Unified field theory

Abstract

The "Unified field theory" (UFT) proposes a novel geometric framework designed

to resolve physical singularities where standard classical models break down,

particularly at coordinate origins (r = 0). By introducing a Planck-scale regulator,

Γ(r), the theory redefines the effective radial distance, replacing divergent infinite

values with finite, observable boundaries. This paper demonstrates the consistency

of the UFT framework across fundamental physical scales, ranging from the Bohr

model of the Hydrogen atom to Newtonian gravity and cosmological expansion. The

mathematical approach presented here effectively eliminates singularities while

preserving the predictive power of established physical laws, ensuring finite and

stable physical values.

Description

The UFT methodology relies on a redefined effective radial distance to prevent the

coordinate system from collapsing into an absolute zero singularity. The primary

framework is defined by the following relation:

reff = √ (r² + lp²) 

Where lp represents the Planck length

(approximately 1.616 ×  10-³⁵ m). By substituting

this regularized distance into standard physical equations, we derive finite results for

critical systems:

Newtonian Gravity: The regularized gravitational acceleration is calculated as: geff = (G × M) / (r²+ lp²) 

2. ElectroΓ(r), the theory redefines the effective radial distance, replacing divergent infinitemagnetism: The point charge potential is regularized into a finite bound:

V(θ) = q / (4πε0× lp) 

3. Hydrogen Atom (Bohr Model): The regularized potential energy is expressed as:

V(r) = - (k × e²) / reff