. Pythagoras believed that the underlying principle of his musical scale and the resulting pleasing musical tones, which he deduced acoustically from the perfect *fifth* by applying simple ratios of the lengths of the two parts of a string on a stringed musical instrument that were expressible in numbers, could be applied to the whole *harmonious universe*.

The Pythagorean notion of a noumenal primary reality that could be glimpsed within the realm of pure thought, as distinguished from a phenomenon or a thing as it appears, was immortalized by Plato's (428-348 b.c.) analogy of a cave in which the objects of our sensory perception are blurred into a shadow of recondite realities and uncertainties. The influence of Pythagoras' ideas of numbers, ratios and music is evident in Plato's later work The Republic, in his description of a celestial *harmony of the spheres.* Consequentially, Plato believed that there exists a simple universal truth, not belonging to the sense world, but to the perfect and eternal world of forms. Such a truth, Plato held, while independent from man could be discovered only through pure thought, reason and reflection, those invariant and immortal *forms of thoughts.* In 1606, Johannes Kepler (1571-1630) extended the principle of Pythagoras' *harmonious universe* through his laws of planetary motions that were explained by the simple ratios of the planets' distance from the sun and the length of each planet's year. French philosopher, physicist and mathematician Rene Descartes (1596-1650) believed that all matter, including planets were moving in the background space that he called *plenum*. Descartes eventually accepted Newton's discoveries and abandoned the idea of the *plenum*. G. W. Liebniz, philosopher and mathematician (1646-1716), considered to be essentially a rationalist, believed in the harmonious relation between capacities of human intellect and the order, structure and measure of the material world of experience. For him, as for Kant and Descartes, matter was identical with *extension. *Through epistemology, a branch of philosophy, man has investigated the origin, nature, methods and limits of human knowledge. Through metaphysics, that includes cosmology and which is always connected with epistemology, man has searched for the* first principle or the first cause --* the *cause of all causes*, an indispensable but elusive antecedent of a proposition, *causa sine qua non*, in his quest to elucidate the first recondite principle of all human knowledge -- *being. *The inherently transcendent reason, analogous to and consistent with the necessity of matter to be identical with extension, intuits that something is or exists through those invariant *forms of thoughts*, the pure primordial fundamental force where the *first principle*, the actualization of reality and the coherence theory's sole criterion of truth -- the universal quantum ħ=c=1, emerges as the universal concept and the geometrodynamic structure of the world, manifesting itself implicitly into each particle, atom, molecule, cell, force, movement, velocity or thought.** **B

Geometry is a science and art of discoveries, a vision and intuition. Immanuel Kant (1724-1804), believed that space is a source of geometry and that, "*Space does not consists of simple parts, but of spaces." *The essential belief that all knowledge reveal an antecedent condition based on the structures of geometry, the descriptive experience of the physical world and the product of reason, was held by the classical realist Plato and the philosophic rationalists Descartes, Liebniz and Kant. A search for truth that can be comprehended through a cognitive interaction between a human and the universe, absolute and eternal, continues. Geometry is a theory and a model of the universe, based on a set of fundamental rules and laws immanent from the outset in its ratio, order, structure, measure and the corresponding symmetries that a* man*, a cosmological fact, an intrinsic *measure of all things* is discovering in nature and not, *homo additus naturae* (man added to nature), a quotation attributed to Francis Bacon 1561-1626). Through art and music man wonders about his interaction and his place within the universe; through intuitive and cognitive processes he experiences the simple yet profound and mysterious recognition of reality where* truth, beauty *and *justice *within our universe are experienced as a dynamic and interactive, fundamentally integrated and intrinsically meaningful unity. This wonder was, for Plato and Aristotle, the beginning of philosophy and science, the search for a logical, rational and comprehensive vision of the origin and the evolution of the universe and our place in it.

The Cartesian coordinate system while appropriate to a description of the world of autonomous and unrelated parts is considered obsolescent and insufficient for the study of the universe as a geometrodynamic spacetime phenomenon. We are proposing that the Cartesian coordinate system, while still retaining its obvious usefulness in regard to its geometric and mathematical exactitude in describing the world of unrelated parts, be superseded by our new coordinate system, an inevasible framework for measuring, predicting and verifying the geometry encoded in the metric causal structure of spacetime from the outset -- thus connecting us to here and there and now and then**.** From each and every stem cell the movement of quantized fields or propagation extends over the whole structure of the universe; it carries within itself implicitly all its past and future *enfolded*. We believe that, as David Bohm had proposed,* "a total order is contained, in some implicit sense, in each region of space and time." *** ^{6 }**As our stem cells are finite but with no boundaries, the propagation law allows the propagation from one stem cell to another in a natural way, bound only by the laws of physics. We are proposing that an infinitesimal sphere with a diameter of 1.054589

1. A particle, energy state, composite state, a body or an event in a single particular spacetime, that is in a *primary stem cell. *Each and every one of the 137 stem cells becomes a *primary stem cell* when a physical phenomenon under observation and research is congruous to its scale. The *primary stem cell *comprises of a harmonic representation of** **five** **consecutive stem cells: 531,441 - 19,683 - 729 - 27 and 1 unit or cell. F

2. By repeatedly dividing by three each step inward along the x-axis the previously identified *primary stem cell*, in order to visualize and analyze its constituent particles, bodies, events and other hidden variables* *under investigation.

3. By tripling each step outward along the single x-axis in order to identify, examine and analyze a particular event or phenomenon in interaction with local-neighbouring, intermediate or global surroundings.

Any one of the 137 *primary stem cells** *or cells of reference whether represented in a photograph, book illustration, diagram, photographic plate in astronomy, computer screen representation or the observing spacetime of the particle accelerator laboratory consists of 531,441 identical stem cells. Each and every *primary stem cell* could be identified by its spherical diameter/radius and to its corresponding side of a cube/stem cell expressed in units of meters, with the four smaller interior spherical diameters/radii and the corresponding side of the cubes/stem cells expressed as sub-measurements. Furthermore, each stem cell would be given a secondary set of measurements expressed in the appropriate, for the scale of the phenomena under observation and research units, such as nanometers, kilometers, AU, light years, parsecs, megaparsecs -- in relation to the Hubble constant and others. Each and every one of the 531,441 stem cells would be described and identified by a combination of only 4 letters** **of the 26 letters of the English alphabet plus xi, -- the 14th letter of the Greek alphabet. With an introduction of a combination of 5, 6, 7... or 13 letters sequence or coordinates each of these combinations would increase the possibility of the exact identification of a relative position of a singular unit of spacetime, a singular stem cell, as one of 14,348,907 - 387,420,489 - 1.04603532 ^{10} and 4.05255515 ^{18 }units or stem cells, respectively. F

Within the central unit** **of the 531,441 units of the *primary stem cell* there is always situated the infinitesimal, indivisible sphere ħ=c=1 which supersedes the point of origin O of the Cartesian coordinate system with its diameter being represented by ħ =1.054589 ^{-34 }meters and its interior as a seven-sphere and zero time. B Thus, in our theory, the sphere of a quantum of spacetime explains the uncertainty of spacetime at the Planck scale, by demonstrating that, indeed, the (un)**certainty **of the measurements is the distance to the center of the smallest quantum of spacetime -- **the radius of the sphere is exactly ½ ** ħ. B When we observe and study the multitude of physical phenomena within a spacetime of a particular stem cell, the reality of the central stem cell becomes transferable, that is each of the other 531,440 stem cells, depending on a particular phenomenon observed within, becomes a central unit of its *newly designated primary stem cell.*

It is clear that in our Theory, as well as in the theory of relativity, the three spatial and one time-coordinate are unified with the spacetime. The idea of the world of more than three dimensions as proposed by a mathematician Bernhard Riemann in 1854 introduced the cogitable three-dimensional space within a four-dimensional hypersphere. It was Herman Minkowski (1864-1909), a mathematician and Riemann's compatriot who in 1908 extended the ordinary three-dimensional Euclidean space in which the imaginary fourth coordinate is time. In Minkowski's space, however, an event is still represented as a** **point. One earlier, but important proposition by a mathematician and philosopher W. K. Clifford (1845-1879), suggested that all the forces of nature and particles of matter are just the curvature of space.

It is not surprising that these geometrical discoveries provided a fertile place for the intuitions of Albert Einstein. In 1915, while extending his special theory of relativity to include the accelerated system, Einstein incorporated Minkowski's and Riemann's geometrical propositions into his own comprehensive theory where matter creates the curvature of spacetime and where gravity is geometry. We notice that at the Planck scale or more precisely at our theory's realm of ħ=c=1 all the forces of nature including gravity become unified within the quantum structure of spacetime. Here, the connection between Einstein's lifelong search for such unification, Kaluza's proposition of introducing the *unseen* fifth dimension of space and subsequent calculation of the circumference of the fifth dimension by Oskar Klein as 10 ^{-34 }meters is merged into a simple visualizible real scale**. **B In describing the search for the grand unified theory, in particular Kaluza's contribution, P. C. Davies ** ^{7 }**states, that,

"...The gravitational field in this five-dimensional universe behaves just like ordinary gravity plus Maxwell's electromagnetic field, when viewed from the restricted perspective of four dimensions....The fact that, mathematically, Einstein's gravitational field in five dimensions is exactly and completely equivalent to gravity plus electromagnetism in four dimensions is surely more than a passing coincidence."

Despite Einstein's triumph, a major problem of how to unify an individual structure within a local region with the multitude of similar regions of different strata

*"...What else is there out of which to build a particle except geometry itself? And what else is there to give discreteness to such an object except the quantum principle?"*

John A. Wheeler 1974

Clearly, our theory reconciles a concept of a *seven-sphere*, a geometrical, topological and symmetrical structure with its seven small dimensions and squashed energy actualization with the quantum structure of spacetime. B Moreover, it clearly demonstrates the relationship between seven enfolded dimensions of our universe, unfolding of three space and one time-dimension and its subsequent hierarchically organized evolutionary strata as manifested through its intervals of 1-5-9-13 stem cells. It provides a new insight in describing the nature of spacetime at the Planck's scale of 1.616 ^{-35 }meters, where the huge quantity of energy, according to Heisenberg's uncertainty principle, break down the spacetime itself. Being topologically equivalent, a cube and a sphere, both with Euler characteristic or number 2 are easily transformed or distorted from one configuration to another. The incipient actualization of the seven *small dimensions* in our theory unequivocally elucidates the concept and structure of spacetime at the Planck's scale where we can *observe* and visualize the real and physical, true up to scale seven *enfolded* space dimensions with their small-scale energy fluctuation, configuration and zero time as being inside a three-space and one time-dimensional *universal quantum *ħ=c=1. B

The fundamental quantum structure of our universe emerges as a dynamic, fundamentally harmonic phenomenon with its *cente**r* ħ=c=1 everywhere and its circumferences clearly definable by its intrinsic, unique and comprehensive coordinate system and by its intervals being our measuring rods -- whose metric value was deciphered by threesmalizing our currently used decimal system by reducing it to a system pertaining to thirds or to a number 3. The principal conclusion of our proposals, though only in broad outlines is, that many of the physical concepts including limitless continuity, the indeterminate notion of a point particle, the space composed of points, the patchwork of the bounding surfaces and coordinates of the Cartesian system, the essence of the material body -- that is extension itself and its universal non-local connections are resolved as the *foamy* veil of shadows in a cave, as in Plato's simile, disappears. The reverberations of the resonances of the Creation become visualizible, discernible and physical when quantum spacetime and the quantum theory of gravity are unified. Consequently, it is not hard to conceive of a photon that travels along the null lines of relativity carrying within and with it the realm of zero time, where nothing separates an *observer and participant* from its source, be it in the sparkle of life in the eye of humanity, the glistening crystals of snow in the moonlight, a gleam from the farthest galaxy or quasar -- the realm of comprehensiveness. The relationship of space to matter and light to time are being clearly identified, revealing the *first principle* or the* first cause *and the rational order of the cosmos of intelligible beings.

**REFERENCES**

1. ** **Wheeler, John, Archibald, pre-print to appear in Jonathan J. Halliwell, J. Perez-Mercader, Wojciech Zurek, eds. Proceedings of Workshop, "Physical Origin of Time Asymmetry, "Cambridge University Press, Cambridge, U. K. CB2 2RU, page 15 (1993)

2. Luminet, J. P., C.N.R.S., Clusters of galaxies, page 377, The Cambridge Atlas of Astronomy, the second edition,1988, Cambridge University Press.

3. (After S. A. Gregory and L. A. Thompson 1982), The Cambridge Atlas of Astronomy, the second edition,1988, Cambridge University Press, page 377.

4. ** **A Source Book in Astronomy and Astrophysics, 1900-1975, Harward University Press, Cambridge, Massachusetts and London, England 1979.

5. Matula and Crum. Science: Guardian Online, Jaunary 21, 1998.

6. ** **Bohm, David, Wholeness and the implicate order, Routledge, 29 West, 35th Street, New York, NY 10001, page 149.

7. ** **Davies, P. C. W. , Superforce: the search for a grand unified theory of nature, Simon and Schuster, c1984, New York, NY, page 151 and 152.

8. ** **Wheeler, J. A., in M. Rees, R. Ruffini and Wheeler, J.A., Black Holes, Gravitational Waves and Cosmology, Ney York: Gordon & Breach 1974, page 290.

* To reduce our currently used decimal system to a system pertaining to thirds and to the number 3.

** **** The theory of truth that holds that every true statement, to the extent that it is true, describes its subject and reality in totality of its relationship with all other things.

***** **Its metric magnitude derived from a sphere with a diameter of 1.054589 ^{-34} meters and its equivalent cube/stem cell with side of 8.499943975 ^{-35} meters, both with Euler characteristic or number 2, and from the approximate size of our solar system with diameter/side of stem cell of 81 Astronomical units (1 AU=149,597,870,000 meters). A continuous expansion of the universe by an exact threesmalized multiple of ħ=c=1 is depicted at the top of Table A.