The flow of emails within the block inbox

As a diversion from the important topics of shaming, anti-shaming, and anti-anti-shaming, I thought I’d share a little email exchange (with my interlocutor’s kind permission), which gives a good example of what I find myself doing all day when I’m not blogging, changing diapers, or thinking about possibly doing some real work (but where did all the time go?).

Dear Professor Aaronson,

I would be very pleased to know your opinion about time.  In a letter of condolence to the Besso family, Albert Einstein wrote: “Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.” I’m a medical doctor and everyday I see time’s effect over human bodies. Is Einstein saying time is an illusion?  For who ‘believe in physics’ is death an illusion?  Don’t we lose our dears and will they continue to live in an ‘eternal world’?

Is time only human perceptive illusion (as some scientists say physics has proved)?

Dear [redacted],

I don’t read Einstein in that famous quote as saying that time itself is an illusion, but rather, that the sense of time flowing from past to present to future is an illusion. He meant, for example, that the differential equations of physics can just as easily be run backward (from future to past) as forward (from past to future), and that studying physics can strongly encourage a perspective—which philosophers call the “block universe” perspective—where you treat the entire history of spacetime as just a fixed, 4-dimensional manifold, with time simply another dimension in addition to the three spatial ones (admittedly, a dimension that the laws of physics treat somewhat differently than the other three). And yes, relativity encourages this perspective, by showing that different observers, moving at different speeds relative to each other, will divide up the 4-dimensional manifold into time slices in different ways, with two events judged to be simultaneous by one observer judged to be happening at different times by another.

But even after Einstein is read this way, I’d personally respond: well, that’s just one perspective you can take. A perfectly understandable one, if you’re Einstein, and especially if you’re Einstein trying to comfort the bereaved. But still: would you want to say, for example, that because physics treats the table in front of you as just a collection of elementary particles held together by forces, therefore the table, as such, doesn’t “exist”? That seems overwrought. Physics deepens your understanding of the table, of course—showing you what its microscopic constituents are and why they hold themselves together—but the table still “exists.”  In much the same way, physics enormously deepened our understanding of what we mean by the “flow of time”—showing how the “flow” emerges from the time-symmetric equations of physics, combined with the time-asymmetric phenomena of thermodynamics, which increase the universe’s entropy as we move away from the Big Bang, and thereby allow for the creation of memories, records, and other irreversible effects (a part of the story that I didn’t even get into here). But it feels overwrought to say that, because physics gives us a perspective from which we can see the “flow of time” as emerging from something deeper, therefore the “flow” doesn’t exist, or is just an illusion.

Hope that helps!


(followup question)

Dear Professor,

I’ve been thinking about the “block universe” and it seems to me that in it past, present and future all coexist.  So on the basis of Einstein’s theory, do all exist eternally, and why do we perceive only the present?


But you don’t perceive only the present!  In the past, you perceived what’s now the past (and which you now remember), and in the future, you’ll perceive what’s now the future (and which you now look forward to), right?  And as for why the present is the present, and not some other point in time?  Well, that strikes me as one of those questions like why you’re you, out of all the possible people who you could have been instead, or why, assuming there are billions of habitable planets, you find yourself on earth and not on any of the other planets.  Maybe the best answer is that you had to be someone, living somewhere, at some particular point in time when you asked this question—and you could’ve wondered the same thing regardless of what the answer had turned out to be.

98 Responses to “The flow of emails within the block inbox”

  1. quax Says:

    Always loved Julian Barbour’s book End of Time. Beautifully written.

    Boils down to taking the a Wheeler–DeWitt equation at its word that time really drops out.

    Incidentally a timeless shape space is the only multiverse theory I can stomach. If you strip time out and view it as an emergent connection, then the whole thing no longer feels too big and arbitrary.

  2. matt Says:

    I think Buckaroo Banzai said it best: “no matter where you go, there you are.”

  3. Observer Says:

    I would have just supplied a link to Wikipedia, such as to B-theory of time.

  4. Alex Says:

    You know, every time I hear one of these anecdotes or quotes, I always sort of end up liking Einstein little bit more.

  5. Rahul Says:

    Naive question: For a long time the laws of Physics seemed to be left-right symmetric. Until they were found to be not so in certain very specific cases- the overthrow of parity.

    Is a similar situation possible with the Time-symmetry of the laws of physics? Or have we reason to believe we won’t find such laws?

  6. Shmi Nux Says:

    When you imagine a block universe compatible with QM, do you see it as a single slab of spacetime or as a tree of Many Worlds with a clear direction “up” into the future, where there are more branches than in the past? Or as something else? (I’m asking about your mental picture, not about any kind of underlying physical reality.)

  7. David Says:

    “So on the basis of Einstein’s theory, do all exist eternally, and why do we perceive only the present?”

    This thought often comes up when philosophy of time is being taught, but it doesn’t really make sense as an interpretation of the block universe picture. The most natural interpretation of existing “eternally” according to the block universe picture is to exist within every single time. Existing eternally would be like occupying every spatial location at a single time.

    And of course, people who believe in the block universe do not believe that every object is located at every time any more than they believe that every object is located at every place. I, for example, was never located anywhere 200 years ago and hence do not exist eternally.

    At every time it will still be true that I exist at some time, just as at every place it is true that I exist at some place. But that is a different matter from existing eternally or existing everywhere.

  8. James Gallagher Says:

    This discussion among philosophers and other smart people usually assumes a deterministic universe.

    But we can note, that if there are random jumps in nature, then there is no time symmetry.

    The present moment is the only thing that exists (ie the last thing that (just) happened in the universe), the past has already happened and can only be derived from recorded information in the present moment , and the future is yet to happen, and is fundamentally random, so no god even can know what the future is.

  9. NKV Says:

    I always used to think that entropy increases with a high probability measure. But I did not know that the measure was actually 1.

  10. Audun Says:

    Rahul #5:

    I believe we already know of processes in particle physics which break time-reversal symmetry.

    At least, we know that they break CP symmetry, e.g. switching all charges and flipping space doesn’t give the same result. We also know that CPT symmetry (combining CP with time-reversal) must hold for the laws to be Lorentz invariant. So, for CP to be broken and CPT to hold, T must be broken.

  11. Audun Says:

    Also, I should link to Sean Carroll explaining that certain processes breaking time-reversal symmetry does not explain the arrow of time.

  12. Job Says:

    Don’t worry about time, it passes. 🙂

    I’ve read in your QCSD notes that a gate set consisting exclusively of the Hadamard and CNOT can be efficiently simulated by a classical machine.

    Without a Toffoli or rotation gates we don’t have a universal gate set. On the other hand, a naive implementation of a Toffoli using one NOT and two CNOTs will produce the right output 75% of the time.

    I imagine that the 25% error will go down with n for n-bit Toffoli gates (with n control bits).

    If that’s the case (and i’m not sure that it is) then does it mean that we can efficiently simulate any Quantum Circuit – with additional bounded error and polynomial overhead – as long as the circuit can be redesigned to use n-bit Toffoli gates, for some value of n?

  13. Ariel Says:


    The QM universe is deterministic, and so is the GR universe.


    Entropy is a property of the distribution, not of an event. It does not increase “with a measure”.

  14. Joshua Zelinsky Says:

    Is this an implicit statement that you won’t mind if I send you via email all the questions I was saving for your end of semester bug-Scott-about-stuff event that didn’t happen?

  15. fred Says:

    I recommend the short novel “Einstein’s dreams”
    each chapter describes a world with a different interpretation of time.

  16. James Gallagher Says:

    Ariel #13

    Many physcists would say that the Schrodinger equation is the only fundamentally deterministic law in Physics.

    But since it’s just a mathematical model of how “probability” evolves I think you can’t say “The QM universe is deterministic”

    In any case, my model is so much more beautiful and poetically inspiring

  17. Scott Says:

    Joshua #14: Here’s an idea—why don’t you come over to MIT and ask me your questions in person? That way we get to discuss them, and I won’t feel like they’re hanging over my head sitting in my inbox. Write to me to set up a time.

  18. Joshua Zelinsky Says:


    I would do that but I’m no longer in Boston! I finished by PhD at BU and I’m post-docing at UMaine. If you want though I can let you know the next time I’m back in Cambridge.

  19. Scott Says:

    Joshua #18: Ah. Then email me your questions. I can’t promise how quickly I’ll get to them, but your questions are always interesting so they’ll surely tempt me.

  20. Shaquille Says:

    While reading the background to your blog debate about Bell’s Theorem a few years ago I remember coming across a paper of Richard Gill (I hope I’m not misremembering and confusing him with Joy Christian, or else what follows could be nonsense) arguing for a model of quantum mechanics in which operators are tweaked to force an “arrow of time” so the past is deterministic and the future is intrinsically stochastic. Instead of rejecting locality he interprets Bell’s Theorem experiments as evidence to reject counterfactual realism, meaning the existence (somewhere in the universe, not sure where) of outcomes that would have happened under other experimental conditions. I’d be interested to know if Shor’s algorithm still works if this is what’s going on under the quantum hood.

  21. Shaquille Says:

    Scott, did you ever weigh in on the relatively recent Wired article that said the de Broglie-Bohm deterministic pilot-wave interpretation of QM may be correct, based on experiments your MIT colleagues have done showing wave particle duality in macroscopic fluid droplets? P = BQP!

  22. Rahul Says:

    Audun #10:

    “I believe we already know of processes in particle physics which break time-reversal symmetry.”


    If so, does that mean that what Scott wrote in his post is not strictly true any more?

    “the differential equations of physics can just as easily be run backward (from future to past) as forward (from past to future)”

    If T-symmetry is already broken we do know at least some cases where backward vs forward leads to different results?

  23. Scott Says:

    Shaquille #21: Yes, I commented on that “oil-drop” stuff in various comment threads when people asked me about it; see for example here. I’d say the same thing about it that I’d say about any other “classical model for what’s under the quantum hood,” including the other thing you asked about:

    (1) If people interpret it as a sort of visualization tool, or the way Bohm originally presented Bohmian mechanics—i.e., yes, the predictions quantum mechanics in every experiment will be perfectly upheld, but we can add some structure onto the gargantuan wavefunction evolving unitarily in Hilbert space (e.g., the “actual” particle positions) that might make us happier about it—then that’s fine (or rather: is an aesthetic choice, to be supported or criticized on aesthetic grounds), and is obviously no challenge to quantum computation.

    (2) If, on the other hand, people make a more aggressive claim for their model—that it proves that “entanglement is an illusion,” and that reality is actually classical (in the usual sense of “classical”) at the lowest level, leading to different predictions—then forget about quantum computing, I demand to know how you explain the violation of the Bell inequality, and a hundred other already-observed quantum phenomena! And no classical proposal I’ve ever seen comes anywhere close to meeting that demand, to the extent it tries to address it head-on at all.

  24. Scott Says:

    Rahul #22: Yes, when you reverse the differential equations of physics (so that they run backward in time), you also need to remember to swap left with right, and particles with antiparticles. Once you do that, everything works perfectly.

    Keep in mind that this “CP violation” in quantum field theory (as it’s called) doesn’t differentiate the past from the future in any serious way (since we could always agree to call left right and right left, call particles antiparticles and vice versa, and get on with it!) The arrow of time that we care about—eggs getting scrambled but not unscrambled, reliable memories and records getting produced, etc.—has nothing whatsoever to do with CP violation, and everything to do with the Second Law of Thermodynamics, and with the universe’s low entropy at the Big Bang.

  25. Rahul Says:


    Given that we had the 2nd Law, why do we still say that “the differential equations of physics can just as easily be run backward (from future to past) as forward (from past to future)”

    Doesn’t the 2nd law make it a lot harder (rarer) for the equations to be run in one direction than the other.

    i.e. Did we have to wait for a CP violation to declare the overthrow of T-symmetry or was T-symmetry already overthrown the moment we accepted the 2nd Law?

  26. Scott Says:

    Rahul #25: The differential equations of physics don’t distinguish between the two directions of time; they can be “run either way.” That was true for Isaac Newton, and it’s just as true in modern quantum field theory, with the one technical complication that when we reverse time, we also need to reverse left with right and particles with antiparticles. (What I wrote in the OP is still completely valid: you can still “run the equations backward”; it’s just that doing so involves not only replacing t with -t, but making two other replacements. The important point is that no information gets created or destroyed as the equations are run—and moreover, the equations have exactly the same mathematical form when run backwards as when run forwards.)

    However, modeling the physical world requires not only differential equations, but also boundary conditions. And the initial boundary condition of our world—the Big Bang—was incredibly “special” and “non-generic,” with a tiny entropy (especially, tiny gravitational entropy). To this day, cosmologists avidly debate the explanation for the low entropy of the initial state, but the fact of it is undisputed.

    Now, the great insight of classical thermodynamics, in the 19th century, was that perfectly-reversible equations of physics, when combined with a special boundary condition, can give the appearance of irreversibility: everything will look more and more “scrambled” the further you move from the boundary condition, but that’s not because the laws have any intrinsic direction to them, it’s just because the boundary condition was special. And moreover, not only can this happen, but as far as modern physics can tell, it is the ultimate explanation for all phenomena in our world that appear to be irreversible (eggs getting scrambled but not unscrambled, quantum states getting measured but not unmeasured, etc). This has been physics’ story about “the direction of time” since Boltzmann: CP asymmetry has nothing to do with it, and even quantum mechanics and the Big Bang are in some sense just minor elaborations on it.

  27. Avi Says:

    >Well, that strikes me as one of those questions like why you’re you, out of all the possible people who you could have been instead, or why, assuming there are billions of habitable planets, you find yourself on earth and not on any of the other planets. Maybe the best answer is that you had to be someone, living somewhere, at some particular point in time when you asked this question—and you could’ve wondered the same thing regardless of what the answer had turned out to be.

    I tend to find this answer unsatisfying. Imagine I ask you why the sky is blue, and you told me “well, if it would be green then you’d ask why it was green. It had to be some color, after all.”

    Anthropic questions deserve real answers, or at least theories.

    Just to give one example of a real theory that’s been proposed for why we’re in this time as opposed to another: If we’re in a simulation, and the simulators want to know how Singularities tend to go, then it’s more likely for them to simulate societies closer to Singularities than other people.

    I personally think this has an extremely low prior probability, but it’s at least the kind of thinking likely to produce correct answers.

    And I know you’ve discussed anthropics in the past, so I’m a little confused on why you’d make a comment that seems to completely dismiss it.

  28. AdamT Says:

    Hi Scott,

    In your response you suggest it goes too far to say the table doesn’t exist. Maybe you will be surprised to hear that Buddhism offers a very deep analysis of the precise way in which it can be said that the table exists and the precise way in which it can be said it does not exist. The same is true for all phenomenon including time.

    The interesting thing is that Buddhism claims that our everyday intuitive ideas about the manner in which tables and time exist is utterly wrong. In some respects it is much the same story that physics gives. What is truly astonishing is that Buddhism claims that it is precisely this wrong everyday intuition that all of us share about the way that phenomena exist is the very root of all the suffering we experience in life. Thus it says that the study of how things truly exist is an imperative moral matter.


  29. Rahul Says:


    Thanks. Understood.

    PS. What about Loschmidt’s Paradox? Doesn’t that essentially say that you cannot get irreversibility from a underlying time-symmetric law?

    Does modern physics have a good way around that? Or is that also a boundary condition symptom?

  30. Scott Says:

    Avi #27: Thanks for correcting that omission. I don’t think we actually disagree much! Yes, I’d say, you should feel free to seek explanations even for facts that seem “anthropic” or “indexical,” as you should feel free to seek explanations for everything. And you should be much happier to have an explanation for an indexical fact than not to have one.

    But you should also realize that, if a certain fact is “true for you right now,” but not true for other people or at other times, that likely puts fundamental limits on how satisfying any explanation for the fact can ever be. For the whole nature of explanations is that they aspire to universality—that any valid reasoner, at any time, can be persuaded by them. How deep could an explanation possibly be for why you “ought to” find yourself living in March 2015, if the explanandum will be obsolete in a month? At most, we could try to say why it’s not unreasonable for you to be alive in March 2015—either by

    (a) pointing to statistical phenomena like the record-breaking human population right now (which, of course, would quickly land us in debates over the Doomsday Argument); or

    (b) speculating (as you did) that we’re all in a computer simulation, and the simulators are particularly interested in simulating March 2015 or thereabouts (really? they are? when did they start this simulation? are you willing to bite the bullet and say that Plato never existed, maybe even that WWII never happened?); or

    (c) throwing up our hands and pointing out that you had to be alive sometime, and other people who were (or will be) alive at other times could ask the same question.

    I wasn’t claiming to know that (c) is the only valid answer, just that I don’t see any way to rule out that it is—i.e., that we seem to be in the same position here as we are with countless other “anthropic mysteries.”

  31. Scott Says:

    AdamT #28: Thanks! The Buddhist view of suffering, as you articulated it in that comment, is clear, interesting, and something that I rebel against on a deep level. If, let’s say, my best friend dies in a drunk driving accident right after leaving my house, I’ll probably experience great suffering, but it seems bizarre to say the “very root” of my suffering is the false intuition that my friend was a first-class entity in the physical universe, rather than an evanescent pattern of quantum fields. I know my friend was an evanescent pattern of quantum fields! But the root of my suffering is still that I let him get in the car.

  32. Scott Says:

    Rahul #29: Loschmidt’s Paradox, as I understand it, is simply the correct observation that you can’t “derive” the Second Law of Thermodynamics from time-symmetric laws of physics, if you don’t assume anything (either implicitly or explicitly) about the low-entropy boundary conditions in our past.

  33. RN Says:

    Sorry, if this question is only vaguely on-topic, but I’ve wondered this for a while: Can the Second Law of Thermodynamics be explained in terms of quantum mechanics, perhaps as a result of increasing entanglement?

  34. anon Says:

    for sure Einstein was referring to the block universe. So, I do not understand why you mention the T-invariance in mechanics.
    BTW, I started reading your QC since Democritus. Nice book although you sense of humour is too “american” for my taste.
    The first philosophical/set theory chapters should be reworked (in my own opinion) also in the notation.
    Also your “dream” that th. computer science can say something about physical reality is..well…a dream. The idea that also in the remote past somebody could have discovered QM just modifying prob. theory (2-norm) is a contorted argument. You can discover everythinng in math, eg quantum field theory, but what are the real fields in nature? Physics will never be replaced nor even helped by math/cs arguments.
    When you start with complexity theory chapters, I really appreciate your deep understanding of the subject: they are really great. Overall, I like the book (a lot): it is something it was missing in the literature. All said from the perspective of an HEP physicist.

  35. Scott Says:

    RN #33:

      Can the Second Law of Thermodynamics be explained in terms of quantum mechanics, perhaps as a result of increasing entanglement?

    No, because that “answer” just pushes the question back to “OK then, why is entanglement increasing”? And the answer is, for the same reason for every other manifestation of the Second Law (increasing entanglement is just one of them), the same reason Boltzmann identified in the 19th century: the low entropy of our universe’s initial state. I don’t see any way to avoid talking about that.

  36. Job Says:

    Physics will never be replaced nor even helped by math/cs arguments.

    I agree, for example a result that BQP = NP wouldn’t help Quantum Physics at all.

  37. Scott Says:

    Job #36: You could hardly have picked a worse example to make that argument. A proof of BQP=NP would mean, among other things, that we could build quantum computers to efficiently solve NP-complete problems for us—something that would have a huge impact on physics (like on everything else)—and also that given any quantum system, there would be a short classical proof for what its behavior was, a proof that moreover, by again exploiting the hypothesized equality, we could use a quantum computer to find efficiently. (BQP=NP would also mean that NP=coNP and that the polynomial hierarchy would collapse, but fine, that’s not a direct implication for quantum physics.)

  38. James Gallagher Says:

    The Second Law of Thermodynamics famously works in a deterministic universe, as long as you have an initial condition with low entropy (Boltzmann brilliantly derived this, with his H-theorem, but didn’t get the importance of the initial condition requirement, and quite a few people still don’t 😉 )

    But the 2nd Law works even better if the evolution is stochastically seeded – then Loschmidt’s paradox is irrelevant, since we have natural “molecular chaos”.

    We still need a low entropy initial universe state though, because otherwise everything would already be noise.

    But, importantly, this initial low entropy is irrelevant to explaining why eggs don’t unbreak

  39. Job Says:

    Scott, if BQP = NP then something in Physics would need to change, that’s my point.

    Are you saying that if it were shown that BQP = NP you wouldn’t be the slightest bit skeptical of the viability of QCs, with severe implications for QM in general?

  40. Scott Says:

    Job #39: In general, I dislike thought experiments where I’m asked to estimate P(A|B), where A and B are both bizarre hypotheticals (from my perspective). For in these scenarios, it’s always imagined that B is dropped on us like a divine command; we’ve never told why B is true, or what other surprising discoveries made it possible for B to be true. So it’s hard to judge. In general, I’d say that a proof of BQP=NP (in fact, of either direction: NP⊆BQP or to a lesser extent, BQP⊆NP) would make me want to reexamine my entire previous set of views about physics and computation, including about the viability of QC. But I don’t know what the outcome would be.

  41. Job Says:

    Well ok, that’s a fair and conservative position that should be shared by HEP physicists.

  42. anon Says:

    If QCs could solve NP-complete problems, this would be a world-changing result. I agree. But there was not a paper (by Seth Lloyd maybe ?) saying that only the introduction of an (even infinitesimally small) non-linearity in QM would result in solving np-complete problems? Since QM is linear, QM or QCs cannot solve NPcomplete problems an that’s it. Or not? As said, I’m not a complexity theorist…

  43. Ajit R. Jadhav Says:

    Scott #26 nailed it more or less perfectly, even though, I think, a deeper—epistemologically guided—explanation should be possible. … Let me give it a try.

    The mathematics of motion is abstract enough for it to allow us to go along both +ve and -ve time directions. Both the choices are mathematically consistent. But only one choice is consistent with its physical context, i.e., with the actual observations of the actual physical world—the physical world runs along the +ve time direction.

    A simpler example: I have $5 in all with me, and I give you $10. How much money do I then have? The arithmetic with the negative numbers is general enough to allow you to directly model this situation in a quantitative manner. No questions asked, such as, what is the meaning of the terms like “give,” “money,” “then,” and “have”. By way of supplying a physical meaning, however, you have to say: I give you all the money I have, and on top of that, I also give you a promise to give you some more money. The amount of money I promise to give you is, $5. [Even simpler examples should be possible; I just thought of this one on the fly.]

    The reason why, in reality, going -ve 5 units in space does make sense but not in time is that space—all of it—can be easily taken to physically exist at the same time (and by implication, this happens at all times), but all of time cannot be taken to physicall exist quite in the same sense at any point in space.

    In the physical thought, you can more easily take all of space to exist at the same time. You can directly perceive widths. All the world is a stage, the Old Bard said famously.

    But you cannot similarly directly perceive all of the time “at the same time.” [Isn’t there a contradiction already?]

    You become conscious of reality in such a way that it takes more than one most basic units of perception when two billiard balls come closer, collide, and fly apart. Three perceptual units (at least), to perceive this physical process.

    But, in contrast, think of the billiard balls table. One perceptual unit.

    Now, of course, the lengths/extents contained in the latter perceptual field (of the entire table) can be sub-divided into three (or more) units.

    What the usual mathematical abstraction for the collision process does is, it models the widths (i.e. space) via a continuum, and then, it also models the two instances of the directly perceived durations occurring between the three directly perceived instances of time, via another continuum.

    The time continuum is a more indirect concept. It is modeled via an analogy to space.

    The mathematics of motion comes after implicitly counting on the latter analogy. It is one of the contexts to the quantitative study of motion. By context, space and time are not on the same footing.

    That’s what I think about it, as of now! … For instance, think: Suppose someone is able to directly perceive all the time at the same time? Not via a process of abstraction and using mathematics, but directly? … Its epistemology will be different. … But at least I cannot conceive of what it would be like.

    Incidentally, fundamentally modeling aging as motion is… I don’t know what’s the word here… Far too simplistic? Even, rationalistic?

    Enough is enough.


  44. Scott Says:

    anon #42:

      the introduction of an (even infinitesimally small) non-linearity in QM would result in solving np-complete problems? Since QM is linear, QM or QCs cannot solve NPcomplete problems an that’s it. Or not? As said, I’m not a complexity theorist…

    You might not be a complexity theorist, but hopefully you can understand that “A implies B” is not the same thing as “not(A) implies not(B)”? 😉

  45. fred Says:

    James #38

    “But, importantly, this initial low entropy is irrelevant to explaining why eggs don’t unbreak”

    Well, eggs do unbreak!
    Unless I’m mistaken, there’s nothing more to entropy than the following example:
    Take two dices. Throw them each.
    Possible states and their sum:
    1 – 1 : 2
    1 – 2 : 3
    1 – 3 : 4
    1 – 5 : 6

    2 – 4 : 6

    3 – 3 : 6

    4 – 2 : 6

    6 – 5 : 11
    6 – 6 : 12

    If we only care about the sum, then the state “sum = 6” is way more likely than any other sum.
    There’s only one way to get “sum = 2”.
    Sum = 6 is the equivalent of your scrambled egg.
    But it’s mainly an illusion. It’s just a result of some arbitrary state labeling (or rather our incapacity to properly observe each dice).
    All the states are really as unique and as likely when you consider each dice individually. If you rewrite each state with explicit labels, then any state for which “sum = 6” is just as likely and unique as “sum = 2”.
    You (almost) never see an egg going unscrambled, sure. But if you pick a particular egg and scramble it, you’ll (almost) never be able to scramble any another egg in exactly the same way either.

    Extend this example where each dice is replaced by an air molecule in a room (the state of the molecule is its x/y/z coordinate in the room). The only thing we perceive is the average density of air in the room. A huge majority of the possible states lead to a density that’s almost perfectly uniform across the room. But any such states leading to a uniform density are just as unique as the very few states where all the molecules would be gathered tightly in the upper right corner of the room (all the rest is vacuum).
    What we perceive as the arrow of time is simply due to the fact that most biological processes that constitute us rely on such statistical averages. Our memories rely on the existence of stable organic compounds, which rely on the existence of stable planetary systems, which rely on star formations, which rely on hydrogen atoms formation at the big-bang, etc. So the arrow of time is obvious for us.

  46. Pascal Says:

    A question about the initial condition of the universe : is it possible to turn the claim about the low entropy of the initial universe into a quantitative statement ? How far was it from our present situation, and how much have we got to go to reach equilibrium ?

  47. Scott Says:

    Pascal #45: Interesting questions! I don’t think anyone knows what the observable universe’s initial entropy was, except that it was negligible compared to its maximum possible value (~10122 bits, assuming the holographic principle and cosmological constant).

    But this might also be largely a matter of definition: if you were willing to assign a pure state to the entire universe, then its “entropy” would start 0 and remain 0 for all time! Fundamentally, entropy is the logarithm of the number of distinguishable microstates compatible with a given macrostate. But making that precise requires some notion of what we mean by a “macrostate” (e.g., which observables can we easily measure and which not?), which is unproblematic when talking about a container of gas, but which might become extremely problematic if we try to extend it to very beginning of the universe, and not just to one part of the initial state but to the whole thing.

    As for how long we have until the universe reaches thermal equilibrium: see here. At the least, the supermassive black holes at the centers of galaxies will need to evaporate into Hawking radiation, which will take 10100 years, give or take. Then there might be quantum tunneling effects on a much longer timescale, but that’s speculative.

    (Physicists who want to add more or correct what I said should feel free to do so…)

  48. Chris W. Says:

    Prompted by Pascal #46 (“quantitative statement”): It might be worth reviewing the relevance (?) of entropy increase associated with gravitational collapse in this context. Some might find the assertion that the early universe was in a low entropy state (relative to now) paradoxical, inasmuch as it was a nearly uniform hot gas of subatomic particles and radiation that cooled and developed structure as the universe expanded.

  49. anon Says:

    Scott @ comment 44:

    I understand the logic! But my question was indeed if notA implies notB
    or not. From your answer, I guess no.
    I have till a long way to go in CT, but in the meanwhile I bought your book 😉 .

  50. Rahul Says:

    Is there an absolute lower bound on how low the entropy of a system can be? Say the universe in its early stages.

    In a sense, what’s the maximum order you can impose on a system of atoms?

  51. Avi Says:

    >(b) speculating (as you did) that we’re all in a computer simulation, and the simulators are particularly interested in simulating March 2015 or thereabouts (really? they are? when did they start this simulation? are you willing to bite the bullet and say that Plato never existed, maybe even that WWII never happened?); or

    >( c) throwing up our hands and pointing out that you had to be alive sometime, and other people who were (or will be) alive at other times could ask the same question.

    >I wasn’t claiming to know that (c ) is the only valid answer, just that I don’t see any way to rule out that it is—i.e., that we seem to be in the same position here as we are with countless other “anthropic mysteries.”

    I don’t consider the simulation theory to imply that history is false. The version I’d consider most likely (though still very improbable) is that some society with exactly our history survived, and got access to a large amount of computing power, and is interested in simulating Singularities. So they simulate thousands or millions of societies in the computer age with their history, which makes the measure of observers in a pre-Sing-but-close-to-one era like ours much higher than that of people in the past, which in turn makes our prior probability of ending up as us higher than ending up as someone in the past (or future).

    For specifically 2015 as opposed to anytime since ~1950- anytime without a Singularity, this doesn’t narrow down any further, and I can’t think of any offhand that would.

    And it isn’t hard to think of ways that (c ) could be falsified; for a trivial example, if tomorrow everyone on Earth heard a voice in their heads telling them that the simulation theory is true, with everything that I just conjectured being part of it, I’m pretty sure you wouldn’t still believe (c ). Or more generally, there have been many ways proposed to tell if we’re in a simulation, and if we are, we should expect science to eventually prove it.

    There are some anthropic questions that might only have a priori answers, but often you will be able to get a prediction out of a theory. The trick is to make sure these predictions are likely. That is, what I said above about a voice is not likely under either hypothesis, so it isn’t a good test. It’s just far more likely under simulation than not!simulation. We really need predictions that are very likely under simulation but not otherwise.

    I suppose the Singularity itself is more probable under the simulation hypothesis, so one not occurring for a while would count as evidence against it. But that isn’t really replicable and priors there can’t really be agreed on anyway.

    (Oh, and anthropic hypotheses can still be useful insofar as they constrain priors, even if they can’t be tested. Any theory that gives a greater probability to me being at this time, place, era, other features of myself, etc, gets a slightly higher prior (or should I say posterior? Since I’m updating on knowing things about my setting) than one which predicted any setting to have the same probability.

  52. Marc Says:

    I think that the explanation of the second law by fundamental dynamics together with special initial conditions which is given here misses a crucial fact.

    The phase space distribution in classical mechanics and the density matrix in quantum mechanics evolve in a way which doesn’t change the entropy (Liouville theorem resp. von Neumann equation). So no matter how “special” the initial conditions were, the final state has the same entropy. If we start with a point in phase space, we end up with a point in phase space. So what’s “special” about the first point?

    The situation is a bit different for a small volume in phase space. Although the volume remains constant, it can change its surface area. Some special volumes have a very small surface because they are concentrated in a small area of the phase space while most volumes have a huge surface and are distributed widely over the phase space. Something like in this pictue:

    But the important point is that the volume and therefore the entropy is the same in the special and the widely distributed case. So Loschmidt’s paradox applies.

    The resolution of the paradox is to consider a different kind of entropy. Let’s say we cannot distinguish between nearby states, but only between cells which contain many states. If we use these cells to define a coarse-grained entropy, the right picture indeed has a bigger entropy than the special case.

    It is only the increase of this coarse-graised entropy which is compatible with fundamental dynamics and which is explained by special initial conditions.

  53. Marc Says:

    Somehow, I missed the last couple of answers. Scott’s #47 at least partly addresses the same thing. I hope my explanations are helpful still.

  54. Scott Says:

    Chris #48: Yes, the fact that gravity “clumps” things together—and therefore, that “clumpy” states must have higher gravitational entropy than “well-mixed” states—is a well-known paradox of thermodynamics and gravity, which Roger Penrose puzzles over at length in his books. Thinking out loud, I wonder whether the AdS/CFT correspondence gives us a new perspective on this puzzle? I.e., gravitational clumping on the AdS side really could look like ordinary thermal mixing, which manifestly increases the entropy, over on the CFT side. (As always, any actual physicists who want to chime in are welcome to do so.)

  55. Scott Says:

    anon #49: Ah, OK. In that case, no, no one has proved that you can’t solve NP-complete problems in polynomial time even just with ordinary linear quantum mechanics, though most of us conjecture it’s impossible. But a prerequisite to proving that conjecture would be to prove P≠NP—i.e., that classical computers can’t solve NP-complete problems in polynomial time!

  56. Scott Says:

    Rahul #50: The absolute lowest entropy of any system is 0, and is achieved when the system is in a pure state known to you: in other words, when the system has exactly one microstate compatible with the observables you count as defining its “macrostate”. For example, a single electron with a localized wavefunction might have an entropy very close to 0 in that sense. (OK, not exactly 0, because of limits of your measuring apparatus, how well you’re able to localize the electron, etc. But pretty damn close.)

  57. Scott Says:

    Marc #52: Thanks! That is indeed what I was trying to explain, in my discussion of why the entropy of a pure state evolving unitarily remains 0 if you don’t do any coarse-graining (and hence, why you need to adjust what you mean by “entropy” to get a nontrivial statement). But your explanation will probably be clearer for many people.

  58. Raoul Ohio Says:

    Forgive me for briefly backsliding from this fun topic to the no-fun topic of e-shaming, but many might be interested in a book (published today?) detailing major e-shaming cases. The author was interviewed this morning on NPR and/or BBC.

  59. wolfgang Says:


    this is off topic, but did you notice this paper
    which suggests an upper bound on the chaos possible in physical systems?

    This should be interesting for (quantum)computing, either if one considers Turing machines sensitive to initial conditions (i.e. the input string) or if one considers a (quantum)computer simulating an arbitrary chaotic system.

  60. Douglas Knight Says:

    Raoul, that book was mentioned in the previous post. Indeed, the post was prompted by an excerpt from the book and much of the discussion was about the examples in the excerpt.

  61. James Gallagher Says:

    fred #45

    The sum 2 for the dice is a “fine-grained” observable – when the #outcomes gets large we really need “coarse-grained” observables to make any useful laws – you’re right that there are lots of configurations in phase space with the gas in the corner of the room, but the phase space volume is tiny compared to configurations where the gas is all over the room.

    Scrambled eggs also have a huge phase space volume compared to an unbroken egg, but once in your lifetime you may taste the most perfect ever scrambled eggs, at a more fine-grained level, individual scrambled egg configurations may of course have unique properties.

    Anyway, I’m just alluding to the fact that the obsession with determinism creates most of the confusion, if we allow nature to do what she surely must do, and randomly “jump” every ~planck time then things are much simpler (Humans or any other dumb creature in the universe surely don’t influence “wavefunction collapse” or similar)

  62. Sniffnoy Says:

    So, I’ve always been a bit suspicious about the whole entropy thing. Because, as Scott points out, in order for one to have that entropy increases, one has to choose a coarse-graining. But why this coarse-graining? And how can “the low entropy of the universe’s initial state” possibly be so important when it depends on a choice of coarse-graining?

    Or, like, imagine time-reserved observers. On their planet there exist processes, anti-replicators, that are caused by multiple copies of themselves. So these anti-replicators propagate backward in time; between mutation and (backward) natural selection, they evolve backward in time. Eventually they evolve brains capable of observing their surroundings, remembering the future, postdicting the past and taking action to ensure that their descendants (ancestors?) existed.

    Of course, they should see entropy increasing over reverse-time — but we see entropy increasing over time. Therefore, they must necessarily be using a very different coarse-graining than us.

    Question: How the hell does that work? What the hell is going on here? Or am I missing something big here?

  63. Scott Says:

    Sniffnoy #62: I’d strongly recommend reading Sean Carroll’s From Eternity to Here, and/or his various blog posts about this subject. He’s argued at length (and to my mind, persuasively) that, while there’s some arbitrariness around the edges in the choice of coarse-graining, there’s also a large amount of inevitability in the choice, which basically comes from the fact that the Hamiltonian of our world is local in the position basis. (And as a consequence, that any “sane” coarse-graining will need to involve averages over nearby spatial positions, rather than over nearby momenta or something else.)

    Regarding your thought experiment, how do you imagine that your time-reversed beings came into existence? If they came into existence via the ordinary process of Darwinian natural selection, etc. in the physical world, then presumably there must be a special, Big-Bang-like boundary condition to their future! (Well, they would call it “the past,” but it’s our future.) In which case, “our” Big Bang and “their,” much later Big Bang would coexist in the same universe. But that would create all sorts of teleological mayhem if communication between us and the time-reversed beings were possible! (In other words: if the same universe were subject to both past and future boundary conditions.) Sure, the definition of entropy would need to be revisited, but in some sense that would be the least of our problems. (If, on the other hand, no communication were possible between the two worlds, then it wouldn’t even be meaningful to ask whether their time ran “backwards” or “forwards” relative to our time.)

    Another possibility is that these time-reversed beings are simply conjured up via computer simulation—simulations that run on “normal” computers, which increase their entropy as you get further away from our Big Bang. In that case, you run into precisely the perplexities that I tried to explore in Could A Quantum Computer Have Subjective Experience?.

  64. Ajit R. Jadhav Says:

    Quite a few interesting points seem to have got thrown up in this thread overnight (i.e., “over-day”/”over-day-and-night”/”over-night-and-day” for some of you).

    Without answering them directly [none except for Scott ever answers me directly here [but I don’t “count” “sheep” anyway!!]], here are a few points that occurred to me while going through them:

    Think: Since the supposed Big Bang is a part of cosmo-logy, and since the physical evidence does not yet rule out a cyclical universe, how would your theoretical answers get impacted if the universe were to be in a shrinking period/epoch/state/whatever?

    In particular, to return to the initial concern of this thread, suppose we are in a shrinking universe.

    Would it then be possible for you to say that the fundamental physical laws (say differential equations) are symmetric w.r.t. time, but that there still remains a certain objective distinction between the past, present and future? That time somehow is unlike space in some sense even if the universe were to be shrinking (or even “constant”: neither shrinking nor expanding)?

    And, how about the more abstract theories of mathematical physics: Would a shrinking universe, too, imply a preferred direction for time in these theories? e.g. thermodynamic theories? statistical mechanical theories? How about a “constant” universe?

    And, about the methods of applying the abstract physical theories to the living beings:

    Even if the universe currently expands, a living being still remains a spatially concentrated/dense form of order (you can recognize it’s the same fellow day in and day out); it remains remarkably orderly throughout life (simply because you do age, and aging may be modelled as disorder, it does not mean that your arm begins sticking out off some other place of your body, after coming to a certain age).

    So, even if the universe as a whole were to shrink, why would a local portion of the universe i.e. a living being, not undergo the processes of aging—even if the entropy for the overall universe were to go on decreasing?

    Can the arrow of life point in a direction opposite to the arrow of time for the entire universe?

    Can we directly “transport” some (say thermodynamic) attributes of the overall physical universe to every specific part of it, in particular, also to a living being? If the beach comes out to be a faint yellow patch in a long shot, must every sand particle be the same yellow, and none can be a near-black, brown or off-white?

    Would a forever deceasing entropy for the univese necessarily imply that people would not age, but would get younger and younger?

    Or is it possible that even if the entropy for the shrinking universe as a whole decreases, people would still age because it’s a process related to life, and life is a de-finite process with a certain death as its terminating point?

    Let me terminate this particular comment and check back later in the evening (i.e. about 12 hours from now).


  65. Moshe Says:

    Scott #48: There are two types of black holes in AdS/CFT that should be discussed separately. The sufficiently large ones are well-understood and as you mention clumping and horizon formation is dual to thermalization in the field theory. The type of things people can discuss now is, for example, how fast does entanglement spread when starting with a highly excited pure state and end with a highly entangled state which looks thermal to most of its subsystems. The answer there is fascinating: it spreads faster than a bunch of Bell pairs moving at the speed of light (see 1311.1200, would be nice to have a good mental picture of how that is possible).

    So, I’d say this is quite a detailed understanding. Alas, the black holes that look most like the ones in flat space are the small ones (i.e. they are insensitive to the differences in the global structure of spacetime). Those are a lot more mysterious, though there are some attempts to discuss them. One of the problems is how to define them in a language-independent way. If you just think about them as quantum mechanical states, they are unstable. Metastable in some limit, but generically unstable. So, it is difficult to state precisely what you are looking for, in an inherently quantum mechanical description.

    (As for the block universe, I’d say there’s no operational distinction between the view that all history exists “simultaneously” and any other view you might want to take on that question. But, you’d probably guess that a physicist would say that).

  66. Sniffnoy Says:

    Scott #63: OK, thanks, I might just have to check that book out! The locality thing seems like indeed it might substantially limit things.

  67. Scott Says:

    Moshe #65: Thanks, that’s extremely helpful!

    To help me understand: are sufficiently-large black holes stable in AdS basically because they’re swallowing new stuff at the same rate that they’re emitting Hawking radiation? And if we made the black hole smaller, the emission rate would go up and also the absorption rate would go down, causing an instability? But if so, then wouldn’t a stable AdS black hole be in a precarious equilibrium, like a pencil balanced on its tip? I.e., it seems like making it ε larger would lead to runaway growth, while making it ε smaller would lead to runaway shrinkage. But I’m probably missing something.

    More broadly, I can certainly see how discussing unstable black holes could be harder than discussing black holes in equilibrium. But why does an AdS state’s being unstable make it difficult to state what we’re looking for? Do I understand correctly that the AdS/CFT correspondence doesn’t really do anything to the time dimension—i.e., that the time coordinate on the CFT side naturally gives rise to a time-slicing on the AdS side? If so, then why isn’t what we’re looking for simply the initial state and Hamiltonian on the CFT side, that are dual to the formation and evaporation of our unstable black hole? (With the “paradox” of gravitational entropy increasing even as matter clumps together, getting “resolved” by saying that we should really be asking such questions on the CFT side, where no clumping behavior occurs?)

    I apologize in advance for the many conceptual errors that are no doubt implicit in the above questions.

  68. Moshe Says:

    Both types of black holes can be at equilibrium, which means detailed balance: they absorb the same amount of energy they radiate. For small black holes this is an unstable equilibrium because their specific heat is negative: if (due to some fluctuation) they absorb slightly more energy than they radiate, they (bizarrely) cool down, thus making them more likely to absorb even more energy, and so on. The large black hole in AdS are more like what you’d expect from a regular quantum system: when they absorb energy they become hotter, thus more likely to emit, which is why their equilibrium state is stable.

    As for the small black hole: if you have a generic many-body interacting system, there are very few states you can fully characterize in any useful way. Some low lying states may be identified by their quantum numbers, and various maximal entropy density matrices can be identified by that property. But, if you want to ask where is the small black hole in the QM description of the system, the difficulty as I see it is phrasing that precisely. If I give you some density matrix in the field theory, how would you know it is the right one?

    I am curious what paradoxes come from the relation between clumping and gravitational entropy. In the field theory these may be resolved, as you mention, by the fact that the clumping occurs in the extra radial direction, not in the field theory directions. In fact, what happens in the field theory directions is precisely what you expect when things thermalize (e.g. diffusion of energy). The way that energy pulses broaden in the field theory directions as they “clump” (e.g gets absorbed by a black hole) in the radial direction is one of the pretty ways the whole thing hangs together.

  69. Scott Says:

    Moshe #68: Thanks again!

    So it sounds like AdS black holes behave a bit differently, even semiclassically, from the black holes I’m used to? I had thought that any black hole gets cooler (less likely to radiate) the larger it grows, and that was causing some of my confusion.

    Regarding well-definedness: given a spacelike hypersurface in AdS, is it physically meaningful to ask whether there’s a small black hole there or not? It seems like it “must” be, never mind if the black hole in unstable. But if so, then shouldn’t there be a projector on the CFT side that projects onto the subspace where there is a small black hole? Again, never mind how complicated that projector might be to implement—shouldn’t the observability of the small black hole on the AdS side be enough to ensure its formal existence?

    (Now that I write this, I worry that the question might be analogous to the length of a wormhole in the thermofield double state, which Lenny Susskind conjectures is dual to the quantum circuit complexity of the state on the CFT side. Since quantum circuit complexity is not an observable, it would follow from this that wormhole length can’t be an observable either. OK, but still, I have a much easier time accepting that, than accepting that the existence or nonexistence of a small black hole isn’t an observable!)

    Regarding the “clumping paradox”: I don’t think there’s any formal paradox; it’s just something Penrose vividly described in some of his books as a clash of intuitions, and as a sign there’s something we don’t yet understand about gravitational entropy. Intuitively, it seems “obvious” that a clumped state should have lower entropy than a non-clumped one, there being fewer ways to arrange matter in clumps than to arrange it in a diffuse gas. Yes, the formal calculations (e.g., of the entropy of two merging black holes) all work out, but there still seems like something deeply strange about it.

    But if you affirm that the clumping only happens in the radial direction, and that what looks like clumping on the AdS side is actually just “ordinary” thermalization and diffusion on the CFT side … that’s awesome!! It might seem like a minor point to you, but this might count as the first argument for AdS/CFT that I’ve ever more-or-less understood, without having to 100% take the experts’ word for it (which I’m happy to do if there’s no alternative, but seeing for yourself is always better 🙂 ).

  70. Chris W. Says:

    Scott (#54, #69): The paradoxical assertion I was thinking of was that the early universe should be in a low entropy state, even though the universe is becoming more structured with time.

    This discounts entropy increase associated with gravitational clumping—specifically, the formation of black holes. Once one realizes that gravitational clumping can lead to the formation of objects with far greater entropy than the matter that went into those objects, one can see how a loss of entropy associated with structure formation is more than balanced by the effects of gravitational collapse.

    Of course, nobody (?) before Jacob Bekenstein in the early 1970s considered that black holes might have a well-defined entropy—one proportional to the horizon area. Before that one did have a paradoxical or at least perplexing situation; how is the second law of thermodynamics obeyed in a system containing black holes interacting with matter and radiation? Once one admitted that the entropy could be defined as proportional to the horizon area one was up against the question of how equilibrium could be attained if black holes absorb but do not emit matter and radiation. The discovery of Hawking radiation substantially resolved that question. Of course, it led to other deep questions.

    Among them is the question of what the entropy of a black hole means, as opposed to how one calculates it. The fact that the ostensibly classical evolution of a black hole as a pure creature of a field theory (or of geometrodynamics, to use John Wheeler’s term) should mirror the laws of thermodynamics seemed profoundly mysterious then. It seems less mysterious now, although there seem to be various schools of thought as to how to resolve the mystery. (I am thinking here in part of Ted Jacobson’s famous 1995 paper.)

    The bottom line is that deciding how to properly define entropy so as to ensure conformity to the second law—as well as properly specifying the scope of the second law—seems to be an ongoing source of deep questions.

  71. John Says:

    #218 (Last thread – now closed)

    John Sidles is my hero. Can there by any blog on the planet *less* likely to ban a poster for being … annoying – he’s pulled it off.
    Long live the tangentially related.

  72. Enervator Says:

    On a similar note somehow, take a look at .

  73. fred Says:

    Physical laws are time-symmetrical.
    But what does it mean in terms of a QM experiment?
    Is there the equivalent of the wave function collapse going backwards?!
    E.g. if we take the double slit electron interference experiment. And somehow run all its equations backwards (we take the state of the universe as it is and reverse all the velocities, charge parity, etc), wouldn’t we get an interference from the slits in the other direction and none of the electrons would end up back into the gun?
    I guess the notions of “observer”, “experiment”, “measure” are even way more ambiguous in that context than they already are.

  74. Scott Says:

    Enervator #72: Similar in what sense? In the sense that it’s something people keep asking me about? We already went over Anderson and Brady’s claims at some length in this blog, and I don’t see that anything has changed that would make me want to spend another minute on this. The hydrodynamic models still can’t correctly reproduce the effects even of two-particle entanglement, Bell’s inequality still explains precisely why no such model will ever be able to do that, and the advocates of the models still can’t formulate a way around Bell’s inequality that makes the slightest bit of sense to those who understand it. Which means that there’s no need even to discuss quantum computing; the proposed classical description of our world fails way before we get there. Move along, folks.

  75. fred Says:

    Similarly in a many-world interpretation, it seems to me that when time is flowing in the “normal” direction, we have a tree structure that’s branching out (splits).
    Then if things were to run in reverse, you would need to have the various worlds “fuse” back together.
    So it’s clearly asymmetrical.
    How to reconcile this with basic physical laws that are symmetrical?
    The universe would have to be intrinsically deterministic.

  76. AdamT Says:


    I think you misunderstand what Buddhism identifies as the root of suffering. This false intuition or root ignorance of how phenomena truly exist is not posited to be at the intellectual level. For if it were, then merely refuting this false intuition by learning graduate level physics would lead to the end of suffering. Which of course is absurd. A graduate degree in physics obviously does not guarantee a happy life 😛

    No, the ignorance is posited as deeply ingrained and at a very subtle level of our mind. Even if we intellectually understand that no conditioned phenomena is permanent this by itself does little harm to this deeply ingrained ignorance.

    Understanding how Buddhism relates this deep ignorance with mundane suffering is a complex discussion. First, we’d have to define out terms and learn the jargon lest there is risk of a lot of misunderstanding.

    With that caveat, I would say that the suffering you’d experience with your friend dying would be of the second category of Buddhist suffering – the suffering of change or impermanence. You’d suffer because you are attached to your friend and do not wish him to exit your life. At a very deep level we rebel against how the world actually is. All of our friends will die. There is absolutely nothing we can do to change this. The very important point is that Buddhism acknowledges this, but says it is within our power to end the suffering we experience with the fact of mortality. Moreover, it lays out the path to do this and invites us to see whether it works by way of our own experience.


  77. Moshe Says:

    Scott, it’s a pleasure to discuss this fun stuff, you are certainly very generous sharing your fun over here.

    For the large black holes, they do behave like conventional systems, and unlike small black holes or black holes in flat space. But, for some purposes the distinction is besides the point: if you surround a flat space black hole by mirrors which reflect its radiation back, you’d get the same structure as in AdS, with large black holes being stable. So, being unstable is maybe a distraction and not a defining property of black holes. The correspondence between gravitational dynamics and conventional finite temperature dynamics is so detailed now that it has been used to discover new effects in good old hydrodynamics, and to simulate and discuss scaling laws in turbulent flows (that one somewhere along the infinite corridor). Really pretty stuff, glad you like it too.

    As for the small black holes, this is at the level of gut feelings. I don’t think any geometrical feature of the bulk can be an observable. We know that geometry is a collective phenomena valid only at certain limit and for certain purposes. That last part is important: even in the limits where geometry is a good description, it is only so for a small subset of observables (which are sufficiently “coarse-grained”). So, I don’t think there’s a projection operator for any geometrical property. For large black hole you can look for non-geometrical property (being at equilibrium at some temperature), but I don’t know what that would be for a small black hole (but someone else might).

  78. Rahul Says:

    Naive question:

    When you guys speak in terms of large & small black holes, what’s the approximate dividing line? How big shall one think of the largest “small” black hole to be?

    What units do you measure black holes in anyways; their mass I suppose?

  79. Scott Says:

    Moshe #77: Thanks once more!

    Are you literally saying that, if you lived in AdS space, there’s no observation you could make that would tell you whether a small black hole was present or not present? What about the types of observations that astronomers use to convince themselves that black holes are present in our universe?

    Is the issue simply that astronomers don’t observe “small” black holes (though they certainly observe black holes that are small compared to the size of the observable universe, which I thought was the relevant criterion here, though I might be wrong, cf. Rahul’s comment #78)?

    Or is the issue that the measurement that tells you whether a small black hole is present or not present wouldn’t correspond to a full quantum-mechanical operator, since the question only makes sense if there’s a smooth spacetime background (which the vast majority of states don’t have)?

    Or is the issue similar to the one with using AdS/CFT to resolve the firewall paradox—namely, that you can only “really” be certain that a black hole was present if you jump into it, but if you jump in then you can’t send signals to infinity, and therefore what you’ve done doesn’t correspond to any possible scattering experiment?

  80. Moshe Says:

    Scott, it is the latter option. I am not saying there is something in principle that doesn’t allow you to define a small black hole, just that the geometrical language is not natural in the fully quantum regime, so this task is difficult. Certainly in some classical limit one can envision defining an experiment that will be sensitive to the black hole horizon, while it exists. The issue is perhaps “only” practical: which observation is that and do we have any hope of calculating it independently on the CFT side.

    The issues with the black hole interior are much more complex, I think it is currently not clear whether it is present in the description of the outside observer for the reasons you mentioned. What I was talking about is simpler in comparison.

    And, large versus small is defined with respect to AdS radius of curvature.

  81. Rahul Says:

    John #71:

    “John Sidles is my hero.”

    …..and Ajit E&OE Jadhav is mine. 🙂

  82. Scott Says:

    OK, circling back to some older comments, Rahul #5:

      Naive question: For a long time the laws of Physics seemed to be left-right symmetric. Until they were found to be not so in certain very specific cases- the overthrow of parity.

      Is a similar situation possible with the Time-symmetry of the laws of physics? Or have we reason to believe we won’t find such laws?

    To maybe add to Audun #10 and #11: it turns out to be a theorem in quantum field theory (whose proof I don’t understand) that the laws of physics must be “CPT-invariant”: that is, symmetric under reversing the direction of time (T), exchanging left with right (parity, P), and exchanging particles with antiparticles (charge, C). The theorem says nothing about what happens if you do only one or two of the three, and indeed, it was experimentally discovered (as you said) that the laws of physics are not invariant under any stronger symmetry, like charge only (C), parity only (P), or charge plus parity (CP). But for CPT invariance to fail, basically the whole framework of quantum field theory would need to be wrong.

    Incidentally, if you just wanted the weaker statement that the laws of physics are reversible—i.e., that they don’t create or destroy information—rather than that they look exactly the same backwards and forwards up to CP symmetry, then that follows immediately from the unitarity of quantum mechanics; you don’t need anything about QFT.

  83. Scott Says:

    Shmi Nux #6:

      When you imagine a block universe compatible with QM, do you see it as a single slab of spacetime or as a tree of Many Worlds with a clear direction “up” into the future, where there are more branches than in the past? Or as something else? (I’m asking about your mental picture, not about any kind of underlying physical reality.)

    I dunno … if someone says “block universe,” I guess I just picture some translucent 3-dimensional block, mostly because of the word “block” (if I called something the “giraffe universe,” what picture would you associate with it? 🙂 ), but also because the philosophers usually talk about the “block universe” within the context of classical special relativity, not bringing in quantum mechanics or even GR.

  84. Scott Says:

    anon #34:

      for sure Einstein was referring to the block universe. So, I do not understand why you mention the T-invariance in mechanics.

    Yeah, I thought about omitting it, for exactly the reason you say. But on reflection, isn’t T-invariance part of the intuition for the block universe? The thought being: given that we could run the equations backward just as easily as forward, should we even think of them as being ‘run’ at all? If T-invariance hadn’t held, then at least we could say that any computer program to reproduce our world from one spacelike slice would presumably need to start at the beginning and work forwards, just as we naïvely imagine time itself to do.

  85. Scott Says:

    fred #73:

      Is there the equivalent of the wave function collapse going backwards?!

    Some people might define the Many-Worlds interpretation (or more broadly, the “modern decoherence view”) to be the assertion that the answer to that question is yes—i.e., that in principle, just as an egg could spontaneously unscramble itself without violating any microscopic laws, so too a measured qubit could spontaneously get disentangled from the measuring apparatus and surrounding environment, and thereby become “unmeasured,” its original quantum state restored. Both of these things are ruled out only on thermodynamic grounds (i.e., once again, because of the specialness of the initial state).

  86. Rahul Says:

    Scott #82:

    “Incidentally, if you just wanted the weaker statement that the laws of physics are reversible—i.e., that they don’t create or destroy information—rather than that they look exactly the same backwards and forwards up to CP symmetry, then that follows immediately from the unitarity of quantum mechanics; you don’t need anything about QFT.”

    I didn’t get the distinction between the weak & strong version.

    e.g. Can you give an example of something that is reversible but the laws do not look exactly the same?

    i.e. What’s “create & destroy information” versus “look the same”?

  87. Scott Says:

    Rahul #86: Suppose the “state of the universe” consisted of an integer mod N. And suppose the “laws of physics” consisted of just applying the map

    x := x+1 (mod N)

    over and over. Then the time-reversed laws of physics would be

    x := x-1 (mod N),

    which is different in form (it involves subtraction rather than addition), but clearly the laws are still perfectly reversible. (In this example, the analogue of “CP reversal” would be interchanging addition with subtraction.)

  88. dorothy Says:

    Scott #74 Is it safe to say that there is nothing new or interesting in ? It is two years since your blog debates on the topic. I expect the answer to be yes 🙂

  89. DB Says:


    “And yes, relativity encourages this perspective, by showing that different observers, moving at different speeds relative to each other, will divide up the 4-dimensional manifold into time slices in different ways, with two events judged to be simultaneous by one observer judged to be happening at different times by another.”

    So why does everybody agree on the age of the universe?

  90. Scott Says:

    DB #89: Unless I’m mistaken, because you can, e.g., define time in the rest frame of the cosmic microwave background radiation (or: the frame in which the observable universe looks roughly isotropic, with no anomalous redshifts in one direction and blueshifts in the other). In effect, even though the underlying laws of physics have no preferred inertial frame, cosmology does pick out a preferred frame. You can even measure the earth’s speed with respect to that frame; it’s apparently about 360 kilometers per second.

  91. Scott Says:

    dorothy #88: Yes, it’s extremely safe to assume that. 🙂 Once again, the authors give a classical vortex model that they claim can violate the CHSH inequality, reproducing the prediction of quantum mechanics. Once again, they wrongly assert that the derivation of the CHSH inequality improperly assumes that any influences between the two detectors have to “travel with the photons,” and that the reason their classical model can violate CHSH is that it doesn’t satisfy that assumption. In fact, as I tried to explain to them about 200 times, the derivation of CHSH assumes nothing except the causal structure of spacetime (i.e., influences between the detectors can travel by any means whatsoever, as long as they don’t go faster than light). This means that either

    (a) there must be signalling between the detectors in their model, perhaps smuggled into the “quadratic terms in Euler’s equation” (which would render the result uninteresting), or else

    (b) there must be an error in their derivation.

    I’ll be extremely grateful to any readers who want to look carefully, and explain to us whether (a) or (b) holds. But if Alice and Bob get to choose polarizations v and w independently, and there’s no communication between them, then they’re not going to produce independently-uniform random bits that are correlated with probability cos2(v-w) and anticorrelated with probability sin2(v-w). I’m as sure of that as I am that √2 is irrational.

  92. fred Says:

    Scott #91
    I read the paper, but they lost me at:

    ” The CHSH assumption is not true in Faraday’s model. Instead there is prior communication of orientation along phase vortices such as (4), communication which the CHSH calculation excludes by its explicit assumption.”

    And (4) refers to
    “GN Cantor and MJS Hodge.
    Conceptions of ether: Studies in the history of ether theories, 1740-1900”


    But I like one of the two authors’ web page (Robert Brady).

    “Computer optimisation algorithms often reach an impasse. A typical example is the travelling salesman problem, […] Biological evolution encounters the same problem. But if you can out-evolve your competitors, you will win in the long run. There have been billions of years to solve this problem – and the answer is sex.”

    We’re getting really close to finally tying up complexity theory and those recent controversial topics you’ve been exploring!

  93. Audun Says:

    Scott #87:
    Thanks, that’s a really nice way of looking at it!

  94. Douglas Knight Says:

    Fred, parentheses (4) means figure 4, while brackets [4] means reference 4. You can kind of test that by clicking on links: a green link in brackets goes to the right place in the bibliography, while a red link in parentheses goes to the bottom of the page that the figure is on, which is not optimal, but which is clearly not the bibliography.

    FWIW, reference 4 is available part 1 2 3. And a bunch of reviews (I’m surprised that google scholar doesn’t find them.)

  95. fred Says:

    Douglas #94
    Aaah, ok, it’s equation (4).
    Thanks for the links!

  96. Serge Says:

    Scott, could you please try to answer this little question that I’ve kept asking myself for a while: if time doesn’t exist at the quantum scale, how is it possible to run a quantum process?

    Scientists like Alain Connes and Carlo Rovelli believe that time emerges out of large quantum systems, as the variable which best stabilizes their statistical equilibrium. In their view, time is just a consequence of our lack of knowledge about quantum systems. Alain Connes has coined the motto: “a non-commutative space generates its own time.” He refers to the non-commutativity of Von Neumann algebras of quantum operators.

    In my personal view, computations can be seen, by contrast, as the natural opposite trend to disorder: an ordering factor which creates knowledge but also destroys time – since time can only emerge out of statistical disorder. An interesting parallel can be made between this quantum situation and the well-known opposition stochastic-and-efficient versus exact-and-slow algorithms in complexity theory. The established fact that randomness is a provider of efficiency in computer science might turn out to be a simple consequence of the true nature of time: quantum disorder, while being an obvious destroyer of accuracy, remains the only possible time engine. What do you think of this hypothesis?

  97. Scott Says:

    Serge #96:

      if time doesn’t exist at the quantum scale, how is it possible to run a quantum process?

    That question barely gets off the ground for me, since I don’t see good evidence right now that “time doesn’t exist on the quantum scale.” Conventional QM has a perfectly-ordinary time parameter t, and AdS/CFT even gives you quantum gravity models where that’s upheld (i.e., where you can have a well-defined time-slicing, at least on the boundary, and there are no closed timelike curves or anything like that).

    Of course, AdS/CFT doesn’t seem to describe our deSitter universe, so it remains conceivable that the true quantum theory of gravity, whatever it is, will have no time at a fundamental level, and will relegate time to an “emergent” status—a possibility that lots of deep thinkers indeed speculate about these days. But it seems to me that the burden is squarely on those deep thinkers to explain how to recover a sensible notion of time from their ideas, in the regimes where we know time makes sense! It’s not on the people like me who have no problem with time at the present time. 🙂 So you should really direct your question to Rovelli or Connes or someone like that.

  98. Serge Says:

    Thank you Scott for your answer. I’m not that interested in quantum gravity for the moment, but I’m looking forward to drawing on the novel conception of time that’s being developed there – in order to back up my own views about complexity. Maybe I’ll try to contact one of those thinkers… but when I think of it, I’m also wary that they might reply in turn that they have no problem at all with quantum computing and P≠NP… This is the problem whenever you’re standing at the frontier between two fields, you have to do all the stuff all alone! There’s also Julian Barbour, mentioned by quax in comment one. Quite possibly, Barbour was among the pioneers who triggered the whole trend of thought – with at least one exception in the person of Alain Connes, who came up with his own ideas about time at the very beginning of his career. He had given them up for decades, until he eventually chanced upon Carlo Rovelli at a congress on quantum gravity. Life is filled with such happy coincidences…