What if Time Really Exists?

The Foundational Questions Institute is sponsoring an essay competition on “The Nature of Time.” Needless to say, I’m in. It’s as if they said: “Here, you keep talking about this stuff you are always talking about anyway, except that we will hold out the possibility of substantial cash prizes for doing so.” Hard to resist.

The deadline for submitting an entry is December 1, so there’s still plenty of time (if you will), for anyone out there who is interested and looking for something to do over Thanksgiving. They are asking for essays under 5000 words, on any of various aspects of the nature of time, pitched “between the level of Scientific American and a review article in Science or Nature.” That last part turns out to be the difficult one — you’re allowed to invoke some technical concepts, and in fact the essay might seem a little thin if you kept it strictly popular, but hopefully it should be accessible to a large range of non-experts. Most entries seem to include a few judicious equations while doing their best to tell a story in words.

All of the entries are put online here, and each comes with its own discussion forum where readers can leave comments. A departure from the usual protocols of scientific communication, but that’s a good thing. (Inevitably there is a great deal of chaff along with the wheat among the submitted essays, but that’s the price you pay.) What is more, in addition to a judging by a jury of experts, there is also a community vote, which comes with its own prizes. So feel free to drop by and vote for mine if you like — or vote for someone else’s if you think it’s better. There’s some good stuff there.

time-flies-clock-10-11-2006.gifMy essay is called “What if Time Really Exists?” A lot of people who think about time tend to emerge from their contemplations and declare that time is just an illusion, or (in modern guise) some sort of semi-classical approximation. And that might very well be true. But it also might not be true; from our experiences with duality in string theory, we have explicit examples of models of quantum gravity which are equivalent to conventional quantum-mechanical systems obeying the time-dependent Schrödinger equation with the time parameter right there where Schrödinger put it.

And from that humble beginning — maybe ordinary quantum mechanics is right, and there exists a formulation of the theory of everything that takes the form of a time-independent Hamiltonian acting on a time-dependent quantum state defined in some Hilbert space — you can actually reach some sweeping conclusions. The fulcrum, of course, is the observed arrow of time in our local universe. When thinking about the low-entropy conditions near the Big Bang, we tend to get caught up in the fact that the Bang is a singularity, forming a boundary to spacetime in classical general relativity. But classical general relativity is not right, and it’s perfectly plausible (although far from inevitable) that there was something before the Bang. If the universe really did come into existence out of nothing 14 billion years ago, we can at least imagine that there was something special about that event, and there is some deep reason for the entropy to have been so low. But if the ordinary rules of quantum mechanics are obeyed, there is no such thing as the “beginning of time”; the Big Bang would just be a transitional stage, for which our current theories don’t provide an adequate spacetime interpretation. In that case, the observed arrow of time in our local universe has to arise dynamically according to the laws of physics governing the evolution of a wave function for all eternity.

Interestingly, that has important implications. If the quantum state evolves in a finite-dimensional Hilbert space, it evolves ergodically through a torus of phases, and will exhibit all of the usual problems of Boltzmann brains and the like (as Dyson, Kleban, and Susskind have emphasized). So, at the very least, the Hilbert space (under these assumptions) must be infinite-dimensional. In fact you can go a bit farther than that, and argue that the spectrum of energy eigenvalues must be arbitrarily closely spaced — there must be at least one accumulation point.

Sexy, I know. The remarkable thing is that you can say anything at all about the Hilbert space of the universe just by making a few simple assumptions and observing that eggs always turn into omelets, never the other way around. Turning it into a respectable cosmological model with an explicit spacetime interpretation is, admittedly, more work, and all we have at the moment are some very speculative ideas. But in the course of the essay I got to name-check Parmenides, Heraclitus, Lucretius, Augustine, and Nietzsche, so overall it was well worth the effort.

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99 Responses to What if Time Really Exists?

  1. Jessica says:

    Good luck!

  2. Big Vlad says:

    Come again?

  3. Elliot Tarabour says:

    I found your essay this morning on the fqxi site and commented. (and voted ;))

    As I said… to paraphrase… “thank god somebody is standing up for time”.

    e.

  4. Sean says:

    Thanks for the vote, Elliot! I feel that time has been maligned for too long, and it’s about time (just can’t stop doing that) that someone stood up for it.

  5. Peter Morgan says:

    Hi, Sean, nice to see another big name in the FQXi contest. Good luck. I see that you’re already a member of FQXi, but for little fish the big call of this contest is that people who place in the first three juried prizes (which means up to 8 essays, if they think there are that many that are good enough) will be invited to FQXi membership.

    I misunderstood the Community Prizes at first, as it also appears you may have, when you say: “So feel free to drop by and vote for mine if you like — or vote for someone else’s if you think it’s better”. Community prizes are the result only of “restricted votes”, of which we, the authors, can cast three each. People who are already members of FQXi can also cast three restricted votes each. To get the coveted restricted votes, most people have to write.

    This is what I missed: “Community Prizes: The top recipients of Restricted Votes will be awarded “Community Prizes.” Prizes will not be awarded directly on the basis of Public Votes, but it is anticipated that Public Voting may influence either Restricted Voting or Expert Judging.” That is, Public Votes seem close to irrelevant.

    Also, there are up to 18 juried prizes available in total, judged, I suppose, by Physicists, Philosophers, and presumably serious academics in other fields, all appointed by FQXi, but only up to 3 community prizes, judged half by members of FQXi and half by the writers of the papers you see there, the result of which can hardly be guessed.

    I’m curious whether this kind of competition, run with more editorial control and tighter rules, could form a new publishing model. Being able to say, “2nd place in 2008 FQXi contest” would seem comparable to “published in minor journal X” for one’s CV. The pre-publication discussion is potentially useful, though some form of access control might improve the condition of the FQXi comment threads. If FQXi provide an archive of winning essays that is as robust over the long-term as is provided by journals, it would not be necessary for the essays to be conventionally published in a journal. The Gravity Research Foundation has been running this kind of competition for years, of course, in partnership with GRG, apparently with good success.

  6. Sean says:

    Peter, thanks. You’re right, I had misunderstood the nature of the community prizes; probably the procedure they are actually using is much more sensible than the one I thought they were.

  7. Anthony A. says:

    Peter & Sean,

    With my FQXi hat on: The biggest reason for basing prizes on restricted votes is that it would be too much of a headache to prevent stuffing of the ballot box in the unrestricted voting. In addition, we were worried that people with ‘celebrity’ status (or big blog followings) would be extra-unfairly advantaged (i.e, nice try Sean! You’ll have fall back on the merits of your essay.)

    Anthony

  8. Sean says:

    What’s the point in selling out to become a celebrity blogger if you can’t stuff the occasional ballot box?

  9. Bruce Kellett says:

    Sean, a most interesting essay. Would I be correct in assuming that one consequence of an infinite dimensional Hilbert space and the existence of an accumulation point for energy eigenvalues would be that time (and hence also space) must be continuous? I can think of only messy arguments for this implication at the moment, but I feel that an elegant demonstration of such a connection should be possible.

    Bruce

  10. Neil B says:

    If you believe that the wave function is real, then nature is not really time-reversible after all. Consider that at an “emission” point the WF expands out and gets bigger and bigger, but then (maybe) “collapses” at the absorption point. Run that backwards in time and it will not go the same way. Well, some people say something like many-worlds takes care of that. I suppose if the wave keeps evolving then there’s no time-asymmetry problem? However, with unobservable worlds/branches, it looks “not even wrong” from here. Also, modified from a point I made at http://scienceblogs.com/principles/2008/11/manyworlds_and_decoherence.php#commentsArea, here’s an issue relating to expansion of the WF and the issue of time:

    Regardless of whether you call it a literal “other world”, I in this one observe a specific outcome. If you think the other outcome/s must be actualized then it has to be “somewhere” in some sense of the term. (It’s gross because we are making more of the total integral of the WF over all spaces/?s combined, to have the whole particle “here” as well as the whole particle “there” – but let that go for a minute.) We still have to justify “my” chance of getting various chances of the outcomes, even granting the bastardization of conventional statistics (one person confronting multiple cases in sequence) into the idea of how likely a random “version of you” will run into a given outcome in multiplications of a given trial. Well, suppose there are two possible outcomes, but the chance is not 50/50. I ask: OK, so how many worlds/?s are created in the split?

    The temptation above is to say “two” since there are two things that could happen. But suppose the amplitudes reaching detectors are 0.8 and 0.6. Then the probabilities are 64% and 36%. So now what, we have 64 “worlds” one way and 36 “worlds” the other way, or 16 and 9, or …. to get the right proportion of chance for observation? What number of versions is appropriate? What if it’s an irrational proportion? If you have infinite branchings, then how can you define “proportion” given such infinite sets? And even if you say, it really isn’t a matter of n specific separate worlds, how then does the proportion manifest if you somehow put “all” the particle into both detectors to avoid collapse into only one of them?

    No, it seems that the WF must actually behave inherently differently during absorption/detection than emission/creation, which is asymmetry in time. I think our problem with “collapse” goes beyond just the “metaphysical” issue of what happens during collapse, but even what sort of “interaction” should cause it to happen. If we leave humans out of it, some might say “detectors” are inherently special, maybe from decoherence. But consider a photon entering a Mach-Zehnder interferometer. Why doesn’t the first beam splitter “collapse” the photon so we don’t even get interference from recombining? That silvered surface has atoms which are excited by the photon for “re-emission”. (Or indeed, why not consider the “split” photon to be one in each world for each possible direction, already?) But if a phototube gets a click, many assume that really happens (unless “awareness” makes it so.)

    Hence I don’t think we can avoid the odd challenge to “time” in physics presented by wave function issues. Wave functions tend to get bigger as time progresses – is that perhaps even more fundamental than thermodynamic issues?

  11. Sean says:

    Bruce, the assumption that time is continuous is put in by hand — I’m assuming conventional evolution according to the time-dependent Schrodinger equation, in which the time parameter is certainly continuous. So we can’t really count that as a conclusion.

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  13. Interested says:

    I read Sean’s 9 page article, referred to in his post above, and New Scientist’s time article “What makes the universe tick?” by Michael Brooks http://www.newscientist.com/article/mg20026831.500-what-makes-the-universe-tick.html. I read the latter first and was thrilled by a large consensus among scientists that it might be better to do away with the common sense notion of time. And Roger Penrose’s middle ground that ‘time pops in and out of existence as the universe matures’.

    Reading Sean’s, I found it difficult to grasp everything ( most of it went over my head) but carried away at least 3 small nuggets for myself to store for winter.

    # (1) One is that, “by taking time seriously we can conclude a great deal about the deep architecture of reality” (page 2 , 4th para, last two lines) By that I infer that, where Sean disagrees with the stance of those who would rather do away with the notion of time ( that to Michael Brooks, [time] makes no sense expect in terms of human experience …. “…..Last month, Smolin and other theorists, along with mathematicians and philosophers, got together at the Perimeter Institute to thrash out time’s problems. So complex is the issue that everyone involved seems to have a different idea. It turns out that if you want to understand time, you might need to grab some measurements from the future, watch a big bang explode at the edge of the universe, or delve into the anomalies presented by the most unruly of the subatomic particles. For some, the only solution is to scrap the notion of time altogether……” While I do not grasp Sean’s “deep architecture of reality” I would think and assume that there is a lot there for the picking and it would be a worthwhile journey to see such an architecture, standing the ground for not doing away with the notion of time, even when the notion of time is problematic and may not exist.

    # (2) The Big Bang is outdated. Sean : “The modern idea that time does have a beginning arises from the existence of a Big Bang singularity in cosmological models based on general relativity. But from our current perspective, that is an outmoded relic of our stubborn insistence to think in terms of spacetime, rather than directly in terms of the quantum state. Classical general relativity, after all, is not correct; at some point it must be subsumed into a quantum description of gravity. We therefore imagine that the classical Big Bang corresponds to some particular kind of quantum state, which may be obscure from the perspective of our current knowledge, but will ultimately be resolved. It follows, under our ssumptions (sic) , that there was something before the Big Bang, and time stretches back into the infinite past.” ( page 4 , 2nd para, last 8 lines) . Over the past few years I gathered on my scanty readings the dawning realization that the scientist’s frontier is not the Big Bang but something more or beyond that, but I guess this says it so clearly it is a relic. If one constructs one philosophy based partly on the Big Bang, when that shifts, one needs to adjust. It is here that it makes me think that, those who construct their philosophy based on the Crucifixion and salvation theme, do not have to make adjustment usually in their life time. Man has about four score or five score years ( 80-100 years old) and dealing with life, exigencies of life, often do not permit many adjustments to philosophy and thus, there is a certain efficacy to a model that changes less ( and to Kevembuangga, this is not about whether that is the better or best model in case it crosses his mind).

    # (3) Sean says “As our universe expands, it is increasingly dominated by vacuum energy. Currently,structures are still forming and complex life forms are riding the wave of entropy generated by hot suns shining in cold skies. But ultimately those stars will grow dim, galaxies will collapse into black holes, black holes will evaporate, and all we will be left with is an increasingly thin gruel of elementary particles in a background of vacuum energy. That, then, is a high-entropy state: a nearly-empty universe suffused with a tiny amount of vacuum energy.” (page 8, 3rd para, last 6 lines). This seems like , we should make hay when the sun shines! ( smile) And that one day in the very far distant future, our known universe could experience the big crunch and it will be no more at least as it once was. I wonder what scientists think and feel about the sort of death of the universe if they do not speculate about personal mortality and life after, then at least of universe mortality and after.

    # These are not exactly scientific contributions to the scientific post and article, but to a lay person, like me, when I read them, these are some of my thoughts. Thank you for your ‘time’ blog post.

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  15. I’d love to see a list of the essays you liked. Otherwise I have to dig through them; that would create too much entropy.

  16. Eunoia says:

    Surely Time is Cantor dust, with all that that implies?

    Such as dark matter being on a neighbouring point, forever unreachable 😉

  17. Don Bronkema says:

    panta rhei, auden menei: a century hence some/most/all of you will be risible

  18. Don Bronkema says:

    Panta rhei, auden menei…a century hence most of your vues will be risible

  19. Don Bronkema says:

    think Boltzman, think Bostrum, think mind of Brahma

  20. Lawrence Crowell says:

    I have only read the start of this paper, but I think I get the “gist” of it. I do have a sort of question concerning this

    One possible local example of an accumulation point might be positronium atoms in the distant future ~ 10^{40} years from now. At that time the universe might likely consist of black holes and proton decay will have dissolved away baryonic matter. So there might be a thin soup of electrons and positron in space. These could then form “atoms” with radii that measure in the light years. The Rydberg levels of such an atom, which the atom shifts between by absorbing weak photons or by being pulled by the cosmic expansion, are tiny. So the frequencies associated with these “atomic clocks” are very small and the time intervals they “compute” very large. As time progresses some of these atoms approach the E = 0 through transitions involving Rydberg states that pile up near that limit.

    I am not sure about there being no upper bound to compuational complexity. In my idea of there being a branching of geodesics in the AdS spacetime with a black hole, there is a renormalizatio group associated with this. It sets the values of gauge parameters, and I think does set some extremization of possible local complexity in the corresponding dS spacetime for the physical universe. However, the universe appears poised to expand into a pure deSitter spacetime as the density of mass-energy approaches zero. Eventually the cosmological event horizon at r = sqrt{3/Lambda} will begin to decay as it emits Hawking-Gibbon radiation of enormous wavelengths (billions of light years!) and as Lambda —> 0 the horizon radius approaches infinity leaving the universe as a complete void or Minkowski spacetime M^{3,1} as the classical attractor point, or the endpoint of the cosmological Feynman path integral. I am not sure there is much complexity of computation going on in M^{3,1}! So if we think of the Minkowski spacetime, the conformal boundary of AdS, as some sort of conformal time mapped to a I^{oo}, then this boundary might represent an upper bound on time computations.

    It is worth pointing out that time a clock computes is something which is measured, or the time computed by the system is decoherently reduced to some classical-like value. So in this incredibly distant future the universe might compute its time with various systems with very long time intervals. In the case of the cosmological event horizon receeding away the emitted quanta are decoherent, and so the universe is computing ever large time intervals (decoherently so as a sort of measurement) as the cosmological event horizon retreats away. So the universe computes longer time intervals as time —> infinity. There is some sort of ratio here at work, say Delta t/t, where the time frame the universe computes for itself is given by the number of these Delta t’s it computes in the future. If the intervals Delta t increase in magnitude slow enough there would then be an infinite number of these “time computations” in the future, yet if they increases faster than some criterion, say the value of Delta(Delta t/t) —> 0 as t –> infinity then there might be some upper bound to the computational complexity (time computations etc) which can exist in the universe.

    Lawrence B. Crowell

  21. matthew kolasinski says:

    Hello Sean,

    re:
    “…and observing that eggs always turn into omelets, never the other way around.”
    noting that an egg left to itself has been known to turn into chicken, and re-emerge an egg.
    sort of a work-around for entropy – a carrying on of the same cyclical energy system which is the point of the form. as long as the cycle isn’t interrupted with an omelet for the egg cycle or a pot for the chicken cycle, the energy system which was the essence of the first egg still exists.

    but these are events in time and not time itself, subject to processes which occur in time and are not time themselves.
    that is, unless you’re religious about some physics model for which time is exclusively the metric of a duration compared to some cyclical event, eh.. in time. noting that this concept of metric time as Time has its origin primarily in western cultural convention, which physics has largely inherited. it has an appeal; physics likes to measure things; casting around for something to measure what people said was time and everybody believed existed and was measurable, they just naturally grabbed a clock – it was handy.

    if you wish to rescue an existence for time, it will require stepping outside of metrics. but what happens in so doing, physics tends to loose interest quickly in things which can’t be quantified in some way – whether it exists or no. in stepping outside of metrics, you also step outside of all flavors of what is presently known as physics.

    it’s not too bad out here. we won’t argue with you if you want to call time real.
    if physicists want to call that an illusion, that’s fine too. judging from the entries in the contest, it’s reasonably clear that physics doesn’t have any better handle on it, highly speculative (“So there might be a thin soup of electrons and positron in space. These could then form “atoms” with radii that measure in the light years…”) and trying to promote their case appears to occasionally have strong potentials for adverse impacts on their blood pressure – that is a quantifiable. nobody argues about it out here.

    which leads us to a choice here. invoking the issue of free will – another topic within the parameters of the Time essay… myself i’d prefer to call it ‘event’ rather than ‘contest’ (not terribly interested in the competition so much as the opportunity to participate in an exchange of ideas – a sort of mega-brainstorming session. and having quite a bit of fun in the process. i doubt there’s any participant who’s taken the time to read some of the other posts who hasn’t learned something themselves in the process).

    so, there’s a choice between time as a reality, or the metrics of physics and no “real” existence for time.
    or to not choose. that’s a choice too.
    what will you do here?
    some wiggle room. you can’t ‘choose’ very well to walk to the moon – some limitations to free will. there appears to be an option when it comes to what we think.

    a momentous fork in the road for Sean, folks.

    let’s watch and see what he does. 🙂

    welcome to Time, Sean; i’m looking forward to reading your post there. i’m afraid i’m falling behind in my reading a little; coming in more quickly than i can keep up with. but i’ll get to it, in due time…

    maybe you’ll get a chance to stop by and read ‘some thoughts on time’.

    you wouldn’t mind my borrowing your blog to promote my entry, would you?

    😉

    thanks, Sean, for promoting interest in the contest.
    and thanks to the folks at FQXi for hosting it. i don’t know what, if anything, you’re going to do with all this stuff your collecting there, but it’s a delightful venue.

    matt kolasinski

  22. Loki says:

    Sean and other knowledgeable people, i’ve got a question about Boltzman Brain problem (and this question doesn’t look stupid to me):

    Why should an isolated B.Brain be more plausible fluctuation than the observable Universe we happen to be in?

    To have a fluctuation in the form of B.Brain, lots of otherwise non-existent particles should form into immensely complex form kind of “out of nothing”. The Universe is apparently much bigger than B.Brain and more complex, but it is not a fluctuation per se – rather the result of 13b years evolution of initial, probably much simpler fluctuation. You get just one very energetic Mega-Fluctuaton popping out of vacuum and voila – Big Bang, inflation, reheating, reionisation etc. etc. .. mathematical physisists on Cosmic Variance!

    I guess the good analogy is Darvin evolution here. Obviously, a sudden appearance of a fully-fledged math physisict on an otherwise abiotic Earth is numerically more possbile than the whole big biosphere with gazillions of different animals. But if you take evolution into account, biosphere looks almost inevitable while single m.ph. keep being an impossible example for discussion.

  23. Lawrence Crowell says:

    The Boltzmann brain is something which comes about from a large number of possible configurations in an equilibrium system. The universe in contrast appears to permit a vast array of complex configurations, lots of stars, different planets, complicated chemistry and so forth, from which life appears to be just one example. The universe has a Goldilock condition where small homegenieties exist which act similar to open thermodynamic systems.

    Lawrence B. Crowell

  24. Steve Esser says:

    That’s a great essay, Sean. We’ve gotten used to science proving common sense dead wrong, so it has been tempting to say time is an illusion. But time is different. It is not some postulated feature of reality. It is the dimension of experience. There is no world to talk about without experience.

  25. Henrik Jonsson says:

    Great, just in time when I’ve started getting the hang of thinking of time as illusory you come and attempt to tell us it might be real all along..! But seriously, fantastic essay, your skill at making esoteric physics understandable is unmatched.

    I did find some mistakes you might want to fix if it’s possible to send in another draft before the deadline:
    Typo on last line of page 6: “..the Poincaré recurrence theorem (and brining to life Friedrich Nietzsche’s image of eternal return).”
    Broken citation towards bottom of page 8: “..eternal cosmologies that feature a low-entropy “bounce” that replaces the Big Bang [?]”