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Why can we remember the past but not the future? It might seem like a bizarre question, but it’s not obvious why our psychological “arrow of time” should move in the same direction as that dictated by the second law of thermodynamics, which implies that events unfold in the direction that increases net entropy. A report in Physical Review E suggests that these two arrows of time are forced to coincide by the constraints on what it actually means to remember something.

The fundamental laws of physics are symmetrical in time: in Newtonian classical mechanics time is in principle reversible, and in general relativity it is just a coordinate much like those of space. Given the positions and velocities of a classical system of interacting particles, the past and future can in principle each be completely calculated from the laws of physics. So predictions of the future are just as accurate as descriptions of the past—they are equally “knowable” based on the present.

The existence of an arrow of time is usually explained in terms of the thermodynamic concept of entropy. In systems of many components, it is overwhelmingly more probable that changes will occur in the direction that increases the total entropy of the universe.

How we actually perceive the flow of time is another matter. Theorists have argued that recording information always involves erasing—for example, initializing a computer memory at the start [1]. Since erasure always increases entropy [2], the psychological arrow of time aligns with the thermodynamic one.

But Leonard Mlodinow of the California Institute of Technology in Pasadena and Todd Brun of the University of Southern California in Los Angeles say that this argument is not quite complete. You can, in principle, get rid of any need for erasure and initialization just by remembering everything—which means that recording information in the memory is then fully reversible in time. But even in that case the arrows of time must align because, says Brun, “there is a broader principle at work.”

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