The Discarded Table: Wigner's Exclusions, Priced

Every physicist learns the same short sentence: a particle is an irreducible unitary representation of the Poincaré group, labelled by its mass and spin. The sentence comes from Eugene Wigner's 1939 classification, and the classification itself is a theorem — complete, correct, and not graded here. What this paper prices is the selection that turns the theorem into a periodic table. Wigner's mathematics returns more classes than nature is said to use: representations of negative energy, representations of imaginary mass, and, in the massless sector, the continuous-spin representations, which carry an infinite tower of helicities and a continuous parameter where the familiar particles carry a single number. The familiar spectrum is obtained from the full table by three postulated inputs with zero derivations among them: the identification of particles with single irreducible representations in the first place; the spectrum condition, which keeps only the positive-energy sheet; and the finite-spin selection, which discards the continuous-spin class. I price each discard. Negative energy has no floor, and energy conservation alone would let nothing split into something and minus-something at any scale — the discard buys the stability of the vacuum, and later frameworks had to re-postulate it as an axiom to keep it. The tachyonic class has no rest frame and makes a computed round trip arrive 0.413223 time units before it was sent. The continuous-spin discard stood for seventy-four years on one thermodynamic argument — an infinite tower means infinite heat capacity, which my notebook reproduces in the naive counting — and has since been overtaken by events: an interacting theory of the discarded class now exists, the thermodynamic objection has been answered with dynamics, and the class's defining parameter carries an experimental bound, below about a milli-electronvolt for the photon. A discard with a measured upper bound is no longer a postulate. It is a measurement that has not finished. Grade: THREE POSTULATED INPUTS, ZERO DERIVATIONS — ONE DISCARD NOW A MEASUREMENT, PRICED, STILL TURNING. This paper stands outside my work on the vacuum catastrophe; it draws nothing from that work and repairs nothing in it, and it touches no claim of that program — quantum gravity stands not solved in my books, and nothing here moves it. Keywords: Wigner classification; Poincaré representations; spectrum condition; tachyons; continuous-spin particles; assumed step; census.