Which Way Is Forward? Charge, Time, and the One Sign That Makes Antimatter

A positron differs from an electron by one sign. Stueckelberg and Feynman showed that the sign can be carried by the charge or by the direction of travel in time. Feynman left it as a picture. This paper takes it at its word and completes his theory. Give every particle a charge arrow q = ±1 and a time arrow t = ±1: a binary T on the same footing as the binary charge, free to point toward or away from the thermodynamic future, and not Wigner's time reversal, which acts on histories. Let observation register only their product χ = qt. A positron moving backward in time is then an electron, an electron moving backward is a positron, and reversing both arrows changes nothing. From this single hypothesis, with no new particles, fields or dimensions, we show the following. Every particle is equally itself moving forward and its antiparticle moving backward, with weight one half each. The T of the CPT theorem, read geometrically, is the particle's arrow: Wigner's time reversal is that flip followed by a charge conjugation, the C of CPT cancels it, and CPT reduces to parity times one arrow flip. Flipping a particle's arrow reverses no history, so backward-running antimatter is thermodynamically ordinary; entropy decrease belongs only to Wigner's operation. Antimatter has positive energy and falls down, as the ALPHA-g experiment observed. The asymmetries of charge sign, energy sign, matter content and antimatter thermodynamics disappear, and those of time, handedness, CP and observed matter dominance become facts about the single alignment χ, which read the same from either direction. The finite algebra is exact, its minimal geometric home is the split Clifford algebra Cl(2,2), and every finite claim is machine-checked. Files: the paper (PDF), and its standard-library Python verification script, verify_wwif.py.