Gravity

Modelled[M] modelled package — not free public theorem; see doctrine v1.0.3 residual chips on /status.

EM–Gravity Double Copy

Modelled reading: gravitational amplitudes obtained by squaring electromagnetic ones, joined to a Mach package. Analogous language, not the BCJ double-copy theorem.

Reading this entry

The EM–gravity double copy places a gravitational amplitude as the square of an electromagnetic amplitude inside the Weber force. That reading supplies the shared velocity structure the gravity book uses when charge coupling is joined to mass coupling and to the Mach package.

What this is used for

Use this page to follow the Weber force into its gravitational copy, term by term, and to read the schematic ratio G/k = (m_e/e)² × α² that the mixed-mass Mach package carries forward.

Walk through

The page writes the Weber force as F_W = (k q q′ / r²) (1 − ṙ²/(2c²) + r r̈/c²). It copies the same bracket onto gravity, F_grav = −(G m₁ m₂ / r²) (1 − ṙ²/(2c²) + r r̈/c²), so the velocity-squared term and the radial-acceleration term are common to both forces. The schematic coupling then reads G/k = (m_e/e)² × α², placing G beside the Coulomb constant k through the electron mass-to-charge ratio and the fine-structure input α. With the gravitational sector written as EM², the page assigns gravitational waves the propagation speed c and spin 2, the square of the spin-1 electromagnetic amplitude. Rule C, that all energy gravitates, is the reading of electromagnetic field energy entering that squared sector.

Integrity note (Doctrine v1.0.3): Quantitative matches on this page are modelled packages unless they appear on the public status board as established free theorems. Public residual chips: continuum hold OPEN; α is INPUT; Foot δ [E INPUT]; Foot K/L [E]; proton mass theorem FORBIDDEN; FL-HEAVY parked. Soft packages are not finished UFT certificates.

The double copy principle dictates that the gravitational amplitude is the square of the electromagnetic amplitude. While this is a known relation in certain quantum gravity formulations (like BCJ/KLT), the CPT framework provides a direct classical implementation through Weber electrodynamics.

The gravitational force between two masses follows the exact same structure as the Weber force, substituting for the electrostatic coupling .

The Weber double copy

The key conceptual point is that gravity is not a separate force. The gravitational coupling of two massive particles is the square of their electromagnetic coupling, properly speaking via the mass-as-EM-drag identification.

Schematic coupling relation

Because gravity is , gravitational waves travel at and carry spin-2 (the amplitude is squared from the spin-1 electromagnetic interaction). Additionally, Rule C (all energy gravitates) naturally follows because electromagnetic field energy is squared in the gravitational sector.

[M]

The double copy relationship in the Weber framework is mathematically established.

Source Documents

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