A direct consequence of the expansion of space?

Abstract

Consider radar ranging of a distant galaxy in a Friedman-Lemaitre cosmological model. In this model the comoving coordinate of the galaxy is constant, hence the equations of null geodesics for photons travelling to the distant galaxy and back imply the following equation: \int_{t_e}^{t_r} dt/a(t) = \int_{t_r}^{t_o} dt/a(t). Here, t_e, t_r and t_o are respectively the times of emission, reflection and observation of the reflected photons, and a(t) is the scale factor. Since the universe is expanding, a(t) is a monotonically increasing function, so the return travel time, t_o - t_r, must be greater than the forward travel time, t_r - t_e. Clearly, space expands, and on their way back, the photons must travel a longer distance! The present paper explains why this argument for the expansion of space is wrong. We argue that, unlike the expansion of the cosmic substratum, the expansion of space is unobservable. We therefore propose to apply to it -- just like to the ether -- Ockham's razor.