I predict a metabolic time bending of body mass evolution in the fossil record. I show that self-replication generates population dynamic feed-back selection for a body mass that increases exponentially on the per generation time-scale of natural selection, and that this increase is driven partly, or fully, by unconstrained selection for an exponential increase in mass specific metabolism. The increase in metabolism contracts natural selection time; but, mass specific metabolism evolves also by a mass-rescaling that generates a partial decline, and time dilation, with an increase in mass. The overall contraction or dilation of natural selection time is bending evolution in physical time, and this is described by an allometry dw/dt = w^x for the rate of evolution in mass (w) in physical time (t). The bending exponent (x) is shown to evolve from the relative importance of metabolism for the evolution of mass, and from the spatial dimensions of interactive competition (1D, 2D, 3D); a prediction that is shown to hold across four scale dependent bending exponents in the fossil record. The exponents are i) 3/2 for 2D and 5/3 for 3D evolution within a niche; as observed for horses over 57 million years of evolution. ii) 5/4 (2D) and 9/8 (3D) for the evolution of maximum mass across niches; as found in four mammalian clades across 30 to 64 million years of evolution. iii) 3/4 (2D) and 5/6 (3D) for fast body mass evolution; found for the maximum mass of trunked, and all terrestrial, mammals. And iv) 1 for 2D and 3D evolution along a metabolic bound, as observed across 3.5 billion years of evolution of the maximum mass in non-sessile organisms.