There has been a long history in physics of the apparent dichotomy between the tidy mathematics that is used to model the laws of nature and the messy universe that those models are supposed to reflect. One way this dichotomy is manifest is in the problem of irreversibility.

The mathematical laws used to model very large and very small physical systems, like the Sun’s orbit of the galactic center and the collisions between atoms of gas in a container are reversible. That means if I replace the time parameter, t, with its negative, -t, the models run backward, undoing everything they did when t was positive. On a human scale real physical processes proceed in only one way, from past to future.

It turns out that if you watch a galaxy sized system long enough you see that it does not precisely follow the time-symmetrical laws used to model it. The time-symmetrical laws are only approximations to what is really going on. For the box of gas atoms, we can use thermodynamic principles based on statistical analysis to rationalize the irreversibility. See the glossary entry on system states for this approach.

George Ellis has proposed an even more fundamental reason why time is irreversible. Irreversibility is a property of all quantum mechanical systems. Quantum state reduction, whatever the description of the unitary evolution of the system, is itself irreversible.

Think of quantum state reduction as choosing one of the many states whose time evolution is described by Schrödinger's Equation. If this state reduction were reversible we would have to recover Schrödinger's Equation from the single state that was realized sometime in the past. I can easily choose a single card from a deck but cannot reconstruct a deck from a single card. Since quantum mechanics underlies the evolution of large scale systems including chemical and biological as well as mechanical, we should not be surprised to find that on these scales past, present and future are distinguished from one another. See Professor Ellis’ paper, On the Flow of Time for details.