Superluminal Gravity Provides Unification Scheme

Searching for Tachyons (continued)

Tiwari On The Experiments

Under the sub-heading "Experimental Searches", Tiwari starts the topic by mentioning a few seemingly serious attempts to detect tachyons, noting that: "The first experimental investigation by T. Alvager and P. Erman was based on the suggestion that tachyons might be present in beta decay. Presence of a charged tachyon in a strong radioactive beta source was searched during the years 1963-65, but in vain." His citation is a 1969 article in Physics Today magazine, in which Bilaniuk and Sudarshan discuss these series of experiments. [See: Physics Today, 22(5) (1969).]

However, I found more details in an obscure archived paper* by Sudarshan, in which it is stated: "The simplest method of identification of a tachyon is to measure its energy and momentum and verify that the momentum is larger than the energy; equivalently one may measure the velocity directly by a time of flight method. The first method has already been employed by T. Alvager and P. Erman who used a magnetic deflection in a double focussing beta spectrometer to select the momentum of the particles, and a semiconductor counter to measure the energy. They concluded that in Thulium 170 there were less than 10^-4 tachyons per electron, if at all." [Nobel Institute Report, 1966.]
* Paper; The Nature of Faster-Than-Light Particles and Their Interactions, by E.C.G. Sudarshan (of the University of Texas at Austin). Sub-topic; Methods of Experimental Detection of Tachyons. This paper is labeled; ARKIV FOR FYSIK Band 39 nr 40. And I obtained it online by a Google search using the keyword "T. Alvager".

Now, Tiwari next writes: "Another experiment was based on detecting Cherenkov radiation emitted by charged tachyons. In the experiment carried out by Alvager and Kreisler gamma rays from a 5-millicurie cesium-134 radioactive source collide with lead. A strong electric field is applied to this presumed source of tachyons so that emission of Cherenkov radiation is detectable; but the results were negative." [Citation: T. Alvager and M.N. Kreisler, Phys.Rev. #171, year 1968, page 1357.] But Sudarshan, citing the 1962 American Journal of Physics article "Meta-Relativity", by Bilaniuk, Deshpande, and himself, correctly points out that: "Both of these experiments presume that the tachyons are electrically charged; if the tachyons are neutral, both the experiments must give negative answers." [Citation: Am. J. Phys. #30, page 718 (1962).]

In my opinion, while the literature abounds with people touting these results as proving tachyons don't exist, what the experiments actually show, and only show, is that tachyons are either electrically neutral, or, if any of them are charged, they simply do not possess the kind of electric charge that we are used to dealing with, and that even this is true only within the detection ranges established by the limits of the experiments. It is more likely, given what we know about tachyons theoretically, that the assumption that any of them have a detectable form of electric charge is not really a valid inference, and the null results of the experiments just cited tend not to support the contention that tachyons do not exist, but rather that it is not logical to demand this assumption.

Because of the alternate-dimensional nature of tachyons, any form of electric charge that any of them might exhibit would probably be a superluminal analog of what we know as electric charge. Hence, any experiment designed to detect tachyons based on the idea that they posses a standard form of electric charge is doomed to failure from the outset. What we can learn from this experiment, then, is simply not to base the designs of new experiments on the initial assumption that charged tachyons could possess the standard form of electric charge, because of the obvious theoretical implication that tachyonic charge is probably not like the electric charge that we know.

In Sudarshan's 1969 paper, he suggested that "there are four experimental methods of searching for tachyons which do not require them to be charged particles." I quote:
(a) Search for "decays in flight" of a stable particle: If we find that a particle which is stable in its own rest frame (like the proton) appears to decay in flight we can be sure that at least one of the "decays" products is a tachyon.
(b) Large angle scattering: If fast particles scatter through large angles with pronounced resonance in the invariant momentum transfer, a tachyon is being emitted (or absorbed!).
(c) Poles in the scattering amplitudes: If the scattering amplitude between two ordinary particles exhibits a pole in the invariant momentum transfer variable for negative (space-
like) values we can conclude that a tachyon is being exchanged. [Footnote: "For suitable kinematics the pole may appear in the physical region; it is therefore desirable to have a tachyon with width."]
(d) Effective mass plots: The original method of identifying pion-pion resonances can be
adapted to the present case by plotting the effective 4-momentum squared of a collection of pions with some of the pions in the initial state and some in the final state. A peak in such an effective squared mass plot at a negative value would be evidence for a tachyon. One has to eliminate, in such an analysis, the purely kinematic enhancements. [Here, for the said "original method", Sudarshan cites an entry by himself, G. PINSKI, and K.T. MAHANTHAPPA, in Proceedings from the Tenth International Conference on High Energy Physics (Rochester, 1960).]

I predict that one or more of these methods will provide proof for the tachyon's existence, but that entirely new kinds of apparatus must be designed to accomplish the task.

Sudarshan next states that: "All these methods presume that the tachyon, whether it is charged or neutral, participates in strong interactions. A fifth method which may be employed consists of a search for the missing mass squared in a suitably selected set of processes. In principle, missing mass spectroscopy can be used independent of the strength of the interactions of tachyons." Tiwari, in the chapter on tachyons, does not comment on the four methods Sudarshan listed above, although he does cite Sudarshan in many other places in his book, and, as of the time of publication (2003), asserted that the missing mass method, with all other experiments based on the detection of Cherenkov radiation, as well as searches associated with cosmic rays, had yielded no hard evidence for the existence of tachyons. But I insist that looking for Cherenkov radiation is a waste of time, in searching for tachyons, so more attention should be paid to other experiments.

Researchers have, of course, calculated a negative value for the squared rest-mass of the muon neutrino; implying that this type of neutrino is a tachyon. However, Tiwari pointed out that, while claims that this is evidence for the imaginary mass of neutrinos in general, "such a claim is not supported by researches in neutrino physics." Yet, Tiwari did not actually provide a citation that contradicts the claim. And he admitted too that "the question remains unsettled"; directing the reader to a summary of the then "current status" on the subject. [Reference: V. Barger, D. Marfatia, and K. Whisnant, Physical Review Letters #88, year 2002, page 011302.] Unfortunately, the review he suggests has grown too dated, and the most up-to-date information on this can be had by doing a web-search using the keywords "tachyons" and "muon neutrinos".

My take on all of this is that the searchers have been searching in the wrong places, because of faulty initial assumptions. For instance, all of the cited experiments relied on the assumption that something unusual would be detectable using the same equipment and instruments used to study bradyons and luxons. But trying to detect tachyons based on detectable electric charge, particle decays, scattering angles, scattering amplitudes, missing mass, or Cherenkov radiation presupposes that tachyons will behave in ways that can be discerned from our bradyonic frame of reference. Even the indication that the muon neutrino may have a negative squared rest-mass, and documented superluminal phenomena (such as superluminal photonic tunneling), seem to me to be revealing more about the underlying nature of the universe (that it has superluminal substructure), rather than serving as dependable indicators of the existence of various kinds of tachyons.

Clearly, whether we use Einstein's STR or Lorentzian Relativity, tachyons exist in an alternate-dimensional frame, as viewed from a real bradyonic frame. Consequently, new research directions are needed, with new conceptualizations, new instrumentation, and new interpretations of the data collected in the experiments. I believe, then, that Tiwari is on the right track, in calling for a re-examination of our definitions of space and of time to gain a deeper understanding of nature, though it will require a revision both of Einstein's theories and of Quantum Mechanics.

However, I see that effort as part of an overall sea-change in our way of thinking; perhaps a key part -- but not the whole story. In my estimation, the initial assumption that brings about the next great leap in our intellectual development, though presently only a kind of science-fiction hypothesis, is that gravity is tachyonic. I contend that the search for the tachyon and the search for the quanta of gravity can be viewed as one in the same search; if it turns out that the quanta of gravity are tachyonic. In fact, I hold that this realization, used to define the parameters on which experiments are based, will yield breakthrough results at some point in the future; maybe even in the near future. Tiwari, of course, does not suggest this, and gives only a review of what is presently understood about tachyonic effects in gravitational fields, and tachyons in superstring theories (discussed next).

[More to come.]



HKurtRichter

Searching for Tachyons (continued)

Gravity and Superstrings

In the final portion of the chapter on tachyons, Tiwari writes: "Recent advances in tachyon physics (in the theoretical domain) originate in quantum electrodynamics in the presence of gravity, and tachyons in superstring theories. Faster-than-light photon propagation due to vacuum polarization effects in a background gravitational field was discovered by Drummond and Hathrell in 1980 [Citation: Physical Review D, #22, page 343.]. On the other hand tachyons have been known to arise from early times in bosonic strings -- both closed and open; their importance in recent years has been due to the developments in the brane theory and non-perturbative techniques in string theory."

He then explains superluminal photons (based on the given citation), noting that the framework that results from combining Quantum Electrodynamics (QED) and STR "has been very successful" at explaining the electromagnetic interactions among subatomic particles, but that attempts to incorporate the General Theory of Relativity (GTR) [i.e., the curvature of space caused by gravity], "is plagued by insurmountable difficulties." Yet, after going into some of the details of the associated research, which included the study of vacuum polarization subjected to the curved geometry of GTR, Tiwari quotes the researchers as stating that "either perturbative QED is inadequate as a theory when extended to a general-relativistic background, or that photons indeed can travel faster-than-light." Huge implications for cosmologists would therefore stem from the later. But Tiwari also points out: "That vacuum polarization leads to photon velocity exceeding the velocity of light in the early times of the evolution of the universe in a rather intriguing way agrees with the time-varying velocity of light hypothesis in some models of cosmology." This includes his own theory, and Inflation Theory. And "we note that not just photons, neutrinos also become superluminal ...", in such models.

On the other hand, after labeling superluminal photons as "quasi-photons", he cautions that such a photon "should not be interpreted as a tachyon." [Note that part of Tiwari's suggestion that we re-evaluate our concept of time depends on whether or not lightspeed varies with time.] From there, he gets into string theory, noting that QED is a point field-theory, in which the path of a particle establishes a "world-line" in space, while strings are one-dimensional objects that sweep out "world-sheets" as they move through space; thus resulting in those branches of string theory called "brane theory" (i.e., membrane theory) and its close but older relative "superstring theory". He then gives a concise overview of the most important aspects of string theory, and how tachyons are involved; noting that the dynamics of tachyons "may provide useful insight into non-perturbative features of superstrings", leading to "an optimal formulation of the theory."

For my part, I accept that string theories, especially their latest incarnation, brane theory, provide deeper understanding of natural processes than can be had from other theories taken without them, but there is simply too much empirical support for the point-particle descriptions associated with subatomic interactions to completely abandon them.

It seems to me that brane theory and quantum mechanics are actually compatible, if they are kept distance specific. Quantum mechanics, for instance, allows us to study all of the subatomic particles down to distances on the order of the Planck length, while brane theory lets us see what reality is like at smaller distances. The two scenarios need not be at odds, nor should one be abandoned in favor of the other too regularly, while yet other ideas are entertained, as necessary for completeness. In that case, since brane theory involves an inherent prediction of tachyonic objects (FTL strings), at sub-Planck-length distance scales, and therefore asks for the acceptance of such objects by the mainstream physics community, then these objects can and should likewise be regarded as possibly manifesting themselves as point-like tachyons at distances larger than the Planck length; most especially in a Lorentzian relativistic, rather than Einsteinian relativistic, format.

Among those point-like tachyons, I am convinced (though Tiwari does not mention the notion in his book) that there is a kind which explains quantum gravity better than any other hypothetical particle suggested to be responsible for the warping of space caused by gravity, described by the "field equations" of GTR -- which tachyon I have explained thoroughly in my thesis. I am, however, willing to concede that such tachyons may be string-like, or, more correctly, may have string-like substructures, when viewed at distances smaller than the Planck length. [An example substructure would be a string that is spiral shaped, and spins in such a way as to drill through space, like a corkscrew; thus providing an action that pulls towards the source, without causing damage.]

Studying Tiwari's book has, in fact, done much to strengthen the conviction that my thesis is valid, because I find in the book no unbiased theory to refute it, and find therein, as well, a great store of reliable information supporting the conclusion that tachyons, of many kinds, probably do exist.

Based on that conviction, and on "faith" in the open-minded researchers actively engaged in the investigation of superluminal phenomena, I predict that a point-like tachyon will be "discovered" someday, and soon thereafter it will be confirmed, beyond doubt, that the contention I and a growing number of other thinkers have been presenting for a while now must be viewed as a scientific fact, instead of science- fiction. Namely, that gravity is faster-than-light, and may actually involve a tachyonic force quantum-unit.

[End of article.]


HKurtRichter

The GET-Particle's Path

For the orientation of a given GET-particle's trajectory, see D.C. Kay's Equation for the Ricci Scalar.

My thesis on Superluminal Gravitation hinges on the acquisition of repeatable detection and manipulation apparatus designed specifically first, to prove that tachyons exist, and second, to test the thesis. But I did not provide a place to look, although I have stated that the GET particle's path and action are along an arbitrary radius-of-curvature (Ricci Scalar) for the path of an object moving while under the influence of the gravitational field of the source-mass. And I had not published a proper equation for it (one that can be used in experimental settings), although I have mentioned it.

So, here it is in detail, in ordinary keyboard symbols.

I use the formula David C. Kay provided for the Ricci Scalar in his contribution to the Schaum's Outline Series, on Tensor Calculus (McGraw-Hill, '88); theorem 8.6, page 106. He displayed the equation in stating that the Ricci Tensor is symmetric, in the chapter on Riemannian Curvature; specifically, while defining Ricci Tensors of second kind.

Here is a rendering, into standard keyboarding symbols, of D.C. Kay's formula for the Ricci Scalar, or "Ricci curvature", Rs, in Einstein's theory of General Relativity;

Rs = [g^(ij)] f(x) ,
where
f(x) = f1(x) - f2(x) + f3(x) ,
with
f1(x) = [ {&/[&(x^i)]}{&/[&(x^)]} ][ ln(sqrt|g|) ] ,
f2(x) = [ 1/(sqrt|g|) ]{ &/[&(x^r)] }[ (sqrt|g|)(F1) ] ,
f3(x) = (F2)(F3) ,
for
F1 = ( Christoffel symbol of second kind; contravariant in r, covariant in i and j. ) ,
F2 = ( Christoffel symbol of second kind; contravariant in r, covariant in i and s. ) ,
F3 = ( Christoffel symbol of second kind; contravariant in s, covariant in r and j. ) .
|g| = ( The determinant of the metric tensor's conjugate matrix; i.e., contravariant in ij. )
i, j, r, s = ( Arbitrary index symbols, with mandatory specific ordering; given. )
& = ( Symbol for partial differentiation; used instead of standard symbol. )
^ = ( Symbol for index; implies indices. Does not indicate an exponent. ).

In words, you take the square-root of the determinant of the conjugate matrix of the standard metric-tensor, then determine its natural logarithm and its inverse, then use these in the terms defining the three functions, f, of the generalized-coordinate sets, x^i and x^j. The first function is written as the partial-derivatives successively taken with respect to x^i and x^j of the logarithm of the square-root of this determinant of the metric-tensor. The next function is written as the product of the inverse of the square-root of the same determinant with the partial-derivative with respect to x^r of the product of the square-root of the determinant of the metric-tensor and a Christoffel symbol of second-kind which is contravariant in r and covariant in i and j. And the last function is written as the product of two such Christoffel symbols; the first contravatiant in r and covariant in i and s, and the second contravariant in s and covariant in r and j.

The difference between the first two functions is added to the last function, and the result is operated on directly by the said second-order contravariant form of the metric-tensor, to get the scalar quantity, Rs (radius-of-curvature; also called the "Ricci curvature invariant").

That's it. Meaning, looking experimentally for my get particle, it must be found moving along a Ricci Scalar (radius-of-curvature), and cannot be found going anywhere else (i.e., it cannot take curved paths; the GET particle always observes a Cartesian-straight path). This does not follow from the foregoing. I'm just saying, this is where a GET resides, and it is not scattered or absorbed by real matter in its path.

It's the objects in the paths of the collection of GET particles radiating from a source that take curved trajectories -- because of the negative radiation-pressure established by the overall flux of radiating GETs, in a time-dependent setting. This is the action that makes gravity work quantum-mechanically; the GET particles' force contributions not only sum to the Newtonian force value, they also physically establish the radius-of-curvature of the space-time described by the field-equations of Einstein's theory of General Relativity.

Having the quantum-mechanical information about a GET particle compacted into some Ricci Scalar, employing a special case of a linearized wave-equation (specifically and only used for GET particles), we can actually derive Quantum Mechanics systematically from the field-equations of General Relativity. And that seems like something seekers of a Grand Unified-Field Theory would be interested in doing, if for nothing else but to use the math as an exercise (for stimulating the imagination).

Note, however, that if GET particles are proven to exist, that will not rule out the existence of superluminal analogs of the standard spin-2 graviton, nor even that such can also constitute gravitational attraction. It just seems that they can additionally explain the life-force of all living things. That is, superluminal gravitons probably account for the imaginary-energy field that living organisms interact with to maintain animation.

Other tachyonic energy fields can be postulated, as well, to account for sentient thought, human emotions, and so on. But that deviates into metaphysics.


Comments welcome. E-mail: HKurtRichter@yahoo.com



HKurtRichter

Let " ^ " denote upper indices (not exponents), and let " _ " indicate subscripts.
Example: Let x^i_j denote a tensor, contravariant in i and covariant in j.
Then Kay's equation for the Ricci Scalar can be written;

R = [g^(ij)]{ f1(x) - f2(x) + f3(x) } ,

where

f1(x) = [{&/[&(x^i)]}{&/[&(x^j)}][ln(sqrt|g|)] ,
f2(x) = [1/(sqrt|g|)]{&/[&(x^r)]}[(sqrt|g|)(F^r_ij)] , and
f3(x) = (F^r_is)(F^s_rj) ,

with the "F" indicating Christoffel symbols (rather than forces or functions),
and the "&" indicating partial differentiation (instead of the standard symbol).



HKurtRichter

Kurt,

Fairly ambitious. And well written. I especially want to commend you for not using too much math. This is after all a physics and astronomy website. Math is vital to our work, but it is not the work itself. A few things caught my eye early on, and I'd like to chat about them.

<b>[Kurt] "... I replace LeSage gravity with my own thesis on Superluminal Gravitation, and which is fully compatible either with Einstein's theory of Special Relativity or with Lorentzian Relativity. In fact, while it was originally developed with Einstein's concepts, it actually works better with the Lorentzian formulation."</b>

<b>[Kurt] "The apparent "pull" of gravity is due to negative radiation pressure from the collective action (due to reversed causality) of a special tachyon ..."</b>

<u>Causality reversal</u> is a feature of Special relativity that arises in part from treating time as a physical thing that can be altered by other physical things like speed or gravitational potential. It slows with speed, for instance. And if speed should ever go above c, time runs backwards and effects begin to precede causes. A first class paradox-generator.

In Lorentzian relativity time is a concept. As such it is not altered by speed or potential or humidity or any other thing with physical existence.

Clocks, on the other hand, do have physical existence. Thus other physical things can influence them, causing them to run faster or slower. Or even to stop working. For example<ul>
<li>sun dials are sensitive to weather</li>
<li>pendulum clocks are sensitive to temperature</li>
<li>atomic clocks are sensitive to gravitational potential</li></ul>
Time does not stop when a cloud passes overhead, causing the sun dial to stop working. Nor does time speed up when it turns cold, causing the pendulum to oscillate more rapidly.

And time does not slow down when an atomic clock is moved deeper into a gravitational potential well, causing it to oscillate less rapidly.

Causality reversal may be required under SR, but it is excluded under LR. For example if we do the famous twins thought experiment under the postulates of LR, the travelling-twin returns to Earth and finds that he has aged the same 60 years as the stay-at-home twin. The travelling-twin's atomic clock, however, shows much less elapsed time. As in many fewer total ticks.

I suspect that you will be able to make suitable adjustements to your otherwise interesting idea so that it does not have to just go away. (Or perhaps you have already done so and just need to provide the details?)

Regards,
LB

Kurt,

Trying to do math in ASCII symbols is possible ... but difficult. Especially if you want to go beyond simple calculus. You are going to loose your audience if do too much of it.

For example, I have little interest in trying to translate the math you have presented here into something readable, so unless it is intuitive at first glance I mostly treat it as noise and skip it. (Later, if I have time, I might come back and play with your custom symbology as a mental exercise. Brain cells, like muscle cells, tend to atrophy if not exercised.) If your message depends on the reader understanding the math, then you have not communicated.

Hmmm. I am speaking for myself only, of course. But I suspect most of the others in the audience would agree to at least some extent. (If not, please speak up.)


LB

(
Use the words, Luke ...

The physics is in the words. And in the art. The standard exchange ratio applies. One art = one thousand words. But art is hard to do also. BTW, we are contemplating a new website, so maybe this will change. Sigh.
)