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 OCTOBER 26, 2008

God, Science & The Secret Doctrine

and Microcosm/Macrocosm

Section V 4b or II 2c

   Sculpting the Void

Seven Hidden Compacted Dimensions in Hyperspace

“... the broken symmetries of a higher dimensional space yield the four big dimensions ...
Perhaps the real world with its four big dimensions corresponds to the broken but stable solutions
 to equations describing the symmetries of a multidimensional geometry.”  (Pagels, 1985, p. 8)

“Seven hidden dimensions of the universe ... have been proposed in a theory that seeks to unify the forces of nature.
 ...  (the seven hidden dimensions) can be pictured as a small, compact structure such as a sphere
that is associated with every point in space and every moment in time.” 
(Freedman, Nieuwenhuizen, Scientific American, March, 1985)

There is no question of, say, an atom going off round the (7 hidden) dimensions.
Rather, we should think of the extra dimensions as somehow inside the atom.
(Davies, 1984, p. 160)

            Profound new ideas have emerged in modern physics about the hidden dimensionality of existence.  Traditionally, space has been regarded as three dimensional and time is considered as a fourth dimension.  Thus, relativity theory describes the curvature of the four-dimensional space-time continuum.  However, in the twentieth century, physicists suggested that the four ordinary dimensions are only the “four large dimensions,” because we experience our lives (seemingly) living within these dimensions.  Physicists now describe the laws of nature evident within the four large dimensions as dependent upon processes occurring within underlying “hidden compacted dimensions.”  As physicists seek to integrated the four forces of physics into one fundamental force, additional higher dimensions of Space were so postulated.  One of the most advanced models of such “hidden dimensions,” designed to explain the four laws of physics, in the 1980s, was the eleven dimensional Kaluza-Klein supergravity theory.

            In 1921, Kaluza, a German physicist, had been inspired by Einstein’s general theory of relativity, which explained gravity in terms of the ‘geometry’ of a four dimensional curved space-time continuum. Kaluza attempted to unify the electromagnetic force with gravity by postulating another fifth dimension of space.  Kaluza demonstrated that Einstein’s gravitational field equations, if written in a five dimensional form, could be arranged to yield the usual four dimensional equations plus the electromagnetic equations of Maxwell.  Kaluza postulated that this extra dimension existed at every point underlying the four dimensional space-time as a “compacted” dimension; a tiny circle in the fifth dimension would allow an extra degree pf freedom of motion to particles.  Kaluza was the first to develop a unified field theory giving a geometric explanation of both the gravitational and electromagnetic forces.

            In 1926, O. Klein, a Swedish physicist, noted that Kaluza’s extra dimension would go unnoticed if it were “rolled up” very small or compacted. An example used to illustrate this is that of a garden hose as seen from a distance, where any point on the line of the hose is actually a small circle extended around the circumference of the hose.  Similarly, Klein suggested that perhaps Kaluza’s extra dimension is so small that we cannot distinguish it from a point, but which is really a small circle extended into the fifth dimension.  Klein computed the circumference of this fifth dimensional loop, was about 10-30 centimeters, approximately 10 to 100 Planckian units.

B. Greene, The Elegant Universe, 1999

           For years, Kaluza-Klein type theories postulating additional hidden dimensions fell out of favor as an approach to unifying the laws of physics.  Instead, physicists attempted to unify gravity and the other quantum field theories using the concept of gauge fields and hidden symmetries.  Gradually, physicists realized that the symmetries associated with K.K. hidden dimensions could be used to yield purely geometric interpretations of the Yang-Mills fields with their gauge symmetries. Pagels explained:

… the extra freedom of movement of a particle around a little circle in the fifth dimension, associated with a little circle symmetry at each point in space-time could be interpreted as the simply gauge symmetry of the electromagnetic field.  This interpretation of is not so surprising to us from a modern viewpoint if we realize that a symmetry (like the little-circle symmetry) automatically implies the existence of a gauge field.  (1985, p. 312)

K.K. theory re-emerged when it was realized that it was compatible with approaches to unification based on the concepts of symmetry and gauge fields.

However, contemporary physicists want not only to unify gravity and the electromagnetic force but also to include the strong and weak forces.  These additional forces required additional symmetries and gauge fields, or additional hidden dimensions. Thus, the new gauge theories came to be reformulated in terms of Kaluza-Klein theories with the addition of extra microscopic hidden dimensions. Pagels explains that:

               Theoretical physicists generalized the original five-dimensional theory to an arbitrary number of higher dimensions.  All the higher dimensions are compact; they are curled up into a tiny multidimensional space that exists at each point of ordinary space and hence is unobservable. But the freedom of moving around these compact tiny spaces with symmetries more general that the simple symmetry of a circle corresponds exactly to the freedom of performing Yang-Mills gauge transformations. Remarkably, the local gauge symmetries are precisely the symmetries of the compact higher-dimensional space. Because of this mathematical fact, all the gauge theories of Yang-Mills fields can be interpreted purely geometrically in terms of such compact higher-dimensional spaces. (Pagels, 1985b, p. 313)

 The term Kaluza-Klein theory is generally used to describe theories within a quantum mechanical framework which attempt to unify the fundamental forces of nature within a spacetime having more than the four large dimensions. Paul Davies (1984) thus noted that the Grand Unification Theories required the existence of seven compacted dimensions.  He wrote:

In the revitalized Kaluza-Klein theory, the gauge field symmetries become concrete; they are the geometric symmetries associated with the extra space dimensions. … A simple count of the number of symmetry operations embodied in the grand unified force leads to a theory in which there must be seven extra dimensions, making ten space dimensions in all, plus time, or theory postulates an eleven-dimensional universe.  (pp. 160-1)

 Paul Davies provides a valuable description of the dynamics and topology of these hidden dimensions:

When it comes to seven dimensions the range of topologies is enormous. What shape is correct? One particularly attractive choice is the seven-dimensional analogue of the sphere, known simply as the seven-sphere. If the unseen space dimensions really do have this form it means that every point in three-dimensional space is in fact a minute seven-dimensional ‘hyperball’ …. if nature had to find a closed geometrical structure that permits anything like the fundamental forces and fields that we perceive in the real world, then the seven-sphere would be the simplest choice. You couldn’t get the sort of structures we see, from atoms to galaxies, out of some simpler mathematical arrangement. A sphere is a highly symmetrical shape, and a seven sphere contains many additional symmetries not found in an ordinary sphere. … symmetry breaking is achieved by distorting the shape of the seven-dimensional structure somewhat away from exact sphericity. …  the structure of force fields depends on the geometrical symmetries of the compacted dimensions. (pp. 161-2)

Seven hidden dimensions are required to accommodate the three major quantum field theories (electromagnetism, the strong and weak forces) with their inherent symmetries and gauge fields.  Geometrically broken symmetries within the seven hidden dimensions are then the ‘nomenal causes’ of the phenomena of nature.  Only gravity remained associated with the four large dimensions of space-time.

            Modern physicists regard the creation of the matter and energies of the universe as resulting from “broken symmetries” within higher dimensional space.  In the beginning, the quantum vacuum was in a state of perfect symmetry, until a random fluctuation broke this symmetry leading to the differentiation of the forces of nature and the quantum particles, which mediate these forces.  As Pagels explains in the opening quotation, “the broken symmetries of a higher dimensional space yield the four big dimensions.” He then refers to “the symmetries of multidimensional geometry” as underlying “the real world.” 

Ideas concerning higher dimensional spaces, or hyperspace, have become a mainstay in the new physics.  The quantum vacuum, on a very low level of differentiation at Planck’s units, is a space-time foam having an inner hidden nature which scientists are seeking to grasp. Any particles or forces can be regarded as the result of broken geometric symmetries within the hyperspace of these compacted dimensions. These models of physics extend a geometric framework into understanding hyperspace dimensions.

            In Superforce: The Search for a Grand Unified Theory of Nature, Paul Davies, provides an inspiring description of the universe as it appears in the newer models of the geometry of hidden higher dimensionality spaces:

“All the forces of nature are revealed as nothing more than hidden geometry at work. ... There is a deep compulsion to believe in the idea that the entire universe, including all the apparently concrete matter that assails our senses, is in reality only a frolic of convoluted nothingness, that in the end the world will turn out to be a sculpture of pure emptiness, a self-organizing void.  Geometry was the midwife of science (for early astronomers), and now, we have come full circle, and the forces and fields are themselves being explained in terms of geometry.”  (1984, p.161-2)

 Davies describes the universe as a “sculpture of pure emptiness” and as emerging out of a “self-organizing void.”  This is the direction in which science has moved—towards the study of the quantum vacuum and hidden dimensions.  The void appears to have a dimensionality and organizing nature latent within its apparent nothingness.  Creation involves the manifestation within/without of the principles latent within the hyperspace of the vacuum.  Indeed “all of physics is in the vacuum” and the zero point field. 

            When it comes to explaining why the universe might happen to be founded on such a seven dimensional hyperspace, Davies raises some interesting questions concerning the meaning of it all:

 “When numbers occur naturally in the world, it is tempting to search for meaning behind them.  Sometimes they seem to be purely accidental, as with the number of planets in our solar system.  Other naturally occurring numbers suggest a deeper significance. ... Is the dimensionality of spacetime merely an accident...?  Or is it a pointer to a profound truth about the logical and mathematical structure of the physical world.”  (1984, p. 163)

 Is there indeed some hidden seven dimensional layering within the root principles of creation–in the apparent void of hyperspace?  Perhaps such patterns of existence are pre-existent in non-existence!  Or perhaps this is just another random feature of the accidental universe?  Scientists’ search to unify the laws of physics has lead to seven hidden spatial dimensions, wherein all elements and forces are ultimately derivatives of one superparticle or superforce–a god-like superparticle, superforce or superstring. 

This basic scientific model of higher dimensions at zero point levels is quite consistent with the bizarre metaphysics suggested by Blavatsky over a century ago.   The Eternal Ceaseless Breath modifies it motion on the basis of seven invisible points existent within the Seven Skinned Eternal Parent Space.  Blavatsky’s Secret Doctrine suggested that the forces of nature manifest outwardly through ‘zero point sources,’ from the Laya or undifferentiated state, and are rooted within a seven-skinned Eternal Parent Space.  Blavatsky describes the seven inside as “digging holes in Space” to channel their intelligence/influences into the material realm.  Thus, seven Laya Centers, seven invisible zero points, are established as a foundation for physical manifestation—seven invisible centers beyond the level of physical differentiation:

... all the so-called Forces of Nature, Electricity, Magnetism, Light, Heat, etc., etc., far from being modes of motion of material particles, are in esse, i.e., in their ultimate constitution, the differentiated aspects of that Universal Motion. ...  When Fohat is said to produce “Seven Laya Centres,” it means that for formative or creative purposes, the GREAT LAW (Theists may call it God) stops, or rather modifies its perpetual motion on seven invisible points within the area of the manifested Universe.  “The great Breath digs through Space seven holes into Laya to cause them to circumgyrate during Manvantara.”  (Occult Catechism). We have said that Laya is what Science may call the Zero-point or line; the realm of absolute negativeness, or the one real absolute Force … the neutral axis, not one of the many aspects, but its centre.  … “Seven Neutral Centres,” then are produced by Fohat ….  (S.D., I , pp.147-8)

In this view, the true foundation for the laws of nature and of material quanta (and the foundation of human consciousness), are these invisible points–the Laya Centres–which extend from physical dimensions into the metaphysical realms of Being/Non-Being—into the Eternal Parent Space and the Eternal Ceaseless Breath.  The Gods and other invisible powers “clothe” themselves in bodies based upon such Zero point neutral centres—or undifferentiated Laya Centres.

       Although on some occasions the Zero Point is described as singular, at other times it is described has having this inner sevenfold differentiation.  Like Fohat, it is One and Seven.  It is from such mysterious zero point conditions that the differentiation of a Cosmos and a quantum or Monad begins.  Paul Davies describes a similar model of 11 dimensional theory, with seven hidden compacted dimensions rolled up into elements at zero point levels.  Davies explained: “think of the extra dimensions as somehow inside the atom.”  (p. 160) Remarkably, Blavatsky explained exactly such a peculiar inner dimensionality to ‘atoms,’ quanta, Monads and the Kosmos over a century ago.  There is a complex metaphysics to reality at zero point levels.   As Blavatsky explains: “God ‘geometrizes!”  (1877, I, p. 508)

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