What if Time Really Exists?

By Sean Carroll | November 24, 2008 12:01 pm

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.

CATEGORIZED UNDER: Science, Time
  • Jessica

    Good luck!

  • Big Vlad

    Come again?

  • Elliot Tarabour

    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.

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

    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.

  • http://pantheon.yale.edu/~pwm22/ Peter Morgan

    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.

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

    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.

  • http://www.fqxi.org Anthony A.

    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

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

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

  • Bruce Kellett

    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

  • http://tyrannogenius.blogspot.com Neil B

    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?

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

    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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  • Interested

    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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  • http://notes.kateva.org John Faughnan

    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.

  • http://www.savory.de/blog.htm Eunoia

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

    Such as dark matter being on a neighbouring point, forever unreachable ;-)

  • http://kloanchoyss@gmail.com Don Bronkema

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

  • http://kloanchoyss@gmail.com Don Bronkema

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

  • http://kloanchoyss@gmail.com Don Bronkema

    think Boltzman, think Bostrum, think mind of Brahma

  • Lawrence Crowell

    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

  • matthew kolasinski

    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

  • Loki

    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.

  • Lawrence Crowell

    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

  • http://guidetoreality.blogspot.com Steve Esser

    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.

  • Henrik Jonsson

    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 [?]”

  • http://magicdragon.com Jonathan Vos Post

    Albert Einstein, in a letter to the widow of his best friend, Michael Besso:

    “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.”

    My coauthors Professor Philp V. Fellman, Prof. Christine M. Carmichael, Andrew C. Post, and others have a series of refereed papers that compare the theories of time of Dr. Sean Carroll (Senior Research Associate in Physics at Caltech), Hawking, Penrose, and the un-institutionally supported New Zealand iconoclast Peter Lynds (born May 17, 1975) is a New Zealander who first drew sudden attention in 2003 with the publication of a physics paper about time, mechanics and Zeno’s paradoxes.

    Lynds attended university for only 6 months. His career as a physicist began in 2001 with his submission of an article entitled “Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity” to the journal Foundations of Physics Letters.

    The papers that I coauthored can easily be found via GoogleScholar. The next will be at Complexity’09, February 2009 in Shanghai, China.

    I am a big fan of Sean Carroll. But I have to keep a very open mind to possibilities such as that the cosmos as a whole in trapped in a closed time-like curve, with the “origin” and “end” of time being the same point. It is hard to analytically continue such curves, which is why I suspect ambiguities in quantum cosmology.

  • Loki

    Lawrence, thanks for responce. Still, what is wrong with my biological analogy?

    I mean: “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”

    Rephrasing B.Brain problem – “It is vastly more probable to be a single human on Earth than see other people around”.

  • Lawrence Crowell

    This all tends to point to the matter of the cosmological constant and the value of coupling gauge terms. The cosmological constant is probably not constant. It depends upon a Higgs-like field which inflated the spacetime rapidly into a flat (or near flat) geometry. The cosmological constant settled into the value we infer today which is involved with the latent accelerated expansion of the universe. We might imagine a universe with a large comsological constant which inflates early on much more rapidly and enters into a latent inflationary (accelerated expansion we observe) that is far more rapid. In such a spacetime mass-energy would rapidly expand away and little local structure (stars, galaxies, planets etc) would occur. Conversely suppose that that cosmological constant is very small. Such a universe might expand more slowly and have matter far more clumped together with far more black holes. In that case too much mass-energy would be tied up in black holes and local complex structure not as possible.

    Sean’s thesis here, which BTW assumes time exist, has quantum systems entering states which accumulate or have some asymptotic bound. These ever closely packed states have a lot of detailed selection rules for transitions between them. In order for all of these states to be occupied it probably requires that the universe becomes colder and for the cosmological arrow of time to march forwards as entropy increases. Robert M. Wald in The Arrow of Time and the Initial Conditions of the Universe (Enrico Fermi Institute and Department of Physics University of Chicago, arXiv:gr-qc/050709 vl 21 Jul 2005) writes:

    “There is no question that our present universe displays a thermodynamic arrow of time: We all have observed phenomena in our everyday lives where entropy is seen to increase significantly, but no one has ever reliably reported an observation of entropy decrease in a macroscopic system.”

    So a universe which expands too fast or one which buries quantum bits into black holes by expanding too slow might not satisfy Sean’s thesis as well. So the running parameters in a renormalization group appear adjust so that the time scales for the universe are appropriate for the “Goldilocks” condition we observe around us. We might be seeing Liebniz thesis about this being the best of all possible world at work! Voltaire’s Pangloss aside :-) In fact, the renormalization group equations (Wilson, Polchinski etc) are remarkably similar to the Navier-Stokes equation! So there is some underlying sense of a flow. The forward march of time, whether that be an emergent macroscopic thing or something absolutely fundamental, appears wrapped up in the structure of the universe, the “fine tuning” of gauge coupling terms and the cosmological constant.

    So this Liebnizian or Goldilock universe we observe appears to permit local inhomogeneities that give rise to structure on a wide range of scales: galaxies, stars, planets, complex chemistry, life and so forth. Some of these local clumps behave approximately as open thermodynamic systems which can give rise to very complex systems. It appears this is how the complex structure arises.

    The Boltzmann brain thesis is still outstanding in some sence. In a sufficiently large sample space of states Einstein could emerge spontaneously. Yet the universe we observe appears to not let this possible. An ever expanding universe is one which prevents incredibly long Poincare recurrences and for any equilibrium system to enter into all possible states.

    Lawrence B. Crowell

  • Loki

    I think i understand now, thanks.
    So, St.Augustine was right when he called the idea that history goes in circles totally preposterous? He used different arguments though :-)

  • CarlN

    Sean seems to think that infinite time is possible. Let’s make ourselves immortal and check.
    From now on we are immortal (regardless what happens to the universe) and we keep track of time. We will realize that after being around for 10^100000 years we can still be around a little longer. We see that there will never come time when we can say that we have lived for an infinite amount of time. Even though we live for ever we will never reach infinite age.
    So time cannot be infinite. By reflection of the argument a physical reality cannot be eternal. There is not enough time that can pass form minus infinity to reach the present time.

    One cannot escape creation from nothing. :-)

  • Lawrence Crowell

    I think it likely that time is infinite into the future, at least as measured by some standard clock which could measure that long. Time going back to the past appears to be bounded by the big bang, though there is room for arguments there whether time pushes further back to some pretunnelling state or other universe and so forth. The “time at infinity” is the attractor point in the (mini)superspace, which might be a Minkowski spacetime that is completely void or empty.

    We humans of course will not be there to see much of it. In fact there is room to question whether we will survive this century. The demise of the sun strikes me as a drop dead end time limit. Paleontology indicates that most large mammalian species are on the Darwinian game table for only a few million years. That is far short of any cosmological time scale, and our historical time frame is far shorter still.

    Lawrence B. Crowell

  • CarlN

    LC, you must realize that there will never come a time when the clock says: “An infinite amount of time has passed!” That time will simply never come even for a clock that runs forever. Jeez. Time is finite no matter how long.

  • Lawrence Crowell

    In part I indicated this with the problem of time intervals. If there is an accumulation point of energy eigenvalues then the energy spacings between these levels becomes very small Delta E_{i,i+1} < Delta E_{i-1,i} for all i, so in the limit i goes to infinity these spacings converge in a Cauchy type of sequence. The corresponding time intervals associated with these transitions which this quantum system computes become larger and larger. This system in order to be a physical clock must exhibit decoherence similar to a measurement. So as the "pure time" goes to infinity what quantum clocks there are which compute this time do so with ever larger time intervals. So there appears to be an issue of detailed balance or ratios here. So depending on how these energy eigenvalues values converge it could be that what quantum clocks the universe provides for itself may in the end compute a finite number (albeit enormously large) of time intervals. I'd need to think more about this to be certain of this conjecture.

    As for this so called pure time, this might be something considered by the Compton wavelength of an electron L = hbar/mc. As the universe expands in this accelerated manner there might in the distant future be some sort of "quantum solipcism," where every quanta which exists does so in isolation within a cosmological event horizon, which in the very distant future will retreat off to infinity. The electron appears absolutely stable, and for argument I will assume it is, even through vast times of 10^{10^{10^{…}}} years. So the quantum oscillations of an electron in its rest frame will beat with a T = hbar/mc^2 = 6.4×10^{-22}sec. So this might be seen as some parameter for the forward direction of time. If the universe expands endlessly and the electron is stable then there will be an infinite number of Compton oscillations.

    Of course this might not count as a quantum clock, for there is no decoherence involved with state transitions. Maybe these lonely quanta become entangled across vast distances across cosmic event horizons, or there are some sort of physics involving transitions, but I will defer opinion on that for now.

    Lawrence B. Crowell

  • CarlN

    LC, you don’t see. There will never be an infinite number of Compton oscillations. The number will keep increasing, from a finite n to n+1 to n+2 etc forever, but the number will NEVER become infinite.

    A transition from a finite value to an infinite “value” cannot take place by finite increments. Such a transition can only happen for an infinite increment.

  • Doug

    Sean,

    I agree with you that this “departure from the usual protocols of scientific communication” is a “good thing.” When I asked Peter Woit if he would be inclined to participate, he didn’t think it would be a good idea, given that he objects to the Templeton funding.

    Did that give you any pause and do you think it might be a more widely spread deterrant?

  • Lawrence Crowell

    CarlN: your argument would then mean the real number line can’t be infinite because nobody could ever count them all. You might in a sense pop out of the picture and think as Einstein told us to and think of the whole spacetime. The temporal part then “goes to infinity” in much the same way that the real number line goes to infinity.

    Lawrence B. Crowell

  • Fermi-Walker Public Transport

    Hi Sean

    Very interesting essay. I have a question, namely that if we are talking about the time evolution of a wave function, then the equations which describe the time evolution of such a wave function in quantum mechanics are invariant under Galilean transformation,
    not Lorentz. Galilean invariance assumes a universal time, does this matter in your argument ?

  • CarlN

    LC, the correct wording is that the real number line is unbounded. For any number you write down I can write a larger one. Then you write one larger still etc. We could go on for all “eternity” without ever reaching the “infinite number”.

    I guess you are starting to see what is wrong with Einsteins spacetime geometry.

  • http://cosmicvariance.com/sean/ Sean

    FWPT– You can certainly have a Lorentz-invariant version of quantum time evolution (the Schrodinger equation). The only trick is that the fundamental variables are not the positions of particles, but the amplitudes of quantum fields. (You can look up “functional Schrodinger equation” in some textbooks.) The notion of a Hamiltonian demands that you choose a frame in which to define it, but the result is independent of the frame you choose, if the underlying theory is Lorentz invariant.

    I discussed this more in the original version of the essay, but space constraints did not permit me to keep it. In a Lorentz-invariant theory, the time parameter is certainly not unique, but any choice is fine.

  • Lawrence Crowell

    CarlN, indeed the real number line is unbounded, and in a deSitter type cosmology the same is the case. I am not sure I see anything particularly wrong with this. We might ponder whether there are really indeed physical systems which demark time intervals endlessly. Sean says they do with the accumulation of eigenvalues. I think the conjecture is fairly reasonable. I suppose I see nothing wrong with the prospect of a quantum system that oscillates endlessly and demarks and infinite number of time intervals. That the system will never count some “final” time does not bother me particularly.

    Lawrence B. Crowell

  • CarlN

    LC, I’ll try one last time. What unbounded means: You can never reach the end of the line, but you can’t reach infinity either with finite increments (you could try by divison by zero, though).

    You could fix your favorite spacetime by a supplementary condition that says only a finite spacetime interval is physical. You will still have other problems though..

    The fact that “time” never can be infinite into the future from the present has very important implications. It means that an infinite amount of time can’t already have passed, even for a physical reality “outside” the BB. In fact all kinds of eternities are eliminated.

    You can work out the implications..

    Keep in mind that apart from what exits, there is nothing.
    If you think that entropy is an important concept:
    It requires less effort to specify low entropy initial conditions than high entropy conditions.
    In fact zero entropy initial conditions are easiest to arrange.

  • http://tyrannogenius.blogspot.com Neil B

    CarlN, I don’t see how you get the idea that time can’t be “infinite into the future.” That was never supposed to mean, there’d be “a time” at which the clock actually read “infinity” (the same as a “highest integer”, or treading “infinity” like another uber-integer somehow beyond each and every other integer ….) What’s to keep things from simply continuing to behave various ways in an ever-expanding universe?

    BTW, it can’t be both the case that time was indefinite into the past and yet constants could change with each iteration of a collapsing universe: the chance of becoming an open universe would always have already happened. (Contradiction: I can’t be even in such an open universe, contemplating “the infinity” of cycles before now, since however tiny the chance, the open cycle must have already happened earlier.)

    One thing throwing a monkey wrench into consideration of infinite time, and space, is how we can mathematically compress infinite extents into a finite length. We can for example (“normalize” as is convenient and use x or t), use t’ = ArcTan t, or x’ = x/sqrt(x^2 + 1) and remap an entire infinite extent onto a finite line or space. That possibility challenges a realist, common sense notion of what can coexist “in the same space.” Why? Because I can imagine that my entire “infinite universe” is mapped onto the space defined with ArcTan of the given value of r distance from me (such as it is.) It then has a pseudoboundary. (Not a true boundary, since the limit is not an actual defined value: it’s like the open circle at unity for x < 1.) Mappings are perfectly valid transformations, right, than cannot affect or "be observed" by the inhabitants. And yet, if I do so I can now imagine another entire universe "beyond" the infinity, mapped onto another finite segment in the new x' or t' container space. Even weirder, we can then compress an entire Aleph null of such compressed infinities via a second iteration onto x'' or t'', etc ….

    One can even imagine apparent absurdities like moving a point along x' such that it will actually blow past "infinity" of x in a finite time, or outwait the entire infinite time extent in t by slowing down appropriately, etc. (Compare "supertask.") Maybe that mathematical trick is not physically realizable. OTOH compare to the old saw about outsiders never being able to see the an object actually fall into a black hole. Yet the faller finds himself reaching not only the event horizon, but the singularity later in a finite time.

    The latter disjunction was the framing of a poignant SF story, "Kyrie" by Poul Anderson. The heroic energy-being type alien falls into the black hole. His telepathic human companion can "hear" his laments forever since for her, the fall never ends. See e.g. http://www.nvcc.edu/home/ataormina/scifi/works/stories/kyrie.htm. I admit to getting a little sniffly, reading the story as a boy (always a sucker for sentimental stuff like "Lassie Come Home.")

  • CarlN

    Neil B, “What’s to keep things from simply continuing to behave various ways in an ever-expanding universe?”

    Exactly. What remains invariant is that the future will always be at a finite (but increasing) “distance” from a given point in the past.

    Mathematical transformations won’t help you. You can’t “remap” the infinite future before it has happened. That time will never come.

  • Lawrence Crowell

    Neil B’s mathematical example is spot on. He did the work and keyboard tapping I was trying to avoid. The Penrose conformal diagram for the universe can put the t = infinity boundary, maybe a Minkowski spacetime, at a finite distance.

    The existence of an accumulation point in Hilbert space permits the continued existence of systems which mark time intervals. Whether they reach the endpoint as a summation of their iterations is besides the point.

    Lawrence B. Crowell

  • CarlN

    That is the other problem with spacetime geometries. People are led to believe that the future actually exists in some 4D (or more) geometry.
    As a calculational tool it is OK, but don’t get confused.

    This is why we never will see a visitor from the future. The future does not exist :-)

  • CarlN

    LC, the point is that the future will ALWAYS remain at a finite “distance” from for example today. This is an invariant fact of reality. Spacetime geometries go in and out of fashion on the other hand :-)

    Come on, is anybody willing to step up and say that there will come a time that is infinite into the future from Dec 1, 2008? I guess at least Sean should do so, since he suggests time going from – to + infinity :-)

  • Lawrence Crowell

    I am reminded of an account of George Bernard Shaw who apparently said he did not think the planets exist at the distances demonstrated by astronomers because nobody could ever walk to them.

    Lawrence B. Crowell

  • Roman

    Invariant fact of reality is that we will have some great new theories like CN’s popping out now and then.
    I don’t have one yet, but I have this question bugging me for some time now: why physics has problems with infinities while mathematics doesn’t?

  • http://tyrannogenius.blogspot.com Neil B

    Roman: of course math has problems with infinities, everything from dividing by zero to the status of infinite sets. BTW, I have yet to find a good rundown of “complex number infinity” descriptions, anyone know? I expect it would be “bifurcated” into two incommensurable limit approaches. One would be along a parallel line (such as 5 + infnty i) as one approached infinity along either the real or complex axes. The other would use r, theta guidelines. It would be in the form r = infinity, theta = whatever. Anyone see this?

    CarlN, your intuitive notions and “common sense” reasoning (reminding me of how “analytical philosophers” think) may not really constrain the real world, and they certainly don’t constrain the conceptual world.

  • CarlN

    My only problem with infinities is getting there :-)

    So if you become eternal you believe that there comes a time when you can say: Gee, look at the calendar. It has passed infinitely many years since 2008.

    Either you believe that or you don’t. Or you are not able to make up your mind.

  • http://tyrannogenius.blogspot.com Neil B

    CarlN, I don’t think there is an actual limit moment you can ID as “infinity”. Just think again of relations like x x’ transformation and the weird time issues about black holes. Maybe *I* can’t ever notice a calendar moment when “infinitely many years” since whenever, but *someone else* operating through mappings might be able to go past all of my infinite time or distance (with my “infinity” like the open circle on “one” at x < 1.)

  • Roman

    Neil B, I agree I put it too broadly – what I meant is that infinity has its place in math, is part of the system. And from my layman perspective it looks like in physics infinity needs to be avoided at all cost.
    I know that there are good reasons for this – it just seams (maybe better would be feel) strange.

  • Lawrence Crowell

    Physics has problems with infinities associated with an observable. These crop up with electric potentials V(r) = qq’/r, where r —>0 at a point charge you get an infinite potential. There are of course ways around this, but singularities regularly crop up as troublesome. However, infinite time is not the same problem. A two body problem in Newtonian mechanics is ideally eternal. Of course we accept that for two stars in a mutual orbit other external factors will probably at some time end it, but there is nothing which causes physicist hair to stand up over the prospect of a two body system ticking away forever.

    The issue Neil B with the black hole is one example. If you fall into a black hole you will cross the event horizon in a short finite period of time. An external observer will see you slow down and never reach the horizon. This has a relationship called the tortoise coordinates, where you never can witness anything cross the horizon. Of course it becomes incredibly redshifted so that you can’t observe much except Planck scale modes. This gets into the whole matter of the stretched horizon, black hole holography and AdS/CFT. The curious thing which happens of course is that the external observer in principle can witness you, or Planck modes (strings etc) associated with you, right up to the moment the black hole quantum evaporates.

    In the case of cosmology there is no evaporation point of the same type. So with respect to some conformally mapped coordinates. So the “infinity” is reduced to something finite. In the Anti de Sitter cosmology, a sort of strange twin of the more physical de Sitter cosmology, the boundary of the space is in Fermat coordinates a finite boundary. Yet particles leave and exit this boundary at +/- infinity along great arcs similar to a Poincare disk. So something which is infinite in one definition (time) is mapped to something finite in Fermat metric coordinates. Of course you can put a black hole in this space and have all sort of fun with dilated times and coordinates for particles on paths between the boundary and horizon.

    Lawrence B. Crowell

  • Interested

    I am not able to follow the discussion, but it comes to my mind, the issue at least to lay people is whether time is an illusion. It seems the scientific discussion focuses on that it is not. ( at least that is what I gather )

    Wanting to get a better grip of whether time is an illusion, I decided to search readable sources— and gather that from New Scientist. http://www.newscientist.com/article/mg19726391.500-is-time-an-illusion.html

    “… Physicists have long struggled to understand what time really is. In fact, they are not even sure it exists at all. In their quest for deeper theories of the universe, some researchers increasingly suspect that time is not a fundamental feature of nature, but rather an artefact (sic) of our perception. One group has recently found a way to do quantum physics without invoking time, which could help pave a path to a time-free “theory of everything”. If correct, the approach suggests that time really is an illusion, and that we may need to rethink how the universe at large works.”

    I thought this is cute, that the holy grail quest for the “theory of everything” will or could soon be a “time free” theory of everything ( smile) (smile) (smile) So to get around, with a time free theory of everything, it seems to get back or return to or come home to square one with the suggestion time really is an illusion.

    So is time an illusion?

    I am a bit rushed for time so did not read the entire 7 page article if the fonts are expanded to size 12 Roman Times font style ( saved for a later day), so I cannot tease out the writer’s suggestion (if any) time is an illusion. http://www.newscientist.com/article/mg19726391.500-is-time-an-illusion.html

  • CarlN

    Ok. So Neil, as an immortal local observer, will not ever turn the calendar page “Year Infinite”. But LC, via some “conformally mapped co-ordinates” probably, will actually see that Neil wraps around to the page “year infinite”. LC, via a strong telescope can actually read “Year Infinte” on Neils calendar.

    Guys, this is not general relativity, this is general inconsistency. You seriously need to get your spacetime straight.

  • Interested

    My apologies, for being insensitive to many great , serious , & genuine attempts at the theory of everything, something dear to the heart, soul & mind of those professionally & scientifically engaged in that worthy pursuit.

    Such efforts are to be commended whether they bear immediate fruit or not. It may be there are several or more baskets of paradigms, and to reconcile the different baskets seem herculean now, with our current perception of separate and distinct baskets with their own self contained logic.

    This comment on New Scientist’s Is time an illusion?” echoes in my being … “It is not reality that has a time flow, it is our very approximate knowledge of reality that has a time flow,” says Rovelli. “Time is the effect of our ignorance.”…. because it comes close to home of ancient buddhist teachings that ignorance is the greatest taint, on the perception of the world as real, when it is not. Science view of and on time, gives a small window to introduce concepts of perception versus fundamental or non fundamental ( of which time is said to be a non fundamental) that seems to defy human understanding based on perception & experience, a rare & unique occasion of possible interface or criss crossing of views or worldviews. But the explanation given by the author is distinctly and admittedly different, “Imagine gas in a box. In principle we could keep track of the position and momentum of each molecule at every instant and have total knowledge of the microscopic state of our surroundings. In this scenario, no such thing as temperature exists; instead we have an ever-changing arrangement of molecules. Keeping track of all that information is not feasible in practice, but we can average the microscopic behaviour to derive a macroscopic description. We condense all the information about the momenta of the molecules into a single measure, an average that we call temperature.” And THUS “According to Connes and Rovelli, the same applies to the universe at large. There are many more constituents to keep track of: not only do we have particles of matter to deal with, we also have space itself and therefore gravity. When we average over this vast microscopic arrangement, the macroscopic feature that emerges is not temperature, but time. ..”

    This brings to my mind somewhere where it is said that time is connected or related to gravity, and the higher we go up a high rise building, and live there, we age faster because of weaker gravity as compared to another who lives on ground level. It also brings to mind something about travelling at speed of light and ?? not aging? Or something odd (forgotten), and so, it is not the usual perception of the clock ticking time as we ordinarily experience.

  • CarlN

    What comes to my mind is the similarity between the thermodynamic partition function and the QM path integral. By “Wick rotation” of the time you get a temperature.

    I guess Rovelli is right by saying that time does not really exist. Classically the present is encoded in the particles positions. The past exists only as encoded in the particles present momenta. And the future does not exist at all.

    Only the present really exist. Any spacetime geometry that allows some kind of time travel is fundamentally wrong.

  • Lawrence Crowell

    Interested: The problem is somewhat beyond whether time exists, but how is it that time in general relativity and quantum mechanics can ever be made to agree with each other about time. In general relativity time is a symmetry of the theory, or in the su(1,1) part of the sl(2,C) group. One can in ADM relativity consider spatial surfaces as foliating a spacetime. How these spatial surfaces link together is chosen by the analyst in a manner similar to a gauge choice. This is of course curious, for we can think of time as some one dimensional space with a fibration given by spatial surfaces. So “choosing” how time acts is equivalent to choosing a section in a fibration of spatial surfaces over a real line which parameterized time.

    Quantum mechanics in the other hand treats time as more concrete. The Schrodinger equation

    [tex]
    ifrac{partialpsi}{partial t}~=~Hpsi
    [/tex]

    holds time as an evolutionary parameter which is not a symmetry of the Hamiltonian. In relativistic quantum theory one must assign fields on a spatial surface of simultaneity (equal time commutators of fields etc), and from there time acts as a parameter which fixes a Hamiltonian, but is not a symmetry of the Hamiltonian. Things get somewhat odd when the space or spacetime is curved. In particular the distinction between a vacuum and a particle state breaks down.

    General relativity does not derive a Schrodinger equation per se, but in the “space plus time” ADM approach the canonical quantization of variables give the above equation with the left hand side zero. This Wheeler-DeWitt equation is then not a wave equation of evolution, but a constraint type of equation which specifies a wave functional on metric configuration variables.

    This dichotomy between how general relativity and quantum mechanics treat time still obtains. The big theory of unification is string theory, which is more particle based based. There general relativity is treated with a background, which adulterates some aspect of gravitation. The other theory called Loop Quantum Gravity is more general relativity oriented, but this theory has difficulty in deriving particle or quantum physics in a workable manner. At the core of this problem is that GR and QM simply regard time in basically different ways.

    In euclidean gravity time is related to a temperature as
    [tex]
    t~=~frac{hbar}{kT}
    [/tex]
    which indicates that on a microscopic level time is the phase description of spinor fields (or whatever substructure there is) to gravitation. There may then be a time, or equivalently a temperature, where the physics is scale invariant, which will occur for some very low temperature (T goes to zero) or equivalently a long time parameter. This is I think a quantum critical point, similar to the “breakdown” of electrons or quasi-particle Fermions in a Landau fluid.

    In this setting time appears to be emergent, but at the critical temperature T = 0 time does “go to infinity,” if you will.

    Lawrence B. Crowell

  • http://tyrannogenius.blogspot.com Neil B

    CarlN, there will not be a way to read the “year infinite” on my calendar since as I have repeatedly said, remapping makes the limit to infinity a “closed” point like the “one” in x < 1. But you may well be right that there is no way for any entity to physcially relate to another one in that remapped way which seems to "include" the limit to infinity within it's own finite coordinates. I could be just a math notion that has no real physical enactment. This is all part of the question, what is really real, wave functions, time itself, "curved space" and "so then, what does it curve into" etc. I think the universe isn't fundamentally real or self-sufficient in itself anyway. It's just a "Matrix" like scheme for generating phenomenal existence, i.e. for "a purpose" as hinted through anthropic fine tuning.

  • Lawrence Crowell

    It is hard to know if the universe expands to its attractor point in an infinite time period for sure. The cosmological horizon, just as with a black hole horizon, might produce exceedingly long wavelength radiation and decay. The following article arxiv.org/abs/0803.1987 discusses this, though I am not sure about part of this. However if this occurs the cosmological horizon at r = sqrt{3/Lambda} will have some temperature T ~ Lambda, and over an immense period of time the cosmological constant (parameter) will approach zero and the horizon will retreat off to “infinity.” The final state of this is an empty Minkowski spacetime. Whether this takes a literal “infinity time” or not is somewhat academic. It might be that as with BEC’s there is some tiny temperature T > 0 where the process stops. So the final state of the universe might then be at some finite time, though enormously large, in the future. Again we are in a domain of great uncertainty, and because of the nature of this subject we obviously will never do an experiment or make any observations!

    It is also curious that the final state might be a Minkowski spacetime, which would be an eternal void with no clock or anything else in it.

    Lawrence B. Crowell

  • CarlN

    Neil, I guess you took the point. You can’t remap infinite time, since it will not ever exist.
    On what is “real” you can only rely on what does not introduce inconsistency. A “thing” that is in conflict with itself cannot exist. It cannot exist more than 2=3.

    Certain spacetime geometries will in fact give rise to inconsistency or “incomputability” like GR regarding the BH singularity or time travel.

    However, the most important point is that “time” is invariably finite. The impossibility of future infinite time means that there is no infinite time in the past. The infinite simply takes too long for time to pass. So the beginning of time is finite in the past. This is of course the BB. And this is creation from nothing.

    Of course one can think about something “before” the BB, that has caused the BB. But the same logic applies. That needs a beginning too. As we have discussed before, you cannot explain anything using eternal (outside of time if necessary) concepts, since there is no way of explaining the properties of eternal “things”. There is no way of explaining something eternal has this set of properties instead of that set of properties. If you go that way all you have is wishful thinking and no explanation.

    You already know that creation “from” nothing is logical. That is simply logically possible.
    And also, it is of course impossible for something not self-consistent to start to exist.

    This is why our physics books is full of math!

    But still there are things to be said. On what it means to exist, for example.

    :-)

  • CarlN

    LC, time (or the size of the universe) will always be finite, but increasing. This is just a mathematical fact. You can’t reach infinity by finite increments applied one after the other. You just move from one finite value to another for ever. That is just the way it is. And how it must be. Physically it is impossible to measure anything infinite.

  • Lawrence Crowell

    Whether or not an alarm clock will ever ring once time reaches infinity is besides the point. Of course that can’t happen. That still does not mean that time can’t continue endlessly. In effect what you are saying is that because there is not the infinite register space for information required to enumberate that infinite time it then must not exist.

    Again one can consider a Zeno type of argument. Suppose that in one second I or some oracle machine counts 1, and then in the next 1/2 second it counts 2, and the in the next 1/4 it counts 3 and so forth. Then this is an infinite sequence of performed in 1 + 1/2 + 1/4 + 1/8 + … = 2 seconds. Now I have invoked a bit of “magic” here, but this does indicate that in a finite time an infinite number of counting steps is possible, at least mathematically.

    So for the universe being infinite in spacial extent, that is of course an interesting question. It indeed could be infinite! Inflation expanded a region the size of an atom to about 1 meter in the first 10^{-20} seconds or so of the universe. Suppose the universe tunnelled out of the vacuum from a wormhole with the Reissnor Nordstrom F(r) = 1 – 2M/r – /r^3/3, for

    ds^2 = -F dt^2 + F^{-1}dr^2 + r^2 dOmega^2

    Suppose the cosmological constant / = /(f, f-dot), for f a Higgian field, this for small scales, such as with a virtual wormhole near the Planck scale, this / might be very large. This will then act to inflate the two 3-balls in the interior of the wormhole boundaries, which compose a three sphere S^3. Now suppose that this Higgsian field is dynamical, say it is composed of gauge particles or quark-like particles. Then there is a theorem by Fred Taubs which says that such fields can be concentrated at a pole on the sphere, associated with a Chern class. This could not only inflate the sphere, but puncture it and push the boundary “off to infinity!” So inflation might not have just blown up a three sphere with a small radius of curvature to one with 10^{-20} that curvature, it might have literally “popped it” and stretched it out to infinity.

    I am not saying this happened with any certainty, but who knows. The universe looks awfully spatially flat, so it could be indeed infinite!

    Lawrence B. Crowell

  • CarlN

    LC, you are almost there. Time can indeed continue endlessly, while always remaining finite. The “transition” from a finite to an infinite value cannot happen by finite steps. Making the steps ever smaller can also prevent you from going past a certain value as your example shows.

    Anything infinite cannot be measured. Any theory involving infinities is impossible to verify.

  • Lawrence Crowell

    There are certain infinities which are more troublesome in physics than others. Physics is really about local principles, so if there is an infinte cosmology in either space or time which permits finite measurements in any local region this is not that troublesome. Infinities which are troublesome in theories is where you get infinite masses for particles or other divergences which would be locally observable.

    Again, I think the problem you raise is somewhat artificial. If there is a Cauchy-like sequence of energy eigenvalues, similar to what Sean argues for, which permit the endless occurrence of time increments to be “measured” by quantum transitions, then just because this will never register the “number” infinity, this does not mean there is not infinite time. By the same token just because there is no meter stick large enough to measure the real number line does not mean there is some consistency problem with the idea of the reals, or infinte spaces, or their application in physical or cosmological models.

    Lawrence B. Crowell

  • http://mccabism.blogspot.com/2008/11/cosmogenic-drift.html Gordon McCabe

    Interesting stuff.

    Any attempt to deny the real existence of time breaks the physicalist notion of the correspondence between brain states and mental states. We subjectively experience the passage of time as a succession of mental states; physicalism assumes, amongst other things, that you cannot have a change of mental state without a change of brain state; hence there is an objective succession of brain states.

  • daemon

    Sean, I think your classification of Parmenides as belonging to ‘presentism’ is incorrect. He would actually belong the the school of thought called ‘eternalism’.

    http://plato.stanford.edu/entries/spacetime-bebecome/

  • Lawrence Crowell

    Parmenides might be the first person to advance something similar to block time, which is the viewpoint in general relativity from a purist perspective.

    L. C.

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

    The classification was only a loose one, as noted in the essay — given the word limit, I couldn’t get into the various specific schools of thought.

  • Interested

    CarlN Says: “Only the present really exist. Any spacetime geometry that allows some kind of time travel is fundamentally wrong”

    I do not personally know, having little maths, but if there is something to this below ( same comment above about this funny script), then time travel might be fundamentally right, albeit progress in this area is slow.

    ” Prof RICHARD GOTT: The greatest time traveller so far is an astronaut, cosmonaut named Sergei Abediev who spent 748 days aboard the Meer space station travelling over 17000 miles per hour. And when he came back because of this he had aged a 50th of a second less than he would have if he had stayed home. In other words when he got back to the earth he found it to be a 50th of a second to the future of where he expected it to be, he has time travelled a 50th of a second into the future.

    NARRATOR (DILLY BARLOW): Admittedly a 50th of a second may not sound dramatic but the cosmonauts of Meer could have travelled much further into the future, all they’d have needed to do was travel even faster.
    Prof PAUL DAVIES: Imagine if I go off in a rocket ship at very close to the speed of light and perhaps I’m gone for about a year whizzing around our part of the galaxy and I come back to earth and I find that you’re ten years older. I’ve been away one year but ten years have elapsed here on earth, and so in effect I’ve just nine years into your future.

    Prof DAVID DEUTSCHE: This sounds like an extremely weird and unbelievable property of nature. It’s actually one of the best corroborated physical effects that we know of. People who build satellites have to routinely take into account the fact that time travels at a different speed in different states of motion.” http://www.bbc.co.uk/science/horizon/2003/timetriptrans.shtml

    Lawrence Crowell ,

    You attempted to explain to me, but I think it had more science than I could manage or chew off. I read this http://www.bbc.co.uk/science/horizon/2003/timetriptrans.shtml It seems like a pretend script, a made up story or dialogue but it also seemed to have some content . Yes ? / No?

    The ending of the script was surprising for it echoes what I felt at the onset of knowing the big question about time, if it exists.

    “Prof FRANK TIPLER: Inside the simulation you can’t tell any difference between the simulated environment, the virtual reality and the real environment. In fact this environment we need find ourselves in could be just a simulation.

    NARRATOR (DILLY BARLOW): Three hundred years ago science set out on a quest to master time, to control it. People didn’t like time being controlled by a super intelligent superior being, we do it for ourselves instead. But every time we made a break through there was a downside. Now we’re told we may not even be real. Instead we may merely be part of a computer program, our free will as Newton suggested is probably an illusion. And just to rub it in, we are being controlled by a super intelligent superior being, who is after all the master of time.

    Prof DAVID DEUTSCHE: From the point of view of science it’s a catastrophic idea, the purpose of science is to understand reality. If we’re living in a virtual reality we are forever barred from understanding nature.

    Prof PAUL DAVIES: Our investigation of the nature of time has lead inevitably to question the nature of reality and it would be a true irony if the culmination of this great scientific story was to undermine the very existence of the whole enterprise and indeed the existence of the rational universe.”

    Back to me – If it were to turn out that, we would walk down the road where, we realize we are not real, and that we are some virtual reality, then it will/could/might open door to other ancient knowledge of what type of virtual reality our rational being and rational universe is. It would/could/might be knowledge converging at some point in future, through the scientific pursuit of the scientific understanding of time, and thus of real nature of reality.

  • CarlN

    Interested, you refer to relativistic time dilatation. This is not time travel in the usual sense. You can slow your time (and aging) with respect to earth (for example) by taking a rocket trip.
    Time travel is stepping into a stationary machine and find that
    you have moved back in time or forward in time more than the time you spent in the machine. I tend take the absence of time travelers as empirical “proof” of the impossibility of this.

    LC, Sean is not using the accumulation point(s) of eigenvalues to “generate” time by quantum transitions. Instead he says nothing about time and uses the superposition of eigenstates to make sure the universe never repeats itself (given time from the outset). However, he does not explain in this setup how an omelet turning into eggs is less probable than eggs turning into an omelet.

  • Lawrence Crowell

    The idea is to provide a large enought a Hilbert space, which has energy gaps small enough for any future cold condition, so that a quantum Poincare recurrence does not set in. An elementary example of a recurrence is a two state atom and photon in a cavity described by the Janes-Cummings Hamiltonian.

    Lawrence B. Crowell

  • CarlN

    LC, what in this setup make sure the future cold condition?

  • Lawrence Crowell

    As the universe expands things get colder. The 3K CMB temperature is a remnant of the period about 380,000 years after the big bang where radiation and matter existed in a plasma. The end of that age released the radiation which is now redshifted and “cooled” to the feeble microwave background we see today. This will continue as the universe expands into a sort of void that approaches absolute zero temperature.

    Lawrence B. Crowell

  • CarlN

    I know, but what about what my question?

  • Lawrence Crowell

    It is the expansion of the universe which keeps temperature dropping. Consider a box, where the boundary points of that box keep expanding out by comoving of coordinates. The wavelength of light in that volume increases as that expansion occurs, if we think of the box as being like an EM cavity. The energy of photons is E = nhc/L, L = wavelength and n = # of photons which is constant. So if these photons are thought of as particles in the box with E = pV, which is decreasing, then an analogy with the natural gas law pV = nkT tells you that temperature must be declining.

    Lawrence B. Crowell

  • Interested

    I feel like I am a parrot. We have a 30 years old parrot at home, and i let him or her out of the cage so he or she is free ( sex/gender cannot be easily determined without DNA or what test as not visible)

    I am parroting the answers I read. CarlN, answers to your question. First what is the source? BBC Space.

    Second what is your question.
    You (CarlN) : Time travel is stepping into a stationary machine and find that you have moved back in time or forward in time more than the time you spent in the machine.

    Paraphrase your question: Is a stationary time machine for travel to future theoretically possible according to science?

    Parroting http://www.bbc.co.uk/science/horizon/2003/timetripqa.shtml : “The Future
    According to Professor Paul Davies “Scientists have no doubt whatever that it is possible to build a time machine to visit the future”. Since the publication of Einstein’s Special Theory of Relativity in 1905, few, if any, scientists would dispute that time travel to the future is perfectly possible. “ What are the different possible time machines we could build?
    There are now a number of different proposals for time machines that have been put forward by well-regarded physicists, for example:…”

    Paraphrase your question : Is travel to past possible as opposed to future ?

    Parroting : The Past
    Time travel to the past is more problematic, but there is nothing in the known laws of physics to prevent it. It is accepted that if you could travel faster than light, you could travel to the past. However, it is impossible to accelerate anything to a speed faster than light because you would need an infinite amount of energy.

    You: I tend take the absence of time travelers as empirical “proof” of the impossibility of this.

    Parroting : If time machines are possible, why haven’t we built one?
    Although the time machines suggested by physicists are theoretically possible, all of them would require massive amounts of energy and a level of engineering technology that we don’t have at the moment, and which we are unlikely to have for quite some time.

    “One of the most famous arguments against time travel is that if time travel is possible, why haven’t we been visited by lots of time travellers from the future? Again, people have come up with ways round this objection: we may be inundated with time travellers and not be aware of it. Maybe that’s what UFOs are. Perhaps civilisations don’t last long enough to develop the knowledge and technology required to build a time machine. And most convincing of all, general relativity says that you can only go back to the time a time machine was created. Since no one has built a time machine yet, no one can come back to this time.” (*I do not know why general relativity says that or has to say that???##@@@)

  • CarlN

    Hi LC, again..I know. To be more precise: What in Seans setup ensure the expansion of space? And what in the setup make sure that an omelet turning into eggs is less probable than eggs turning into an omelet? I can’t find any of that.

    Interested, people who believe in time travel are people who think that spacetime is a “structure” where the past and future actually exist (“block” time view) instead of viewing it as a calculating tool. In some of these proposed geometries time travel is indeed possible. Which only prove that the geometry is badly “constructed”, since there is no way of preventing future time travelers of visiting us. Remember that the future already exists in Einsteins 4D spacetime (if you view it the “wrong” way), which of course is nonsense.

    Please, no conspiracy theory about secret visitors from the future.

  • Interested

    CarlN, would it be apt to paraphrase or capture your expressed and implied point of view, that time is a calculating tool (epxressed), but does not exist as a real dimension (implied). That ordinary people perceive time as a real dimension, the past, present and future, 13.7 billion years ago, and the time in future of LC’s ” This will continue as the universe expands into a sort of void that approaches absolute zero temperature.” when the distant future, approaches absolute zero coldness, is then a common defect of perception (implied), a prevailing shared defect of humans (implied). That it takes skilful science or maths understanding to see or accept time merely as a calculating tool, and not a real entity by itself.

  • CarlN

    Interested, I do not belive that time (as something fundamental) really exists at all. Time can only be measured by comparing one motion (or change) to another. So motion seems to be more fundamental than time.

    It seems you belive that the universe not only exists as we see it today, but that it also exists in the cold, expanded “future” state, and also in all stages in between. In this view the universe is also still in the Big Bang state, probably.

    I agree that it is possible to view the 4D spacetime this way. I only say that the absence of time travelers shows that this view is probably wrong.
    So yes, the 4D spacetime geometry is only a calculating tool. Be careful when you use it :-)

  • Lawrence Crowell

    Time machines? Why yes of course, or well … uhmm maybe, but on second thought probably no. Kip Thorne showed that a worm hole can act as a time machine. A worm hole is like a blackhole, but if one enters it you pop out elsewhere from a connected identical opening. So there are two connected openings with a boundary which have points identified with each other. Now suppose you hang a clock near each of these openings. If one opening is Lorentz boosted to near the speed of light and then brought back near the speed of light on another boost the so called twin paradox has the clock near that opening far behind that of the first. As a result a person can loop through the worm hole and travel back in time. There is a null congurence of rays, like a light cone, which connect the openings at equal times on their clocks where the time machine is “turned on.”

    This sounds simple, right? What is the problem? It requires that some exotic quantum field of matter exist right around where the event horizon would otherwise exist. This field acts to defocus geodesics and connect them to this other region. This exotic field violates some energy conditions established by Hawking and Penrose, in particular T^{00} > 0 is violated. The momentum-energy tensor terms are ultimately determined by a quantum field, and if they violate this energy condition it leads to a big problem. In particular the quantum states are not bounded below, such as the elementary case of the minimum S-wave for the electron in a hydrogen atom. This means that quanta can endlessly transition to lower energy states and produce an infinite amount of energy. The result for spacetime is that it would lead to enormous fluctuations which would destroy the worm hole. Ford and Roman have in connection to this demonstrated a quantum interest conjecture which indicates that attempting to accumulate negative energy, T^{00} < 0, always results in more positive energy which overwhelms your attempt.

    The Dirac sea of the electron suggests this as well. The negative energy states are "occupied," so no real quanta can fill them. If you try to excite a state there you generate an electron with opposite quantum numbers, but with positive mass, which is called the positron. Quantum mechanics has other hints as well. For space and time translations are determined by the momentum and energy operators, as with Noether's theorem. Yet worm holes, multiply connected spacetimes and time machines indicate there exist nonunique maps, or operator determined translations, which connect these points. This leads to problems with the uniqueness of operators on Hilbert space.

    There are other exotic spacetime solutions. The Alcubierre warp drive and the Krasnikov tube are examples. These all rely upon T^{00} = 0, and appears as some sort of protection that ensures this. This connects with worm holes as well, for one could imagine generating an opening into a black hole, pulling out hidden information in the interior and thus violating the laws of thermodynamics which apply to black holes.

    On the matter of time as something fundamental, say linked with quantum gravity and field theory, it is best to keep an open mind.

    Lawrence B. Crowell

  • CarlN

    LC, good job. Yes the entropy keeps increasing.. Note that it by definition can’t be negative. That is interesting as we rewind time (evolution of the universe). We can’t rewind anymore when we reach S=0. We reach the beginning of time. The big bang, the creation from nothing. The beginning of time follows from the second law. Note that you logically (and thermodynamically) can’t have periods (finite or infinite) where dS/dt = 0 for the universe as a whole somewhere in the past.

    From our earlier discussion we noted that time will always be finite in the future, hence it must be finite in the past. Nice to note that the second law comply with this purely mathematical result. Well, it would indeed need to comply!

  • Interested

    You: Interested, I do not belive (sic) that time (as something fundamental) really exists at all. Time can only be measured by comparing one motion (or change) to another. So motion seems to be more fundamental than time.

    CarlN, if time ( to you) does not exist ( to put it plainly and to then dispense with the coating of “fundamental” ),

    (i) then how would you tell a lay person, why time does not exist when he or she sees time exist in so many ways every day every minute.

    (ii) If time which is so commonly experience and thought of as real and existing, what is there to suggest that the same cannot be said of other equally real things that we take as real in our everyday day to day life?

    (iii) There has to be a way that scientists can explain the science time rules to the “12 jurors and their alternates” so that, these every day jurors, people who live down your street, can apply these rules to the facts that they have to figure out. Every juror has to know what the community of scientists say the rules of time are. Like in a trial court, opposing counsels will not agree with the rules of law for the judge to direct the jury, and they will split hairs over the rules, and the judge rules on what the rules are when there is lack of disagreement, taking note later, of the objections of the counsel whose version of the rules have been sidelined. So to spare the jury the torment of knowing what the conflicting rules are, the judge hears the disagreement of the opposing counsel when the jury is out, and makes his or her decision as to what the rules should be for the instant case, and when the time is right, the judge tells the jury in no uncertain way, what the rules of law are and how they should apply it to the facts of the case. The jury then only has to weigh the facts. As lay people, we have our experiences of time, we look at the picture of ourselves when we look hip, had moustache, dark hair, lean and slim and with a big dog beside us when the snap was taken, we pass by our alma mater where we studied, and the grave stone of our loved ones where we place a bouquet of flowers now and then and on Thanksgiving too, as they are not around us to celebrate the day. What are the time rules that we the jury should know and follow and apply to determine the case?

    You : It seems you belive (sic) that the universe not only exists as we see it today, but that it also exists in the cold, expanded “future” state, and also in all stages in between. In this view the universe is also still in the Big Bang state, probably.

    CarlN, I have not till now thought of it that way. Reading and re reading and again rereading it several times, I ponder is that so? I see that you see it that way. The I ponder what is the difference between the way I see it and the way you perceive I see it. I ask myself if I infer from the way I see it, would I come to the derived at position that you describe of my perception?

    (i) I see it I existed before I was conceived and before I was born, and after I die. As to the form of existence, I do not know. I have no idea. I have no clue. A part of my Buddhist grounding, and I read widely across the three branches of Buddhism, for some years, and had a personal collection library of Buddhist books I bought, and helped to proof read the Theravada Buddhist bible ( The Dhammapada ) for the Chief Reverend of the temple I was somewhat connected with, is that maybe I might be born again as a human being in my next life ( after death of this life). I see the Big Bang ( as scientists tell us it happened probably) and see or imagine that you were there, I was there, all of us were there – how I do not know – but that all of us were there somehow and participated in it. The birds too that fly over the river.

    (ii) I disagree with the bleak outlook and end of the universe when we get the deep freeze in the far future expanded state and life can no longer be supported or at least as we know it. I tend to have some optimistic outlook that, if we can come from those who began to use fire, use and shape tools, and hunt and farm, and start factories, and invent technology, in that short span of time, if we compare the bigger time span of 13.7 billion years, then the exponential curve of progress we have made, can continue its exponential curve, how I do not know, where I do not know, but it would be to some fine end, the beauty of it we cannot imagine or conceive as the man who first learnt to build a fire could not imagine, how we can built a furnace to melt iron and make steel. Even if the universe has be very cold, something would still be going on in that exponential curve, what and how I have no inkling whatsoever. I grew up with no landline home phone and now there is easily accessible cell phones.

    (iii) CarlN, if you see that I see things as (i) (ii) can you see how difficult it is for me to capture your “the universe not only exists as we see it today, but that it also exists in the cold, expanded “future” state, and also in all stages in between. In this view the universe is also still in the Big Bang state, probably” and bring it within my fold of perception and worldview and personal view? Tell me what missing links must I fill in, to move from (i) and (ii) to “the universe not only exists as we see it today, but that it also exists in the cold, expanded “future” state, and also in all stages in between. In this view the universe is also still in the Big Bang state, probably” so that there can be a logical progression of thoughts.

    You: I agree that it is possible to view the 4D spacetime this way. I only say that the absence of time travelers shows that this view is probably wrong.
    So yes, the 4D spacetime geometry is only a calculating tool. Be careful when you use it

    CarlN, you have slipped through the fence. Let me break it down and see if I understand what you are saying. Are you saying –
    (i) Time does not exist . So time cannot be a calculating tool. Thus time is not a calculating tool.
    (ii) Space time ( as opposed to time itself) is a calculating tool.
    (iii) Space time is 4Dimension (4D) and the everyday world where we see hear feel is 3 dimension.
    (iv) Mathematics, geometry, algebra are calculating tools. Space time geometry as other branches of geometry as other branches of mathematics are all calculating tools.

  • CarlN

    Interested, I don’t know if time is real or not. All I know is that the more I think about it, the more unreal it gets. It is like gravity. It seems natural that things fall down when dropped until we start to think about it. Then it gets difficult. We are all born as idiots with stupid instincts so that whatever we see or “feel” it seems natural. And we remain idiots until we start to think about things.

    Distance (space) can be measured by comparing with a unit distance (one meter). Same with mass and electric charge. Not so with time. Time can only be measured indirectly by comparing one motion to another. Why is it so? Why is there no time “quantity” that we just can “pick up” and use as a unit? Why do we have go through all this stuff with motion and change in order to be able to measure time?

    I guess this is the main reason for my worries about time. Looks like time is not fundamental, but it is of course still a very useful concept.

    Anyway, science is not settled via consensus, democracy or jury. Science is all about consistency and reductionism. Explain ever more using fewer and fewer hypothesis. In the end all will be explained using nothing unexplained.

    I normally get Gødel thrown at me at this stage. By people who has not understood Gødel :-)

  • Lawrence Crowell

    In general relativity the proper time ds = sqrt(g_{ab}dx^adx^b) has a relationship to a clock. The coordinate variable t is a chart dependent calculating device. This coordinate time only approximately has a clock meaning for a spacetime with some asymptotically flat region, such as a black hole sitting in a spacetime that is flat far removed from r = 2GM/c^2. Spacetimes in general do not provide this convenience. Quantum mechanics on the other hand involves dynamical wave equations which explicitly use the coordinate time t. The Schrodinger equation and relativistic wave equations all do this. So the coordinate time is treated as a physical parameter for the dynamics of a quantum wave. As a result some hard work is required to place quantum fields in spacetime (equal time commutators etc), and this leads to some curious physics for quantum fields in curved spacetimes, which in turn leads to the radiation emitted by black holes.

    Because of this there exists a dichotomy in our concepts of time between general relativity and quantum mechanics. This is related in part to the problem of quantizing gravity, for you are attempting to quantize a field theory with one concept of time according to a procedure which requires another concept of time.

    As for comparing different times according to different moving objects, we sure do this! I worked on how to synchronize clocks in Earth orbit before GPS devices got embedded in nearly everything these days. General relativity tells us that clocks moving in different regions of the gravity field will mark time according to different intervals or proper times. For GPS purposes this will cause time on these different satellite frames to drift apart, which will result in errors in the triangulation of a point on Earth.

    So time is measured in a sense relative to other “times.” Galileo measured the periodicity of a chandelier by using his pulse, presumably as the story goes during a mass. He then later used a clock to measure the periodicity of a pulse. If you have one clock you always know what time it is, but if you have two you might not. With measuring spatial distance we compare one distance according to some established length, a meter stick. So in some ways we do much the same thing. If one is to consider time as strange and maybe not existing the same really has to apply to space.

    General relativity is a relationship system between particles that involves geometry. Quantum mechanics is another relationship system which fundamentally relates particles to each other by an abstract Hilbert space of states. Quantum wave equations emerge by our representations of quantum states in spacetime, which have some funny elements to it. The fact that general relativity and quantum mechanics are different relationship systems between particles is manifested in the dichotomy in how the two define time.

    Lawrence B. Crowell

  • Interested

    CarlN : Interested, I don’t know if time is real or not. All I know is that the more I think about it, the more unreal it gets. It is like gravity. It seems natural that things fall down when dropped until we start to think about it. Then it gets difficult. We are all born as idiots with stupid instincts so that whatever we see or “feel” it seems natural. And we remain idiots until we start to think about things.

    I guess we all know what is real and what is real, and so we do not define ‘real’. But when it comes to ‘time’, when you say, ‘real’ or ‘not real’, you may mean something than what I think and I may not be aware of that. So I would like to see what you mean by ‘real’ and ‘unreal’ or ‘not real’.

    As for me, I am more drawn to time is not real than real, since scientists have come out in the open in public domain to discuss them. Before the recent understanding of a month or so back, I did not even know scientists have been concerned ( or as you say ‘worried’ about time). The reason I am more drawn to the idea that time is not real, is my own limited understanding of intuition in meditation, which I do not pursue to achieve enlightenment this life time or on paced program of within seven human lifetimes ( seven rebirths to go through all the levels of meditation to enlightenment) though at one stage of my life, such was my sincere and avowed aspiration to pursue it for seven life times, this lifetime included, but I support the institution that preserves that ancient method for others and for posterity, giving it the benefit of doubt ( as absent attainment, there will be reasonable doubt) The core of Buddhism is this world is not real, and there is no self, quaintly put, the light is on but no one is at home. If that be the perception of the conventional world, then time is but an element of the conventional world, and thus to see time as not real, is a sub part of the whole seeing the world as not real. Because of my limited experience in meditation, and other human experiences, and in the face of the open conflict between scientists as to whether time is real or not, I lean to think or infer that time is not real. But at this juncture, absent clearer more understandable science advice, I do not think I fully grasp what scientists have in mind when they worry whether time is real or not real or unreal. IF scientists can clarify in plain simple lay people language and modes of understanding absent abstract calculations, what it means when you say time is real, when you say time is not real, when you say time is unreal.

    All of us are born much the same way, we cry for food, comfort and through environment, and genetic advantages, we learn to speak write think research. Not many of us will have the advantage of further education, much less advanced higher maths and science education. Thus not many of us will have the scientific and mathematical ability to think in a structured way about gravity and time. Does it mean that absent scientific and mathematical training, we will never have the avenue to think about reality ( gravity, time, universe)? The people who can provide the avenue for those without the special science and maths training to think of reality, would have to step down their explanation to reach the ordinary man in the street.

    In today’s time and age & for the future, why should such avenues of thinking about reality be made popular knowledge or in public domain? There could be many reasons, but the reason that I wish to articulate here is that, every life lived lives philosophy examined or not. If we see or “feel” with our instincts, we imbibe a philosophy of life, and if we do not have the avenue to think about things, we will go by our instinct, but if society gives us the avenue, then we can think about reality even absent a higher science or maths qualification.

    You: Distance (space) can be measured by comparing with a unit distance (one meter). Same with mass and electric charge. Not so with time. Time can only be measured indirectly by comparing one motion to another. Why is it so? Why is there no time “quantity” that we just can “pick up” and use as a unit? Why do we have go through all this stuff with motion and change in order to be able to measure time?

    If time is measured indirectly by comparing one motion to another, what does this say about process of ageing, where we experience time in the most intimate of way. We grow old, the day we are born, we age every day every year. What happened to the baby the child teenager that we once were? What does 1 year old mean , 4 years old mean, 6 years old mean, 25 years old mean, 45 years old mean, 70 years old mean? IF time is measured indirectly by comparing one motion to another, than what motions are we supposed ( IF supposed to ) to compare? The motion of our cells , human cells with each other? With the earth? With other humans or other human cells?

    You: I normally get Gødel thrown at me at this stage. By people who has not understood Gødel

    I had to look up wikipedia to know who Godel is. It was too deep. So I looked up MSN Encarta and it made easier reading though in terms of content, it is understandably negligible. Absent understanding of Godel’s work, and absent maths training of even undergraduate level, and just based on MSN Encarta, which is really scanty, and for kids, my knee jerk response, is that, logic within a certain paradigm is self contained, and outside the parameters, it tends to become illogical. If so, then, the proof of a matter within a paradigm ( be it a field of maths or any field of human enquiry of recent centuries) can only be proven within the enclosed paradigm. Godel’s is thus another example of this human adventure to understand the universe and humans, where to contain that understanding we map out a field of understanding and the basis for it, and then, we delve into it and unfold many things in that field.

  • http://magicdragon.com Jonathan Vos Post

    I just submitted a link to this thread at

    The Status of Coalgebra
    Posted by David Corfield
    , the n-Category Cafe, because of the issues raised there about infinite-dimensional (even still countable-dimensional) topological vector space, whose underlying discrete vector space is (by the axiom of choice) uncountable-dimensional.

  • http://magicdragon.com Jonathan Vos Post

    Specifically, see what my friend Dr. Jonathan Farley writes: “Birkhoff and von Neumann developed the logic of quantum mechanics in the 1930’s. One central question is to characterize lattice theoretically lattices of closed subspaces of Hilbert spaces: they satisfy the orthomodular law at least [I read that this term was coined by Kaplansky, just to drop more names: as someone working in a field (lattice theory) a number theorist at Princeton has called ‘not interesting or important’ I am somewhat self-conscious].”

    “I may be wrong—my memory is poor—but I believe this question may only be interesting in the infinite-dimensional case because otherwise you just get orthocomplemented modular lattices.”

    In the n-Category Cafe thread I then expand on his correct citation and, correcting notation to be ASCII-ized, explain what orthocomplemented modular lattices are about, as T. S. Fofanova outlined roughly 30 years ago.

    I’ve not yet thrashed the matter to death with another friend, Dr. George Hockney, but he thinks that the foundational difference between countable-dimensional and uncountable-dimensional Hilbert Spaces for QM does not matter FOR PHYSICS as such, in part because a physical system is not quantized as such, but second-quantized. That it doesn’t matter how we renormalize is morally the same as that it doesn’t matter if we have countable-dimensional and uncountable-dimensional Hilbert Spaces for QM. What is the order of the renormalization group (countable or uncountable?) Another way to look at this is in terms of gauge invariance. We can’t get away from ghosts. For the gauge invariance, we must have that the Lorentz-transformed EM is a subspace of the Minkowski-transformed system as a whole. The real particles mix with virtual particles whether we like it or not.

    Philosophically, this relates to a question that I’ve been asking for 35 years: what is the topology of the space of all possible ideas (what Fritz Zwicky called the “ideocosm”)? What is the topology of the space of all mathematical theories? How do we make a hyperplane or hypersurface to separate the physical theories from the nonphysical theories within the space of all mathematical theories? (this is touched on in S. Majid, Principle of representation-theoretic self-duality, Phys. Essays. 4 (1991) 395-405). To avoid paradox, that seems to me neither a mathematical nor a physical meta-theory, that partition. But what is it?

  • Lawrence Crowell

    I would need to think to a bit about this. A countable Hilbert space, the classic case being a harmonic oscillator, is what is used in second quantization.

    A ghost field is employed to define a supergenerator so that unphysical fields are cancelled out. This is done so that Q^2 = 0 (eg fermionic) and the ghost anticommuting scalars are used to insure this condition.

    Where the size of Hilbert space comes in, which might have some bearing on ghosts and gauge theory is with the quantum cohomology of the generators. If one wants to get fussy this does depend upon issues of compactness, paracompactness and the rest. If states cluster up and become dense on some base of support then these subtle issues might crop up.

    Lawrence B. Crowell

  • Interested

    Jonathan : Philosophically, this relates to a question that I’ve been asking for 35 years:“what is the topology of the space of all possible ideas (what Fritz Zwicky called the “ideocosm”)?

    Of what good would it do to collect and store and archive all possible ideas? Not knowing what ideas Fritz Zwicky stored and archived, and retrieved for his research use, would it not suggest a storage has to be tailored to the intended use and needs of the specific user/s? The usual general storage area is the library. Some may collect and archive many things, like a human sponge. It is said that babies before age 5 are like sponges, and they can absorb many new things easily and learning is effortless then. It is said that Sanskrit is difficult to learn but a child below 5 who lives in that environment can learn it easily and speak it then. Those who collect sort out and compartmentalise and archive, are like the before 5 babies, human sponges, brains that absorb all. http://www.amazon.com/Absorbent-Mind-Maria-Montessori/dp/0805041567 Is that one of the further along human evolutionary process/es? On a parallel tangent, I have met 2 people who have told me that when some very good meditator monks die, and are cremated, their remains, include some crystals besides the ashes and bones ( as they have been privileged by circumstances to have a few of them.) I have also read that in one book on the monk who purchased the land in Northern CA, for his temple (something like ten thousand buddhas) and before he died, he donated a part of the forest land to the monks of a different buddhist branch (something like Redwood Valley area in Northern CA). ( I just pulled out the book to get his name Hsuan Hua, city of ten thousand buddhas) These people do not collect such worldly knowledge but it seems they are different and their difference is in what forms their body so that when cremated they leave behind things that others do not.

    What is the topology of the space of all mathematical theories?

    Do not know

    How do we make a hyperplane or hypersurface to separate the physical theories from the nonphysical theories within the space of all mathematical theories?

    Do not know

  • http://magicdragon.com Jonathan Vos Post

    The issue is not to store all ideas, but to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas. I’ve discussed that with Zwicky himself (whose first words to me were “who the hell are you?”) and Herman Kahn, and Linus Pauling, Jr. — they all agreed on this. Stephen Wolfram asked me the sneaky question: if you have a computer search for you, who owns the intellectual property to what is discovered?

  • Interested

    Jonathan: “The issue is not to store all ideas, but to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas.”

    Books are stored in libraries, catalogued, so they can be searched by topic, specific subject matter, author, etc. Abstracts enable easy overview of the longer works.

    What then would be methodologies to systematically explore the Ideocosm? How different would they be from that used by libraries?

    One apparent difference between “to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas” for public use versus private system of Zwicky ( not having spoken to him, nor met him, and not being called ……. [ seven letters] by him would be design of the system, made easier when ( imagine) Zwicky employs it for his own research & his area of interest is limited to his field of study.
    Given that, the world has many areas of studies that humanity has come up with and more yet to come, how can there be same methodologies for different areas of studies? For example, sciences differ from social sciences & humanities & arts. Even within broad categorisation, differences would appear in the different sub fields.

    How can mankind conceive of perfecting “methodologies” to cover all areas of human studies and explorations?

    Who determines what ‘really great ideas” are? If that be the criteria to selection for the Ideocosm?

    What is this ideocosm? The reality of nature , of the universe? Who determines what is the ideocosm? Zwicky? Based on what he collected and stored and the method he employed for himself for his limited area of study? Is that to be exponentially transferred to the whole world, whole of humanity, whole of universe, from beginning of time to end of time ( if there is a beginning and if there is an end since there is some doubt serious doubt whether time even exists)

  • http://magicdragon.com Jonathan Vos Post

    See also equation (5) of On the consistency of the constraint algebra in spin network quantum gravity, R Gambini, J Lewandowski, D Marolf, J Pullin – Arxiv preprint gr-qc/9710018, 1997:

    “While this sum involves an (uncountable) infinity of terms, its action on spin network states|Γ′is well-defined since only one term (the one in which σ maps the vertices of Γ to the vertices of Γ′ in the proper way) can be nonzero…”

    And also:

    Unimodular eigenvalues and linear chaos in Hilbert spaces
    Journal Geometric And Functional Analysis
    Publisher Birkhäuser Basel
    ISSN 1016-443X (Print) 1420-8970 (Online)
    Issue Volume 5, Number 1 / January, 1995
    DOI 10.1007/BF01928214
    Pages 1-13

    PDF (722.1 KB)

    Unimodular eigenvalues and linear chaos in Hilbert spaces
    E. Flytzanis1

    (1) Athens University of Economics and Business, 76 Patission Street, 104 34 Athens, Greece

    Received: 15 May 1993 Accepted: 15 October 1994

    Abstract For linear operators T in a complex separable Hilbert space H we consider the problem of existence of invariant Gaussian measuresm:
    mT^–1 = m. We relate the size of the unimodular point spectrum of T to mixing properties of the measure preserving transformations defined by T with respect to such invariant measures, and we draw some conclusions concerning orbit structure properties of T.
    The research for this work has been supported by a grant from the Research Center (KoE) of the Athens University of Economics and Business.

    “Unimodular eignevalues of linear operators in Hilbert space are usually associated with periodic or quasiperiodic orbits. We will show that this is indeed the case if they are countable. However if the unimodular point spectrum is uncountable then we will show that the orbits of the operator are also characterized by erratic behavior associated with chaotic motion. This happens because the linear transformations defined by such operators accept invariant probability measures having mixing properties in the context of ergodic theory.”

    Does someone want to draw a Cosmological conclusion from this?

  • Interested

    Jonathan: “Stephen Wolfram asked me the sneaky question: if you have a computer search for you, who owns the intellectual property to what is discovered?”

    http://www.outlinedepot.com/textbookoutlines.aspx?textbookid=385
    If you go to Outlinedepot.com you can preview the various law school outlines on intellectual property , and purchase them. I think they cost about $ 10 per subject outline. Many schools offer their outlines and so you have a choice of outlines. The preview section will give you an idea of the writing and pedagogical style that suits your taste.
    To answer your question, will require visiting those outlines and then framing them in a way that meets your expectations. It will take very much time and some cost. Maybe it may be done if circumstances permit, but otherwise this is the direction you are looking at on the net.
    In a broad brush, some things you want to watch out for- (i) intellectual property rights to protect writing (books) music [ copy right] patents, trademarks, service marks (?) and of course intellectual property rights and technology (ii) intellectual property rights at international level, TRIPS – Trade Related Intellectual Property rightS and concomitant 153 states’ obligation vide TRIPS Agreement and interlinked with about 40 (?) agreements through membership of World Trade Organisation, of which it was about 120 in 1994 at inception and 153 today.

    153: –
    [Albania 8 September 2000 Angola 23 November 1996 Antigua and Barbuda 1 January 1995 Argentina 1 January 1995 Armenia 5 February 2003 Australia 1 January 1995 Austria 1 January 1995 Bahrain, Kingdom of 1 January 1995 Bangladesh 1 January 1995 Barbados 1 January 1995 Belgium 1 January 1995 Belize 1 January 1995 Benin 22 February 1996 Bolivia 12 September 1995 Botswana 31 May 1995 Brazil 1 January 1995 Brunei Darussalam 1 January 1995 Bulgaria 1 December 1996 Burkina Faso 3 June 1995 Burundi 23 July 1995 Cambodia 13 October 2004 Cameroon 13 December 1995 Canada 1 January 1995 Cape Verde 23 July 2008 Central African Republic 31 May 1995 Chad 19 October 1996 Chile 1 January 1995 China 11 December 2001 Colombia 30 April 1995 Congo 27 March 1997 Costa Rica 1 January 1995 Côte d’Ivoire 1 January 1995 Croatia 30 November 2000 Cuba 20 April 1995 Cyprus 30 July 1995 Czech Republic 1 January 1995 Democratic Republic of the Congo 1 January 1997 Denmark 1 January 1995 Djibouti 31 May 1995 Dominica 1 January 1995 Dominican Republic 9 March 1995 Ecuador 21 January 1996 Egypt 30 June 1995 El Salvador 7 May 1995 Estonia 13 November 1999 European Communities 1 January 1995 Fiji 14 January 1996
    Finland 1 January 1995 Former Yugoslav Republic of Macedonia (FYROM) 4 April 2003 France 1 January 1995 Gabon 1 January 1995 The Gambia 23 October 1996 Georgia 14 June 2000 Germany 1 January 1995 Ghana 1 January 1995 Greece 1 January 1995 Grenada 22 February 1996 Guatemala 21 July 1995 Guinea 25 October 1995 Guinea Bissau 31 May 1995 Guyana 1 January 1995 Haiti 30 January 1996 Honduras 1 January 1995 Hong Kong, China 1 January 1995 Hungary 1 January 1995 Iceland 1 January 1995 India 1 January 1995 Indonesia 1 January 1995 Ireland 1 January 1995 Israel 21 April 1995 Italy 1 January 1995 Jamaica 9 March 1995 Japan 1 January 1995
    Jordan 11 April 2000 Kenya 1 January 1995 Korea, Republic of 1 January 1995 Kuwait 1 January 1995 Kyrgyz Republic 20 December 1998 Latvia 10 February 1999 Lesotho 31 May 1995 Liechtenstein 1 September 1995 Lithuania 31 May 2001 Luxembourg 1 January 1995 Macao, China 1 January 1995 Madagascar 17 November 1995 Malawi 31 May 1995 Malaysia 1 January 1995 Maldives 31 May 1995 Mali 31 May 1995 Malta 1 January 1995
    Mauritania 31 May 1995 Mauritius 1 January 1995 Mexico 1 January 1995 Moldova 26 July 2001 Mongolia 29 January 1997 Morocco 1 January 1995 Mozambique 26 August 1995 Myanmar 1 January 1995 Namibia 1 January 1995 Nepal 23 April 2004 Netherlands — For the Kingdom in Europe and for the Netherlands Antilles 1 January 1995 New Zealand 1 January 1995 Nicaragua 3 September 1995 Niger 13 December 1996 Nigeria 1 January 1995 Norway 1 January 1995 Oman 9 November 2000 Pakistan 1 January 1995 Panama 6 September 1997 Papua New Guinea 9 June 1996 Paraguay 1 January 1995 Peru 1 January 1995 Philippines 1 January 1995 Poland 1 July 1995
    Portugal 1 January 1995 Qatar 13 January 1996 Romania 1 January 1995 Rwanda 22 May 1996 Saint Kitts and Nevis 21 February 1996 Saint Lucia 1 January 1995 Saint Vincent & the Grenadines 1 January 1995 Saudi Arabia 11 December 2005 Senegal 1 January 1995 Sierra Leone 23 July 1995
    Singapore 1 January 1995 Slovak Republic 1 January 1995 Slovenia 30 July 1995 Solomon Islands 26 July 1996 South Africa 1 January 1995 Spain 1 January 1995 Sri Lanka 1 January 1995 Suriname 1 January 1995 Swaziland 1 January 1995 Sweden 1 January 1995 Switzerland 1 July 1995 Chinese Taipei 1 January 2002 Tanzania 1 January 1995 Thailand 1 January 1995 Togo 31 May 1995 Tonga 27 July 2007 Trinidad and Tobago 1 March 1995 Tunisia 29 March 1995 Turkey 26 March 1995 Uganda 1 January 1995 Ukraine 16 May 2008 United Arab Emirates 10 April 1996 United Kingdom 1 January 1995 United States of America 1 January 1995 Uruguay 1 January 1995
    Venezuela (Bolivarian Republic of) 1 January 1995 Viet Nam 11 January 2007 Zambia 1 January 1995 Zimbabwe 5 March 1995 ]

    The legal text for TRIPS agreement and others are in the website http://www.wto.org/ . Your question also crosses states borders through technology and you might wish to look at the user in any of the above 153 states or outside those 153 states, that is 42 states [ 195-153]

  • http://magicdragon.com Jonathan Vos Post

    Thank you, Interested. Although my wife and I have earned over $100,000.00 in consulting for top Intellectual Property law firms, I now delegate that subject to my son. My son, after all, is smarter than me. I was a ripe old 16 when I arrived at Caltech on full scholarship and worked with family friend Feynman. My son started full time at university at age 13, and got his double B.S. in Math and Computer Science at 18. He’s halfway through his J.D. program, specializing in Intellectual Property, at the Gould School of Law, University of Southern California. Stephen Wolfram (who met my son when my son presented a paper years ago at a Wolfram NKS conference) is in no way naive about IP, having won his showdown with Caltech, a complicated story dating back to when Wolfram left his Computational Physics professorship to commercialize Mathematica.

    Referring back to the title of this blog thread, “What if Time Really Exists?”, the deeper questions involve the period with which IP grants monopoly to the patent holder, versus the benefits to Arts & Sciences that it confers on society as a whole. Once computers have legal rights (inevitable when a system that passes the Turing Test has a good enough lawyer) then the whole game changes. Time really exists alright (though Sean Carroll opened a cute loophole with the uncountably infinite Hilbert Space notion) but the computers of the future, merged in ways we can’t yet describe with human beings, explore the Ideocosm dramatically faster with quantum hardware and genetic algorithm software.

  • Interested

    Jonathan,

    Thank you. You are welcomed. I cannot imagine such a computer, though one sees the likes of it in movies, where the computer takes on a life of its own. One of my favorites was the robot who opened his own bank account, and decided to go out and find other robots like him and he found none and lived by himself near the sea. But this http://www.poodwaddle.com/worldclock.swf that is circulating among my husband’s friends and sent to me just now, is a far cry but still something : – )))

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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