Relation between the psychological and thermodynamic arrows of time
Leonard Mlodinow and Todd A. Brun
Phys. Rev. E 89, 052102 (2014)
Published May 2, 2014
No photos of the future. Since the laws of physics could allow time to run forward or backward, it’s not obvious why time as we perceive it must move in the same direction as that required by thermodynamics (entropy always increases). But theorists propose that a proper definition of “memory” shows why we can’t “remember the future.”
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 . Since erasure always increases entropy , 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.”
The researchers argue that this extra ingredient is something they call generality. They illustrate the argument with a rotating turnstile that records the passage of gas molecules from one chamber to another. The system starts with most of the molecules in the left-hand chamber, and at any instant the rotor reveals the net number that have passed from left to right since some earlier reference time. But since the system follows predictable and reversible Newtonian laws, the readout could also be interpreted as showing the number of molecules that will pass between the time of the reading and some future reference time. One can show that this would be a correct anticipation, since that number can, in principle, be calculated. “Why can’t we call that a memory of the future?” asks Brun.
The reason we cannot is that for the rotor to work as a memory of the past, the system’s state at an earlier reference time need not be precisely specified; any slight changes in the molecules’ positions at that time will not affect the readout at a later time. But equivalent small changes in the state at a future reference time—say, due to some unforeseen influence intervening—lead to inconsistencies.
To see this, recall that the molecules started mostly in the left-hand chamber and are gradually equalizing their numbers on both sides of the rotor. Imagine “running the movie backward” (according to Newtonian equations) from the future reference time to the readout time and seeing the molecules collectively move back toward the left-hand chamber. That extremely improbable event can only occur from one very specific arrangement of the molecules at the future time. If, before running time backward, you made any small changes, say, in the molecules’ positions, new collisions would occur during the time reversal that would rapidly set the system on a completely different course. The molecules would take the much more probable path of equalizing the populations and would not get close to the original state of the system at the readout time.
As Mlodinow and Brun put it, this kind of “future memory” lacks generality—a requirement that the memory accurately reflects the future state of the system regardless of unexpected events. The readout indicates a future state, but only one specific future state. They compare it to a camera that needs a different type of memory card to accommodate each photo. A real memory, they say, cannot be contingent on the system behaving a certain way.
“They have emphasized a very important problem in the meaning-of-time debate and provided an interesting solution,” says Lorenzo Maccone of the University of Pavia in Italy, who has previously considered the origin of the thermodynamic arrow of time in quantum physics .
But he isn’t yet persuaded by the answer, because the researchers allow the memory to track the system only in the “forward” time direction. “It seems to me that they are somehow introducing surreptitiously an arrow of time when they say that the memory tracks the system only in one direction.” But Maccone adds that “in such a difficult field, even highlighting what are the relevant questions to ask is already big progress.”
Philip Ball is a freelance science writer in London and author of Curiosity: How Science Became Interested in Everything (2012).
D. H. Wolpert, “Memory Systems, Computation, and the Second Law of Thermodynamics,” Int. J. Theor. Phys. 31, 743 (1992).
R. Landauer, “Irreversibility and Heat Generation in the Computing Process,” IBM J. Res. Dev. 5, 183 (1961).
Lorenzo Maccone, “Quantum Solution to the Arrow-of-Time Dilemma,” Phys. Rev. Lett. 103, 080401 (2009).
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