The phenomenon of time dilation demands the existence of a field that supports the propagation of photons. Historical references identify this field as the luminiferous ether. I will call it the temporal-inertial field (TI field), because I may attribute properties to this field not obtained by classical versions of the luminiferous ether. Time dilation occurs when an ongoing process moves relative to space, relative to this ether, relative to this TI field. The greater the velocity of the process relative to space the greater is the time dilation experienced by that process. The rate at which a process is slowed or accelerated is intrinsic, absolute and depends solely on the velocity of the process relative to space. If space has no properties other than dimensionality, motion relative to that space is undefined and meaningless and can have no influence on any ongoing process moving through that space. Accordingly I assert the existence of the so-called TI field that supports the propagation of photons and occupies and permeates all of space, including the space of atoms. The entire thrust of this paper is that geometry does not govern the physics of time dilation; motion relative to the TI field of space does.