Tachyonics

Part 2, Introduction to Superluminal Gravitation

Foreword

I describe gravity as a superluminal force by suggesting that point-like tachyons give rise to the causally-reversed radiation pressure we experience as Newton’s law of universal gravitation.

The idea involves setting SchrÃ¶dinger’s wave equation equivalent to the equation of a line in space, for the tachyon held as causing gravitation. In particular, this model of gravity envisions an infinitesimally small point-particle, epitomizing the mathematical notion of a point in space, and suggests that there may exist such point-like tachyons radiating naturally (and constantly) from all real masses in all directions; each such tachyon traveling perfect Euclidean-straight lines from their sources to infinity, imparting some of their causally-reversed momentum to all of the “real” objects through which they pass on their journey. And since reversed causality orients an imparted momentum-vector in the opposite direction to the direction of the tachyon's travel, then such tachyons would collectively establish negative radiation pressure in ordinary space. This is what we understand as the gravity described by Newton’s law of gravitation, locally, and by Einstein’s General Theory of Relativity, when dealing with large astronomical reaches.

Also, if gravity is tachyonic, and there is a superluminal universe in connection with the detectable universe (but unseen due to existing in alternate-dimensional space-time), then the gravity from tachyonic matter would cause repulsion for all ordinary matter, and this could explain the "dark energy" and "dark matter" that astronomers are interested in understanding more completely.

I provide here a textual rendering of my theory. Readers are invited to check my work (e.g., search keywords). But since it is speculative, it can be ignored.

The Concept of Tachyons and Tachyonic Spacetime

Einstein’s famous equation for the rest-mass of a real particle is;

E = m(c^2),

where E is energy, m is mass, and c is the lightspeed constant. But it is derived from the energy equation for a moving mass, involving momentum;

E^2 = (pc)^2 + [m(c^c]^2,

where p is the particle’s momentum.

The difference is that momentum at rest is zero. And the problem with that is; the reference-frame for a resting particle is relative to the observer, and must be specified case-by-case. There is no absolute rest-frame; everything in existence moves somehow, relative to everything else. Nevertheless, let us use the simplified formula, because it is easier to work with.

If E = m(c^2) is positive, for a real mass, m , then -E = -m(c^2) can designate the analogous tachyonic mass, -m ; i.e., particle of mass -m and energy -E is a tachyon (faster-than-light, FTL), where, if v is any velocity. Thus, we have the three cases:

(1) 0 < v < c for ordinary particles, called “bradyons”,

(2) v = c for massless particles, called “photons” and “luxons“, and

(3) c < v < (infinity) for tachyons obtained as analogs of bradyons.

[Other tachyons can be imagined, including those traveling infinitely fast, but I view most of those as accounting for other phenomena.]

Next, let's define convenient variables, to make for concise text;

v+ = v where 0 < v < c , for bradyons,

v = c , for photons, and

v- = v where c < v < (infinity), for tachyons.

Also, assign special symbols for other important variables.

For a bradyon, let m+ be the mass, E+ the energy, and p+ the momentum.

For a photon or luxon, let m = 0 , E be energy, and p be the momentum.

For a tachyon, let m- be the mass, E- the energy, and p+ the momentum.

The Empirical Variables:

{bradyons: v+, m+, E+, p+ | (E+)^2 = [(p+)c]^2 + [(m+)(c^2)]^2 **

{photons: v = c , m = 0 , E , p | E^2 = (pc)^2 **

{tachyons: v- , m- , E- , p- | (E-)^2 = [(pt-)c]^2 + [(m-)(c^2)]^2 **

These are the most important empirical (testable) quantities and formulas, here.

Notice that there is no absolute zero velocity, regardless of the reference-frame; even for the center of the detectable universe, because we do not know if the center of the universe is moving with respect to empty space. Consequently, a zero velocity specified for a given real reference-frame is purely relative, while an absolute zero velocity is an imaginary quantity. And there exists no absolute infinite velocity for a tachyon, although a relative infinite velocity can be specified, theoretically, in a tachyonic reference-frame.

We should also address the issue of the lightspeed constant, to remove possible ambiguity. For example, we now know that all the physical constants (including lightspeed) change slowly with time, as the universe expands, although we can continue to use the latest confirmed values of the “constants” for most purposes. But the knowledge that the lightspeed constant changes along with the evolution of the universe begets important ramifications for cosmologists. It does not, as a rule, however, alter the present discussion very much. Yet, it warrants mention. And regardless of it, I make use of the lightspeed constant just as Einstein did. Hence, to stress my reliance on the lightspeed constant, c , recall the relativity operator, R, Einstein made use of, and which is derived from the Lorentz Transformations. It is defined;

R = 1 / sqrt{1 - [(v/c)^2]** .

[Einstein preferred the Greek letter alpha for this.]

Applying R multiplicatively to some quantity associated with a rest-state for a particle results in the corresponding quantity for the particle in motion; assuming standard coordinate systems. For instance, if m+ is a resting particle‘s mass, we can let M+ = Rm+ be the moving mass. Similarly, R can be applied to other measurable or calculable quantities, such as velocity, momentum, and time (rendering them “relativistic”).

It's this operator, R, that implies the existence of tachyons (particles that always travel FTL, and which are said to be “superluminal” in character), due to the presence of the velocity ratio, v/c , under a radical-sign in the denominator. To the point, the three overall categories of particles (bradyons, photons, and tachyons) arise directly from applying the operator in describing reality.

Take a generic rest-mass, m , as an example, where M = Rm defines the corresponding moving mass. So, whenever v < c , then R is a real number, and therefore M is real.

But if v = c , then, by convention, R = 0 (or else it is said to be “undefined”), making M = 0 , which is the specific case for photons.

Thus, if v > c , then R is an imaginary number, making M an imaginary mass.

We thus justify the nomenclature; m+ is bradyonic rest-mass, m = 0 is photonic rest-mass, and m- is tachyonic rest-mass -- so moving masses are;

M+ = Rm+ , M = Rm = 0 , and M- = Rm- .

With velocities, we can let; V+ = Rv+ , V = Rv = c , and V- = Rv- .

And with time, let T+ = Rt+ , T = Rt , and T- = Rt- .

Important! Use the equation for R to plot a graph setting velocity against time in three-dimensional space, to give the “light cone” of Special Relativity.

[Online reference

http://en.wikipedia.org/wiki/Light_cone.]
[Print reference, textbook Modern Physics for Scientists and Engineers, by Thornton & Rex, Saunders College Publishing, '93. Pg. 50, 1st edition.]

Mere inspection of the light-cone (and test-runs of the formula for R) suggests that the universe has three time-dependent "regions"; the past, present, and future for an event, or for a moving object. It can also suggest the existence of objects (such as subatomic particles) that are not "real", mathematically, but which are not strictly forbidden, theoretically, on the other side of lightspeed.

A tachyon is one such object, with negative time (reversed causality), and imaginary mass (compared to bradyons, with real mass and positive time).

Tachyons travel backwards in time as viewed from a standard bradyonic system in which time-flow is counted as "forward" for positive real mass. However, a tachyon would have positive time as viewed from a superluminal system, from which normal bradyons would appear to have negative time.

The important consequence in context is that a tachyon's momentum will appear opposite to that of an analogous bradyon, as seen from a bradyonic system. One can assume, then, that a collision between a tachyon and bradyon would result in post-collision trajectories, momenta, and various anomalies that take into account the reversed causality of the tachyon, observed from a standard bradyonic frame.

If bradyons radiating from a radioactive object give rise to radiation pressure, pushing things away from the object in the space surrounding it, then perfectly analogous tachyons radiating from the same sample would produce radiation pressure that pushes in towards the object. Radiating tachyons would impart negative radiation pressure. We might conclude, then, that this negative-radiation-pressure accounts for the pull of gravity between all real massive bodies; assuming tachyons actually do radiate spontaneously in all directions.

Prime Implication: The universe we observe from bradyonic space-time has a counterpart, or more correctly an extension, in tachyonic space-time. That is, for a given bradyon, we can speculate an analogous tachyon in a superluminal manifold, which further implies that a superluminal universe may co-exist, and is interactive, with the visible universe. What that means experimentally is that we should start considering the influences of super-dimensional factors in our tests. In fact, we should continue looking for a universal superluminal substructure.