From Eternity to Book Club: Chapter Seven

Welcome to this week’s installment of the From Eternity to Here book club. We next take a look at Chapter Seven, “Running Time Backward.” Now we’re getting serious! (Where “serious” means “fun.”)


The important concept isn’t “time reversal” at all, but the similar-sounding notion of reversibility–our ability to reconstruct the past from the present, as Laplace’s Demon is purportedly able to do, even if it’s more complicated than simply reversing time. And the key concept that ensures reversibility is conservation of information–if the information needed to specify the state of the world is preserved as time passes, we will always be able to run the clock backward and recover any previous state. That’s where the real puzzle concerning the arrow of time will arise.

With this chapter we begin Part Three of the book, which is the most important (and my favorite) of the four parts. Over the course of the next five chapters we’ll be exploring the statistical definition of entropy and its various implications, as well as the puzzles it raises.

But before getting to entropy, and the arrow of time that depends on it, we first have to understand life without an arrow of time. The only reason the Second Law is puzzling is because the rules of fundamental physics don’t exhibit an arrow of time on their own — they’re perfectly reversible. In this chapter we discuss what “reversible” really means, and contrast it with “time reversal invariance,” which is related by not quite the same. If a theory is both reversible and time-translation invariant (same rules at all times), it’s always possible to define time reversal so that your theory is invariant under it. (E.g. in most quantum field theories, “CPT” does the trick.)

Reversibility is a very deep idea; it implies that the state of the universe at any one moment in time is sufficient (along with the laws of physics) to precisely determine the state at any other time, past or future. But not many popular physics books spend much time explaining this idea. So we reach all the way back to very simplified models of discrete systems on a lattice (“checkerboard world”). What we’re after is an understanding of what it really means to have “laws of physics” in the first place — rules that the universe obeys as it evolves through time. That lets us explore different kinds of rules, in particular ones that are and are not reversible.

Along the way we talk about time-reversal invariance in the weak interactions of particle physics, and emphasize how this is not related to the thermodynamic arrow of time that is our concern in this book. Which gives me a good excuse to quote a touching passage from C.S. Wu. This chapter has everything, I tell you.

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22 Responses to From Eternity to Book Club: Chapter Seven

  1. Philoponus says:

    On page 135 you talk about the reversibility of beta-minus decay (and the wanton ways of that notorious drama queen, the free neutron). Excellent! I’m looking at a Feynman diagram of that reaction, and having a Humpty-Dumpty moment: however shall we ever manage to put that neutron back together again? Does this reverse reaction ever actually occur in nature or experimentally, creating a free neutron from a proton, etc? A second question if I may. If we can associate entropy with the neutron as a quark system (udd), does it tell us anything that the weak interaction seem to take us from a low entropy system of 3 confined quarks to much higher entropy system of one udu proton plus escaping high-energy electron plus electron anti-neutrino?

  2. Sean says:

    In principle you could have an electron and anti-neutrino combine with a proton to make a neutron; but in practice you’d never get the energies to exactly match. (It’s just like in principle a cool glass of water can separate into warm water plus an ice cube, but in practice it doesn’t happen.) However, the closely related reactions of having an electron plus a proton turn into a neutron plus a neutrino, or an anti-neutrino plus a proton turning into a neutron plus a positron, happen all the time. Indeed, that’s where most of the neutrons in your body came from.

    I’m not sure about the second question. We go from one particle to three, or (if you want to count individual quarks) from three particles to five. In either case, entropy goes up. Just like it’s supposed to!

  3. Lab Lemming says:

    Has anyone ever looked in an environment with a high density of all those particles?

  4. Sean says:

    The early universe certainly counts, and the success of Big Bang nucleosynthesis is evidence that the theory is well understood. See also electron capture.

  5. Clifford says:

    Can someone quickly give a good example of something that breaks the symmetry for each of the pairs of symmetry: CP, CT and PT? Thanks.

  6. LastAncientGreek says:

    You say

    ” Reversibility is a very deep idea; it implies that the state of the universe at any one moment in time is sufficient (along with the laws of physics) to precisely determine the state at any other time, past or future. …”

    But, isn’t that ‘determinism’ which i thought Quantum Mechanics forces us to abandon because we cannot *fully* measure the state of the universe at any one moment and furthermore, whatever happens next is *not* precisely determinable since it is quantum probabilistic ?

    So isn’t reversibility inconsistent with the ‘facts on the ground’ so to speak ?

  7. Sean says:

    Clifford– I don’t have good examples off the top of my head. Probably simplest to imagine processes that violate each transformation individually (e.g. beta decay violating P) and then combine with the other transformation (e.g. switch particles to antiparticles for C).

    LAG– It is basically determinism, and QM raises questions there, which I discuss in Chapter 11. QM certain violates determinism at an apparent level, but I’ll argue that at a deeper level it does not. The Schrodinger equation, in particular, is perfectly deterministic.

  8. KiwiDamien says:

    Hi Sean and LAG,

    I disagree that reverisibility is essentially the same as determinism. In Sean’s book with the “Checkerboard” rules he gives examples of deterministic evolution (i.e. with knowledge of the present state, you can predict the future state at an arbitrarily *later* time) but the lack of reversibility means that how you evolved to a particular state is ambiguous. You can predict, but not retrodict. If you knew the initial state (if it exists) then it is perfectly consistent in such a world for evolution to be deterministic but irreversible. However that does not seem to be the type of rules that nature has employed.

    As for LAG’s second comment about determinism and quantum mechanics, if we believe that quantum mechanics is the true story (with no collapse) quantum mechanics does not tell us that we cannot fully measure the state of the universe at one time. QM tells us that the state of the universe (or a isolated system) is given by the wavefunction, which we can write down, and this *is* the full information in the state. The issue with “uncertainty relations” is that things that we have been mislead by classical mechanics into thinking as a complete description of the state (e.g. position + momentum for every particle) cannot be well defined — that technically information about different observables is obtained by projecting the *same* state in terms of different bases that do not line up with one another.

    So it may be more useful to say that quantum mechanics fundamentally changes what we mean by “state of the system”, rather than what many popular science books try to do under the guise of uncertainty relations. (Heisenberg’s microscope argument is a particularly blatent offender here.)

  9. Sean says:

    You’re right about reversibility not being the same as determinism, that was sloppiness on my part. Determinism is typically a statement about “the future” being determined, while reversibility is a stronger statement because it works in both directions of time.

  10. Ahmed says:

    Even if we leave the actual act of measurement out of this, it seems rather unfair to use ‘determinism’ to denote the propagation (with certainty) of a probabilistic ensemble. This is inherent uncertainty, not some frequency distribution upon realization. Looking forward to the coming chapter snippets.

  11. KiwiDamien says:

    Hi Ahmed (10),

    As you point out, with measurement left out of the picture the evolution of the wave function is in fact deterministic. If you subscribe to something akin to the Cophenhagen interpretation then what you are saying is correct — I am stating that the evolution of a joint probability distribution is deterministic.

    If you take an Everettian point of view, quantum mechanics really is the whole story and the “uncertainty” and “probability” are put upon you partially by insisting that you can use a classical description — QM tells you about a wave function that is perfectly well described and uncertainty relations only come about by us trying to use classical notations of position and momentum that CM lead us to believe could be simultaneously determined. It is not that QM is “missing” information, it is that CM gave us the wrong impression of what “complete” information would look like.

    The Everett picture tells us that interactions tend to destroy coherence and makes the macroscopic world look like a (very) weakly coupled set of (almost) classical systems. If this is in fact the right way to think about it, QM is in fact a deterministic theory, and the probabilities arise in a manner similar to the way they arose in (classical) stat mech — from our course graining and assigning ourselves to only one of the possible (almost) classical worlds.

  12. OXO says:

    Sean, Is there anywhere I can get a personally signed copy? (I’m in Europe btw)..

  13. Sean says:

    Ahmed– I agree with KiwiDamien. It’s not right to think of the wave function as a “probabilistic ensemble”; it’s simply “the state of the system,” and it evolves deterministically. Probabilities only enter when we make observations, and that’s where the interpretational difficulties lie.

    OXO– I don’t know of any place you can buy a signed copy. If you mail a copy to me with a stamped return envelope, I’m happy to sign it and mail it back.

  14. uncle sam says:

    (Ignore, I sent in twice and can’t cancel comment it seems.)

  15. uncle sam says:

    As I wrote once before, letting time run backward causes weird paradoxes if anything can intervene in the process – but not if something external intervenes in time running forward. For example, someone shoots at a tree and the bullet smacks into it. Now suppose that is running backward and I can intervene “from another universe.” The bullet springs out of the tree, and say I can push something that was nearby into the path of it going back into the barrel. So if the bullet his that obstruction going backwards, it will appear to the people of that world (whatever their experience would be like) to spring from the obstruction rather than the gun. It will be “absurd” in that world, even if (because of still being physically possible) it does not break laws per se.

    Note also that in QM, and per Sean’s previous comment: such a reversed world is not like a Laplacian clockwork that is just running backwards and will reliably continue to do so for deterministic reasons. The wave functions have to behave differently (I don’t think their backwards evolution is quite the same – consider how wave packets of particles are supposed to expand inherently as different velocities. Am I missing something? In any case, a reversed world should be constantly under the threat (in model theory …) of the game screwing up as probabilities eventually fail to cooperate in the “conspiracy” to pretend to support a t-reversed world. IOW, the screen that now photons are being emitted *from* will not continue to have them absorbed on the little spot that is (in the reversed world) the presumptive “emitter” of those photons! See more at my link on QM issues of decoherence etc. that might relate to that. (,sorry it didn’t go thru system OK. )

  16. Ahmed says:

    Hi Damien! See, this is what happens when you start talking about measurement. Which in a way is completely unavoidable because the model is built around it, and ultimately caters to it, but I intentionally avoid all issues of interpretation, paradox, “philosophy” and so on and prefer to let Sean do the hard work of summarizing all these things in his nice blog entries.

    As for the particular issue we are discussing, of course we all accept what the basic model is. There is not much room for disagreement once you do take the wavefunction as the model. I certainly do agree with the Bohr-type view, but I disagree with your saying that it involves things going “missing”. As you know, when things are inherently uncertain, in that the (nature dictates) info cannot exist, that is different from when the info only doesn’t exist. We do not cling to classicism when we are at peace with the notion that the uncertainty is okay.

    I hope there is a mention of Feynman’s “can we simulate physics with computers” paper in the book. It would make for a great blog entry!

  17. Robert Price says:

    You gentlemen will forgive my ignorance in this post. I am a lawyer not a particle physicist; I know you’re all thinking, “Lawyers have never known anything about astrophysics.”

    I have read a little, about Hubble, the laws of thermodynamics and how they don’t appear to apply to the universe, donut shaped universes etc., and these ideas remind me of something I saw as a young boy.

    I live by the sea, and would sit and watch the waves roll in, break, then rapidly spread across the sand as they lost energy (at least rapidly from my perspective). It occurs to me that the universe is just energy, as was the energy in the wave. That sitting on the cusp of the wave we would know nothing of the depths of the ocean or the heights of the sky. We would only know the energy we were part of, and we would also have the perspective that the wave was increasing in velocity as it was affective by other medium, and as it spread and lost energy.

    Is this a completely illfounded idea?

  18. Robert Price says:

    Of course from such possibly errouneous assumptions, it may be thought that time was just another form of energy.

  19. Will says:

    Hi Sean,

    I’ve been following along pretty well so far, but I had a couple questions come up on a couple points. I hope that they don’t seem like ridiculously easy questions, but I think I might have missed an assumption or two along the line.

    1. On p.129 you specifically state that we don’t need to know the acceleration of the ball to predict the next state. But I’m confused as to how you can safely ignore it. Obviously, by knowing the position and momentum, you can predict the next position of the ball. But since acceleration would change velocity and hence momentum, wouldn’t you need to have that to predict the momentum of the ball at the next instant?

    2. On p.132 you described the 4-dimensional space of states for a billiard ball. Then you said that a baseball in 3-space would have a 6-dimensional space of states. I don’t know if I’m counting correctly. Is that 3 for the position, 2 for the direction of momentum, and 1 for the magnitude of momentum? Are there always n-1 dimensions for direction of momentum for n-space? I think I am close to understanding this, but I guess what’s confusing me is that the number of directions of momentum seems to be somewhat arbitrary – it seems like it is possible to use a single dimension to describe that direction even in 3-space (even if it is not very practical). Or you could use two dimensions to describe the direction in 2-space by splitting it into x and y components. What am I missing?

    I’m really enjoying the book and discussion so far, and recommending it to my friends. Thanks!

  20. Sean says:

    Robert– There is certainly energy in the universe, but I don’t think it’s right to say that the universe simply “is” energy. That doesn’t get us very far; we need to be more specific. My book is just one attempt to move in that direction.

    Will– The point is that the laws of physics tell us what the acceleration is, if we know the position and momentum. (a = F/m, in Newtonian language.) We don’t need to specify it independently.

    On momentum, yes that’s right. The rule is simple: there is one dimension of momentum for every one dimension of space, since the particles can move independently in each direction of space.

  21. jeff says:

    Looks like I have a book to buy!
    I just read the article on wired and a lightbulb appeared above my head. I apologise if this is an old or useless idea to those of you who have thought about it all for more than 30 seconds.
    In that article the ‘static’ universe in the multiverse has half-life moments with a decay product of a universe with an arrow of time. Is this like the ‘spin’ property, with antimatter universes having an opposite direction of spin?

  22. Sean says:

    Jeff– It’s not really like that. The original universe has no arrow of time (in most places); the newly-born universe has an arrow when it’s first formed, but it eventually dies out as we approach thermal equilibrium.