THE ARROW OF TIME AS A CONSEQUENCE OF THE GROWTH IN PARTICLE NUMBER: DERIVATION OF THE MONOTONIC QUANTITY AND AN EQUILIBRIUM PAST INSTEAD OF THE PAST HYPOTHESIS

This paper proposes a hypothesis according to which the directionality of time (the "arrow of time") has as its physical basis the monotonic, irreversible growth of the total number of particles in the Universe. Relative to the previous version, the growth law is no longer postulated but derived from the equations of the self-replication cosmological model: from the continuity equation with a creation source, ṅ + 3Hn = Γn, the total particle number N = n·a³ obeys Ṅ = ΓN, so that N(t) = N₀·exp(Γt) exactly, for any expansion history. A point essential to the argument is established: in this model the Hubble parameter approaches a finite limiting value H∞ = Γ/3 and therefore ceases to distinguish states, whereas N grows without bound and does not cease to distinguish them — which is precisely why N, rather than the expansion rate, is taken as the carrier of directionality. The falsification condition has been revised: in its previous form it was refuted by any laboratory experiment, since in a closed system the particle number does not grow while time still runs forward; in the picture proposed here the arrow is cosmological and local directionalities are derivative from it. The difference from the "past hypothesis" has also been sharpened: the past state of the model is not special but equilibrium, and in it, since nothing changes, no directionality exists — the arrow is not imposed by a boundary condition but comes into being together with the growth process.