Gravitational Vortexes of Cosmic Plenum
| Scientific Paper | |
|---|---|
| Title | Gravitational Vortexes of Cosmic Plenum |
| Read in full | Link to paper |
| Author(s) | Mario Ludovico |
| Keywords | Fluid plenum, vortices, velocity fields, acceleration gradients, gravity, gravitational equations |
| Published | 2011 |
| Journal | Proceedings of the NPA |
| Volume | 9 |
| No. of pages | 12 |
| Pages | 346-357 |
Read the full paper here
Abstract
Against the conservative attitude of the academic world, a massive number of clues indicate that our universe consists substantially in an undetectable fundamental essence, which is commonly referred to as "ether". The need for the "ether" was finally and openly admitted even by Einstein; whereas quantum physics lingers still on fuzzy concepts like "zero/ground energy level" or similar ones, with no capacity of re-founding physics from the bottom up. The basic problem is now to try hypotheses on what the ether is and which properties are inherent in it. This paper draws materials also from a book of mine, to try suggestions for a different approach to physics. The space of our universe is here addressed as it were a finite physical—though undetectable—fluid continuum (not consisting of component particles), here dubbed the "plenum", which is surrounded (and partly permeated) by a boundless space of "true vacuum" (the void). In the void no physical event occurs. All material elements and detectable phenomena are effects of kinematical states of the "plenum". Allowing for such a basic assumption, the principal issue addressed here regards gravity and gravitation. Instead of "mutual attraction between masses", gravitation is here viewed and described as one particular effect associated with vortexes of plenum that establish gravitational fields. Also the formation of mass and the aggregation of matter components are viewed as states of plenum around nuclei of void, which "enters" the physical space through tears and openings caused by motions and/or turbulence of the plenum. The analysis leads to the formulation of tentative gravity and gravitational equations, though a complete solution to them requires further research.
Overview
Mario Ludovico presented this paper to the ninth NPA proceedings (Albuquerque, 2012) as an introduction to his book Vacuum, Vortices and Gravitation. Its distinguishing move is a sharp separation between two things usually run together. What physics calls "the vacuum" Ludovico renames the "plenum": a finite, continuous, incompressible, massless fluid, not made of particles, in which every physical event takes place. Beyond and partly through it lies the "true void" — genuine nothingness, unbounded, in which nothing can happen and through which light cannot travel.
From that dichotomy everything else follows. Matter is not a substance immersed in the plenum but a kinematic state of it: vortices form, their cores tear open, and true void intrudes through the tear. The volume of void trapped inside a vortex is its mass, so "the greater the density of matter the greater the volume of true void it includes". Gravity is then not attraction between masses at all but the local acceleration field of a large vortex, acting on smaller structures through the Kutta-Joukowski (Magnus) mechanism of ordinary fluid dynamics. Ludovico is explicit that he is not attempting a theory of everything — such attempts "become metaphysical very soon" — and that his interest is gravity, ideally gravity that could be controlled.
The argument
Shift conservation and the 1/r velocity law
Because the plenum is perfectly continuous and cohesive, no point can slide past an adjacent point. Ludovico converts this into a "principle of shift conservation": if the points of a reference circle of radius R complete a revolution in time T, then the points of every concentric circle must traverse the same total path length in the same time. Hence for a circle of radius r,
- v = VR/r, V = 2πR/T
Speed therefore falls off as the inverse distance, which he presents as the only way to handle "different infinities of adjacent points in a continuum". Extended from a flat sheet to coaxial cylinders, the same law gives v = Vρ/r with ρ the radius of the core.
The law immediately implies infinite speed at r = 0, and Ludovico takes this as forcing a choice: either the fluid becomes rigid below some radius, or it tears and leaves a nucleus of true void. He argues for the second on the grounds that a rotating solid core would have to slide against the surrounding plenum and would invert the speed law, both incompatible with the assumed cohesion. He also appeals to the familiar empty-cored whirls on the surface of a stream. So the void enters physical space through the centres of vortices, and every vortex line develops along "its own central spine-line of true void". Invoking the fluid-dynamical theorem that vortex lines in a homogeneous incompressible fluid cannot end inside the fluid, he concludes that the simplest self-contained vortex is the ring, which behaves as a dipole — sucking fluid in at one pole and ejecting it at the other, and tending to be shaped by its own flux into a sphere. Turbulence within a large vortex generates chains of sub-vortices at many scales, and this cascade "is just the process of mass and matter formation".
Centrifugal force and the Magnus mechanism
Before reaching gravity, Ludovico offers an account of centrifugal force, which he insists is real rather than fictitious. A stone whirled on a sling rotates as a rigid body, so the plenum's relative speed differs at the stone's inner and outer orbital lines; this velocity gradient establishes a circulation Γ = ∮v·î dS around the stone. Applying the Kutta-Joukowski theorem gives a double force, the centrifugal force ω2mr together with the sling's opposite constraint. He draws a strong conclusion: "in my opinion, centrifugal force proves both the existence of the plenum and the existence of absolute motion with respect to the plenum", supporting it with the observation that a massless point on a curved path undergoes only centripetal acceleration.
He also flags, in passing, the substitution on which the whole later derivation depends: "in the Kutta-Jukowski theorem density ρ relates to the fluid's density, whereas the mass density σ in Eq. (5) regards the mass density of the stone, since the fluid plenum has by hypothesis no mass".
A sample spherical vortex
Section 5 constructs a specific velocity field. At distance r the velocity vector has constant modulus 𝒱r = nVc/r, where Vc is the plenum's speed at the core surface and n the core radius, but its direction varies with position on the sphere, decomposing into parallel and meridian components Vcos θ and Vsin θ. Each concentric shell then rotates as if solid, at angular velocity ωr = nVc/r2. Ludovico computes the Cartesian components of the curl ∇ × Vr and finds it non-zero almost everywhere — at θ = π/4 its modulus is 1.6213 𝒱r/r — and divergent at the poles and equator. He treats the divergence not as a defect but as a signal: an infinite rotational intensity "shall conventionally imply the intrusion of a true-vacuum nucleus whose radius is greater than zero", so the curl is capped at some finite maximum Ω. What sets Ω is deferred: "in a subsequent paper, it will be shown that the values of Ω are connected with both the vortex size and the plenum's kinetic viscosity."
The gravity law
A small body of radius ρ at distance r is wrapped in a geometrical sphere, and Stokes' theorem gives the circulation of the vortex field around it, Γ = 4πρ2g(θ)𝒱r/r, where g(θ) collects the angular functions. Applying Kutta-Joukowski slice by slice with σ the density of the void inside the body, and integrating, gives the gravity force
- F = 6H2g(θ)m/r3, H2 = n2Vc2
The result is an inverse-cube law, modulated by g(θ), which grows as the body approaches the vortex's equatorial plane. It is centripetal provided the body's own motion does not reverse the sign of the circulation; otherwise it can become centrifugal, so the same field can both "pull-in" and "push-out". Ludovico stresses that no force is transmitted: once formed, the vortex field is stationary in time, and the effect on an immersed body is instantaneous and local, like an ice ball in a canal drifting toward the fast central thread — "neither is there an attraction force inherent in flux thread c... nor is there a repulsive force inherent in the concrete edges". He contrasts this explicitly with quantised gravitation, noting that no graviton has ever been detected.
Orbits
Since the force is central, motion stays in a plane. Near the equatorial plane g(θ) is treated as constant and Binet's formula converts the equation of motion into a linear second-order equation in 1/r:
- d2(1/r)/dθ2 + [1 − 6H2g(θ)/ω2](1/r) = 0
Writing λ for the bracket, the solutions are: circles when λ = 0; parabolas focused on the vortex centre when λ > 0; and spirals — approaching or receding asymptotically, terminating on or starting from the vortex core — when λ < 0. Ludovico then generalises D'Alembert's principle to F − ma = f0, adding a constraint term for the other influences to which every body in the universe is subject, since "it is conceptually impossible to think of any material body as in a perfect rest condition". With f0 included the equation becomes non-linear; he obtains a quadrature but reports honestly that "the integration of this non-linear equation seems difficult. Actually, I could not yet determine its general solution."
Assessment
The paper has genuine conceptual interest. Separating a physical continuum from true nothingness is a clean idea, and identifying mass with trapped void rather than with stuff in the fluid at least attempts an answer to a question — what is mass made of — that the standard account largely declines. The vortex-line theorem is used correctly, the observation that a ring vortex behaves as a self-propelling dipole is sound fluid mechanics, and the canal analogy is a genuinely useful way of showing how a stationary velocity field can mimic attraction without transmitting anything. Ludovico is also unusually candid about what he has not done: he flags his own unjustified substitution in Kutta-Joukowski, admits he cannot integrate his general orbit equation, and defers the constant Ω to a later paper. That is better scientific manners than most papers of this kind display.
But the physics does not survive its own central result. An inverse-cube central force is not a small correction to Newton — it is a different regime. By Bertrand's theorem, the only central force laws producing closed non-circular bound orbits are the inverse square and the linear (harmonic) law; an inverse-cube force produces Cotes' spirals, and Ludovico's own equation (29)-(30) reproduces exactly that catalogue: spirals, parabolas, and circles only in the fine-tuned case λ = 0. There are no ellipses. The paper therefore cannot generate Kepler's first law, and its circular orbits exist only on a knife-edge condition and are neutrally stable at best. Kepler's third law fails too: under F ∝ 1/r3 a circular orbit has v ∝ 1/r and hence period T ∝ r2, whereas the solar system obeys T ∝ r3/2. Neptune's orbital radius is 77.7 times Mercury's and its period 684 times Mercury's; Kepler's exponent gives 77.73/2 = 685, while the inverse-cube law demands 77.72 = 6040. That is not a discrepancy to be absorbed by the "constraint term" f0; it is a factor of nearly nine across the solar system.
The derivation's key step is also the one Ludovico himself marks as irregular. The Kutta-Joukowski theorem F = ρfluidΓv is a statement about momentum flux in the fluid; replacing ρfluid by the density of the immersed body removes the theorem's derivation entirely and leaves only its algebraic form. This is not a technicality — it is what converts a fluid-mechanical result into a gravity law, and it is unsupported. The underlying reason for the substitution, that the plenum is massless by hypothesis, creates a second problem: a massless fluid cannot carry momentum, so there is nothing for Γ to multiply and no mechanism for the Magnus effect in the first place.
The "shift conservation" principle is likewise asserted rather than derived. That every concentric circle traverses equal path length in equal time is not a property of any real incompressible fluid and does not follow from Euler's equations; it is chosen because it yields v ∝ 1/r, which happens to be the exterior velocity field of a line vortex. Real vortices have that profile outside a rotational core and a solid-body profile inside it — precisely the option [a] Ludovico rejects — and this is directly observed in tornadoes, bathtub vortices and laboratory flows.
Quantitatively, the law is unusable as it stands. Its strength is set by H2 = n2Vc2 and by g(θ), whose cap Ω is explicitly left to a future paper. No value of G is derived and no measured gravitational quantity is computed anywhere in the paper. The angular factor g(θ) also predicts something striking that goes untested: gravity should be markedly stronger near the vortex's equatorial plane than away from it, so the Earth's own gravity — being, on this account, the acceleration field of the vortex from which the Earth formed — should vary substantially with latitude beyond the small rotational and oblateness effects actually observed. Terrestrial gravity is measured to parts in 109 and is fully accounted for by mass distribution, rotation and shape.
Finally, the claim that gravitational effects are stationary and involve no propagation is now directly contradicted by measurement. GW170817 delivered a gravitational-wave signal and a gamma-ray burst from the same event arriving within about 1.7 seconds after 130 million years of travel, fixing the propagation speed of gravitational disturbances to that of light to within a part in 1015; the Hulse-Taylor binary's orbital decay has matched the general-relativistic radiated power for four decades. A theory in which "the propagation of the vortex velocity field is in no case the transmission of a force" has no room for either. Nor does the paper address light deflection, Gravitational Lensing, or the Perihelion Precession of Mercury — though it is worth noting that an inverse-cube term added to an inverse-square law was historically the standard way of modelling precession, so a version of this mechanism as a small correction rather than as the whole of gravity would be a more defensible programme than the one attempted here.
As the opening chapter of a longer project, the paper sets out its assumptions plainly and does not overclaim its results. As a theory of gravity it is refuted by Kepler's laws, which the author does not test it against.