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Superluminal Quantum Gravitation
Another take on the hypothesis that gravity is faster than light.
"Science Fiction"
by
H.K. Richter
As a mathematical exercise, designed to stimulate the imagination, suppose that gravity is faster than light, and is therefore a tachyonic force. That is, view gravity as a monopole radiation field, unlike the electrodynamic and chromodynamic fields, where the speed of propagation of the virtual exchange particle responsible for gravity is faster than light. In such a case, it may be that the spatial size of each radiated quantum of the gravitational field is the literal embodiement of an infinitessimal point in space, observed at some specified instant in time, so that it gives a physical definition to a point in 3-dimensional space, and each such moving particle maintains an absolutely straight-line path from its source-mass to some arbitrary location at an infinite distance, thereby giving a physical definition for an absolutely straight line in 3-dimensional space.
It can also be conjectured that the most likely reason physicists have been unable to detect the exchange particle responsible for gravity at the quantum (or any other) level is probably because gravity is tachyonic, and our technology is not yet sufficiently advanced to provide scientists with instruments capable of detecting or manipulating tachyons.
Presently, using relativistic gauge-field theory (Griffiths, 343-368; Lerner, 427), physicists can, of course, specify a standard picture of quantum gravity as a quadrupole field, involving spin-2 massless bosons, called "gravitons", traveling at lightspeed. (Lerner, 394) But that model has two major shortcomings; (1) it results in an exchange particle so energetic that the particle could not possibly have evaded detection for so long, after we have been able to detect all of the other fundamental particles necessary for establishing a viable Unified Field Theory, and (2) the notion that gravity is a quadrupole field is not supported by experimental evidence, which indicates (and has done so ever since measurements were first conducted) that gravity is actually a monopole field, whose force is given by Newton's equation involving his universal gravitational constant (Berkey, 1037), and whose observable macrocosmic effects are given by the field equations of Einstein's theory of General Relativity (Lerner, 1048). On the other hand, if we impart faster-than-light velocities to the gravitational interactions, making gravity a wholly imaginary thing (mathematically), and say that its virtual exchange particles radiate to infinity (like the real particles that stream from a radioactive substance), then we obtain an elementary representation by which gravity can be unified with the other forces of nature symbolically, wherein the overall Grand Unified-Field is displayed as a complex number (n) in which the real-number part (a) represents the detectable unified-field (involving the electro-weak and the chromodynamic interaction fields), while the imaginary-number part (b) is the superluminal analog of a central force field [such as that obtained using Coulomb's Law (Berkey, 1038)], with the imaginary-number, ib, representing superluminal gravitation; n = a + ib , where i is the standard imaginary-unit, defined: i = (-1)^(1/2); i^2 = -1.
We can therefore invent a complex specifier, F, representing the Grand Unified-Field, which incorporates the detectable unified fields, Fu, of electromagnetism, the weak nuclear, and the strong nuclear fields as the real-number part, and attach by addition the classical gravitational-field, Fg, as the imaginary-number part, and write; F = Fu + iFg . However, since Fu is itself complex, then we need a new operator (i), called, for instance, the "imagination-unit", which allows us to distinguish the complex numbers in Fu (which can be referred to as "standard" complex numbers) from complex numbers in Fg (which can be referred to as "actual" complex numbers), where i is defined as imposing a transformation that restricts the velocity of gravity to propogation speeds between lightspeed and infinite speed, exclusively.
That done, if iFg is replaced by iFg, we obtain a crude sort of quantum-field unification of all the forces of nature, given as a single super-complex number; F = Fu + iFg, wherein the imagination-unit (i) transforms Fg, the classical representation of gravity, into a certain non-instantaneuos analog of itself, but which still interacts faster than light. (Berkey, 1038)
Unification of tachyonic gravity with the other forces is readily accomplished by constructing a gauge-field scaling-format for hyperlight velocities, by which format one-to-one correspondences can be established between speeds above and below lightspeed; necessarily confining the velocities of gravity-inducing tachyons so that they exist only between lightspeed and infinite speed, exclusively, to ensure that the model, involving the representations of all of the fields of a specified source (such as, for instance, a single hydrogen atom), contains no unmanageable infinities.
The tachyonic gauge itself is obtained by relating a well-defined definite integral with exclusive limits at 0 velocity and lightspeed (it being sufficient, formally, to exclude both parameters from the integration), by means of a transformation equation, to an analogous integral defined between lightspeed and infinite speed (likewise involving exclusive limits). (Griffiths, 343-368; Lerner, 427-429)
For a more detailed pure mathematical explanation of the imagination-unit, i, and how it can be used to explain quantum gravity, click the following link; http://hometown.aol.com/HKurtRichter/TachyonMath.html , read the article there (which describes the integrals mentioned above), then click the link "Application to Gravity" at the bottom of that page, and read on. A link back to this page, labeled "Tachyonic Gravity", is provided on each of those pages.
Here, while the imagination-unit i enables us to present an hypothetical unification of tachyonic gravity with the other forces of nature, making for a Grand Unified-Field that explains physical reality almost completely, we may yet wonder: "what about the rest of existence?" There are, in fact, numerous other aspects to reality that are not explained by this, or any other, Grand Unified-Field which encompasses only those physical considerations which we are accustomed to investigating experimentally. These other aspects include human thought, the life-force of living creatures, and a plethora of unexplained natural and supernatural phenomena. To solve that dilemna, we can call upon Interdiscipline Synthesis Cosmology to go beyond the Grand Unified-Field (though it must include that theory), and let yet another new imaginary, named the "infinity-unit", ii, be employed as an operator that imparts infinite speed to a given real particle or to a sub-infinite tachyon. Then we have two classes of tachyons to consider, where the gravity-inducing tachyons cannot reach infinite velocity (just as real masses and massless particles are constrained to having lightspeed as a velocity limit), but infinite-speed tachyons supply the necessary additional level of complexity. A scenario involving both i and ii can then be used to explain any number of previously unexplained natural and supernatural phenomena; for these are the tools by which anything we imagine becomes not just conceptual but quantifiable, metaphysically.
Next, assign to gravity an infinite distance range but to all other forces a limited range of distance, where only gravity may act across truly infinite distance (within the detectable universe) -- meaning electromagnetism cannot have an infinite range (as traditionally held), but must be restricted to having all its energy fall to zero well-before reaching an infinite distance from its source.
Note now that we employ the word "actual" as a label, in an attempt to distinguish between the detectable and nondetectable. Furthermore, in saying "detectable," we include anything that is implied by empirical observation and/or experiment, even if it cannot be detected directly, while "undetectable" refers to different imaginary things than the usual symbolically imaginary things. Yet, in naming something as an actual imaginary, we do not imply nonexistence. We are only saying the entity is so named in order to categorize it theoretically. But, of course, since tachyonic gravity is itself an actual imaginary idea, by definition, it can be ignored in other considerations of our spacetime reality, so that the gravity-tachyon hypothesis need not interfere with any other model purporting to describe physical aspects of our real existence.
Consider now a tachyon generated by a bit of real mass in outer-space. The tachyon, unrestrained by physical objects in its path, sails off to infinity at incredible speed, faster-than-light, and therefore describes a true straight line in real space, from the origin to an infinite distance away. Not just a localized line, mind you, but the literal embodiment of an absolutely straight line in 3-d space. [We are therefore creating a physical definition for the straight line.] If it is also allowed that the energy of the tachyon is sufficiently small that it is easily generated by any bit of mass, and that its spatial size is such that it epitomizes a point in space, then there is no barrier to its spontaneous creation by any massive object, no matter how small the object. If it is further allowed that a free tachyon imparts some of its time-reversed momentum to some of the real masses through which it passes on its journey from its source to an arbitrary point at infinity, then its passage esstablishes an attractive force between other masses in its path and the source-mass. Collectively, therefore, all of the radiated tachyons from a given source constitute a true monopole in spacetime, the effect of which is the bringing about of perpetual attractions between all physical bodies in the universe.
So, this is superluminal quantum gravitation; the gravitational energy-exchange particle is an infinitessimally small tachyon, traveling an absolutely straight-line path from its origin to some infinite distance away, all the while imparting a pull rather than a push upon passing through objects in real spacetime, where Einstein's theory of General Relativity describes the observable effect of all radiated tachyons on space. Thus, in accordance with Einstein's rather artistic use of Reimannian geometry, the imaginary monopole radiation responsible for the curvature gives rise to gravitational field shapes around each source-mass, which shapes are determined using fractal geometry to depict concentric gravity "shells" propagating through the universe, which is itself replete with violent and/or unpredictable activity at every measureable scale.
The conclusion to all of this is the implication that the search for the quantum of gravity and the search for the tachyon are one in the same search, and it therefore behooves those seeking the quantum of gravity to join forces with those seeking tachyons, and perhaps together come up with a way to detect tachyons; gaining the means of proving or disproving the hypothesis that gravity is faster than light.
Conclusion: Gravity is faster than light, and is therefore a tachyonic force.
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Text References (w. Additional Selected Works):
Berkey, D.D. & Blanchard, P. Calculus, 3rd Ed., Saunders Col. Pub., '92.
Einstein, A. Relativity: The Special And General Theory, Crown Publishers, Inc., '61.
Griffiths, D. Introduction to Elementary Particles, John Wiley & Sons, Inc., '87.
Lerner, R.G. & Trigg, G.L. Encyclopedia of Physics, VCH Publishers, '91.
Matthews, P.T. Introduction to Quantum Mechanics, McGraw Hill, '65.
Thornton, S.T. & Rex, A. Modern Physics ..., Saunders Col. Pub., '93.
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To correspond with the author, send email to HKurtRichter@aol.com.
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Copyright 2003, H.K. Richter. All rights reserved.
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