Planck Scales from Coherence Geometry: A Swarm Theory Derivation

Please feel free to email me with questions.  Jpcrumpler@swarmfieldtheory.org  

This paper derives the Planck scales — mass, energy, length, and time — directly from coherence geometry within the Unified Field Equation (Budget form, UFEB). In conventional physics these scales are defined combinations of G, hbar, and c. Here they arise naturally from the lattice update interval (tau), with no additional parameters.

Key results:

• Planck mass mP = hbar / (pi · c² · tau).

• Planck energy EP = hbar / (pi · tau).

• Planck length l* = c · tau = lP / pi.

• Planck time tau = tP / pi.

These expressions show that once tau is fixed by the same update rule that yields G, all Planck scales follow immediately. The values agree with CODATA 2022 within experimental uncertainty.

This result extends Swarm Theory by closing the system of natural units, showing that Planck scales are geometric consequences of lattice coherence rather than independent definitions.