This week, Dr Alastair Wilson introduces a philosophical puzzle arising out of the nature of chance.
We live in a world with a pronounced arrow of time running from the past to the future. Eggs crack but don't uncrack, milk can't be unmixed from coffee, and all living things age and die. Puzzlingly, though, our best physical theories tell us that the fundamental laws of nature are nearly all temporally symmetric. If a fundamental physical process is possible, then an appropriate time-reversal of that process is also generally physically possible*. How can our world of temporally asymmetric processes result from a set of fundamental laws which our best physics says are largely time-symmetric?
One important part of this puzzle concerns objective chance: real probabilities in nature. It seems that events in the future are often chancy in a way that events in the past are not: it may still be a matter of chance what the weather will be like next month, but it's not a matter of chance what it's like right now. We may be uncertain about the present whether, but it isn't objectively probabilistic. How, in particular, does this asymmetry of chance arise?
One bold answer derives from the work of Ludwig Boltzmann (1844-1906). Boltzmann's idea traces the source of the time asymmetry we observe to a very special initial state, which is in a rigorous sense extremely orderly: technically, the initial state has exceptionally low entropy. Since the initial state is assumed to obtain at the beginning of the universe but not at the end, we recover an asymmetry in processes that go on in between.
But Boltzmann's answer can't be the whole story about the temporal asymmetry of chance. The low-entropy initial state is compatible with deterministic theories like classical mechanics, according to which the state of the universe at one time fixes the state of the universe at every time. This wouldn't allow for any temporal asymmetry of chances, on the usual philosophical understanding of chance: the chance of any given event occurring would always be either 1 or 0, and it wouldn't change over time.
*(There is a fascinating exception involving the weak nuclear force, which has recently been experimentally verified by an amazing experiment called BABAR - but that violation of time symmetry isn't able to produce the radical asymmetries we see in the world around us.)
Fellow in Philosophy Birmingham