Book review: The Direction of Time

The Direction of Time
by Hans Reichenbach (1956)

Reichenbach died before writing the final chapter of this book, but the unfinished manuscript was edited and published by his widow, Maria.  The topic is our experience of the flow of time and the asymmetry between past and future.  The mystery, recognized for centuries, is that the laws of mechanics contain no such asymmetry.  They can equally well be run backward as forward.  This has led some philosophers to deny that causality, as opposed to correlation, is a real feature of the world.  However, the identification of causality with temporal succession is not the classical position, but that of Hume.  We pre-modern philosophers thus have little investment in an intrinsic past/future asymmetry, and can watch with disinterested curiosity what physics does to the concept.

As I anticipated, Reichenbach decided to refine his “mark” model of the direction of time by noting the centrality of having some type of process, empirically found to be irreversible, to define the sense of before and after.  The natural place to look would be irreversible thermodynamic processes, and most of the book is dedicated to the theory of entropy.  There are problems, though, with using the entropy of the observable universe as a clock.  First of all, our actual sense of the flow of time is much more local than that.  Second, while it is true that a low entropy state is likely to be followed by a higher entropy state, one can run the laws of mechanics backward to show that it is equally likely to be preceded by a higher entropy state.  For an isolated system evolving from infinity in the past to infinity in the future, one can’t use entropy to define a direction of time.

Nowadays, speculations on the direction of time give a central role to the big bang (or inflation) having somehow left the universe in a low entropy state.  Perhaps because cosmology was less settled at the time, or because he had already decided to leave the universe at large scales out of it, Reichenbach follows a different strategy.  He posits a “branch structure” of the universe.  Systems spend blocks of time relatively isolated from their environment, but the isolation usually only lasts a finite time and terminates with strong interactions with outside beings in both time directions.  I said “both time directions” because the goal is to find a statistical criterion for identifying one as the start and the other the finish.  The direction of the “t” axis in one’s equations is to be regarded as arbitrary.  Interventions tend to leave systems in improbable states (records) from which they generally evolve into more probable configurations in one direction of time (but not the other, because we have assumed that the system is not isolated in that direction, that improbable arrangements are the result of outside intervention, not incredibly improbable fluctuation), and this gives Reichenbach his statistical marker of time direction and causality.  He shows how the same statistical arguments go through for systems with macroscopic components, so long as we introduce some loose form of coarse graining, and information plays a role mathematically identical to that of entropy.

The last chapter considers new features of the problem of time related to quantum mechanics.  Because Reichenbach’s whole model of time direction is statistical, he gives a careful derivation and discussion of Fermi-Dirac (FD) and Bose-Einstein (BE) statistics.  This leads to considerations of genidentity:  in what cases can we identify distinct spacetime events as different stages of an enduring object?  This is of course a restatement of the ancient problem of substances which endure through time and accidental change.  FD and BE statistics are often taken to show that elementary particles are indistinguishable–that it makes no sense to speak of “this electron” or “this photon” because swapping two indistinguishable particles does not result in a distinct configuration.

Reichenbach points out that it’s not quite that simple.  One might ask how we know that swapping two particles does change the system but simply makes no observable difference?  He poses as an example two tossed coins.  If we can distinguish them, there are 4 possible states:  HH, HT, TH, and TT, where “HT” means heads for the first coin and tails for the second, and so forth.  If they are indistinguishable, the middle two are not distinct states, so there are only 3 possible states:  HH, TT, and HT.  Now we let nature decide by measuring the probability of each state.  If the coins are distinguishable and the tosses independent, we would expect probability 1/4 for two heads, 1/4 for two tails, and 1/2 for one of each–Boltzmann statistics, essentially.  If the coins are indistinguishable and the tosses independent, we would get probability 1/3 for two heads, 1/3 for two tails, and 1/3 for one of each–BE statistics, essentially.  Now, nature actually chooses BE (or FD, depending on the particle).  However, Reichenbach points out that we could also drop the assumption of independence, say that coins exert some weird attraction to each other, so that a coin in one state makes it more likely that another one will be present.  (For FD statistics, it would be a repulsion.)  Which description we use he takes to be a matter of choice, another one of his coordinative definitions.  We choose to regard fermions and bosons as indistinguishable because we don’t like the “causal anomalies” of such strangely acting forces.

I agree with this reduction to definition in issues of space and time, as Reichenbach uses it in The Philosophy of Space and Time, because space and time measurements and questions of the geometry and topology of space are intrinsically questions of structure, of the relations of parts of the system to each other, of mathematics.  There is no reason for metaphysics to intrude.  With the question of genidentity, of the endurance of substances through time, we seem to be intruding more into the properly metaphysical realm, and I am less likely to accept the assertion that whether or not beings persist through time can be answered according to our convenience.