This observation seems to me to provide a clue towards the solution of Smart's puzzle, for whatever the exact analysis of the concept of trace, some causal element must be involved-if feature f is a trace of events e, then the occurrence of e must be a cause of the appearance of f. It seems to me that Smart must admit this much, for otherwise his puzzle disappears. Consider, for example, an inscription which records the correct prediction of the position of Mars at some future time. If we do not want to call this inscription a trace of the future (and neither Smart nor I do) it seems to me it must be because we believe that the future position of Mars does not have any causal influence on the production of the inscription. But once this much is admitted, the pieces of the puzzle fall into place. For, first of all, it follows that if there could be backward (i.e. future to past) causation of a certain type, then there could be traces of the future. I believe that backward causation is a conceptual possibility and that the question of whether backward causation exists in nature is a question which must be settled not by armchair philosophers but by natural philosophers. A possible mechanism for backward causation is contained in the Dirac-Plass theory of classical relativistic electrodynamics. According to this theory, an impulsive force causes (I believe that 'causes' is the right word) a particle to accelerate before the pulse arrives. For an electron, the preacceleration effect is on the order of 10-23 seconds, and, therefore, it is unlikely that it could be detected by any classical apparatus; so even if it exists in nature, preacceleration may not give rise to any recognizable future analogues of traces. But still the point remains that a coherent mechanism for the production of traces of the future is at hand.

A second point which follows is that, contrary to Smart, the asymmetries of traces with respect to past and future may well lie in the laws of physics even if these laws are invariant under time reversal. Time reversal invariance of a law does mean in a sense that the law is symmetric with respect to past and future, but the relevant sense has to be carefully specified. In particular, the time reversal invariance of a theory T does not mean that T allows forward causation if and only if it allows backward causation. I have argued elsewhere, that there is a well-defined sense in which Newton's laws of motion with certain force functions, though invariant under time reversal, allow forward but not backward causation in the sense that past states affect future states but not vice versa. If true, something along this line would be sufficient to account for the asymmetry of traces with respect to past and future.