Introduction
Hello,
This paper hand waves at a theory of everything, as in the physics kind. It might be unorthodox, somewhat irreverent, and just as likely to describe an elaborate delusion, so please enjoy then pass it along.
Sincerely,
The wishdrops
Foreword
Much gratitude is owed to the physicists, philosophers, teachers, and ordinary citizens who, over the course of time, have managed to distill the puzzles of the heavens into something resolvable with a notebook, a pencil, and an internet connection.
Yes, the gratitude applies even if this is delusional. Memories made along the way 🙂
Table of contents
Introduction
Foreword
Table of contents
The wishdrops conjecture
The Pythagorean theorem
The golden ratio
The speed of light
Mass-energy equivalence
Dark matter
A compendium of physical constants
The expansion of space
1 / 137
The color spectrum apices
The frequency of the universe
Sensory harmonies
Ancient philosophy
Incompleteness, infinity, and existence
The wishdrops conjecture
In physics, a theory of everything would reconcile the two predominant sets of laws – general relativity and quantum mechanics. It might furthermore address concepts like the sensory apparatus, rationalizing color and note wavelengths, for example. Indeed, this is the domain of the wishdrops conjecture:
The latent form of the universe is a spinning sphere of infinitesimal radius and infinite dimension. The manifest form, a dilation of the omnipresent point.
Supportive overtures follow.
The premise is hard to reason about, thus naturally superpositions truth and delusion. Its favorability, drawn in isolation, becomes either. The hedge against truth – it may be nothing, in which case the exposition that follows will hopefully be nonetheless interesting or at least entertaining. The hedge against delusion – but maybe it is something ! Like maybe it’s just enough to inspire one intrepid string theorist to launch the next superstring revolution ! Of course, if they do, and in this spirit, they might want to rename it to have something to do with spheres instead.
!
Ok, let’s not get ahead of ourselves.
The Pythagorean theorem
Consider orthogonal segments of length 1, composed.
The Pythagorean theorem – a² + b² = c² – can be used to derive the following:
A path of p such segments assembled end to end projects a length √p
A front balanced on f such segments of common origin is at its center 1 / √f from the origin
These basic forms are amenable to the principle of least action, which is prevalent in nature:
√p is the shortest possible projection of a trace that wanders ever further from the origin until reaching length p while breaching not more than p dimensions
1 / √f is the shortest possible distance between the origin and a front balanced on not more than f segments
The abstract notions of path and front theoretically apply to the infinite sphere, in that their combined, reciprocal effects can be observed at a node, or a cohesive point of interrelation between spinning subspheres. Propagation of a node relative to a spherical frame – hence frequency, given the cyclical nature of a sphere – would be the function of a dimensional ratio:
v = √(p / f) – frequency of a node in relation to a frame
p – count of dimensions in the path
f – count of dimensions in the front
Path and front here are somewhat akin to perpendicular spins into and out of the frame where the node is observed, measured in dimensions, thus integers. Imagine them as superimposed convergence and divergence; source and sink; gain and loss. The path aligns with the direction of propagation, thus contributes to acceleration; the front is perpendicular, thus decelerates.
Recognize that the universe – itself, space, and particles alike – is replete with nodes and frames; that this is the fractal substance of everything. Every node — indeed, every physical construct — shares a common albeit inaccessible center, and is arbitrarily close to every other, however distinguished by unrelated spins of potentially unfathomable proportions. Assume subspherical intersections with orientation embody frequencies, and that physical constants are, among these, of common recurrence. Expect in particular, and hereby emphasized:
Physical constants correlate to square roots of integer ratios, and those integers count dimensions.
This lends to an entirely dimensionless system of units, based on counting dimensions, compatible with known physical formulas, to be elaborated hereupon.
The golden ratio
To divine order from the naturally infinite, employ the golden ratio, which has equivalent infinite and finite forms:
continuing fraction form of Φ
1 + 1 / Φ = Φ
1 + 1 / (1 + 1 / Φ) = Φ
1 + 1 / (1 + 1 / (1 + 1 / Φ)) = Φ
…
algebraic form of Φ
(1 + √5) / 2
The algebraic form consists of additive terms that separately conform to spherical frequencies:
1 / √4 + √5 / √4
The first term – 1 / √4 – implies four dimensions of front; divergence; sink; loss. The second term – √5 / √4 – implies five dimensions of path; convergence; source; gain; and four dimensions of front; divergence; sink; loss.
Expect the golden ratio to model the rest path of physical nodes.
Nodes are depicted as right triangles to show the orthogonal vectors of path and front have a vector sum that is also of interest. This hints at a fractal, for the resulting vector is as legitimate as its constituents. Since these vectors are always square roots of counts of dimensions, the Pythagorean theorem becomes both convenient to use and easy to reason about – just add the dimensions. Indeed, the count of dimensions implied by a and b combined is equal to the count of dimensions implied by c. This suggests a and b simply segment the dimensions implied by c into two groups, thereby forming a simple ratio, the basis of frequency.
The speed of light
Scale by √8 and theorize related constants.
Proposed constants include:
c — speed of light — √8
mₑ — mass of the electron — √10
e — electric charge — 1 / √18
Formulas that relate the speed of light and the mass of the electron are therefore:
c / 2 + mₑ = Φc
1 / 2 + mₑ / c = Φ
mₑ / c = √5 / 2
Mass-energy equivalence
Scale again, by the speed of light squared.
The additive terms correspond to mass and energy, or:
The curvature of spacetime
The distribution of mass-energy
These are the two sides to Einstein’s field equations describing general relativity:
𝑅𝜇𝜈 - (1 / 2) 𝑅𝑔𝜇𝜈 = (8π𝐺) 𝑇𝜇𝜈
The application of the golden ratio at different scales predicts the relationship between the gravitational constant (G), Coulomb’s constant (k), and the speed of light (c):
2πG = 1 / c
2πk = c
Which also means:
G⁻¹ = k
G = k⁻¹
Gk = 1
G / k = 1 / c²
And furthermore:
𝑅𝜇𝜈 - (1 / 2) 𝑅𝑔𝜇𝜈 = (8π𝐺) 𝑇𝜇𝜈
𝑅𝜇𝜈 - (1 / 2) 𝑅𝑔𝜇𝜈 = (4 / c) 𝑇𝜇𝜈
𝑅𝜇𝜈 - (1 / 2) 𝑅𝑔𝜇𝜈 = (√2) 𝑇𝜇𝜈
Dark matter
Dark matter and energy proportions are also predicted by the universal form. Light only penetrates the darkness by the inverse proportion to the speed of light squared – 1 / 8 – the same theoretical relationship G bears to k.
Ordinary matter, dark matter, and energy should account for:
ordinary matter — 1 / 8 / 2 / Φ — 3.9%
dark matter — 7 / 8 / 2 / Φ — 27%
energy — √5 / 2 / Φ — 69.1%
Or, as simple proportions:
ordinary matter — 1
dark matter — 7
energy — 8 * √5
A compendium of physical constants
Here are frequency assignments for a number of physical constants:
w₀ = √162 — wishdrops ratio of convenience
c = √8 — speed of light
mₑ = √10 — electron mass
e = 1 / √18 — electric charge
2πk = √8 — Coulomb’s circumference
2πG = 1 / √8 — gravitational circumference
h = √20 / w₀ — Planck’s constant
Ry = 1 / √10 — Rydberg energy
λᵣ = 40 / w₀ — Rydberg wavelength
R = w₀ / 40 — Rydberg constant
vᵣ = w₀ / √200 — Rydberg frequency
α = 1 / √40 — fine structure constant
μ₀ = 1 / √2 — magnetic constant (vacuum permeability)
ε₀ = 1 / √32 — electric constant (vacuum permittivity)
2πa₀ = √10 / w₀ — Bohr circumference
mₑc² = √640 — electron rest energy
λᵥᵥ = 40 — wishdrops wavelength
vᵥᵥ = 1 / √200 = wishdrops frequency
Here are some of the physical formulas they satisfy:
c² = 1 / ε₀ / μ₀
ε₀ = e² / 2 / α / c / h
Ry = mₑ * e⁴ / 8 / ε₀² / h²
Ry = R * h * c
R = α² * mₑ * c / 2 / h
2πa₀ = α * λᵣ / 2
2πk = 1 / 2 / ε₀
And here’s how they relate to each other:
The expansion of space
The expansion of space, observed to outpace light by a factor of approximately 10 / 3, may be owed to the perpendicular application of golden ratio components corresponding to the inversely proportional electron mass (mₑ = √10) and Rydberg energy (Ry = 1 / √10). This underpinning accelerates into “ten by ten” dimensions, upon which light accelerates at a substantially lesser rate.
mₑ / Ry / √(c² + 1) = 10 / 3
Ten by ten may also be the square of either / both:
mₑ² / √(c² + 1) = 10 / 3
1 / Ry² / √(c² + 1) = 10 / 3
1 / 137
The proposed frequency of the dimensionless fine structure constant — 1 / √40 — is theorized to relate its observed value — 0.00729735…, or approximately 1 / 137 — by an exponent of 8 / 3:
1 / √40 ^ (8 / 3) = 0.00731004… =~ 1 / 137
The discrepancy casts doubt, admittedly, or at a minimum invites curiosity.
The rationale is to apply the frequency 8 times, per the 8 dimensions into which light converges, and submit to a cube root, or 3 reverse applications, per 3 dimensions of spatial divergence, hence observance.
Assume the strong force takes the universal form as well, however at a different scale of cⁿ, which may explain the observation that the coupling strength ratio between electromagnetism and the strong force is roughly equal to the fine structure constant.
The color spectrum apices
The observed electromagnetic frequencies of the color spectrum apices can be derived from the Rydberg frequency (~3.29 * 10 ^ 15 hertz) scaled by the inverse wishdrops ratio (1 / √162):
v(n) = (vᵣ / w₀) * √n = ~3.29 * 10 ^ 15 * √(n / 162) hz
n = 3 — red — ~4.48 * 10 ^ 14 hz
n = 4 — yellow — ~5.17 * 10 ^ 14 hz
n = 5 — green — ~5.78 * 10 ^ 14 hz
n = 6 — blue — ~6.33 * 10 ^ 14 hz
n = 7 — indigo — ~6.84 * 10 ^ 14 hz
n = 8 — violet — ~7.31 * 10 ^ 14 hz
n = 9 — ultraviolet — ~7.75 * 10 ^ 14 hz
The variable term – √n – suggests the pure colors each correspond to a different number of dimensions. More specifically, harmonies occur when electromagnetic waves converge with balance, or with spin equally apportioned to a number of dimensions (in the range of integers 3 through 9).
Substituting w₀ * c / 40 for vᵣ yields:
v(n) = (c / 40) * √n
Color wavelength is its inverse, factoring out the speed of light:
λ(n) = 40 / √n
Expect the observed wavelength ratios for pure colors to mirror a sequence of inverse square roots for integers 3 through 9, representing harmonic balance in n dimensions of divergence.
The root wavelength manifests as ~1160 nm, which is the Rydberg wavelength (~91 nm) multiplied by the wishdrops ratio (√162).
The frequency of the universe
The frequency of the universe, which is around 432 hertz, sometimes used to tune pianos and our proposed center of the audible range, adds 40 octaves, or 480 notes, to the color frequency formula for n = 10:
vᵤ = v₁₀ * (c / √(c² + 1)) ^ 480
vᵤ = (vᵣ / w₀) * √10 * (c / √(c² + 1)) ^ 480
vᵤ = (vᵣ / √162) * √10 * (√8 / √9) ^ 480 = ~432 hertz
Alternatively:
vᵤ = v₁₀ * (c / √(c² + 1)) ^ 480
vᵤ = c / 40 * √10 * (c / √(c² + 1)) ^ 480
vᵤ = c / √160 * (c / √(c² + 1)) ^ 480
Notice 160 + 480 corresponds to the number of dimensions implied by electron rest energy — 640. The first half accounts for 160 and is perceived flatly, traversed by light naturally. The second half accounts for 480 and is perceived dilated, or in space iteratively calibrated to the speed of light once per each of 480 dimensions.
Sensory harmonies
The generalized formula for a musical note is proposed as:
v(♪) = c / √160 * (c / √(c² + 1)) ^ ♪
The suggestion is that c / √(c² + 1), or √8 / √9, is the ratio of frequencies for adjacent notes — more important even than (1 / 2) ^ (1 / 12), the ratio when octaves are a precise factor of two apart. Of course, the audible range only covers 10 octaves, which means ♪ must be in the range of 480 plus or minus 60. Perhaps other ranges correspond to other senses, all of which seem to share the same spectral profile of three plausible opposites plus a center of balance.
color
red — blue
yellow — indigo
green — violet
ultraviolet onset
note
C — F
D — G
E — A
B
taste
sweet — soft bitter
sour — hard bitter
salt — umami
savory
sense of direction
backward — forward
left — right
down — up
center
passive moods
lust — sloth
pride — envy
gluttony — greed
wrath
active moods
abstinence — zeal
humility — kindness
temperance — charity
patience
chakras
root — heart
sacral — throat
solar — third eye
crown
Ancient philosophy
The Book of the 24 Philosophers contains among its aphorisms:
God: an infinite sphere whose centre is everywhere and whose circumference is nowhere.
God: the sphere which has as many circumferences as points.
Are these to be taken literally ? Knowledge we have since lost ?
Pythagoras is known for his promotion of musica universalis, which literally means universal music, but has since come to be known as the music of the spheres. Did the namesake of the right triangle formula and philosopher of spheres and music appreciate their interrelation more deeply than we have in the interim been capable of giving credit for ?
Are the platonic solids of sacred geometry not just quirky curiosities but rather woven directly into the natural universe ?
Incompleteness, infinity, and existence
Per a loose interpretation of Gödel’s incompleteness theorems, the formalism that is physics cannot account for everything. Unless infinity is a loophole ? Or is sheer existence perhaps the only thing unaccounted for ?