Compactification of Quantum Mechanics: Collapsing the Constants of Nature to Two Postulates and Integrating Gravity

Note:  Feel free to email me should you have any questions.  jpcrumpler@swarmfieldtheory.org

This paper presents a compactification of quantum mechanics, reducing the apparent independence of the fundamental constants of nature to two postulates:

1. Quantized patch action — one coherence patch of area A = pi·lambda² acting over one response interval tau under membrane tension DeltaI yields one quantum of action:
   hbar = pi·DeltaI·lambda²·tau

2. Helical projection — the observed speed of light is the projection of the intrinsic ratio lambda/tau:
   c_obs = kappa·(lambda/tau)

From these two postulates, Planck’s constant, the speed of light, vacuum permittivity, vacuum permeability, the fine-structure constant, and the elementary charge follow directly. Extending the framework to thermal physics shows that Boltzmann’s constant, the Stefan–Boltzmann constant, the radiation constant, Wien’s displacement constant, and the Planck temperature also condense from the same postulates. All values match CODATA 2022 to machine precision.

Gravitational scaling arises consistently, compressing the Unified Field Equation (UFE) into a minimal Lagrangian with no free parameters. If future measurements of lambda and tau deviate from the gate-predicted values, the framework requires at most a single universal scaling factor linking hbar, lambda, and tau.

This work integrates prior Swarm Theory derivations into a unified presentation, offering a simple, testable, and complete foundation in which the constants of nature are not arbitrary but necessary consequences of geometry, tension, and coherence.

This framework does not seek to impose new values on nature. Instead, it demonstrates that the constants measured with extraordinary experimental precision are exactly those demanded by simple geometric and temporal structure. The match is not coincidence or curve-fitting: it is the observation that the empirical values were always accurate reflections of an underlying coherence. The role of the model is not to correct experiment, but to reveal why experiment never needed correction in the first place.

Website:  https://www.swarmfieldtheory.org/
GitHub:   https://github.com/crumpler4/Swarm-Theory-Unified-Field-Equation-Series