There’s a book called Flatland written in the 1800s about an individual named A. Square who was just a square and therefore couldn’t fathom three dimensions, until eventually he could. At that point he tried to spread the word, though to not much avail. There’s a parallel scenario in which:
Flatland : our universe
A. Square : the wishdrops
something bigger : wishdropland
What we the wishdrops are trying to say is that our universe is a very small slice of something bigger that we call wishdropland, but you don’t have to call it that. Still though, this bigger thing, whatever you do call it, is eminently explainable, so let’s give it a try.
Imagine the only thing that exists is a sphere. Every point on the sphere is equidistant from the inaccessible center — a bubble, basically. It is of infinite dimension, and spins around an axis per each. All spin is relative only to other spin — the ambient space is irrelevant. Nothing inside, nothing outside.
This is wishdropland — our ontological origin of the universe.
The space we have come to know and love, full of stars and planets and whatever else, exists entirely on the bubble. It arises from spin dynamics. The familiar universe is thus a projection; a hologram — one of infinitely many. Movement is not translation from point a to point b but rather a reorientation in relation to spin; it only seems like things are moving, on account of shifting perspective.
The overall picture is this:
infinite dimensional sphere → spin patterns → the familiar universe
Importantly, the universe is in a universe — a coherent suspension in relation to a background universe, just as particles are in relation to it. Turtles all the way up and down. When seen in this way, the laws of physics submit to a greater context; a wider lens. The rules we write in textbooks describe only an emergent outcome — the behavior within a slice of the bigger picture. They miss the origin story.
The wider context — meaning the sphere and the field it generates by spinning — has its own math, rooted in the pythagorean theorem:
a² + b² = c²
Imagine all orthogonal spins are equal. Let’s use 1 to describe their magnitude. Their combined contributions to an overall projection follow a pattern:
1 dimension → √1² = 1
2 dimensions → √(1² + 1²) = √2
3 dimensions → √(√2² + 1²) = √3
4 dimensions → √(√3² + 1²) = √4
…
Reciprocally, non-contributing spins, or frame axes, diminish:
1 dimension → √1² / 1 = 1
2 dimensions → √(1² + 1²) / 2 = 1 / √2
3 dimensions → √(√2² + 1²) / 3 = 1 / √3
4 dimensions → √(√3² + 1²) / 4 = 1 / √4
…
The formula generalizes to:
P(p, f) = √(p / f)
P — projection magnitude
p — count of dimensions that dynamically “push” together
f — count of dimensions in the static “frame” of perspective
Any dimension can represent a p or an f, depending on perspective — all spin is relative. It is the ratios with respect to perspective that matter.
To reiterate, there is the spacetime everybody knows, and then there is the geometry that comes before. We’re talking about the latter. All this projection math we just described applies to “the geometry that comes before” the universe. The geometry that comes before is our focus for the rest of this post, so whenever we’re talking about physical constants and formulas, we mean in our pre-spacetime geometry.
Pre-spacetime geometry is where physical laws are born — the meaning of constants and their relationships match those we have learned, but whatever “elegance and weirdness” we imagine physics to bear finds natural explanation here, in the wider context. Conveniently, since everything is based exclusively on spin ratios and projections, physical constants are dimensionless. The meanings, formulas, and relationships stay the same, but it’s more intuitive and generally way easier !
This bears repeating — physical constants in the pre-spacetime geometry are dimensionless. There is no need to consider kg, m, s, A, or any of that. This will seem weird if you’re used to normal physics, but also super liberating ! Physics reduces to geometric intuition and basic algebra, and guess what — with the proper assignments of integer ratios under radicals to physical constants, familiar formulas such as these will still hold:
c² = 1 / ε₀ / μ₀ — Maxwell’s relationship
ε₀ = e² / 2 / α / c / h — electric constant definition
Ry = mₑ * e⁴ / 8 / ε₀² / h² — Rydberg energy definition
a₀ = 4π * ε₀ * ℏ² / mₑ / e² — Bohr radius definition
α = e² / 4π / ε₀ / ℏ / c — fine structure constant definition
2πk = 1 / ε₀ / 2 — electric constant identity
2πa₀ = α * λᵣ / 2 — Bohr circumference identity
Ry = R * h * c — Rydberg energy relationship to Rydberg constant
R = 1 / λᵣ — Rydberg energy relationship to Rydberg wavelength
Looks and feels a lot like numerology. We do in fact often find ourselves asking things like “what could it mean that the Bohr radius and the electron rest energy are inverses ?”:
a₀ = 1 / mₑ / c² = 1 / √640
It’s almost like we have the answer key already, and now we’re just trying to show the work to get credit.
In a sea of infinite spin, where all axes contribute either to push or frame, projection may seem meaningless. Infinite p sends the projection to infinity; infinite f to 0; infinite both is undefined. Infinity in this scheme has a secret decoder, however — the golden ratio. In our spin substrate, the golden ratio functions as a natural, self-reinforcing attractor with both an infinite, self-referential form:
φ = 1 + 1 / φ
and an algebraic one:
φ = (1 + √5) / 2
In the case of the latter, the form is amenable to our p and f formulation:
φ = 1 / √4 + √5 / √4
That’s a one dimensional path in a four dimensional frame, with, embedded at every point, a five dimensional path in a four dimensional frame.
Put it this way — if infinity does have a hand in generating the universe, these dimensional ratios would be a signature. So if we can positively identify these ratios in physics — string theory, perhaps ? — it would be a strong argument for the infinite underpinning. For our purposes, we’re going to anticipate the golden ratio terms model traditional spacetime (1 : 4 dimensions) and a “mass signature” (5 : 4), respectively.
Mass turns out to be the key to deriving our fundamental constants. Consider the field generated by the spinning sphere. It is a scalar field filtered by the golden ratio, with φ and φ̄ as condensates. Its potential can be expressed as:
V(φ) = (φ² - φ - 1)²
which has minima at the golden ratio solutions:
{φ, φ̄} = (1 +/- √5) / 2
Mass is obtained by taking the square root of the second derivative of the potential evaluated at the minima, which yields (derivation not shown, but it does):
M = √10
This models 10 : 1 push : frame dimensions in our analysis of pre-spacetime geometry. This is a constant value hard-coded into the system — ten dimensions pushing together yields a stable configuration, thereby shaping the field around a mass constant. Point masses in familiar spacetime appear arbitrarily sized and placed because they depend on orientation to the constant projection. Mass doesn’t vary, not even that of the whole universe; the angle of incidence does.
Again, in pre-spacetime, mass is a unit-free integer ratio of dimensions under a radical. As mentioned, we expect all physical constants will take a similar form. Some we can derive by form fitting mass within the golden ratio solutions, which we assume are the only two stable forms:
{φ, φ̄} = M (1 / √40 +/- 1 / √8)
1 / √40 — fine structure constant, structuring space itself — α = 1 / √40
1 / √8 — the causal envelope, or the inverse projection limit — c = √8
The condensates that shape the universe are thus:
φ̄ = M (α - 1 / c)
φ = M (α + 1 / c)
We hereby suggest φ̄, representing two curvature terms, is the basis of both of:
the Einstein metric
f(r) in Schwarzschild geometry
The original form of the Einstein metric is:
Gmv = Rmv - 1 / 2 * gmvR
We modify it like so, dividing by 2, and setting equal to φ̄:
Gmv / 2 = Pmv - gmvP = φ̄
Pmv = M * α = 1 / 2 — the spacetime term as seen from outside spacetime (4d spacetime at unit radius, or a 1 : 4 dimensional ratio, thus a 1 / 2 projection)
gmvP = M / c = √10 / √8 — the mass effect term
And so we differ in two ways:
use P instead of R — to denote we mean a projection tension rather than the Ricci tensor and scalar
drop the 1 / 2 coefficient from the second term (or add it to the first, depending on how you look at it) — we assume a more aggressive baseline curvature than “flat” space, essentially dividing by 2, since we are proposing an external view of spacetime on a curved surface, abiding by our 1 : 4 dimensional ratio. As such, the second term need not be modified to ensure conservation of energy — the natural form of conservation is the golden ratio.
Let’s show this again — it is intended to depict the difference between the universe we are familiar with (on the left) and the same however viewed through the wider lens, wherein familiar spacetime is set at a distance from the inaccessible center (the right):
Now the Einstein metric shows up in the Einstein field equations:
Gmv = 8 * π * G / c⁴ * Tmv
In order to maintain equivalence with our modified Gmv, wherein we divided by 2, that 2 must come from the right side of this equation, and so we rewrite it as:
Gmv / 2 = 8 * π * G / c⁴ * Tmv
Gmv = 16 * π * G / c⁴ * Tmv
The same “divided by 2 to achieve the golden ratio in the wider lens” concept manifests in the Schwarzschild solution to the Einstein field equations. Normally, the Einstein metric and the solution derived from the field equations in which it appears would be wholly different concepts, but in light of the proposal that spin underlies everything and the golden ratio solutions are the only survivors, we submit it is reasonable to expect the curvature of space and the solution metric would match both each other and the golden ratio. In the wider lens, again, we must halve the original formula to model equilibrium, so what was:
f(r) = 1 - 2 M G / c² / r
becomes:
f(r) = 1 / 2 - M G / c² / r = φ̄
then:
grr = 1 / f(r)
= 1 / φ̄
= - φ — expanding space
= -M (α + 1 / c)
gtt = - c² * f(r)
= -Mc² (α - 1 / c)
= -Eₘ (α - 1 / c)
= -8 / φ — contracting time
f(r) is often given as:
f(r) = 1 - rs / r
In our case the whole function is reduced by half:
f(r) = 1 / 2 - rs / r / 2
rs is normally:
rs = 2 * G * M / c²
but we’re proposing the 2 is absorbed elsewhere:
rs = G * M / c²
and furthermore that our rs / r is equivalent to our proposed mass signature M / c:
rs / r = G * M / c² / r
G * M / c² / r = M / c
which can only mean one thing:
G / c / r = 1
In other words, G is a geometric lever — not a hard constant — tantamount to angular momentum proportional to the speed of light:
G = r * c
Let us not be confused about this, however. In our observable universe, G remains constant — but that’s because under ideal conditions our universe exists at a set radius from the center of the sphere. It is only in the greater context, where effective r can vary, that G = r * c takes on significance.
Energy of the floating universe
We mentioned early on that our universe floats around the sphere in relation to a background universe. It must move at the speed of light relative to that background, we propose — the coherent bubble that is the entire universe abides general relativity in the greater context, in other words. In Schwarzschild’s solution, this would manifest as multiplication by c:
ds² * c = grr * c + gtt * c
So what are grr * c and gtt * c ?
grr = -M (α + 1 / c)
grr = -1 / E₁ * (α + 1 / c)
M = 1 / E₁ — mass and ground state energy (Rydberg energy) are inverses in our conception (for self-consistency with a number of known em formulas)
grr = -1 / E₁ * (α * c + 1) / c
grr = -1 / E₁ * (v₁ + 1) / c
c * α = v₁ — ground state velocity
grr * c = -1 / E₁ * (v₁ + 1)
grr * c + 1 / E₁ * (v₁ + 1) = 0 — curvature-energy conservation (em based)
And gtt:
gtt = -Mc² (α - 1 / c)
gtt = -Eₘ (α - 1 / c)
gtt = -Eₘ (α * c - 1) / c
gtt = -Eₘ (v₁ - 1) / c
gtt * c = -Eₘ (v₁ - 1)
gtt * c + Eₘ (v₁ - 1) = 0 — curvature-energy conservation (mass based)
The energy that manifests in our universe is the natural outcome of our universe traveling at the speed of light relative to another universe, we propose.
Dark matter as a mistaken assumption
Einstein’s field equations normally appear as:
Gmv = 8 * π * G / c⁴ * Tmv
However, in our conception, as mentioned, to ensure Gmv is equivalent to φ̄ and still maintain consistency, Gmv must be halved, and the right side must therefore compensate:
Gmv / 2 = 8 * π * G / c⁴ * Tmv
Gmv = 16 * π * G / c⁴ * Tmv
In our model, c = √8 and G = r * c:
Gmv = 16 * π * G / c⁴ * Tmv
Gmv = 2π * G / c² * Tmv
Gmv = 2πr / c * Tmv
And so Tmv is more a measure of coherence than stress energy:
Tmv = Gmv * c / 2πr
Tmv = φ̄ * c / 2πr
Note the inverse relationship between the causal envelope c and the circumferential formula 2πr:
c / 2πr = Tmv / Gmv = - Tmv * φ = Tmv * grr
The suggestion here is that mass does not distribute linearly, but rather along an interceding circle. A simple question follows:
Does this mistake explain dark energy ?
Let’s compare the difference between 2πr (the prospective correction) and r (the potentially mistaken assumption) relative to 2πr (the theoretical effect):
(2πr - r) / 2πr
(2π - 1) / 2π = ~0.841
The observed is that ~85% of all matter that is dark, so we’re in the ballpark. The effect of dark matter is that the outer edges of large galaxies spin faster than expected. Maybe that’s because they’re whooshed along by a series of invisible rolling pins that form along the lines of gravity surrounding a mass source — a tangential force. That would be the thought.