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








“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.

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40 Responses to Time-Reversal Violation Is Not the "Arrow of Time"

  1. John Campion says:

    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”

  2. T Monroe says:

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

  3. Jeff Merkey says:

    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.


  4. Matt says:

    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?

  5. Sean Carroll says:

    Matt– It’s not a matter of the size of the effect. Particle physics, no matter how big T violation is, is completely reversible (unitary). The arrow of time is all about irreversibility.

    John– See here:


  6. SpeakerToManagers says:

    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?

  7. Sean Carroll says:

    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.

  8. Ranting Nerd says:

    So this is really a kaon koan?

    <ducks and runs>

  9. Daniel Ucko says:

    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.

  10. Chris says:

    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.

  11. Pingback: ☆ First Evidence for an Arrow of Time – or not? « Mostly physics

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

  13. nate says:

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

  14. James Gallagher says:

    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 :-)

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

  16. Cole says:

    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!

  17. David Lau says:

    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.

  18. dmck says:

    “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!

  19. Meh says:

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

  20. martenvandijk says:

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

  21. Aatish says:

    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?

  22. Sean Carroll says:

    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.

  23. Ian Durham says:

    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?

  24. Sean Carroll says:

    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.

  25. Ian Durham says:

    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.

  26. ohwilleke says:

    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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  28. melior says:

    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?

  29. Harold says:

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

  30. Joan Vaccaro says:

    Nice blog Sean.


    Found. Phys. 41, 1569-1596 (2011) http://dx.doi.org/10.1007/s10701-011-9568-x (http://arxiv.org/abs/0911.4528)



    So T violation may well underpin the thermodynamic arrow.

  31. Ian Durham says:



  32. Bob says:


  33. James Gallagher says:

    Hi Bob


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




  34. Bob says:


  35. James Gallagher says:





  36. Bob says:


  37. James Gallagher says:


    er, NO.



  38. Valatan says:

    I think you do get irreversibility in the following sense:



  39. Ian Durham says:

    Excellent point, Valatan. Again, it is statistical.