Spacetime Unification Equation — Unifying Three Theories

\frac{4\pi^2 r^3 C^2}{T^2 G h \nu} = 1

Symbol Definitions

Symbol	Meaning	Theory
G	Gravitational constant	Newtonian gravity / General relativity
r	Radius of helical spatial motion around matter (equivalent to the orbital radius in Kepler's law)	Unified Field Theory
C	Speed of light	Special relativity
T	Period of helical motion	Unified Field Theory
h	Planck's constant	Quantum mechanics
ν	de Broglie frequency ( $\nu = mc^2/h$ )	Quantum mechanics

Three-Step Derivation

Kepler's Third Law (1687)

\frac{4\pi^2 r^3}{T^2 G M} = 1

For an object of mass M, orbital radius r and period T satisfy this relation.

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de Broglie Mass-Frequency Relation (1924)

\nu = \frac{mc^2}{h} \quad \Rightarrow \quad M = \frac{h\nu}{c^2}

The mass of an object is equivalent to a quantum frequency.

↓

Substitution

Substitute $M = h\nu / c^2$ into Kepler's law, where r is the helical radius:

\frac{4\pi^2 r^3 c^2}{T^2 G h \nu} = 1

Three independent physical laws merged into a single equation.

Why Does This Matter?

In human physics, $G$ belongs to gravitational theory, $h$ belongs to quantum mechanics, $c$ belongs to relativity. The three are mutually incompatible. Physicists have asked for 100 years: what is the relationship between $G$ and $h$ ? This equation answers: $G$ and $h$ are precisely constrained in the same equation through helical spatial motion. Gravity, quantum mechanics, and relativity are not three independent theories — they are three facets of the same helical spatial motion.

A Stunning Corollary

If we assume helical rotation speed equals light speed (UFT basic assumption), i.e., $T = 2\pi r / c$ , substituting into the equation yields:

r = \frac{Gm}{c^2}

This means: the radius of helical spatial motion around every particle precisely equals half of that particle's Schwarzschild radius. The Schwarzschild radius is the event horizon radius of black holes in general relativity. Humans have always thought it only applies to black holes. This equation says: every fundamental particle — even an electron — has its own gravitational radius, and this radius is the scale of helical spatial motion.

Numerical Verification

Verification using electron parameters:

// Electron parameters

m_e = 9.10938 × 10⁻³¹ kg

ν = m_e·c²/h = 1.236 × 10²⁰ Hz

r = G·m_e/c² = 6.765 × 10⁻⁵⁸ m

T = 2πr/c = 1.418 × 10⁻⁶⁵ s

// Substitute into equation

4π²r³c² / (T²·G·h·ν)

= 1.000000 ✓ Perfectly equals 1

Disclaimer: The above derivation is based on Zhang Xiangqian's unified field theory framework and basic assumptions. The mathematical structure of the equation is rigorous, but its physical interpretation has not undergone academic peer review. This site presents this equation for researchers' reference and independent verification.