I am tackling this material because it is important. Yet my own work has advanced wonderfully while depending primarily on a 3D manifold and will suffice to describe accurately our physical universe. Thus i am hesitant to use any hyper dimension because it will need to be constrained and that can be also a source of severe error.
In the meantime we learn here that all our Gas Giants are radiating excess heat. My first conjecture is that this is caused by magnetic release of free electrons followed by electron decay to produce heat. This is only a first conjecture informed by our knowledge of dark matter.
As important we learn that Heaviside stripped Maxwell's equations to loose a greet deal of information..
Part I
In the meantime we learn here that all our Gas Giants are radiating excess heat. My first conjecture is that this is caused by magnetic release of free electrons followed by electron decay to produce heat. This is only a first conjecture informed by our knowledge of dark matter.
As important we learn that Heaviside stripped Maxwell's equations to loose a greet deal of information..
Part I
\
\Hubble's New "Runaway Planet"
- A Unique Opportunity for Testing the Exploding Planet Hypothesis and Hyperdimensional Physics -
For some time, we have been asked to
provide an overview of a subject intimately connected with -- but
not dependent upon -- the confirmation of "intelligent ruins at Cydonia," on Mars:
The arcane subject of "Hyperdimensional Physics."
Unknown to most current physicists and students of science (if not
the general media and public), the beginnings of modern physics
launched over 100 years ago by the so-called "giants" --
Helmholtz,
Lord Kelvin, Faraday, Maxwell and many others -- laid a full and
rich tradition in this currently little-known field: the open,
heatedly debated scientific and philosophical premise that
three-dimensional reality is only a subset of a series of higher, hyperspatial,
additional dimensions, which control not only the
physics of our very existence, from stars to galaxies to life itself
... but potentially, through time-variable changes in its
foundations--
Dramatic coming changes in our lives
This bold theoretical and experimental era, at the very dawn of science as we know it, came to an abrupt end at the close of the 19th Century. That was when our currently accepted (and very different) view of "physics" -- everything from the "Big Bang" Expanding Universe Cosmology, to Relativistic limitations imposed by "flat" space and non-simultaneous time, complicated by a non-intuitive "Quantum Mechanics" of suddenly uncertain atomic "realities" -- all took a very different turn ... from where they had been headed. Imagine our surprise, when -- as part of our Enterprise Mission effort to verify the existence of intelligently-created ruins at "Cydonia" -- we suddenly realized we might have stumbled across the geometry of this same 19th Century, pre-Relativity "hyperdimensional physics" (click below image)But encoded on a completely separate world!
Even more startling: this "lost science" was -- somehow --geometrically memorialized on the same planet ... the planet Mars ... that may have seen its "end" as a direct result of this same physics ...
According to the former Chief of the Celestial Mechanics Branch of the U.S. Naval Observatory, astronomer Thomas Van Flandern, Mars may once having been the satellite of a former major 10th planet of the solar system, that once orbited between current Jupiter and Mars. Sixty-five million years ago, for some currently unknown reason (according to Van Flandern’s 25-year-old theory ) -- that planet suddenly exploded-- releasing Mars into its currently "anomalously elliptical" orbit of the Sun ...
With NASA’s recent announcement of the potential discovery of the first "extrasolar, Jovian-class planet" physically detected beyond the confines of our solar system, the timing seemed particularly appropriate to update our original description of "hyperdimensional physics" at the United Nations, in 1992. And to call for some unique tests of this hypothesis, now that extensive new NASA observations of "the planet" are being planned for the next few months.
It is particularly ironic that these same tests could also provide striking new evidence supporting Van Flandern’s 25 year-old "exploding planet hypothesis" ...
On May 28,
1998, NASA held the
latest in a recent series of unprecedented news conferences in
Washington D.C.; the announcement of the first direct detection
(as opposed to inferences deduced from "stellar wobbles") of a
possible planet located beyond our local solar system.
The discoverer -- Dr. Susan Terebey (image left), founder of the "Extrasolar Research Corporation" -- serendipitously located the potential planet while using the Hubble Space Telescope (HST) and the newly-installed "NICMOS" Camera last year to study newly-forming stars.
Officially termed "TMR-1C," (watch below video) at the announcement NASA press conference Dr. Terebey described her at first slow realization of the uniqueness and potential importance of this "find"; ultimately her attention was drawn to a mere "pinprick of infrared light" in close association (on the Hubble "NICMOS" image -- click image below) with two much brighter stars.
 |
TMR-1C
|
Immersed in a dense
cloud of interstellar dust, this faint, solitary object -- the
only other IR source (besides the stars themselves) visible
against the dust -- was strategically located at the precise end
of a long, slender filament of light.
Terebey discovered, upon
preliminary measurement, that this "filament" extended
over a
100 billion miles ... directly connecting the "pinprick" with
the twin, newborn parent suns.
Several months into her analysis, Terebey reached the tentative conclusion that this tiny "IR speck" was most likely the first Hubble image (if not any image!) of a newborn, runaway giant planet -- "recently" ejected from a prior orbit of the nearby stars themselves (above image). From the faint infrared luminosity of this isolated object and contemporary models of planetary formation, Terebey estimated that its mass has to be only "2 to 3 times Jupiter’s."
The "filament," she theorized, is most likely a "tunnel" literally bored through the dense cloud of surrounding gas and dust by the passage of the ejected planet itself -- a tunnel that, acting like a "lightpipe," is scattering infrared energy down its entire 130 billion-mile length from the nearby stars themselves.
Because Taurus (the celestial region in which these remarkable objects are located) is now behind the Sun as seen from Earth, it will be several months before Hubble can be used to acquire additional data on the "planet." There are also plans to enlist major ground-based telescopes in this campaign.
What is critically needed is spectroscopic data on this object; if it is not merely a misidentified small star (such as a red dwarf, drastically dimmed by the copious dust still swirling in the vicinity of the nearby brighter stars), but is in fact a cooling planet, this will be instantly apparent from its spectrum.
Which brings us to the unique hyperdimensional possibilities this discovery has now presented.
Astrophysical discovery of "glowing planets" -- planetary bodies which shine in the infrared via internal energy sources, not just by reflected light -- stems from completely unexpected ground-based telescopic observations of this solar system, beginning in the mid-1960’s: the startling detection of "anomalous internal infrared radiation" (click image left) coming from the planet Jupiter.
Later Pioneer and Voyager insitu spacecraft observations
across the 70s and 80s added the other "giant planets," Saturn,
Uranus and Neptune, to the list of solar system worlds that --
somehow, without internal nuclear fusion processes, like stars --
still manage to radiate more energy out into space than they receive
directly from the Sun. (click image below)
After much initial debate, the conventional understanding of these anomalous "infrared excesses" eventually settled on three possible internal sources:
After much initial debate, the conventional understanding of these anomalous "infrared excesses" eventually settled on three possible internal sources:
1) left-over "primordial heat" from the literal formation of the planet2) heating caused by eventual internal separation of light elements in so-called "gas giant" planets (helium from hydrogen), releasing potential energy as the helium falls further toward the center of the planet (a form of ultra-slow, "continued gravitational contraction")3), anomalous energy release due to excess radioactive decay of heavy element concentrations located within gas giant rocky cores
[ What is startling here is that the giants are radiating a net heat. ]
Of the three current explanations for these "energy anomalies," only the first applies to Jupiter ... because of its mass -- 318 times the Earth’s; a planet of that minimum mass is required (in the model) if it’s to retain significant thermal energy across the immense lifetime of the solar system ... almost 5 billion years since the planet’s formation ... and still be able to radiate observable heat.
Of the three current explanations for these "energy anomalies," only the first applies to Jupiter ... because of its mass -- 318 times the Earth’s; a planet of that minimum mass is required (in the model) if it’s to retain significant thermal energy across the immense lifetime of the solar system ... almost 5 billion years since the planet’s formation ... and still be able to radiate observable heat.
And, as can be seen from this diagram
(click image right), the current
ratio of absorbed solar energy to emitted 5-billion-year-old
internal Jovian energy is still almost two to one!
After the Voyager fly-bys of the 1980’s, the second "internal heat" proposal -- the "helium drip model" -- was favored for the observed heat excess in the Saturn situation. But, because of their relatively light masses (less than 30 times the Earth’s), only the third possibility -- massive internal radioactive decay -- has been seriously attempted as an explanation for Uranus’ and Neptune’s more puzzling "anomalous infrared emissions."
There are, however, serious problems with all of these "conventional" explanations -- particularly after these spacecraft flybys, for all planets less massive than Jupiter.
For instance, during the Voyager encounters of Uranus and Neptune, spacecraft instruments detected a barely measurable (but significant) "infrared excess" (as opposed to merely infrared re-emission of absorbed solar energy) for Uranus of about "1 to 1.14"; whereas for Neptune (essentially its planetary "twin") the ratio of internal heat to intercepted sunlight was a striking "three to one!"
However, simultaneous "doppler tracking" gravity measurements conducted during the fly-bys (looking for anomalous trajectory changes to the spacecraft motion, caused by gravitational effects from increased percentages of heavy radioactive elements in the cores of Uranus and Neptune) detected no anomalous central concentrations in either planet ... necessary, if the excess observed IR radiation is in fact caused by "excessive internal radioactive element concentrations."
Even more perplexing, Uranus has a pronounced axial tilt ("obliquity" is the technical term) compared to all the other planets of the solar system -- some 98 degrees to the plane of its orbit of the Sun; Neptune’s is much more "normal": about 30 degrees. [For comparison, Earth’s obliquity is about 23.5 degrees]. One recently proposed alternative to the "internal radioactivity model" is "the recent collision model": that Uranus -- somehow, long after its formation -- suffered a massive impact with another major object, perhaps an errant moon ...
After the Voyager fly-bys of the 1980’s, the second "internal heat" proposal -- the "helium drip model" -- was favored for the observed heat excess in the Saturn situation. But, because of their relatively light masses (less than 30 times the Earth’s), only the third possibility -- massive internal radioactive decay -- has been seriously attempted as an explanation for Uranus’ and Neptune’s more puzzling "anomalous infrared emissions."
There are, however, serious problems with all of these "conventional" explanations -- particularly after these spacecraft flybys, for all planets less massive than Jupiter.
For instance, during the Voyager encounters of Uranus and Neptune, spacecraft instruments detected a barely measurable (but significant) "infrared excess" (as opposed to merely infrared re-emission of absorbed solar energy) for Uranus of about "1 to 1.14"; whereas for Neptune (essentially its planetary "twin") the ratio of internal heat to intercepted sunlight was a striking "three to one!"
However, simultaneous "doppler tracking" gravity measurements conducted during the fly-bys (looking for anomalous trajectory changes to the spacecraft motion, caused by gravitational effects from increased percentages of heavy radioactive elements in the cores of Uranus and Neptune) detected no anomalous central concentrations in either planet ... necessary, if the excess observed IR radiation is in fact caused by "excessive internal radioactive element concentrations."
Even more perplexing, Uranus has a pronounced axial tilt ("obliquity" is the technical term) compared to all the other planets of the solar system -- some 98 degrees to the plane of its orbit of the Sun; Neptune’s is much more "normal": about 30 degrees. [For comparison, Earth’s obliquity is about 23.5 degrees]. One recently proposed alternative to the "internal radioactivity model" is "the recent collision model": that Uranus -- somehow, long after its formation -- suffered a massive impact with another major object, perhaps an errant moon ...
This, according to the theorists,
in addition to accounting for the current "tipped over situation" of
the planet, would have also added a significant amount of
geologically "recent" internal energy to Uranus, driving up internal
temperatures by equivalent amounts. This model argues that these
resulting elevated temperatures in Uranus, derived from a massive
"cosmic collision," could thus account for Uranus’ current "infrared
excess," as observed by Voyager in 1986.
There is only one problem with these ideas: the "excess radioactivity theory," and the "cosmic collision model" are both apparently dead wrong.
There is only one problem with these ideas: the "excess radioactivity theory," and the "cosmic collision model" are both apparently dead wrong.
Uranus, with no apparent core concentration of "heavy radioactive elements" (so said Voyager), yet the one solar system planet with an axial "tilt" consistent with a major interplanetary collision -- is barely radiating "over unity" at its distance from the Sun ("over unity" = more energy coming out than is going in); Neptune -- essentially Uranus’ twin (image above) -- by striking contrast, and with a perfectly "normal" obliquity, is radiating almost three times more energy "out" than it’s getting from the Sun.
When these two planets
are "normalized" (i.e., when their differing distances from the Sun
are taken into account), their absolute internal "over unity" energy
emissions, in fact, are just about the same.
So, based on these "local" solar system observations, there’s apparently something drastically wrong with current astrophysical theories relating to "anomalous internal planetary energy resources" ... the same theories that Dr. Susan Terebey and NASA are now relying on to tell them (and us) both the age and mass of her newly-discovered "runaway planet."
So, based on these "local" solar system observations, there’s apparently something drastically wrong with current astrophysical theories relating to "anomalous internal planetary energy resources" ... the same theories that Dr. Susan Terebey and NASA are now relying on to tell them (and us) both the age and mass of her newly-discovered "runaway planet."
Enter
Hyperdimensional Physics
The cornerstone of the hyperdimensional model (as applied to the
problem of "unexplained" astrophysical energy sources) is that
historically, there is a perfectly natural explanation for such
"anomalous energy" appearing in celestial bodies ... which,
unfortunately, hasn’t been seriously considered by Science for over
100 years:
The existence of unseen hyperspatial realities ... that, through information transfer between dimensions, are the literal "foundation substrate" maintaining the reality of everything in this dimension.
The mathematical and physical parameters required for such "information/energy gating" into this spatial dimension from potential "n-dimensions" were primarily founded in the pioneering work of several 19th Century founders of modern mathematics and physics: among these, German mathematician Georg Riemann; Scottish physicist Sir William Thompson (who would eventually be Knighted by the British Crown as "Baron Kelvin of Largs" for his scientific and technological contributions); Scottish physicist James Clerk Maxwell; and British mathematician Sir William Rowan Hamilton.
In 1867 Thompson (image left), following decades of inquiry into the fundamental properties of both matter and the space between, proposed a radical new explanation for the most fundamental properties of solid objects -- the existence of "the vortex atom." This was in direct contradiction to then prevailing 19th Century theories of matter, in which atoms were still viewed as infinitesimal "small, hard bodies [as] imagined by [the Roman poet] Lucretius, and endorsed by Newton ..."
Thompson’s "vortex atoms" were envisioned, instead, as tiny, self-sustaining "whirlpools" in the so-called "aether" -- which Thompson and his 19th Century contemporaries increasingly believed extended throughout the Universe as an all-pervasive, incompressible fluid.
Even as Thompson published his revolutionary model for the atom, Maxwell (image below right), building on Thompson’s earlier explorations of the underlying properties of this "aetheric fluid," was well on the way to devising a highly successful "mechanical" vortex model of the "incompressible aether" itself, in which Thompson’s vortex atom could live -- a model derived in part from the laboratory-observed elastic and dynamical properties of solids.
.
Ultimately, in 1873, he would succeed in uniting a couple hundred years of electrical and magnetic scientific observations into a comprehensive, overarching electromagnetic theory of light vibrations ... carried across space by this "incompressible and highly stressed universal aetheric fluid ..."
Maxwell’s mathematical basis for his triumphant unification of these two great mystery forces of 19th Century physics were "quaternions" -- a term invented (adopted would be a more precise description) in the 1840s by mathematician Sir William Rowan Hamilton, for "an ordered pair of complex numbers" (quaternion = four).
Complex
numbers themselves, according to Hamilton’s clarifications of
long-mysterious terms such as "imaginary" and "real" numbers
utilized in earlier definitions, were nothing more than "pairs of
real numbers which are added or multiplied according to certain
formal rules." In 1897, A.S. Hathaway formally extended Hamilton’s
ideas regarding quaternions as "sets of four real numbers" to the
idea of four spatial dimensions, in a paper entitled "Quaternions as
numbers of four-dimensional space," published in the Bulletin of the
American Mathematical Society [4 (1887), 54-7].
It is obvious from Maxwell’s own writings that, even before Hathaway’s formalization, his choice of quaternions as mathematical operators for his electromagnetic theory was based on his belief that three-dimensional physical phenomena (including even perhaps the basis of human consciousness itself) are dependent upon higher dimensional realities.
It is obvious from Maxwell’s own writings that, even before Hathaway’s formalization, his choice of quaternions as mathematical operators for his electromagnetic theory was based on his belief that three-dimensional physical phenomena (including even perhaps the basis of human consciousness itself) are dependent upon higher dimensional realities.
For, in honor of another great mathematician
of the time, multi-dimensional geometer Arthur Cayley, Maxwell wrote
...
"Oh WRETCHED race of men, to space confined!
What honour can ye pay to him, whose mind
To that which lies beyond hath penetrated?
The symbols he hath formed shall sound his praise,
And lead him on through unimagined ways
To conquests new, in worlds not yet created.
First, ye Determinants! In ordered row
And massive column ranged, before him go,
To form a phalanx for his safe protection.
Ye powers of the nth roots of - 1!
Around his head in ceaseless* cycles run,
As unembodied spirits of direction.
And you, ye undevelopable scrolls!
Above the host wave your emblazoned rolls,
Ruled for the record of his bright inventions.
Ye cubic surfaces! By threes and nines
Draw round his camp your seven-and-twenty lines-
The seal of Solomon in three dimensions.
March on, symbolic host! With step sublime,
Up to the flaming bounds of Space and Time!
There pause, until by Dickenson depicted,
In two dimensions, we the form may trace
Of him whose soul, too large for vulgar space,
In n dimensions flourished unrestricted."
-- James Clerk Maxwell
To the Committee of the Cayley Portrait Fund -- 1887
Confirmation that Maxwell’s
"hyper-dimensional" inquiries extended far beyond "mere" physical
interactions can be seen from another of his "unknown" poems ...
"My soul is an entangled knot,
Upon a liquid vortex wrought
By Intellect in the Unseen residing.
And thine doth like a convict sit,
With marlinspike untwisting it,
Only to find its knottiness abiding;
Since all the tool for its untying
In four-dimensional space are lying."
In another work ("The Aether," 1876), Maxwell underscored the "ultimate" significance of these inquiries ...
"Whether this vast homogeneous expanse of isotropic matter [the aether] is fitted not only to be a medium of physical Interaction between distant bodies, and to fulfill other physical functions of which, perhaps we have as yet no conception, but also as the authors of The Unseen Universe seem to suggest, to constitute the material organism of beings exercising functions of life and mind as high or higher than ours are at resent, is a question far transcending the limits of physical speculation ..."
This startling connection -- between
Maxwell’s demonstrably deep interest in questions "hyperdimensional,"
including his direct homage to one of his scientific mentors’,
Arthur Cayley’s hyperdimensional geometry (the "27 lines on the
general cubic surface" problem -- see diagram,
below); and our
rediscovery over a century later of that same geometry ... at a
place called "Cydonia" ... on Mars -- is nothing short of
astonishing.
But, if you doubt such a compelling connection, just
reread those key lines.
"...Ye cubic surfaces! By threes and nines, Draw round his camp your seven-and-twenty lines- The seal of Solomon in three dimensions [emphasis added] .." (click above image)
Which, of course, are nothing less than the geometrical and mathematical underpinnings of the infamous "circumscribed tetrahedral latitude" memorialized all over Cydonia ... 19.5 degrees (click above image), the identical, hyper-dimensional quaternion geometry whose physical effects (see below) we have now rediscovered all across the solar system ... and beyond!
In a tragedy for science (if not for society in general) whose outlines we are only now beginning to appreciate, after Maxwell’s death, two other 19th Century "mathematical physicists" -- Oliver Heaviside and William Gibbs -- "streamlined" Maxwell’s original equations down to four simple (if woefully incomplete!) expressions.
Because Heaviside openly felt the
quaternions were "an abomination" -- never fully understanding the
linkage between the critical scalar and vector components in
Maxwell’s use of them to describe the potentials of empty space
("apples and oranges," he termed them) -- he eliminated over 200
quaternions from Maxwell’s original theory in his attempted
"simplification."
[Oliver Heaviside (image right), described by Scientific American (Sept. 1950) as "self-taught and ... never connected with any university ... had [however] a remarkable and inexplicable ability (which was possessed also by Newton and Laplace ...) to arrive at mathematical results of considerable complexity without going through any conscious process of proof ..." According to other observers, Heaviside actually felt that Maxwell’s use of quaternions and their description of the "potentials" of space was "... mystical, and should be murdered from the theory ..." which -- by drastically editing Maxwell’s original work after the latter’s untimely death (from cancer), excising the scalar component of the quaternions and eliminating the hyperspatial characteristics of the directional (vector) components -- Oliver Heaviside effectively accomplished singlehanded.]
This means, of course, that the four
surviving "classic" Maxwell’s Equations -- which appear in every
electrical and physics text the world over, as the underpinnings of
all 20th Century electrical and electromagnetic engineering, from
radio to radar, from television to computer science, if not
inclusive of every "hard" science from physics to chemistry to
astrophysics that deals with electromagnetic radiative processes --
never appeared in any original Maxwell’ paper or treatise!
They are,
in fact...,
"Heaviside’s
equations!"
Lest anyone doubt this is the case, they merely have to read a highly revealing paper on the subject by another renowned British mathematical physicist of this century, Sir Edmund Whittaker, titled simply "Oliver Heaviside" (Bulletin of the Calcutta Mathematical Society, Vol. 20, 1928-29, p.202); or, another overview of Heaviside by Paul J. Nahin, "Oliver Heaviside: Sage in Solitude" (IEEE Press, New York, 1988, p.9, note 3.).
The end result was that physics lost its promising theoretical beginnings to becoming truly "hyperdimensional" physics ... over a century ago ... and all that that implies.
Lest anyone doubt this is the case, they merely have to read a highly revealing paper on the subject by another renowned British mathematical physicist of this century, Sir Edmund Whittaker, titled simply "Oliver Heaviside" (Bulletin of the Calcutta Mathematical Society, Vol. 20, 1928-29, p.202); or, another overview of Heaviside by Paul J. Nahin, "Oliver Heaviside: Sage in Solitude" (IEEE Press, New York, 1988, p.9, note 3.).
The end result was that physics lost its promising theoretical beginnings to becoming truly "hyperdimensional" physics ... over a century ago ... and all that that implies.
Georg Bernard Riemann mathematically initiated the 19th Century scientific community (if not the rest of Victorian society) into the "unsettling" idea of "hyperspace," on June 10, 1854. In a seminal presentation made at the University of Gottinggen in Germany, Riemann put forth the first mathematical description of the possibility of "higher, unseen dimensions ..." under the deceptively simple title: "On the Hypotheses Which Lie at the Foundation of Geometry."
Riemann’s paper was a fundamental assault on the 2000-year old assumptions of "Euclidian Geometry" -- the ordered, rectilinear laws of "ordinary" three dimensional reality. In its place, Riemann proposed a four-dimensional reality (of which our 3-D reality was merely a "subset"), in which the geometric rules were radically different, but also internally self-consistent.
Even more radical:
Riemann proposed that the basic laws of nature in 3-space, the three
mysterious forces then known to physics -- electrostatics, magnetism
and gravity -- were all fundamentally united in 4-space, and merely
"looked different" because of the resulting "crumpled geometry" of
our three-dimensional reality ...
In terms of actual physics, Riemann was suggesting something clearly revolutionary: a major break with Newton’s "force creates action-at-a-distance" theories of the time, which had been proposed to explain the "magical" properties of magnetic and electrical attraction and repulsion, gravitationally-curved motions of planets ... and falling apples, for over 200 years; in place of Newton, Riemann was proposing that such "apparent forces’" are a direct result of objects moving through 3-space "geometry" ... distorted by the intruding geometry of "4-space!"
It is clear that Maxwell and other "giants" of 19th Century physics (Kelvin, for one), as well as an entire contemporary generation of 19th Century mathematicians (like Cayle, Tait, etc.) , took Riemann’s ideas very much to heart; Maxwell’s original selection of 4-space quaternions as the mathematical operators for his force equations and descriptions of electrical and magnetic interaction, clearly demonstrate his belief in Riemann’s approach; and, his surprising literary excursions into poetry -- vividly extolling the implications of "higher-dimensional realities" ... including musings on their relationship to the ultimate origin of the human soul (above) -- emphatically confirm this outlook.
So, how can modern "hyperdimensional physicists" -- like Michio Kaku, at City College of the City University of New York -- representative of an entirely new generation of physical scientists now reexamining these century-old implications of "hyperspatial geometries" for generating the basic laws of Reality itself, almost casually claim:
In terms of actual physics, Riemann was suggesting something clearly revolutionary: a major break with Newton’s "force creates action-at-a-distance" theories of the time, which had been proposed to explain the "magical" properties of magnetic and electrical attraction and repulsion, gravitationally-curved motions of planets ... and falling apples, for over 200 years; in place of Newton, Riemann was proposing that such "apparent forces’" are a direct result of objects moving through 3-space "geometry" ... distorted by the intruding geometry of "4-space!"
It is clear that Maxwell and other "giants" of 19th Century physics (Kelvin, for one), as well as an entire contemporary generation of 19th Century mathematicians (like Cayle, Tait, etc.) , took Riemann’s ideas very much to heart; Maxwell’s original selection of 4-space quaternions as the mathematical operators for his force equations and descriptions of electrical and magnetic interaction, clearly demonstrate his belief in Riemann’s approach; and, his surprising literary excursions into poetry -- vividly extolling the implications of "higher-dimensional realities" ... including musings on their relationship to the ultimate origin of the human soul (above) -- emphatically confirm this outlook.
So, how can modern "hyperdimensional physicists" -- like Michio Kaku, at City College of the City University of New York -- representative of an entirely new generation of physical scientists now reexamining these century-old implications of "hyperspatial geometries" for generating the basic laws of Reality itself, almost casually claim:
"... In retrospect, Riemann’s famous lecture was popularized to a wide audience via mystics, philosophers and artists, but did little to further our understanding of nature ... First, there was no attempt to use hyperspace to simplify the laws of nature. Without Riemann’s original guiding principle -- that the laws of nature become simple in higher dimensions -- scientists during this period were groping in the dark.
Riemann’s seminal idea of using geometry -- that is, crumpled hyperspace -- to explain the essence of a a force’ was forgotten during those years ... The mathematical apparatus developed by Riemann became a province of pure mathematics, contrary to Riemann’s original intentions. Without field theory, you cannot make any predictions with hyperspace [emphasis added]..."
-- M. Kaku, "Hyperspace"
Doubleday (Anchor Books): New York, 1994
Kaku’s statement belies the entire "modern" outlook on 19th Century physics, and leaves the distinct impression of an apparently unconscious "bias" similar to Heaviside’s, regarding Maxwell’s actual treatment of such matters; certainly, in completely ignoring Maxwell’s true discussion of the importance of the underlying four-dimensional "scalar potentials" for creating such "fields." And remember: Heaviside also thought of such "potentials" as ... "mystical ..."
The use of little-known Hamiltonian 4-space quaternions, to represent the effect of "scalar potentials" on electric charges (as opposed to Heaviside’s vectorial descriptions of direct "electric force fields") obviously have led to great confusion; because ... Maxwell’s "scalar potentials" are, of course, nothing short of exactly what Riemann initially proposed:
Quantifiable "geometric spatial distortions" ... the exact marriage of hyperspatial geometry and field theory that Kaku and others mistakenly believe (because they’re basing their analysis on Heaviside’s surviving vectorial version of Maxwell’s original "Equations") is totally missing from this greatest achievement of 19th Century physics!
The major source of confusion surrounding Maxwell’s actual Theory, versus what Heaviside reduced it to, is its math -- a notation system perhaps best described by H.J. Josephs ("The Heaviside Papers found at Paignton in 1957," Electromagnetic Theory by Oliver Heaviside, Including an account of Heaviside’s unpublished notes for a fourth volume, and with a forward by Sir Edmund Whittaker, Vol. III, Third Edition, Chelsea Publishing Co., New York, 1971).
According to Josephs:
"Hamilton’s algebra of quaternions, unlike Heaviside’s algebra of vectors, is not a mere abbreviated mode of expressing Cartesian analysis, but is an independent branch of mathematics with its own rules of operation and its own special theorems. A quaternion is, in fact, a generalized or hypercomplex number ... [emphasis added]"
And, you will remember, in 1897 Hathaway
published a paper specifically identifying these hypercomplex
numbers as "... numbers in four-dimensional space" (above).
Thus,
modern physics’ apparent ignorance of Maxwell’s 19th Century success
-- a mathematically-based, four-dimensional "field-theory" -- would
seem to originate from a basic lack of knowledge of the true nature
of Hamilton’s quaternion algebra itself!
[Apparently, unless a "hyperdimensional theory" is narrowly expressed in terms of a separate technique Riemann himself invented for his own N-dimensional mapping -- the so-called "metric tensor" -- modern physicists don’t seem to be able to recognize it as a valid higher-dimensional model ... not even when it was written in its own, specifically-designed, four-dimensional mathematical notation! (Riemann’s "metric tensor," BTW, is essentially a graphical checkerboard composed, for a 4-space description, of 16 numbers defining, for instance, field strength at each point in that four-dimensional space. It is NOT written in quaternions.)
And, unless you track down an original 1873 copy of Maxwell’s "Treatise," there is no easy way to verify the existence of Maxwell’s "hyperdimensional" quaternion notation; for, by 1892, the Third Edition incorporated a "correction" to Maxwell’s original use of "scalar potentials" (contributed by George Francis Fitzgerald -- whom Heaviside heavily admired) -- thus removing a crucial distinction between 4-space "geometric potential," and a 3-space "vector field," from all subsequent "Maxwellian theory." Which is why Kaku apparently doesn’t realize that Maxwell’s original equations were, in fact, the first geometric 4-space field theory ... expressed in specific 4-space terms ... the language of quaternions!
Just another measure of Heaviside’s effectiveness ...]
One of the difficulties of proposing a
"higher dimension" is that, inevitably, people (and scientists are
people!), will ask: "Ok, where is it? Where is the fourth dimension’
..?"
One of the most persistent objections to the 4-space geometries of Riemann, Cayley, Tait ... and Maxwell, was that no experimental proof of a "fourth dimension" was readily apparent; one of the more easily understandable aspects of "higher dimensionality" was that, a being from a "lower dimension" (a two-dimensional "Flatlander," for instance) entering our "higher" three-dimensional reality, would appear to vanish instantly from the lower-dimensional world (and, consequently, appear just as suddenly in the higher dimension -- but geometrically distorted.) When she returned to her own dimension, she would just as "magically" reappear ...
Unfortunately (or fortunately, depending on your perspective ...) to the scientific mind, people in our dimension don’t just "turn a corner one day ... and promptly vanish into Riemann’s fourth dimension.’" While mathematically derivable and beautifully consistent, to "experimentalists" (and all real science ultimately has to be based on verifiable, independently repeatable experiments) there seemed no testable, physical proof of "hyperdimensional physics."
Thus "hyperspace"-- as a potential solution to unifying the major laws of physics -- after Maxwell’s death, and the major rewriting of his Theory, quietly disappeared ... not to resurface for almost half a century ... Until April of 1919.
At that time, a remarkable letter was delivered to one "Albert Einstein." Written by an obscure mathematician at the University of Konigsberg in Germany, Theodr Kaluza, the letter’s first few lines offered a startling solution (at least, to Einstein -- unknowing of Maxwell’s original quaternion equations) to one of physics’ still most intractable problems: the mathematical unification of his own theory of gravity with Maxwell’s theory of electromagnetic radiation ... via introduction of a fifth dimension.
One of the most persistent objections to the 4-space geometries of Riemann, Cayley, Tait ... and Maxwell, was that no experimental proof of a "fourth dimension" was readily apparent; one of the more easily understandable aspects of "higher dimensionality" was that, a being from a "lower dimension" (a two-dimensional "Flatlander," for instance) entering our "higher" three-dimensional reality, would appear to vanish instantly from the lower-dimensional world (and, consequently, appear just as suddenly in the higher dimension -- but geometrically distorted.) When she returned to her own dimension, she would just as "magically" reappear ...
Unfortunately (or fortunately, depending on your perspective ...) to the scientific mind, people in our dimension don’t just "turn a corner one day ... and promptly vanish into Riemann’s fourth dimension.’" While mathematically derivable and beautifully consistent, to "experimentalists" (and all real science ultimately has to be based on verifiable, independently repeatable experiments) there seemed no testable, physical proof of "hyperdimensional physics."
Thus "hyperspace"-- as a potential solution to unifying the major laws of physics -- after Maxwell’s death, and the major rewriting of his Theory, quietly disappeared ... not to resurface for almost half a century ... Until April of 1919.
At that time, a remarkable letter was delivered to one "Albert Einstein." Written by an obscure mathematician at the University of Konigsberg in Germany, Theodr Kaluza, the letter’s first few lines offered a startling solution (at least, to Einstein -- unknowing of Maxwell’s original quaternion equations) to one of physics’ still most intractable problems: the mathematical unification of his own theory of gravity with Maxwell’s theory of electromagnetic radiation ... via introduction of a fifth dimension.
(Because Einstein, in formulating the General and Special Theory of Relativity in the intervening years since Riemann, had already appropriated time as the "fourth dimension," Kaluza was forced to specify his additional spatial dimension as "the fifth." In fact, this was the same spatial dimension as the 4-space designations used by Maxwell and his colleagues in their models ... over 50 years before.)
Despite its stunning (Einstein mulled over the paper’s implications for more than two years, before finally supporting its scientific publication) mathematical success, in apparently -- finally -- uniting "gravity" and "light," the same question, "OK, where is it?" was asked of Kaluza as had been asked of Riemann, over 60 years before; because, there was no overt experimental proof (for instance, people and things up and "disappearing") of the physical existence of another spatial dimension.
To which Kaluza this time
had a very clever answer:
he proposed that this "fourth dimension" -- unlike the other three we are familiar with -- somehow had collapsed down to a tiny circle ... "smaller than the smallest atom ..."
In 1926, another essentially unknown mathematician, Oskar Klein, was investigating the peculiar implications of Kaluza’s ideas in the context of the newly-invented atomic theory of "quantum mechanics." [Klein was a specialist in the truly arcane field of mathematical topology -- the higher dimensional surfaces of objects; the twisted 3-D topology of the 2-D surface of a "Klein Bottle" (image left) is named specifically in his honor].
Quantum mechanics had just been proposed
a year or so before Klein’s further topological investigation of Kaluza’s ideas, by
Max Planck and many others rebelling against
perceived limitations of Maxwell’s (remember, heavily sanitized by
Gibbs and Heaviside) classical Electromagnetic Theory.
The "quantum
mechanics " theory would eventually become a highly successful (if
bizarre, by common-sense standards) non-geometric effort to describe
interactions between "fundamental particles," exchanging "forces"
through discrete "quantitized" particles and energy in the
sub-atomic world.
Eventually, combining the two inquiries,
Klein
theorized that, if it truly existed, Kaluza’s new dimension likely
had somehow collapsed down to the "Planck length" itself --
supposedly the smallest possible size allowed by these fundamental
interactions. However, that size was only about ... 10-33 cm long!
Thus, the main obstacle to experimental verification of the Kaluza-Klein Theory (and the reason why people simply didn’t "walk into the fourth dimension"), was that quantum mechanics calculations affirmed that the only way to physically probe such an infinitesimally tiny dimension was with a new machine ... an "atom smasher." (click image below) There was only one small "technical" problem ...
Thus, the main obstacle to experimental verification of the Kaluza-Klein Theory (and the reason why people simply didn’t "walk into the fourth dimension"), was that quantum mechanics calculations affirmed that the only way to physically probe such an infinitesimally tiny dimension was with a new machine ... an "atom smasher." (click image below) There was only one small "technical" problem ...
The energy required would exceed the output of all the power plants on Earth ... and then some!
Thus, the brief "blip" of new interest in "hyperdimensional physics" -- the discussions of Kaluza-Klein among physicists and topologists -- "dropped through the floor" by the 1930’s. This occurred both because of Klein’s "proof" of the apparent impossibility of any direct experimental verification of additional dimensions ... and because of the dramatic revolution then sweeping the increasingly technological world of Big Science...
The flood of "verifications" gushing forth from atom smashers all around the world, feverishly engaged in probing the new area the experimentalists apparently could verify: the multiplying populations of "fundamental particles" spawned by the bizarre mathematical world (even more bizarre than "N-dimensions") of Quantum Mechanics.
30 more years would pass ... before (almost by mathematical "accident") in 1968, the current mainstream "flap" of renewed scientific interest in "hyperspace" would be, like the legendary Phoenix, "magically" reborn -- a theory now known as "Superstrings" ... in which fundamental particles, and "fields," are viewed as hyperspace vibrations of infinitesimal, multi-dimensional strings ... From those relatively inauspicious beginnings, stretching across more than 60 years, the current focus of scientific research papers on "hyperspace" -- from continued research into updated versions of the old "Kaluza-Klein Theory"; to discussions of the much newer "Supergravity" hyperspace unification model; to the exotic "String Theory" itself -- has grown geometrically (over 5000 papers by 1994 alone, according to Michio Kaku -- see above).
This much attention to a
subject involving realities you can’t even see, represents nothing
short of a fundamental psychological revolution sweeping across a
major segment of the worldwide scientific community.
For most physicists currently interested in the problem, the "Superstring" hyper-dimensional model has overwhelming advantages over all its predecessors. Besides effectively unifying all the known forces of the Universe ... from electromagnetism to the nuclear force ... in a literally beautiful "ultimate" picture of Reality, it also makes a specific prediction about the total number of N-dimensions that can form:
For most physicists currently interested in the problem, the "Superstring" hyper-dimensional model has overwhelming advantages over all its predecessors. Besides effectively unifying all the known forces of the Universe ... from electromagnetism to the nuclear force ... in a literally beautiful "ultimate" picture of Reality, it also makes a specific prediction about the total number of N-dimensions that can form:
"Ten" (or "26," depending on the rotation of the "strings").
The bad news is: they can’t be tested
either ...
As all ten dimensions are curled up (in the model) inside the same experimentally unreachable "Planck length" which spelled the scientific demise of the original Kaluza-Klein ...
Impasse.
As all ten dimensions are curled up (in the model) inside the same experimentally unreachable "Planck length" which spelled the scientific demise of the original Kaluza-Klein ...
Impasse.
This, then is the current situation.
The "hottest" mainstream scientific theory to come along in more than half a century, the next best thing to a "Theory of Everything" (and seriously attempting to become precisely that ...), is not only a Hyperdimensional Model of Reality ... it is another one which, by its fundamental nature... can’t scientifically be tested!
While a "hyperdimensional model" which can be tested easily -- as this paper will unequivocally show -- for over a 100 years has been systematically ignored.
Is it just us ... or is there something truly wrong with this picture?
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