a note about the einstein tensor
a guess that it represents the difference between spacetime regime and mass regime, different thresholds of the same underpinning curvature
hey wishdrops diary, today we had a new idea. you know how we had been a bit uneasy ascribing the golden ratio’s algebraic solution to both the schwarzschild solution and the einstein field equations themselves ? well today we changed perspective on that. whereas the schwarzschild metric we continue to assume has two terms that combined represent the golden ratio, we now believe the field equations, particularly the einstein tensor, or the left side, model the difference between two stable thresholds of the golden ratio:
Gmv = Rmv - 1 / 2 gmvR = 8 pi G / c^4 * Tmv
we’re guessing both Rmv and gmvR represent phi bar now, and that the 1 / 2 coefficient is there to modulate the effect of mass relative to spacetime. mass would be a scalar — a 1d phenomenon — whereas spacetime is 4d. in wishmath, this corresponds to a projection ratio of sqrt(1 / 4), or 1 / 2. so both Rmv and gmvR represent phi bar, however at different thresholds.
regarding the schwarzschild geometry, we’ve been working with a modified theory for a while now… it’s that its traditional form is just the “n = 2” configuration of this:
f(r, n) = n * M * (fine - 1 / c) = n * phi bar
fine = 1 / sqrt(40)
c = sqrt(8)
so:
f(r, 2) = 2 * M * (fine - 1 / c)
which corresponds to the known schwarzschild metric:
f(r) = 1 - 2 * M * G / c^2 / r
G = c * r (we assume)
the schwarzschild radius including a 2 * M — where 4d space becomes the surface of a sphere — is somewhat intuitive in this sense. mass itself obviously corresponds to 1 * M. charge corresponds to 3 * M — this would be the photon sphere, where light maintains stable trajectory at a particular set radius. and so on, presumably. this is the stratification of space, with thresholds everywhere that the square of the count of dimensions yields an integer, thus a rational number.