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
  • John Campion

    I know you are explaining Entropy but what’s your opinion about Free Will? “we can make choices about our upcoming actions but not about our past”

  • T Monroe

    Great post. You’ve clarified a lot for me. Thanks!

  • Jeff Merkey

    I reviewed their analysis and they are correct about the preferred direction of time direction theory and its effects on matter vs. anti-metter, but they are off on the reason. Your position about their research is technically correct, but their assumption is also correct. Time has a preferred direction of flow — forward. Look around you — see reality shifting backwards time ever or have you ever seen something travel backwards in time without a lot of energy to cause it? Well, no. Some things are obvious I would think.

    But you are correct that time can be made to flow backwards, that’s what a nuke does — creates a flow of time and anti-time in both directions, that’s why Plank’s quantum theory of thermal radiation only shows specific bands or quanta of energy being produced from a nuclear blast — the missing bands are travelling in both directions — forward and backward through time — it does not release energy in a 0 to infinity scale which is counter-intuitive to most folks.

    Their assumtion is correct — time has a preferred flow and its forward — reality around us is the proof of that theory and the fact anti-matter has such a punch — its rest energy is greater than matter, but they are flat wrong about supersymmetry — chiral symmetry is not a physical law that is enforced unless chiral forces choose to enfore it, reality is assemmetric in nature, so you are right about that for sure, but their premise is correct based uypon my analysis of their data.


  • Matt

    Sean, could you conceive of a scenario where the arrow of time that matters is due somewhat to T violation (for instance, the fact physics isn’t T invariant somehow conspires to create low entropy Big Bang)? I know the effect is small, but T violation is still an example of physics working one way when time is played in one direction, and a different way in another direction. I could image some wacky scenario where B meson (or Kaon) oscillation pushes entropy in one direction for a long time, then the big bang happens.

    I know this is jargon, any easy answer for why I’m wrong?

  • SpeakerToManagers

    The field theory needs to be local and Lorenz-invariant. But this experiment used quantum-entangled pairs of particles; wouldn’t that require using a non-local field? Or am I confusing two different things?

    • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean Carroll

      Different senses of the word “locality.” QFT is local in the sense that interactions take place between fields at the same space-time point; that’s completely compatible with the “non-locality” of quantum correlations.

  • http://rantingnerd.blogspot.com/ Ranting Nerd

    So this is really a kaon koan?

    <ducks and runs>

  • http://physics.aps.org Daniel Ucko

    Hi, great write-up. Just one small pedantic point, all articles covered by Physics Viewpoints are free to read if you access them from physics.aps.org, so this article is not behind a paywall at all.

  • Chris

    Thanks for the explanation. I read about the CPT theorem as a kid and I always wondered how could they hope to measure T reversal properties without building a time machine. Now I know.

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  • http://gnomonicablog.com Fernando Curiel

    Guilty as charged… A physicist that confused these two things in the past. Thanks again Sean!

  • nate

    Does Noether’s theorem have anything to say about the consequences of T-violations, or the preservation of CPT symmetry?

  • James Gallagher

    Jesus, how many times do I have to explain this, the reason we have an arrow of time is because the universe isn’t friggin deterministic.

    But the violations in this experiment are (ironically) probably from deterministic schrödinger evolution rules at the microscopic scale.

    BUT the microscopic evolution is almost surely seeded by random quantum jumps every ~plank time (10^-43 secs)

    Think about it Sean – a unique probablistic evolution of the universe or zillions of deterministic Many Worlds.

    Really think about it, you have free will after all :-)

  • http://www.flickr.com/photos/sedary_raymaker/ Naked Bunny with a Whip

    So those kaon-enriched eggs I bought won’t scramble themselves? Darn it.

  • Cole

    When I saw the headline of this article, I was so happy to see the author. I read From Eternity to Here and it was fantastic! Excellent explanation!

  • David Lau

    Another excellent post, Sean. I learned a lot from it. T-violation is not the same as time reversibility. Thanks.
    By the way, I am in the middle of reading your new book.

  • dmck

    “Love the B mesons, but they aren’t the reason why we can’t put Humpty Dumpty back together again.” That should be in someone’s fortune cookie!

  • Meh

    This is beyond full comprehension for me, but very informative.

  • martenvandijk

    I am afraid that this is another example of fallacy from not recognizing the difference between exogenous and endogenous processes.

  • Aatish

    Interesting post, Sean. So, now that you’ve got us going, is there an answer to your question “why is the preserved notion of time reversal one that involves what we label C and P as well?”

    And another question. When you say that any unitary, information-conserving theory will have a ‘good symmetry’ related to time reversal, I suppose this must be related to the quantum version of Noether’s theorem. But does this result extend to quantum field theories as well?

    • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean Carroll

      Not sure what the most convincing explanation is for why we need to include CP to get a good time reversal symmetry, except to point to the CPT theorem.

      Noether’s theorem isn’t really involved, as far as I can tell. And the statement should be true in classical mechanics, QM, or QFT. It’s just a statement about trajectories evolving within a space of states.

  • http://quantummoxie.wordpress.com Ian Durham

    I’m not sure I’d say it has absolutely nothing to do with the arrow of time, per sé. I mean, I get your point (I’ve got an on-going project with some quantum information folks on CPT-symmetry so we’ve been dealing directly with this problem). But, it seems to me that, if one were to take the Feynman-Stueckelberg interpretation of anti-particles literally (and that is admittedly a big ‘if’), i.e. that anti-particles are particles moving backward in time, then one could potentially view this result as saying something important about the arrow of macroscopic time. The question, of course, is whether or not we can take that interpretation literally or as merely a convenient way to look at the problem.

    That said, time-reversal symmetry is exactly as you describe it. As my operationalist colleague sees it, time-reversal is, in a sense, merely motion reversal without other distinguishing factors. But even there one potentially gets at the heart of macroscopic time if, as we suspect, it is related to irreversibility. In fact, couldn’t the BaBar results be interpreted as indicating some amount of “stochastic” or “statistical” (i.e. bulk) irreversibility, in which case there could be a relation to the arrow of time?

    • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean Carroll

      I don’t think the BaBar results indicate irreversibility in any sense. If they did, it would amount to an experimental observation of non-unitary evolution (apart from the measurement process), and would be the most important discovery since the invention of quantum mechanics. But in fact this result (as I understand it) is just what the Standard Model predicts, given CP violation in the CKM matrix.

  • http://quantummoxie.wordpress.com Ian Durham

    I don’t mean irreversibility for an isolated process. Clearly it is not and that is what is consistent with CP violation in the Standard Model. But on a bulk level, if you take it as being “directional” in a sense, then you have statistics showing that the process seems to favor one direction over another. To me, that is a kind of “bulk” irreversibility of the kind Eddington talked about when he was discussing the arrow of time.

  • http://dispatchesfromturtleisland.blogspot.com ohwilleke

    BaBar’s results indicate that there is a difference between going forward in time and going backward in time, which is indeed an arrow of time. BaBar’s results don’t actually say which way is forward and which way is backward, but it does show experimentally that physicals laws are not identical going forward and backward in time.

    More deeply, that forward and backward in time are different at a fundamental physical way in a sense that, for example, going east and going west are not. Directions in the three dimensions of space are arbitrary in a way that directions in the one dimension of space are not, even at the very fundamental particle level.

    In other words, a definition of an arrow of time as being uniquely a question of irreversibility, is not the only or best definition of the concept of an “arrow of time.” Irreversibility due to the Second Law of Thermodynamics or any other number of reasons is indeed an arrow of time, but that is not the only kind of arrow of time or even, for all purposes, the most important one.

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  • melior

    I’ve read about time-symmetrical interpretations of QM, such as arxiv.org/abs/1211.4645, which postulate a superposition of forward and backward propagating conjugate wavefunctions to address the measurement problem… does violation of T-symmetry complicate this idea?

  • Harold

    What shall Cosmic Variance give thanks to this year, Sean? The suspense is overwhelming!

    • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean Carroll


  • Joan Vaccaro

    Nice blog Sean.

    “….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…..”

    I agree up to a point. The new work is evidence for a different arrow of time, that’s certainly true. But T violation may well underpin all other arrows. T violation is associated with a time-asymmetric dynamical law (the weak interaction). All the other arrows, including the thermodynamic arrow, are associated with time-symmetric dymanical laws. Their asymmetry arises from time-asymmetric boundary conditions – starting from a low entropy state, for example. I published some work last year on this very topic:
    Found. Phys. 41, 1569-1596 (2011) http://dx.doi.org/10.1007/s10701-011-9568-x (http://arxiv.org/abs/0911.4528)

    The way I like to think of the situation is like this. Imagine a tree loosing its leaves in autumn. The position on the ground where the leaves fall depends on the direction of the wind. If you see the leaves lying on only one side of the tree, you can say which direction the wind was blowing. The pattern of fallen leaves is evidence of the direction of the wind. But this evidence doesn’t make the wind blow in any direction! This is like the thermodynamical arrow – increasing entropy is evidence of the direction of time evolution. But it doesn’t tell you why the universe evolves in one particular direction.

    The T violation work I am doing is really embryonic at this stage. But it does show that T violation can induce large scale effects via interference. T violation may give an explanation of why the universe appears to continue to move in one direction. This is like explaining why the wind blows continuously in one direction.

    So T violation may well underpin the thermodynamic arrow.

  • http://quantummoxie.wordpress.com Ian Durham

    Excellent analogy Joan. That was the point I was trying to make. The BaBar results demonstrate a preference for one process over another. Ergo, if you assume the Feynman-Stueckelberg interpretation of anti-particles is correct, then these results appear to demonstrate a preference for one time direction over another.

    And, in fact, I would think these results fit very nicely with the concept that the macroscopic arrow of time (via entropy and irreversibility) arise from microscopic statistical processes.

  • Bob

    Sean is partly right and partly wrong. He is partly right in that this microscopic process is unitary, and has nothing to do with the thermodynamic arrow of time. The latter is completely well understood from basic statistics with large numbers. He is partly wrong in claiming we need a new theory to understood why the entropy was low at the beginning (big bang); it had to be low, or it wouldn’t be the beginning, now would it?
    So indeed all these things are very well understood but get confused by different groups/people — the SLAC headline of the discovery of the quantum arrow of time totally confuses the issue, and Sean’s claims that the thermodynamic arrow of time is a great mystery also totally confuses the issue.

  • James Gallagher

    Hi Bob

    Sean is correct if Nature is deterministic, since in a deterministic theory we could just reverse all microscopic dynamics and have the entropy decreasing from an initial high-entopy state, then this state would be the past

    eg see http://www.scholarpedia.org/article/Time%27s_arrow_and_Boltzmann%27s_entropy

    However, if the universe is non-deterministic then the only possible global behaviour is increasing entropy or equilibrium at max entropy – except in ultra improbable scenarios (unlikely in exponential googolplexes of universes).

    However, even in this non-deterministic universe we have a low-entropy initial state (otherwise we would just have noise everywhere today) – BUT this low entropy initial state just explains why we haven’t reached heat death yet, IT IS NOT THE REASON EGGS DON’T UNBREAK – eggs can hardly ever ever unbreak anywhere in any universe because Nature is not deterministic, not because the initial state was a low entropy one.

    (local decreases in entropy are of course possible – otherwise life wouldn’t exist)

  • Bob

    James, if you just reversed all microscopic dynamics, then the arrow of time would be reversed relative to the usual one, so we would just perceive that as forwards in time — everything would appear the same. So that is irrelevant to the discussion.

  • James Gallagher


    You know how a backwards entropy human would think? – impressive.

    Well, no, perhaps it’s not impressive, a backwards in time human would no doubt perceive the high entropy state as the past (Which is a big deal, no?)

    However, I don’t believe such a backwards in time human is possible, since I don’t believe the world is deterministic.

  • Bob

    James, the point is the low entropy state is the past and high entropy is the future, even if you reversed the microscopic dynamics. You seem to be very confused about this simple point.

  • James Gallagher

    Oh I see, your reversed entropy humans would still see high entropy as the future.

    er, NO.


    But I’m at least arguing that such a scenario is not possible, so I don’t have to defend my position so much as yours – but frankly, if you believe in determinism – then any way is ok. :–)

  • Valatan

    I think you do get irreversibility in the following sense:

    Let’s say you have a cycle where you start with a particle B and it’s antiparticle B*. You have a cyclical decay process whereby B -> C -> B* -> D -> B and the time reverse of this decay process B* -> C -> B -> D -> B*. You start with B and B* in exact 50/50 equilibrium. If the decay rates are different, however, after time, you will favor either B or B* over the other. You know the arrow of time, so long as you look at time scales less than the period of the longer oscillation.

    How is this any different from ergodic recurrance, other than the fact that we typically can’t measure time scales large enough to see the gas recompress into the left half of the piston? And given the short times in the early universe, couldn’t this have had something to do with picking out the direction of time in the early universe?

  • http://quantummoxie.wordpress.com Ian Durham

    Excellent point, Valatan. Again, it is statistical.


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Cosmic Variance

Random samplings from a universe of ideas.

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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