The First Priniciples of Aether
| Scientific Paper | |
|---|---|
| Title | The First Priniciples of Aether |
| Read in full | Link to paper |
| Author(s) | William R Hohenberger |
| Keywords | aether, fine structure constant, electromagnetic waves, electron, fractal |
| Published | 2011 |
| Journal | Proceedings of the NPA |
| Volume | 8 |
| No. of pages | 11 |
| Pages | 258-268 |
Read the full paper here
Abstract
Various fractals are both defined and described that exist within the Aether Fractal Plenum. Mathematical equations are developed from those fractals that define the distribution of energy within the Aether Fractal Plenum. Sierpinski's Triangle and Pascal's Fractal are unified yielding additional mathematical descriptions for those fractals. Structures for electromagnetic waves, charged fibers, and charged particles are referenced from previous papers. A Periodic Table is developed for the various fractals that form within the Aether Fractal Plenum yielding methods for calculating the masses of the electron, proton and neutron, and for the values of the Fine Structure Constant and Planck's Length. Alternate mathematical methods are proposed for verifying the previous calculated values. Structures for the electron and the nucleon are proposed, and atomic structure and the structure of aether is reviewed.
Overview
William R. Hohenberger's contribution to the 2011 NPA proceedings develops what he calls the Aether Fractal Plenum: space is not empty but is filled with discrete "energy cells" at or near the Planck length, and every particle is a fractal arrangement of those cells. The paper rests on four stated assumptions — that an aether pervades everything, that its fine structure is set by the Planck length, that all particles are fractal structures built from scalar multiples of the smallest electromagnetic wave, and that the aether is "a hyper-dynamic, non-homogeneous, elastic substance".
The departure from the mainstream account is total rather than local. Instead of fields on a continuum with masses and coupling constants determined by measurement, Hohenberger proposes that counting loops in geometric fractals should yield those constants. Building on Don Briddell's field-structure theory, he tries to derive the proton-to-electron mass ratio, the fine structure constant and the Planck length from loop counts in Sierpinski/Pascal triangles and in a new six-loop hexagonal fractal. He is unusually frank about the state of the result: the closing section says that reconciling his table with the accepted values of alpha and the Planck length "must be done by others as I do not have the necessary skills or knowledge to complete it".
The argument
Twist-loops and the scaling ratio
From Briddell, even-numbered looped structures are energy loops (they close on the first circuit) and odd-numbered ones are mass loops (they must circulate many times before closing), so only odd twist-loops can build fractals. For N small circles of radius r packed around a large circle of radius R, N isosceles triangles fill 2π radians, each with half-angle π/N, giving the scaling ratio
- S = r/R = sin(π/N)
Each generation doubles the number of trip-loops; half-integer twist-loops (9½) need four trip-loops per generation instead of two. Hohenberger compares the whole construction to helically laid rope, citing Bohr and Olsen's "The ancient art of laying rope", and notes that a real drawing would need a computer.
The 1836 ratio
Superimposing Sierpinski's triangle on Pascal's fractal and highlighting the odd numbers, he tabulates running totals of mass loops and trip-loops. In the mass-loop column appear the powers of three: 1, 3, 9, 27, 81, 243, 729, 2187. Briddell's claim is that 1 is the electron and the proton is 1836 out of 2187, obtained by successively dividing 2187 by three and subtracting. The ratio recurs: 1836/2187 = 612/729 = 204/243 = 68/81. Moving to the hexagonal six-loop fractal, where everything is a multiple of six, the same ratio appears as 1088/1296 = 6528/7776 = 39,168/46,656 = 235,008/279,936.
The obstacle is that the measured ratio is 1836.15, not 1836, and "there cannot be a portion of a loop". Hohenberger's answer is resolution: successive layers of the fractal do not grow the object but zoom in on it, "like increasing the number of pixels in a picture". Zooming four more layers gives 362,797,056 cells, and applying the CODATA ratio yields 304,595,694, a whole number inside the experimental range. The gap between that and the integer count from 1836 is 25,326 loops, which he interprets as mass gained in transforming from a hexagonal to a twist-loop structure.
A periodic table of fractals
Tables 4 and 5 take the scaling factor 2 to twenty-two powers, subtract from each "a correction factor equal to one half of the quantum limit of the fine structure of the aether" (justified on the ground that a fractal needs a finite centre circle: "if there is no limit to the infinitely small, then fractals cannot form and we are not here"), and multiply the resulting factors in every combination across one- to eleven-layer fractals. Hohenberger reports the outcome as a mass of near-miraculous regularity: whole numbers emerging from ten-digit decimals, an exact 33 and 63 in the five-layer column, a stair-step in which each column's lowest highlighted number is two less than the next column's highest, the skipping of 64 "since 64 is an even multiple of 2", the recurring decimal .1428574, and a crossing point at 136.4666667. "There are so many coincidences apparent, that they can no longer be considered coincidences."
Constants
The weighted average scaling factor for a seven-loop eleven-layer fractal, 136.4666667, is offered as the fine structure constant. Table 6 builds the electromagnetic spectrum on eleven platforms starting from the Planck length; when platform eleven failed to match Table 7, "Planck's Length was calculated backwards from the eleventh platform" to 1.611096×10−35 m. Table 7 then converts CODATA particle masses to electron volts, multiplies by 128 (the three-loop to six-loop conversion) and by 1296 (four more layers), and reports the electron as 165,888 cells, with masses recovered "with a zero percentage error". The paper acknowledges a 0.42% variance in alpha and a 0.320% variance in the Planck length. An alternative route to alpha is proposed: taking S = π/N with N = 2 and introducing an unknown correction x for the shortening of a collapsed loop under helical twisting, alpha = [(π/2) − x]11, with x to be derived by rope-laying mathematics not carried out here.
Particles and aether
The electron is 165,888 cells = 1296 strings of 128 cells, the seven layers corresponding to seven atomic orbits with sub-orbits doubling. Charge splits 2/3 to 1/3 when the loops break, which he takes to validate quark charges — though "quarks are not particles, but only charge segments of an electromagnetic wave". The neutron is an electron encased in a proton. Nuclei are 4-loop tetrahedral fused structures with arms, bands and groups. Each energy cell carries about 3 eV, "well within the parameters for the definition of a neutrino", and the pre-existing aether energy that must be present before a particle can form is identified with dark energy and, once wound into particles, dark matter.
Assessment
There is something genuinely appealing in the ambition — a single substance, a single construction rule, and constants that fall out of counting rather than being measured — and Hohenberger is honest in a way that deserves saying: he flags his own 0.42% and 0.32% discrepancies rather than burying them, he admits the reverse-engineering of the Planck length, and he closes by handing the unresolved reconciliation to others.
Where the arithmetic is right. Most of the number work checks out. 1836 = 37 − 35 − 34 − 33 = 2187 − 243 − 81 − 27, and 1836/2187 = 68/81 exactly; the whole hexagonal chain 1088/1296 = 6528/7776 = 39,168/46,656 = 235,008/279,936 is also exactly 68/81. The factor 128 is right for a good reason he does not state: 67/37 = 27. 362,797,056 = 611, and 611/2187 = 165,888 = 64×27 exactly, so 165,888 × 1836.15267 = 304,595,694 as printed, and 165,888 × 0.15267 = 25,326 as printed. The scaling law S = sin(π/N) is the correct packing geometry, and it gives sin(π/6) = 0.5, i.e. the factor-of-two scaling he claims for the six-loop fractal. 0.511 MeV / 165,888 = 3.08 eV per cell, so "about 3 electron volts" is right. And 136.4666667 versus the CODATA 1/α = 137.035999 is a 0.415% miss, so his "0.42%" is honest; likewise 1.611092 versus 1.616252 (×10−35 m) is 0.320%, exactly as stated.
Two printed numbers are wrong. Multiplying 1836.15267 by 128 gives 235,027.54, not the 237,027.54 in the text — a slip of exactly 2,000, and the correct value sits right beside the 235,008 he compares it to. Similarly, 165,888 × 1836 = 304,570,368, not the 304,705,366 printed; the paper's own difference of 25,326 only works with 304,570,368, so the error is in transcription, not in the underlying calculation. The stated absolute Planck-length discrepancy, ".051560128E-35", is ten times too large: the difference is 0.00516×10−35 m, which is what his own 0.320% implies. There is also an internal inconsistency of substance: section 3 derives S = sin(π/N), but section 7 quotes it back as "S = π/N" and builds the alternative alpha formula on the version without the sine. With the sine, N = 2 gives S = 1, not π/2, and the formula alpha = [(π/2) − x]11 does not follow from anything in the paper.
The constants are not derived. This is the decisive problem, and it is a case of a free parameter doing the work. The alternative alpha formula contains an unknown x that is never computed; solving [(π/2) − x]11 = 137.036 simply gives x = 0.00667, so the equation is not a prediction but a definition of x. The Planck length is worse: Hohenberger says outright that it "was calculated backwards from the eleventh platform", so it is an output of the fit, and in any case the Planck length is not an independent measurement — it is defined as √(ħG/c3), and its uncertainty is entirely inherited from G. And the whole-number "coincidences" in Tables 4 and 5 come from twenty-two scaling factors multiplied in every combination across eleven layer-depths — thousands of products, searched afterwards for round results, with no prior specification of what would have counted as a hit and no count of the trials. Under those conditions whole numbers are expected, not evidence.
Conflicts with measurement. Three are specific. The fine structure constant is known to about 1.6×10−10 relative uncertainty from the electron anomalous magnetic moment and from atom-recoil measurements; a 0.42% discrepancy is roughly 2×107 times that uncertainty, so 136.4667 is not a slightly imperfect value of 1/α but a different number. Three electron volts per cell is not "well within the parameters for the definition of a neutrino": the KATRIN tritium beta-decay experiment bounds the effective electron-neutrino mass below 0.8 eV, and cosmological limits on the sum of neutrino masses are tighter still. And the quark scheme of "up, down, charm, strange and their anti-quarks" omits bottom and top, discovered in 1977 and 1995; more fundamentally, the proton's mass is overwhelmingly QCD binding energy rather than a count of constituents, which is why treating 1836.15 as a ratio of integers has no purchase on the deep inelastic scattering and lattice results that fix the proton's internal structure. The paper's largest claim — that fractal counting yields the constants — is therefore not yet supported by the paper's own numbers, a conclusion Hohenberger comes close to conceding himself.