Pattern Field Theory’s Correction of Einstein’s Relativity

Allen, James Johan Sebastian

Pattern Field Theory’s Correction of Einstein’s Relativity

How Pattern Field Theory (PFT) models spacetime and gravity beyond Einstein—while reproducing the correct Newtonian limit

Pattern Field Theory (PFT) correction to Einstein’s spacetime

Summary

General Relativity (GR) models gravity as curvature of spacetime and has been confirmed across a broad range of observations. GR does not, however, specify how spacetime arises or what its underlying structure is. Pattern Field Theory (PFT) treats spacetime, matter, and gravitational effects as emergent properties of motion organizing under constraint. GR appears naturally within PFT as a subsystem, and in weak-field domains PFT reproduces the Newtonian limit.

PFT: structural replacements for GR primitives

PFT provides structural quantities that take the role of curvature, metric, and time rate. The relations below are schematic and used as analytical tools within PFT.

Gravity (emergent field strength):

G = γ · Σ ( M² · D ) / C

G: effective emergent gravitational strength
M: local motion magnitude
D: pattern density
C: curvature resistance
γ: proportionality constant

Spacetime metric (emergent):

S = Σ ( P_n · C_n ) / D

S: metric-like emergent quantity
P_n: pattern coherence at layer n
C_n: curvature contribution at layer n
D: dimensional density

Local time rate:

T_local = dC / dM

T_local: local rate of time
C: curvature
M: motion intensity

In stable, low-curvature environments, these structures converge to an inverse-square attraction and GR’s weak-field behavior, maintaining consistency with tested physics.

AFCL: even perfect numbers as closure counts

The Allen Fractal Closure Law (AFCL) relates even perfect numbers to binary pair closures on a curvature-seeded two-dimensional lattice. The classical perfect-number form is:

Perfect(p) = 2^p-1( 2^p − 1 )

When (2^p − 1) is a Mersenne prime, this expression yields an even perfect number. Examples include 6, 28, 496, 8128, 33,550,336, 8,589,869,056, and 137,438,691,328. In PFT, these correspond to the number of undirected pair closures for N = 2^p anchors:

κ(N) = C(N,2) = N(N-1)/2 → κ(2^p) = 2^p-1(2^p − 1)

The AFCL diagram on this site visualizes these values on a logarithmic scale for reference.

Relation to Einstein and current literature

GR remains the accurate macroscopic theory in all tested regimes. PFT does not contradict GR; it extends it by providing explicit structural foundations for curvature and metric emergence, addressing singularities, and unifying cross-scale behavior under a single vocabulary of motion, constraint, and closure.

Recent context: Modern reformulations of GR highlight the Newtonian correspondence more transparently, clarifying the inverse-square limit without altering physical predictions. [See Physics World summary.]

Predictions and checks

Measurable micro-variations in local time rate correlated with pattern-density gradients.
Specific weak-lensing offsets at cluster boundaries attributable to non-terminal resonance features.
Reproducible curvature-based light behavior in engineered environments without particulate assumptions.

Note on Einstein’s contribution

Einstein’s theory remains foundational in physics. Pattern Field Theory (PFT) incorporates GR’s verified predictions while offering a structured substrate for emergence, removing singularities and supplying a unifying geometric and field-based logic suitable for both classical and quantum regimes.

Pattern Field Theory