Focus: A Quantum Arrow of Time

Published August 17, 2009  |  Phys. Rev. Focus 24, 7 (2009)  |  DOI: 10.1103/PhysRevFocus.24.7
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Entropy with your coffee. No matter how many times you mix milk into your coffee, you will never see them spontaneously unmix, thanks to the relentless increase in the entropy of the Universe. But the fundamental laws of physics have no preference for a direction in time. A theory suggests that entropy-reducing events are possible, but they always erase any evidence of ever having occurred.

The mathematical laws of physics work just as well for events going forward or going backward in time. Yet in the real world, hot coffee never unmixes itself from cold milk. A theorist publishing in the 21 August Physical Review Letters offers a new explanation for this apparent conflict between the time-symmetry of the physical laws and the forward “arrow of time” we see in everyday events. When viewed in quantum terms, events that increase the entropy of the Universe leave records of themselves in their environment. The researcher proposes that events that go “backward,” reducing entropy, cannot leave any trace of having occurred, which is equivalent to not happening.

Thermodynamically speaking, whenever two bodies of unequal temperature are joined together, energy flows between them until the two temperatures equalize. Associated with this heat diffusion is an increase in the quantity known as entropy. As far as we know, heat never spontaneously flows in reverse, and the entropy of the Universe always goes up.

Reversing time’s arrow would be equivalent to lowering entropy, for example if an object at uniform temperature were to spontaneously warm up in one spot and cool elsewhere. In a 19th century thought experiment, a powerful imp called Maxwell’s demon is able to perform such a separation for a gas by knowing the position and speed of every gas molecule in a box with a partition. Using a shutter over a hole in the partition, the demon restricts high-energy molecules to one side and allows the low-energy molecules to collect on the other side. It turns out that the demon would have to expend energy and raise its own entropy, so the Universe’s total entropy would still rise.

In the quantum world, an entropy-lowering demon would have a different chore, because in the quantum mechanical version of entropy, it isn’t heat that flows when entropy changes, it’s information. Lorenzo Maccone of the University of Pavia, Italy, and the Massachusetts Institute of Technology, describes a thought experiment to illustrate the consequences of reducing quantum entropy. An experimenter, Alice, measures the spin state of an atom sent by her friend Bob, who is otherwise isolated from Alice’s laboratory. The atom is in a combined state (superposition) of spin-up and spin-down until Alice measures it as either up or down.

From Alice’s perspective, her lab gains a single bit of information from outside, and it’s then copied and recorded in her memory and on her computer’s hard drive. That information flow from atom to lab increases entropy, according to Alice. Maccone argues that because Bob doesn’t see the result, from his perspective the spin state of the atom never resolves itself into up or down. Instead it becomes quantum mechanically correlated, or “entangled,” with the quantum state of the lab. He sees no information flow and no change in entropy.

Bob plays the role of Maxwell’s demon; he has total control of the quantum state of her lab. To reduce the entropy of the lab from Alice’s point-of-view, Bob reverses the flow of that one bit of information by removing any record of the atom’s spin from Alice’s hard drive and her brain. He does so by performing a complicated transformation that disentangles the lab’s quantum state from that of the atom.

Maccone writes that such a reversal violates no laws of quantum physics. In fact, from Bob’s perspective, the quantum information of the atom plus Alice’s lab is the same whether or not the two are entangled–there is no change in entropy as viewed from the outside. Such reversals could happen in real life, Maccone says, but because the Universe–like Alice–would retain no memory of them, they would have no effect on how we perceive the world. His paper goes on to show mathematically how this reasoning applies in general, with the Universe taking the place of Alice.

Jos Uffink of Utrecht University in the Netherlands accepts some aspects of the work but is not completely convinced. “The observer might very well retain a partial memory of the event,” after the entropy-reducing process, he says. Still, he calls the approach of the paper “quite novel” and its conclusions “startling.” He says a vigorous debate continues about the relationship between information as an objective, physical quantity and the apparent “irreversibility” of so many events in the world around us.

–JR Minkel


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New in Physics