Time-Reversal Violation Is Not the "Arrow of Time"

By Sean Carroll | November 20, 2012 10:01 am

Looks like the good folks at the BaBar experiment at SLAC, feeling that my attention has been distracted by the Higgs boson, decided that they might be able to slip a pet peeve of mine past an unsuspecting public without drawing my ire. Not so fast, good folks at BaBar!

They are good folks, actually, and they’ve carried out an extremely impressive bit of experimental virtuosity: obtaining a direct measurement of the asymmetry between a particle-physics process and its time-reverse, thereby establishing very direct evidence that the time-reversal operation “T” is not a good symmetry of nature. Here’s the technical paper, the SLAC press release, and a semi-popular explanation by the APS. (I could link you to the Physical Review Letters journal server rather than the arxiv, but the former is behind a paywall while the latter is free, and they’re the same content, so why would I do that? [Update: the PRL version is available free here, but not from the PRL page directly.])

The reason why it’s an impressive experiment is that it’s very difficult to directly compare the rate of one process to its precise time-reverse. You can measure the lifetime of a muon, for example, as it decays into an electron, a neutrino, and an anti-neutrino. But it’s very difficult (utterly impractical, actually) to shoot a neutrino and an anti-neutrino directly at an electron and measure the probability that it all turns into a muon. So what you want to look at are oscillations: one particle turning into another, which can also convert back. That usually doesn’t happen — electrons can’t convert into positrons because charge is conserved, and they can’t convert into negatively-charged pions because energy and lepton number are conserved, etc. But you can get the trick to work with certain quark-antiquark pairs, like neutral kaons or neutral B mesons, where the particle and its antiparticle can oscillate back and forth into each other. If you can somehow distinguish between the particle and antiparticle, for example if they decay into different things, you can in principle measure the oscillation rates in each direction. If the rates are different, we say that we have measured a violation of T reversal symmetry, or T-violation for short.

As I discuss in From Eternity to Here, this kind of phenomenon has been measured before, for example by the CPLEAR experiment at CERN in 1998. They used kaons and anti-kaons, and watched them decay into different offspring particles. If the BaBar press release is to be believed there is some controversy over whether that was “really” was measuring T-violation. I didn’t know about that, but in any event it’s always good to do a completely independent measurement.

So BaBar looked at B mesons. I won’t go into the details (see the explainer here), but they were able to precisely time the oscillations between one kind of neutral B meson, and the exact reverse of that operation. (Okay, tiny detail: one kind was an eigenstate of CP, the other was an eigenstate of flavor. Happy now?)

They found that T is indeed violated. This is a great result, although it surprises absolutely nobody. There is a famous result called the CPT theorem, which says that whenever you have an ordinary quantum field theory (“ordinary” means “local and Lorentz-invariant”), the combined operations of time-reversal T, parity P, and particle/antiparticle switching C will always be a good symmetry of the theory. And we know that CP is violated in nature; that won the Nobel Prize for Cronin and Fitch in 1980. So T has to be violated, to cancel out the fact that CP is violated and make the combination CPT a good symmetry. Either that, or the universe does not run according to an ordinary quantum field theory, and that would be big news indeed.

All perfectly fine and glorious. The pet peeve only comes up in the sub-headline of the SLAC press release: “Time’s quantum arrow has a preferred direction, new analysis shows.” Colorful language rather than precise statement, to be sure, but colorful language that is extremely misleading.

“Time’s arrow,” in the sense that the phrase is conventionally used (by the kind of folks who would conventionally use such a phrase), refers to the myriad ways in which the past is different from the future in our macroscopic experiential reality. Entropy increases with time; we remember yesterday and not tomorrow; ice cubes melt, and don’t spontaneously generate in warm glasses of water; cream and coffee mix and don’t unmix; we are born young and grow older; we can make choices about our upcoming actions but not about our past. This new measurement in the B meson system — indeed, the entire phenomenon of T violation — has absolutely nothing to do with that arrow of time.

The reason is pretty simple to understand. The arrow of time centers on the concept of irreversibility — things happen in one direction of time but not the other. You can scramble eggs, but not unscramble them, etc. That’s not at all what’s going on in the B mesons. The oscillations between different types of meson happen perfectly well in both directions of time, just with ever-so-slightly different rates. What’s more, there aren’t any B mesons (or kaons) playing a crucial role in what happens when you scramble eggs.

The particle-physics processes in question, in other words, are perfectly reversible. Information is not lost over time; you can figure out exactly what the quantum state used to be by knowing what it is now. (It’s “unitary,” to use the jargon word.) That’s utterly different from the macroscopic arrow of time. Indeed, there’s a sense in which T-violation is simply an accident of nomenclature. We could simply choose to define what we mean by “time reversal” as what most textbooks now define as “CPT.” Then time reversal would be a good symmetry of nature! You can actually prove that any theory that is fundamentally reversible (unitary, information-conserving) will have an operation corresponding to time reversal that is a good symmetry. So the carefully posed physics question is not “why is T violated?”, but “why is the preserved notion of time reversal one that involves what we label C and P as well?”

The reason why this is a peeve worth keeping as a pet is that the confusion between time reversal and the arrow of time often leads smart working physicists to think they have discovered something interesting about the arrow of time when really they’re addressing a completely different problem. We understand why there is an arrow of time: because the early universe started with a low entropy, and generic evolution from such a state leads to an increase in entropy. If you have a theory that explains why the early universe had a low entropy, you have successfully accounted for the observed arrow of time; likewise, if you have a theory that does not explain the low entropy near the Big Bang, you have not successfully accounted for the observed arrow of time. Love the B mesons, but they aren’t the reason why we can’t put Humpty Dumpty back together again.

CATEGORIZED UNDER: arxiv, Science, Time, Top Posts
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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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