Gravitation, Matter, and the Expanding Universe
| Scientific Paper | |
|---|---|
| Title | Gravitation, Matter, and the Expanding Universe |
| Read in full | Link to paper |
| Author(s) | Henrik Vilhelm Broberg |
| Keywords | expanding universe, gravitation, matter, gravitational field, Potential Energy |
| Published | 2011 |
| Journal | Proceedings of the NPA |
| Volume | 8 |
| No. of pages | 10 |
| Pages | 86-95 |
Read the full paper here
Abstract
The Lorenz and Einstein theories are here revisited from the perspective of our present pragmatic knowledge of the universe. The field of gravitation emerges in a chain of Lorenz transformations, while linking the micro cosmos of the particles to the macro cosmos of the Universe. In this context, the precession of the Mercury orbit is reconfirmed as a consequence of the field itself. The acceleration in the gravitational field is attributed to a flow velocity which covers up a subluminal deficit left by the world-lines in the Lorenz transformations in the direction towards singularities in the gravitational centers.
The nuclear force emerges as a local variety of gravitation in the micro-scales of the particles within the macro-scale of the Universe. In this context a revised Planck length returns a proper mass in the dimension of the nucleon quarks. From this follows also that force balance is achieved in the local fields of the electron. These examples indicate that the universe is functioning in a holographic way.
In the overall picture it seems to be the Arrow of Time which governs the development of the Universe, resulting in a general inflation in time, space and mass, as well as gravitation, while the mass-increase is offset by negative potential energy in the gravitational fields, thus allowing for a still ongoing avalanche creation of the Universe without any requirement for external energy.
Overview
Presented at the Natural Philosophy Alliance's 2011 College Park meeting, this is the compact statement of a programme Henrik Vilhelm Broberg had been developing in Apeiron and in Selleri's Open Questions in Relativistic Physics since 1991. Its ambition is unusual in its breadth: from a single geometric construction — a chain of Lorentz transformations, drawn as rotating world-lines, quantized in steps of the Schwarzschild radius — Broberg proposes to recover the Newtonian field, the perihelion advance of Mercury, the radius of the observable universe, the nuclear force, the nucleon mass and the mass of the electron. "These examples indicate that the universe is functioning in a holographic way."
The organising idea is that gravitational acceleration is not a force but a flow. Each Lorentz cycle in the chain leaves a small "subluminal deficit" between the two world-lines, and that gap has to be bridged by a real motion of space toward the centre at a velocity vf. The second idea is that Newton's G is not constant. Broberg defines a new universal constant A, an area per unit mass representing each particle's share of the surface of the cosmic event horizon, and writes G in terms of A, c and the age of the universe TU — so that G falls as the universe ages while every particle's mass grows. The mass increase is paid for by negative gravitational potential energy, "thus allowing for a still ongoing avalanche creation of the Universe without any requirement for external energy". (Broberg writes "Lorenz" throughout for Lorentz.)
The argument
World-lines and the quantized field
Figure 1 sets a rotating world-line against a stationary one, with sin θ = v/c, so that the relativistic factor becomes γ = 1/cos θ. Integrating the momentum P = M0c tan θ gives the kinetic energy as M0c2(1/cos θ − 1), reducing to M0v2/2 for v ≪ c.
Gravity enters by requiring one side of the triangle to equal the Schwarzschild radius RS. This forces v2 = c2RS/R0 = 2GMG/R0, the escape speed, and the field is then built as a sequence of such transformations subject to the quantum condition
- R0 = νRS, ν a natural number (1.21)
with sin θν = 1/√ν and a "handshake" sin θν = tan θν+1 linking consecutive cycles. The innermost cycle, ν = 1, sits at RS with θ = π/2; the outermost reaches the event horizon of the universe. At large distances the kinetic energy recovers EK = GMGM0/R.
Mercury
The circular elements joining consecutive Lorentz loops represent a rotation of the field itself. Approximating sin θ ≈ θ, the two hemispheres together give a field rotation of 2 sin3θ per interval R0/c, so the precession rate is c sin3θ/R0. Using the geometric mean of Mercury's perihelion and aphelion distances, 5.6745 × 1010 m, Broberg obtains 6.268 × 10−14 rad/s, which over a century is
- 6.5048 × 1014 × 6.268 × 10−14 ≈ 41 arcsec (2.5)
He calls this "as good as could be expected", noting agreement with the observed value and with the 42 arcsec of general relativity.
The universe as its own black hole
Taking 1011 galaxies of 1011 stars gives a total mass of order 1053 kg, whose Schwarzschild radius is 1.5 × 1026 m — about 15 billion light years, and so, Broberg argues, equal to the radius of the expanding "time-front". The constant A is fixed by requiring each particle's mass to claim a proportionate share of that horizon surface, giving A ≈ 1.5 m2/kg, and G becomes Ac2/(4RU) = Ac/(4TU). The same A applied to a proton returns a radius of about 2 × 10−14 m, which he calls "a realistic radius for a proton interface at interaction with other particles".
Two rates follow: mass grows as dM/dt = 2M/TU and length as dR/dt = R/TU, the latter identified with Hubble's expansion.
The gravitational flow
The density in a world-tube is ρ = 1/(AR), singular at zero radius. Balancing the outward flow of negative energy at one periphery against the inward flow of positive energy at another yields a residue proportional to the gravitating mass, and requiring the sub-luminal flow to carry it gives vf = c(1 − cos θ) and the acceleration
- af = 2GMG/(R0Ri) (5.14)
which becomes Newton's GM/R2 far out and c2/RS at the horizon. Combining with the varying G gives the absorption rate quoted at 3.4 × 10−18 kg/s per kilogram — for the Earth "an absorption rate of 20 million kg/s, which should be enough to explain all observed disturbances of different kinds, such as volcanic activities, tsunamis" — or, in energy terms, about 0.3 W/kg. Broberg adds that diverting a fraction of this would satisfy "all human energy requirements... for all foreseeable future".
A modified Planck length
The classical Planck construction gives a length of 5.722 × 10−35 m and a mass of 3.86 × 10−8 kg, "about 1020 times larger than the mass of a typical nuclear particle". Substituting the A-based expression for G and solving for the length instead gives RX ≈ 0.8 × 10−14 m and MX ≈ 2.7 × 10−28 kg — "approximately one sixth of a nucleon mass". Six such components, one for each of ±X, ±Y, ±Z, give a nucleon: with A ≈ 1.42 m2/kg, 6MX = 1.67 × 10−27 kg. The associated force is about 3.2 kN acting over ~10−14 m at a pressure of 4 × 1030 Pa — "all indications of the nuclear force". Balancing electrostatic expansion against this contraction yields the electron mass, 0.91093 × 10−30 kg, with A = 1.3874 and a fine-tuning factor κ = 1, or A = 1.41103 with κ = 1.00852.
Assessment
Broberg is doing something few in this literature attempt: building one framework and then holding it to account across twenty orders of magnitude, from Mercury's orbit to the nucleon. The holographic instinct — that a particle's mass buys it a share of the cosmic horizon area — anticipates in spirit the Bekenstein-bound reasoning that mainstream gravity was moving toward at the same period, and the flow picture of gravitational acceleration is a recognisable cousin of the Gullstrand–Painlevé "river" description of the Schwarzschild field. Several of the intermediate results are simply correct: γ = 1/cos θ with sin θ = v/c is a legitimate parametrisation; the kinetic-energy integral gives M0c2(γ − 1) exactly; the escape-speed relation v2 = 2GM/R and the far-field limit EK = GMm/R are right. The Planck arithmetic checks: with his own definitions (using h and a factor 2) 5.722 × 10−35 m and 3.86 × 10−8 kg are the correct values, and the modified versions RX = (Aħ/c)1/3 ≈ 8.1 × 10−15 m and MX = h/(cRX) ≈ 2.7 × 10−28 kg reproduce as printed, as do the 3 kN force and the 4 × 1030 Pa pressure, which is indeed the right order for the nuclear scale.
The trouble begins where the results are compared with measurement.
Mercury is 5 per cent short, and the paper's rounding conceals it. Reduced to a per-orbit advance, Broberg's rate c(RS/R0)3/2/R0 combined with Kepler's law gives 2√2·πRS/R per revolution, against general relativity's 3πRS/p where p = a(1 − e2) is the semi-latus rectum. His coefficient is 2√2 = 2.828 where the correct one is 3 — a 5.7 per cent deficit — and he substitutes the geometric mean of perihelion and aphelion, 5.6745 × 1010 m, for the semi-latus rectum, 5.546 × 1010 m, which offsets part of it. His 6.268 × 10−14 rad/s is 40.8 arcsec per century, not the 41 he rounds to and certainly not 43. The anomalous advance is measured, from radar and spacecraft ranging, as 42.98 arcsec/century with an uncertainty well under 0.1 arcsec; a 5 per cent shortfall is not "as good as could be expected", it is a discrepancy of tens of standard deviations. A theory of gravity that reproduces the effect to within a factor of 2√2/3 has reproduced the scale of the effect, which is what dimensional analysis gives for free.
The 0.3 W/kg absorption rate is fatal. This is the paper's most striking number, and it can be tested against the paper itself. Multiply it by the mass of the Earth and one gets 1.8 × 1024 W of mass-equivalent energy delivered continuously to the planet. The Earth's entire measured internal heat flow — the budget that actually powers the volcanism and tectonics Broberg invokes — is about 4.7 × 1013 W. He is over by a factor of nearly 4 × 1010. If that power were radiated from the Earth's surface, the equilibrium temperature would be roughly 16,000 K, hotter than the photosphere of the Sun. Applied to the Sun itself, 0.3 W/kg gives 6 × 1029 W against a measured luminosity of 3.8 × 1026 W — a factor of 1,600. A seventy-kilogram person would absorb about 21 W, comparable to a quarter of basal metabolism. The mechanism the paper offers as an explanation of geological activity, and as a limitless energy source, is excluded by the most elementary energy budget available.
A varying G at this rate is ruled out. From G = Ac/(4TU) with A constant, Ġ/G = −1/TU ≈ −6 × 10−11 per year. Lunar laser ranging constrains Ġ/G to about 7 × 10−14 per year, and binary-pulsar timing and Big Bang nucleosynthesis tighten it further. Broberg's rate is roughly a thousand times the observational limit.
A is a fitted parameter, not a constant that emerges. It is calibrated three separate ways and the values do not agree: A ≈ 1.5 m2/kg from the cosmological relation with a 15-billion-year age, A ≈ 1.42 chosen to make 6MX equal the nucleon mass, A = 1.3874 (with κ = 1) or 1.41103 (with κ = 1.00852) to give the electron mass. Broberg then revises the age of the universe upward to 16 billion years to reconcile them. But the age is measured: the Planck results give 13.8 billion years. Since A scales with the age and MX as A−1/3, putting 13.8 into his own chain gives 6MX ≈ 1.76 × 10−27 kg, five per cent above the nucleon mass. The nucleon "prediction" survives only by adopting an age of the universe that the CMB excludes. Likewise, the electron-mass result carries two adjustable quantities, A and κ, to reach one number, and the proton "radius" of 2 × 10−14 m is more than twenty times the measured charge radius of 0.84 × 10−15 m — it is the size of a heavy nucleus, not a proton. That one sixth of the nucleon mass is called the quark scale also sits oddly: a nucleon has three quarks, so the constituent-quark value is one third, about 5.6 × 10−28 kg.
One much-advertised agreement is a known identity. That the Schwarzschild radius of the observable universe comes out close to its Hubble radius is not evidence for a horizon-flow model — it is the statement that the mean density is near the critical density, which is what a spatially flat universe means, and flatness is measured independently from the CMB. Broberg's chain of reasoning here is arithmetically sound (2GM/c2 = 1.5 × 1026 m for M = 1053 kg is correct) but it re-derives a standard result.
Beyond the numbers, the paper is discursive where it needs to be tight. The step from the geometric "handshake" between Lorentz loops to a physical rotation of the field is asserted rather than derived, and the factor of two from the northern and southern hemispheres is stated without justification — yet the whole Mercury result rests on it. The identification of the flow deficit with a real motion of space, the choice of one sixth rather than one third for the nucleon components, and the introduction of κ are all decisions taken because they produce the desired number rather than because the construction demands them. What survives is an interesting geometric reformulation of free fall and a genuine holographic intuition, attached to a set of cosmological consequences that observation has since closed off.