Half from the Future: Hoyle and Narlikar's Absorber, Priced

In 1964 Fred Hoyle and Jayant Narlikar built a theory of gravity out of direct action between particles: no independent gravitational field, only particles acting on each other along their world-lines, through a propagator that is half retarded and half advanced — half the influence arriving from the past, half from the future. The theory is Machian by construction: a particle's mass is not its own but the summed response of every other particle in the universe, and Einstein's equations come out in the smooth-fluid limit. This paper prices the joint the whole construction stands on, and only that joint. The count is three assumed steps with zero derivations: the time-symmetric propagator itself; the demand that the universe's total response be finite and sum to the same constant at every point; and a cosmology whose absorber asymmetry points the response the way we observe. The middle demand is a boundary condition on the whole universe, postulated, not established — and Stephen Hawking priced it in 1965, within a year: in an expanding universe of masses that all carry the same sign, the advanced half of the response is infinite while the retarded half is finite. I have recomputed his reduced integrals in both cosmologies he calculates: the retarded sum comes out finite (0.500000 in the normalised units of my notebook), the advanced sum diverges quadratically — in the Einstein–de Sitter model with the future cutoff, in the steady-state model with the approach to its future boundary. The universe supplies the required response in zero of the two models calculated, and the one rescue Hawking himself proposed — negative mass — costs half of all mass-energy in the universe carrying the opposite sign, of which none has ever been observed. Grade: THREE ASSUMED STEPS, ZERO DERIVATIONS — THE RESPONSE DIVERGES, 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: Hoyle–Narlikar theory; absorber theory; Wheeler–Feynman; Hawking 1965; Mach's principle; assumed step; census.