Superluminal Interaction, or The Same, de Broglie Relationship, As Imposed By The Law of Energy Conservation. Part II: Gravitationally Bound Particles
| Scientific Paper | |
|---|---|
| Title | Superluminal Interaction, or The Same, de Broglie Relationship, As Imposed By The Law of Energy Conservation. Part II: Gravitationally Bound Particles |
| Read in full | Link to paper |
| Author(s) | Tolga Yarman |
| Keywords | Special Theory of Relativity, Electric Interaction, Tachyons, Superluminal Interaction, General Theory of Relativity, Gravitation |
| Published | 2008 |
| No. of pages | 29 |
Read the full paper here
Abstract
Previously, based on just the law of energy conservation, we figured out that, the gravitational motion depicts a "rest mass variation", throughout. The same applies to a motion driven by electrical charges; this constituted the topic of the preceding article (Part I of this work). One way to conceive the mass exchange phenomenon we disclosed, is to consider a "jet effect". Accordingly, an object on a given orbit, through its journey, must eject mass to accelerate, or must pile up mass, to decelerate. The speed of the jet, strikingly points to the de Broglie wavelength, coupled with the inverse of the frequency, delineated by the electromagnetic energy content, of the object. This makes that, jet speed becomes a superluminal speed. This result seems to be important in many ways. Amongst other things, it means that, either gravitationally interacting macroscopic bodies, or electrically interacting microscopic objects, sense each other, with a speed much greater than that of light, and this, in exactly the same way. In which case though, the interaction coming into play, excludes any energy exchange. Thus, energy cannot of course go faster than light, but information can be carried without any basis of energy. Furthermore, our approach, induces immediately the quantization of the "gravitational field", in exactly the same manner, the "electric field" is quantized.
Overview
This is the second half of a two-part paper by Tolga Yarman of Okan University, Istanbul. Part I treated an electron bound to a proton; Part II applies the identical machinery to a planet bound to the Sun. The governing idea is a single postulate: the rest mass of an object bound to a celestial body amounts to less than its rest mass measured in empty space, the difference being as much as the mass equivalent of the binding energy. From that, plus the special-relativistic mass–energy equivalence, Yarman derives an equation of celestial motion in three lines, claims it reproduces the observational results of general relativity to second order in a Taylor expansion, and — the paper's main point — extracts the de Broglie relationship from it.
The route to de Broglie runs through a mechanical picture Yarman calls the jet model. If total relativistic energy is conserved along an orbit while rest mass varies with radius, then a body speeding up toward perihelion is converting rest mass into kinetic energy and a body slowing toward aphelion is doing the reverse. Modelled as a rocket, this requires ejecting mass to accelerate and absorbing mass to decelerate. Imposing momentum conservation on that jet fixes its speed, and the speed turns out to be U = (c02/v0)√(1 − v02/c02) — greater than c0 for all sub-luminal v0, and exactly the quantity λB/T0 whose identification yields the de Broglie wavelength. Yarman's conclusion is that gravitating bodies and charged particles "sense each other" superluminally in precisely the same way, that no energy crosses the gap so relativity is not violated, and that gravitation is thereby quantized on the same footing as the electric field. Along the way he sets aside the principle of equivalence entirely — not, he insists, by refuting it, but by not needing it.
The argument
Rest-mass deficiency instead of potential energy
For an object of rest mass m0 at infinity brought quasistatically to radius r from a body of mass M, Yarman writes m(r) = m0e−α(r) with α(r) = GM/rc02. Because the exponential never vanishes, "the present theory excludes singularities, thus black holes." Setting the object into orbital motion adds a Lorentz factor, so the total relativistic energy
mγ(r)c02 = m0c02e−α(r) / √(1 − v02/c02) = constant
is the integrated equation of motion. Differentiating gives the differential form, in which Newton's inverse-square force is multiplied by e−α√(1 − v02/c02). Yarman shows by taking the cross product with r0 that angular momentum is conserved, so Kepler's laws survive; he also asserts linear momentum conservation, which he says GR breaks. He compares his energy expression with the GR result m0c02√(1 − 2α)/√(1 − v02/c02), noting they agree to second order but that his exponential has no singular numerator. He points out that the same exponential form is what Huseyin Yilmaz would have obtained from his proposed correction to Einstein's metric, and that Logunov reached a similar singularity-free result.
The postulate has consequences that run opposite to GR: in Yarman's scheme the bound object's mass decreases and its length stretches uniformly in all directions, where GR has mass increasing and contraction only along the radial direction. He also derives gravitational redshift directly — a smaller mass gives a smaller frequency by hν0 = m0c02, and a correspondingly stretched size by λ0 = h/m0c0.
Gravitational and inertial mass
A long preliminary section defends the claim that [gravitational mass] = [inertial mass]/[Lorentz dilation factor]2. Yarman argues that Newton posed the equality question using tools — force, inertial mass, the inverse-square attraction law — that GR itself discards, so the textbook framing of the equivalence principle is ambiguous. He cites V. Andreev's report at the 2005 PIRT conference in Moscow that a duralumin load irradiated with high-energy electrons at the General Physics Institute weighed less than an untouched twin, and offers his own reading: the energized valence electrons become practically weightless. On the null results of precision equivalence tests, he argues they are all performed on Earth, where the Galilean principle of relativity forbids detection of the effect, and that the required precision — of order v02/2c02, roughly 2.6 × 10−12 for the Earth's rotation — is only barely at the edge of what has been achieved. He suggests instead a Newton-inspired test using the polarization of the Earth–Moon system, requiring Earth–Moon distance measurement to about 4 × 10−12. He also notes that even binary stars at ~1000 km/s would leave the difference undetectable. His stated position is not that the principle is false but that "we are in no way bound to utilize it," since energy conservation "does all the job."
The jet model
Since mγ(r0)c02 is constant, an accelerating planet must shed rest mass and a decelerating one must gain it. Momentum conservation for the ejected element gives mγ(r)dv0 = −U dm(r). Yarman is careful to say he does not claim a literal rocket: "Whether in reality, the whole thing works out this way or not, we do not know it. For the present purpose, we do not need to know it, either." He then decomposes the jet momentum as γVV dm0(r), calling V = c0√(1 − v02/c02) the "relativistic jet speed" and U = γVV the "wave-like" or "superluminal jet speed." The crucial observation is that U depends only on v0, so U remains finite and well-defined even when the jet mass dm0(r) vanishes — as it does for a circular orbit. Yarman reads this as wave–particle duality appearing in a celestial context: the grouping (γVdm0)·V is the particle-like relativistic momentum, while γVV taken as an indivisible whole is the wave-like character.
Deriving de Broglie
Multiplying the momentum relation by c02 and equating the rest-mass change to the change in static gravitational binding energy, c02dm(r) = (GM m(r)/r2)dr, then substituting dv0 from the equation of motion, gives
U = (c02/v0)√(1 − v02/c02),
identical to the expression obtained in Part I from the electric interaction. Writing U = λ/T0 with T0 the period associated with hν0 = m0c02 makes λ the de Broglie wavelength λB = (c0/v0)λ0√(1 − v02/c02). Applying the quantization condition nλB = 2πrn to the Earth's orbit gives n ≈ 1.22 × 1072, a number Yarman regards as large but harmless. The jet speed relative to the moving body, u ≈ U + v0, runs from infinity for a body at rest down to c0 for a body moving at light speed — a range Yarman notes matches the standard tachyon picture, and which implies "light cannot interact with anything via a speed above the speed of light."
He closes by invoking Laplace, who calculated more than two centuries ago that if gravity propagated at c the solar system would fly apart, doubling the Earth–Sun distance in 1200 years, and who therefore required a propagation speed at least 109 times c. Yarman treats his result as an answer to that quest, argues that because no energy is transported nothing in relativity is violated, and suggests the mechanism may bear on the EPR correlations and quantum collapse. He is deliberately cautious about turning interaction into communication: extracting information from a closed system requires disturbing it, so while faster-than-light computation may be plausible, faster-than-light communication "should be considered with care."
Assessment
The paper's most attractive feature is its economy. Replacing gravitational potential energy with a rest-mass deficiency m(r) = m0e−GM/rc2 is a single, clearly stated postulate, and Yarman genuinely does get an integrated equation of motion out of it in three lines, with angular momentum conservation following from a one-line cross product and Kepler's laws intact. Treating gravitational redshift as a straightforward consequence of hν = mc2 applied to a lighter bound object is clean and physically transparent. The exponential metric coefficient is also not idiosyncratic: it coincides with the Yilmaz exponential metric and with Logunov's field-theoretic gravity, both of which are singularity-free and both of which agree with GR at the level of the classical tests, so Yarman's version sits within a recognized family rather than standing alone. And the observation that the same algebra produces the de Broglie wavelength in both the electric (Part I) and gravitational (Part II) cases is a real formal parallel worth noticing, since the derivation nowhere uses the strength of the coupling.
The difficulties are severe. The central result rests on treating U as a physical propagation speed, but U is defined as the ratio dp/dm in a hypothetical jet whose reality the author explicitly declines to claim, and it is then evaluated in exactly the limit — vanishing jet mass — where the jet does not exist. A quantity that goes to infinity as v0 → 0 is a signal that a denominator has vanished, not that an interaction has become instantaneous; the same expression, c2/v, is familiar as the phase velocity of a de Broglie wave, which carries no signal and is not a rate of interaction. Yarman's identification of it with a "superluminal jet speed" and then with the speed at which bodies "sense each other" is asserted rather than derived, and the paper offers no mechanism by which information — even energy-free information — is carried.
The appeal to Laplace is the weakest empirical link. Laplace's argument establishes only that gravity in a Newtonian force-propagation picture must be near-instantaneous; in GR the near-cancellation of aberration arises from velocity-dependent terms in the field, so no superluminal propagation is required, and the binary pulsar PSR B1913+16 shows orbital decay matching the quadrupole prediction to better than 0.2% — a result that assumes propagation at c. Similarly, the equivalence-principle discussion sets up a target the modern experiments do not occupy: Eöt-Wash torsion balance and lunar laser ranging tests bound the Eötvös parameter at the 10−13–10−15 level and the MICROSCOPE satellite reached ~10−15, comfortably past the ~2.6 × 10−12 threshold Yarman computes as necessary; and the argument that terrestrial experiments are forbidden by the Galilean principle from seeing a velocity-dependent effect would, if correct, also forbid the effect from being real in any frame-independent sense. The Andreev weight-loss report is a single unreplicated conference claim carrying a great deal of load.
Internally, the treatment of the equivalence principle is also unstable. The paper alternately says the principle is "totally erroneous," that it is "a prodigious and useful analogy," and that "we do not really bother" whether it is valid — three positions that cannot all be held while the paper simultaneously derives a definite, testable violation ([gravitational mass] = [inertial mass]/γ2). The prose is also unusually polemical for a technical paper, and the extended anecdote about the principle of equivalence and the digs at "conservative reactions" occupy space that the derivation of U badly needs. Where the paper is on firmest ground is the narrow formal claim: that a rest-mass-deficiency postulate plus energy conservation reproduces the standard weak-field results and yields the de Broglie relation in both the atomic and celestial cases. The superluminal interpretation built on top of that is a further step the paper does not establish.