The Gravitational Exchange Tachyon (GET)

If, for any function F , we can define derivatives with respect to x , so that F(x) = f'(x) = df(x) / d(x) , then, for functions f and F , we can give a definite integral between positive and negative infinity, for the variable x , equal to the sum of the integrals that take negative and positive infinity separately. And if we let x be the time t , then the positive integral can be used for studying bradyons, with positive time, and the negative for tachyons, with negative time. Then, imposing exclusivity on the two time integrals, to remove absolute-zero and infinite-velocity solutions, pertinent parameters corresponding to each type of particle (bradyons, photons, and tachyons) are rendered empirical.

That said, the functional operator *a* , used to impose Einsteinian relativity on an object of rest-mass m , is given as a function of the ratio between the velocity (v) of the object and the lightspeed constant (c) ; *a* = 1 / { sqrt[ 1 - (v/c)^{2} ] } , where the moving mass *m* , is defined; *m* = *a*m . This formula is an example of how we get the three categories of particles; standard, massless, and superluminal. And its use to plot time against velocity in two dimensional space results in the Light Cone of Special Relativity, which itself implies a tachyonic universe that coexists with the detectable universe.

A tachyon that we could attempt to devise detection and manipulation apparatus for, might reside in a superluminal analog of the standard space-time manifold, so the limits on it are easily specified;

c < v_{t} < i^{i}(+ infinity) , 0 > t_{t} > i^{i}(- infinity) , 0 < x_{t} < i^{i}(infinity) , ... .

It is simple, then, to imagine a tachyonic analog of all known particles, and obtain hypothetical sets of characteristics for each of the analogs. The tack is to give an integration example to establish specific one-to-one correspondences across the lightspeed barrier required for a given parameter or parameter set. This is the purpose of my Tachyonics Operator, i^{i} ; to imply superluminality, while removing possible interference with the standard imaginary-unit, i .

Using the Tachyonics Operator, let us describe a new particle, not in analogy to any known particle, except perhaps that we allow it to resemble some particles with respect to their macrocosmic behavior. I'm looking for a point-like, spin-less, completely classical tachyon that shoots off to an infinite distance, faster-than-light, seeming instantly, upon being spontaneously generated in some real mass. It is not affected much, or at all, by real objects it encounters (and probably not by other tachyons, as well), and barely registers a whisper of affect on those objects, except that it transfers (by a theoretical twisting-string substructure) some of its forward momentum to the bodies it passes through on a perfect or near-perfectly straight Cartesian path. [The twisting substructure is not necessarily actual. It is an hypothetical means of obtaining the action integral in a string-theory model.]

Being point-like means this tachyon epitomizes the concept of a point in space, and its path therefore serves as a justification for the concept of a line in space. And being spin-less means its Schrödinger Equation is reduced to the equation of a line in space (i.e., no wave characteristics whatsoever). We have thus been given a particle that is wholly compatible with all Modern Quantum-Field Theories, albeit, by reducing the wave-equation for this tachyon to a mere linear reference.

Collectively, such tachyons radiating spontaneously from a real object would give rise to radiation pressure on other bodies in the Universe, but due to the reversed causality of tachyons, of any kind, this is imparted as negative radiation pressure; causing a pull toward the source, instead of pushing things away from the source. So, we have obtained a particle, consistent with Quantum-Field Theory, that can account for Newton's law of Universal Gravitation; F = G[Mm/(r^2)] , where F is the attractive force an object of mass M exerts on some other mass m located the center-to-center distance r away from M (and G is Newton's constant).

In particular, if we let ^{t}F_{i} denote the amount of force each such special tachyon contributes to F , then we can define F as their sum; F = ^{t}F_{1} + ^{t}F_{2} + ^{t}F_{3} + ... .

Let me call this attraction-imposing tachyon the Gravitational Exchange Tachyon, or GET particle, and note that, using its reversed causality to establish a negative radiation pressure, and equating this with Newtonian Gravity (NG), I am greatly encouraged to think this model (superluminal quantum gravity) is compatible with the field equations of Einstein’s theory of General Relativity (GR) -- by means of the equivalence of GR to NG at the weak-field limit of GR, where the Ricci Scalar (radius of curvature), in the field equations of GR, orients the Euclidean direction of the individual GET trajectories.

Conclusion: Gravity is faster than light, and is therefore a tachyonic force.

An intriguing result of such speculation is to realize that, should there truly exist a superluminal universe coexisting with the visible universe, complete with analogs of all known particles [as well as many tachyons for which exact bradyon analogs do not exist (thus explaining why so many particles predicted by string theorists are not currently detectable)], then the gravity of a superluminal body composed of tachyonic mass would correspondingly produce its own version of gravity (also faster-than-light) that imparts positive radiation pressure on all bradyonic matter it passes through; thus setting-up a universal repulsive force (true antigravity) in the visible universe, from seemingly invisible matter. Consequently, I believe this is an explanation for the so-called “dark matter” and “dark energy” astronomers are attempting to investigate more thoroughly, these days.

In short, if the gravity of a bradyon is a universally attractive superluminal force in the visible universe, then the gravity of a tachyon is a universally repulsive force in the visible universe, where tachyons collectively account for dark matter, and their superluminal gravity accounts for dark energy. However, there could also be other superluminal forces at work, and some of these may have influences on the visible universe, as well. For example, tachyonic energy fields could be used to explain the life force of animate things, the seat of consciousness, and how it is that humans have minds, exactly what emotions really are, and a whole array of other previously unexplained natural and supernatural phenomena.

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