Once Before Time - Martin Bojowald [118]
Why is time so different from space when both together, according to general relativity, constitute space-time and are even partially transformable into each other?
CONCEPTS OF TIME:
MOTION IN RELATION
Does time not have time?
—FRIEDRICH NIETZSCHE, The Gay Science
Time in everyday life bears the deep imprint of its unstoppable (and subjectively nonuniform) progress, clearly distinguishing the past from the future. Crucial here is memory, which makes us recall (and often forget) the past, only in this way showing us the existence of the future: The recent part of the past in our experience is reconstructed as the partial future of our older past. Some events, even unimportant ones, have direct consequences; in the memorized reconstruction, they are given the status of causal relationships. One then expects similar consequences of present events in the future, even if they have not yet happened.
Though common, this concept of time is extremely complex and must be distinguished from mathematical time, which is supposed to describe nature independently of a memory. Time here is like the labeling of a movie’s frames, not a player in the action but a mere mark of the physical happenings in their causal order. Shown are either the positions of bodies in classical physics, or the form of the wave function in quantum theory. Even in general relativity this is the case, although time assumes a more active role and can, for instance, come to an end. Time no longer provides absolute marks due to its transformability with space, but marks depending on an observer; it does, however, still determine which events can make others happen and those where no causal connection is possible.
The mathematical picture of time is useful for concrete investigations, but it is idealized. For such a time is not being observed; what we see are rather changes in matter configurations such as the position of the sun relative to the earth, or the hand of a clock relative to the dial. Clocks of any kind are made from matter, subject to natural laws as well as to influence by other matter. One says that a clock keeps good time if the influence from other objects is small, but weak influence always exists; this is the reason why the picture of time completely independent of matter is idealized. Real physical motion is always relational, just as the swing of a pendulum, for instance, is measured relative to the position of hands on a clock. Only matter is ever observed, never time itself.1 This is especially important in cosmology and its quantum version, as we will soon see. While current conditions on Earth easily allow the construction of useful clocks, there may be regions, in particular in early phases of the universe, where strong interactions between all matter components, including clocks, can never be avoided, for instance owing to high densities. In such cases, one could at best use cosmological quantities themselves, such as the changing volume of the universe or its density, as a measure for time.
Independently of whether in mathematical or physical time, natural laws determine general behavior, while initial values govern special situations. This duality has a direct imprint on mathematical description by differential equations. If, for instance, one provides the positions and velocities of the planets at a fixed initial time, the laws of general relativity determine their whole orbits around the sun and their traverse in the course of time. No difference between past and future exists here: Stopping the motion at some later time, reversing the velocities of the planets, and again using