Superluminal Interaction, or The Same, de Broglie Relationship, As Imposed By The Law of Energy Conservation, In All Kinds of Interaction, Making a Whole New Unification
| Scientific Paper | |
|---|---|
| Title | Superluminal Interaction, or The Same, de Broglie Relationship, As Imposed By The Law of Energy Conservation, In All Kinds of Interaction, Making a Whole New Unification |
| Read in full | Link to paper |
| Author(s) | Tolga Yarman |
| Keywords | conservation, superluminal, Unification, energy, Special Theory of Relativity |
| Published | 2009 |
| No. of pages | 13 |
Read the full paper here
Abstract
Previously, based on the law of energy conservation, we figured out that, the steady state elliptic motion of an electron around a given nucleus depicts a rest mass variation throughout. We happened to develop our theory, originally vis-a-vis gravitational bodies in motion with regards to each other, providing us, with all known end results of the General Theory of Relativity. Hence, it is comforting to have both the atomic scale and the celestial scale, described, on just the same conceptual basis. One way to conceive the phenomenon we disclosed, is to consider a "jet effect". Accordingly, a particle on a given orbit through its journey, can be conceived to eject a net mass from its back to accelerate, or must pile up a net mass from its front to decelerate, while its overall relativistic energy stays constant throughout. The speed of the jet, strikingly, points to the de Broglie wavelength, thus coupled with the inverse of the frequency, delineated by the electromagnetic energy content of the object of concern.This makes that, on the whole, the "jet speed" becomes a superluminal speed, a fortiori excluding any transport of energy. We call it wavelike speed. This result, in any case, seems to be important in many ways. Amongst other things, it may mean that, either gravitationally interacting macroscopic bodies, or electrically interacting microscopic objects, sense each other, with a speed greater than that of light, and this, in exactly the same manner, in both worlds. Note that what we do, well stays within the frame of quantum mechanics, since in fact, we ultimately land at the de Broglie relationship. Note also that, we well stay within the frame of the Special Theory of Relativity. Our disclosure seems to be capable to explain the spooky experimental results recently reported.
Overview
This paper is the text of Tolga Yarman's presentation to the 2007 PIRT (Physical Interpretation of Relativity Theory) meeting in Moscow and to the Lebedev Physics Institute, and it summarises two longer articles on electrically and gravitationally bound particles. Its full title in the PDF is "Superluminal Wave-Like Interaction, or the Same, de Broglie Relationship, as Imposed by the Law of Energy Conservation, in All Kinds of Interaction, Making a Whole New Unification".
The organising claim is a single postulate — that a bound object's rest mass is less than its free rest mass by exactly the mass equivalent of its static binding energy — pushed through consistently. Yarman argues that this is nothing more than the relativistic law of energy conservation taken seriously, but that standard practice violates it by writing the total energy of an orbiting electron as γm0c² − Ze²/r, an equation he marks in the text with the word "Wrong!". If rest mass really varies along the orbit, some mechanism must effect the variation, and Yarman proposes a "jet": the particle ejects rest mass rearward to accelerate and absorbs it frontward to decelerate, exactly like a rocket. Imposing momentum conservation on that jet then yields, he shows, the de Broglie relationship — and a jet speed that he claims always exceeds the speed of light while carrying no energy at all. He calls this a "wave-like interaction speed" and offers it as the same mechanism for electric and gravitational binding alike.
The argument
Starting from de Broglie
Yarman begins by re-deriving a kinematic identity. De Broglie's 1925 thesis posited an internal periodic phenomenon of frequency ν0 with hν0 = m0c0², which with λ0 = c0T0 gives λ0 = h/m0c0. For an object in uniform motion the frequency decreases while the mass increases — an asymmetry that, as de Broglie himself said, puzzled him for years — and the resolution was the wavelength λB = h/mv0 with m the relativistic mass. Combining these, Yarman writes λB in terms of λ0, then divides by the rest period T0 to define
- U = λB/T0 = (c0²/v0)√(1 − v0²/c0²)
He notes explicitly that λB can also be written for v0 = 0, in which case it becomes infinitely long, and takes this to be the basis of an immediate action at a distance involving no exchange of mass or energy.
The energy-conservation postulate
The postulate is stated plainly: the rest mass of an object bound gravitationally, electrically or otherwise is less than its free rest mass by the mass equivalent of the static binding energy. For an electron bound at r0 to a much heavier proton this gives m0(r0) = m0·κ(r0) with κ(r0) = 1 − Ze²/r0m0c0². The total relativistic energy of the orbiting electron, m0(r0)c0²·γ, is then held constant along a stationary orbit — his equation (10), which he contrasts with the classical (11). Yarman is candid that this "somewhat negates the Maxwell equations" and that new field equations and a new force law would properly be required; he defers to the pure bound field theory (PBFT) of Kholmetskii, Missevitch and himself, which he says supplies exactly that for quantum-mechanically bound, non-radiating charges, and which he stresses "is not a controversial approach, at all".
The jet model
On an elliptic orbit, constancy of total energy forces an alternation: as the electron speeds up near the nucleus its rest mass "sublimes" into kinetic energy, and as it slows it "condenses" back. The jet model supplies the mechanism. Writing momentum conservation for the closed system of electron plus jet gives the kick equation
- m0 dv0 = dm(r0)·U
with dm negative during acceleration. Yarman observes that the jet momentum should relativistically be dmV(r0)·γV·V, and that this can be grouped either as (dmVγV)V — the conventional relativistic momentum, expressing the particle character — or as dmV(γVV) with U = γVV taken en bloc, which he offers as "a clue for the wave-particle duality", operating "as the heart of the wave-like character of the electron". The grouping matters most when dm vanishes, as in circular motion.
Multiplying the kick equation by c0², substituting −c0²dm for the change in electrostatic binding energy, and eliminating dv0 with the differentiated equation of motion, he recovers U = (c0²/v0)√(1 − v0²/c0²) — the same expression obtained kinematically from de Broglie, but now, he emphasises, "through just the relativistic law of energy conservation". Multiplying through by T0 returns λB = h/mv0. He concludes that "the 'jet mass assumption' comes to be well equivalent to the 'de Broglie relationship assumption'".
Generalisation, and gravity
The derivation is then repeated with an arbitrary static binding energy B(r0) in place of the Coulomb term, giving the same U for any field, "even a straight non-inertial centrifugal field". For gravitation Yarman quotes his earlier result in which the constancy condition carries a factor exp(−α) with α = GM/Rc0², and B(r0) = m0c0²(1 − e−α) — an exponential rather than a Schwarzschild metric, which he says reproduces all known end results of general relativity.
Circular motion is treated as a special case: both dv (scalar) and dm vanish, so the radial wave-like velocity UR must be infinite while its tangential component U = UR cos θ, with θ = π/2, stays finite. Yarman suggests "we have here, perhaps an expression of the Mach Principle".
Claimed consequences
Information, he concludes, can be transferred with no energy at all, always faster than light and occasionally instantaneously; everything in the universe therefore affects everything else from great distances at superluminal speed. He cites Salart et al. (Nature 454, 2008) and the March 2009 Scientific American piece "Was Einstein Wrong?" as recent experimental support, and claims the result answers Laplace's two-centuries-old inference of a gravitational propagation speed far exceeding c. Because rest mass decreases for any bound particle, the metric must change near a nucleus as well as near a star, and this he says is testable: the decay rate of a muon bound to a nucleus is retarded relative to a free muon, and "our prediction about this remains better than any other available predictions". Since the de Broglie relation emerges, quantization follows for all fields — so no choice between quantum mechanics and special relativity is needed.
Assessment
The paper's central postulate is neither exotic nor wrong. That a bound system weighs less than its separated constituents by the binding energy divided by c² is standard and precisely measured — the mass defect of nuclei is the textbook case, and it holds for atoms too. What Yarman does that is distinctive is to attribute the entire defect to the orbiting particle alone and then let it vary continuously around the orbit, so that rest mass becomes a function of position. The insistence that the classical energy expression is inconsistent with mass–energy equivalence is a sharp and legitimate provocation, and the derivation itself is honest: he genuinely does obtain λB = h/mv from momentum conservation applied to his jet, without assuming it. The reappearance of the same U by two independent routes — kinematic and dynamical — is a real internal consistency check, and Yarman deserves credit for stating openly that his approach "somewhat negates the Maxwell equations" rather than concealing the cost.
The difficulties are substantial. First, the quantity U is not new physics but the de Broglie phase velocity, known since 1924 to satisfy vphasevgroup = c², and known equally long to carry no energy or information precisely because it is a phase velocity. That a phase velocity exceeds c is not a discovery and does not license the paper's inference that bodies "sense each other" superluminally; nothing in the derivation shows that U is the speed of anything physical propagating between two bodies.
Second, the paper's own algebra does not support its headline claim. From equations (1)–(5), U = λB/T0 = c0²/(γv0) = (c0²/v0)√(1 − v0²/c0²). This exceeds c0 only when v0 < c0/√2 ≈ 0.707c0; above that speed it falls below c0 and tends to zero as v0 → c0. The conclusion's statement that "the greater v0, the smaller is U, but always exceeding the speed of light" is therefore correct in its first half and false in its second. The discrepancy arises because Yarman divides the moving-frame wavelength by the rest-frame period, mixing frames; the conventional phase velocity c²/v, which is superluminal for all v < c, uses the moving-frame frequency throughout.
Third, the jet is asserted rather than established, and Yarman concedes as much — "of course we do not know whether or not this is so… in the worse case, Eq.(16) becomes an artifact". But it cannot be both. If dm is real ejected rest mass it carries energy dm c², contradicting the claim that the jet transports no energy; if it is bookkeeping, the momentum-conservation equation that yields U has no physical content. The circular-orbit case makes this acute: with dm = 0 and dv scalar zero, UR is set to infinity purely so that an indeterminate product may come out finite, and the invocation of Mach's principle at that point is a label, not an argument.
Fourth, the experimental appeals do not do the work claimed. The Salart 2008 experiment set a lower bound on the speed of any hypothetical causal influence behind entanglement correlations; it did not detect superluminal signalling, and the no-signalling theorem forbids using such correlations to transmit information — the very thing Yarman says his U accomplishes. Laplace's superluminal gravity inference rests on aberration in a static-force picture and is voided in any field theory with velocity-dependent terms, general relativity included. The bound-muon decay retardation is the paper's one genuinely discriminating prediction, but no number is given here; the claim that it beats all rivals is stated without figures, and cannot be assessed from this text.
Finally, the gravitational side is asserted, not derived: the exponential metric factor e−α arrives by citation with no demonstration that it reproduces the perihelion precession of Mercury, light deflection and Shapiro delay to the precision those measurements now reach. The exponential and Schwarzschild forms agree to first order in GM/Rc² but part company at second order, which is the order at which perihelion advance is tested.
Read as a demonstration that de Broglie's relation can be recovered from relativistic energy and momentum conservation applied to a variable-rest-mass bound particle, the paper is ingenious and internally coherent. Read as evidence for superluminal interaction, it identifies a phase velocity with a signal velocity, and its own formula does not stay superluminal.