Two spaceships, A and B, are in motion relative to each other. Their motion relative to the empty space they are in is undefined and undefinable. We can consider ship A to be stationary relative to space and ship B to be moving or vice versa. The two situations are entirely equivalent. Each ship’s motion relative to the other is symmetric. Relative to a clock in either ship, an identical clock in the other ship appears to tick more slowly. This reciprocity paradox, also termed the twin paradox, is unresolvable in a geometric analysis. The history of which ship accelerated to produce their velocity difference is irrelevant and offers no solution to the paradox. If the two ships are brought together, motionless relative to each other, their clocks will tick at the same rate and neither clock will have lost time relative to the other. The symmetry of their motion relative to each other is inviolable. Both clocks cannot tick more slowly than their counterparts. Therefore, neither clock can tick more slowly than the other. The reciprocity paradox is an illusion. The motion between two reference frames in a space without properties that yields the inviolable symmetry of the reciprocity paradox tells us that geometric relationships cannot govern the physics of time dilation. The motion that violates this symmetry must be motion relative to a space with properties. This space must contain something that can be used to reckon motion. This something is a field that supports the propagation of photons and other force particles. This field is identified as the temporal-inertial (TI) field.