Electrodynamics

EstablishedLab OP-F12 = Darwin [E] under named hypotheses. Weber ≠ that operator. Hold is another book.

Darwin Table (Not Weber)

Retarded Liénard–Wiechert at O(v²/c²) equals the Darwin table. Historical Weber is a different eight-number table. The Darwin Lagrangian is already particle-only — no field in L.

Last updated: 19 August 2026

Reading this entry

This entry writes the laboratory order-v²/c² interaction as the Darwin Lagrangian, already a particle-only expression, the slow form of the Liénard–Wiechert force, and the scored two-seat table under the named hypotheses. Historical Weber stays the hold packaging beside that table.

What this is used for

The Maxwell-limit identity and the laboratory two-seat lock both take this Darwin Lagrangian as their slow force table. Acceleration and Weber notes use the same split when they keep rr̈ for the one-seat hold book and leave pair measurements on the Darwin side.

Walk through

The interaction written here is L_Darwin=Σ_(i<j)(e_i e_j)/(2c² r_ij)[v_i·v_j+(v_i·r̂_ij)(v_j·r̂_ij)], the standard order-v²/c² electromagnetic Lagrangian in particle variables alone. That expression is the slow expansion scored as the laboratory table, the same content as retarded Liénard–Wiechert at this order, under the hypotheses of the lab lock OP-F12. Mutual odd order v/c vanishes on the Darwin map, on Liénard–Wiechert, and on Weber, so Newton's third law holds for those mutual forces, and naive retarded Coulomb carries the light-time coefficient b₂=−2. Bradley aberration is the incoming-null map Δθ=βsinθ. Historical Weber remains the hold packaging beside this Lagrangian.

Honesty (19 August 2026): Historical Weber is not equivalent to Darwin at

. The scored laboratory table is Darwin / Liénard–Wiechert. Weber observer channels

are absent. Mutual

keeps Newton III in Darwin/LW; Bradley aberration is incoming-null kinematics — a different operator. Darwin

is already particle-only. Not Maxwell recovered.

The Darwin Lagrangian

The Darwin Lagrangian is the standard electromagnetic Lagrangian used in QED.

Darwin Term

Not an expansion identity

Expanding the historical Weber potential does not recover Darwin. The eight-number tables differ (DW-RET / H-D16). Laboratory two-seat force is the Darwin / Liénard–Wiechert table. Weber is retained as hold packaging, not as that laboratory operator.

Mutual odd vanishes for Darwin, Liénard–Wiechert, and Weber (Newton III holds). Naive retarded Coulomb has a light-time coefficient and fails Newton III. Bradley stellar aberration is the Lorentz map of an incoming null direction, — not the two-seat term (DW-ABR).

What this does not close

Scoring Darwin as the lab table does not prove CPT atomic fine structure as a free theorem, does not recover Maxwell as ontology, and does not close continuum hold. Lamb and hyperfine remain separate books.

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