The Arrow of Time in a Restless Universe

By Sean Carroll | March 2, 2012 9:21 am

A group of philosophers and scientists interested in cosmology have started a new project, funded by the Templeton Foundation, imaginatively titled the Rutgers Templeton Project on Philosophy of Cosmology. It’s a great group of people, led by David Albert and Barry Loewer, and I’m looking forward to interesting things from them. (Getting tiresome questions quickly out of the way: like the Foundational Questions Institute or the World Science Festival, I’m totally in favor of this project even though I’m not a big fan of the Templeton Foundation. This isn’t the place to talk about that, okay?)

They also have a blog, because blogs are awesome. It has a humble title: What There Is and Why There Is Anything. They have a new post up, by Eric Winsberg, that brings up the issue of whether the multiverse can help explain the arrow of time. The post is basically a pointer to this paper by Eric, which is a close analysis of the kind of scenario I’ve been pursuing since my 2004 paper with Jennifer Chen. If this kind of thing is your bag, consider going over there and commenting on Eric’s paper.

I am working on a real science paper about some of these issues myself, but going has been admittedly slow. Let me just lay out a couple of the major issues here. One is, naturally, the question of whether the Farhi-Guth process of baby-universe creation really happens. In 2004 I was pretty confident that it did, but now I’m less sure. Aguirre and Johnson have looked closely at these kinds of tunneling events and come back pessimistic; others have looked at similar processes from the perspective of the AdS/CFT correspondence with similarly unpromising results. I don’t think the issue is settled, however; for the moment I’m willing to take the possibility of spontaneous baby-universe creation as an allowed hypothesis, while continuing to search for more well-grounded alternatives.

The other issue, which I think it should be more possible to make progress on, is a problem of counting — comparing the likelihood of different occurrences. In fact there are two sub-problems here. One is what’s now called the measure problem in cosmology. Assuming that many things (like the appearance of people exactly like you) happen an infinite number of times, how can we compare appearances to calculate probabilities? In this context the question is how we can compare the number of observers who appear in a nice warm post-Big-Bang environment to the number who pop randomly out of the nothingness as thermal fluctuations. In a scenario like ours, you need thermal fluctuations to create new universes, so there is always some possibility of making observers as well. I think that our picture is much better than most versions of eternal inflation from this perspective, as it seems easier to make a baby universe than to make an observer — the magic of inflation is that a bubble ready to inflate can be almost arbitrarily tiny, while an observer needs space for its thinking apparatus. But it’s harder to actually calculate things in a well-defined measure once your spacetime becomes disconnected by the appearance of new universes, so it’s certainly a legitimate question.

The other sub-problem, more subtle, might be called the “genericity problem.” The most important point of my paper with Jennie was to argue that a dynamical origin of the arrow of time is possible if and only if the space of states is infinitely big — the universe can keep evolving forever without reaching an equilibrium or entering a recurrent cycle. Baby universes were just the means to that end. But if there are an infinite number of possible states, how do you pick a “generic” one?

We tried to argue that “almost any” initial state would robustly evolve to a condition where baby universes were produced and became the dominant channel for creating observers. Our strategy for doing so was to say that a low-energy de Sitter vacuum was the highest-entropy state you could be in where space was still connected, and that most conditions evolve toward such a state. (At least if we discount Minkowski space with exactly vanishing vacuum energy, maybe for anthropic reasons.) Of course we then immediately evolve to a state with more than one connected component via the nucleation of baby universes. So then you could ask why we didn’t start there. Our idea is that there is no maximum number of components (separate universes), so any finite number can still grow. So why don’t we have an infinite number?

It’s a legitimate question, but not a show-stopper. In toy models it’s certainly easy to construct examples where there is no equilibrium state (as we mentioned in the paper). It could be difficult in those cases to fix what counts as a generic initial condition, but it might not be impossible. That’s something worth further investigation.

Nobody ever said explaining what there is and why there is anything would be easy.

CATEGORIZED UNDER: Philosophy, Science, Time, Top Posts
  • Bob McElrath

    An “initial condition” presupposes time, from which you intend to derive the existence of or arrow of time. It’s circular. To find time, you must rid yourself of the notion that there is a “state” that evolves into another “state”, because by invoking “evolution” you inject a suppostion about time into the problem. Time must be an inherent property of the “state”.

  • Torbjörn Larsson, OM

    One is, naturally, the question of whether the Farhi-Guth process of baby-universe creation really happens.

    Is it? I don’t know the technical details of course. But just reading from Aguirre & Johnson’s abstract they “comment on the relation of these solutions to possible mechanisms whereby inflating regions may be spawned from non-inflating ones.”

    “These studies found that the inflating (false vacuum)
    region could not avoid collapse unless either the null
    energy condition or cosmic censorship were violated in
    the full spacetime [1], but that the creation of an enduring
    inflating region might be possible via quantum
    tunneling [2, 3]. In this picture, henceforth denoted
    the Farhi-Guth-Guven (FGG) mechanism,”.

    But if we live in an observationally inflated universe the natural question would be if inflating regions may spawn several non-inflating regions. (Say, by inflation locally stopping.)

    Then we could live in a multiverse. The question about initial conditions, which the article seems to return to later, seems an over-reach.

    Our idea is that there is no maximum number of components (separate universes), so any finite number can still grow. So why don’t we have an infinite number?

    I take it that if inflation always existed, this would not be a problem. And an infinite number of universes would then be consistent.

    The only reason to bother about initial conditions among otherwise infinite seeming systems (potentially forward time infinite, potentially infinite volumes) is if one wants to posit that the arrow of time needs to have another explanation than the anthropic principle. (Having the latter case by, say, both the 2LOT and long enough lasting universes for observers from the expansion.)

    Or does fluctuations making observers come into it, despite “it seems easier to make a baby universe than to make an observer”? That would be somewhat confusing.

  • David Brown

    Is Milgrom the Kepler of modern cosmology?
    See http://vixra.org/pdf/1202.0083v1.pdf “Anomalous Gravitational Acceleration and the OPERA Neutrino Anomaly”.
    If nature is finite and digital then is there a way of circumventing the measure problem in quantum gravitational theory?
    See http://vixra.org/pdf/1202.0092v1.pdf “Finite Nature Hypothesis and Space Roar Profile Prediction”

  • Martin Ciupa

    Thanks for the opportunity to post. I would like to make three observations in terms of the philosophy of cosmology.

    1 There is a need to revisit Kant on the the attribute of existence in the ontological question (in its Godel form).
    2 Something kinetic coming from Nothing is not dealing with the concept of Nothing, since that Nothing is Something potential.
    3 Wheeler’s “it is bit” and the role of the observer in collapsing the (Everett) universal wavefunction and his resulting participatory anthropic principle is an interesting viewpoint given Hawking’s recent top down quantum cosmology views.

  • http://www.thdyoung.com/scrapbook/ Tom

    i thought this mordant quote from the king of psychotic honesty Philip K Dick might be salutary in these purlieus..

    “During the years — outright years! — that he labored…[he] must have come up with more theories than there are stars in the universe. Every day he developed a new one, more cunning, more exciting and more fucked.”

  • Jim Graber

    About time passing… Actually, totally off topic: I for one would like to hear more about Julianne’s accident, and particularly her recovery. I hope she is doing much better.

  • Jimbo

    Two points of view on time’s arrow which bloggers may find interesting are:

    Mathematician’s: http://arxiv.org/abs/physics/0608312

    Physicist’s: http://arxiv.org/abs/0909.2330

    I believe Steven Weinberg wrote that the computed convergence of the 3-gauge couplings at precisely the GUT scale of ~ 2×10^16 Gev was highly improbable unless the concepts behind it (MSSM) were actualized in nature.
    Watching Brian Greene’s NOVA special on the Multiverse, it occurred to me that the evidence for the reality of the Multiverse was even more compelling, since 4 prominent notions of modern physics (not 3) all point to its existence: Landscape, Eternal Inflation, Cosmological Constant, & Many-Worlds Interpretation of QM.
    Is there some degeneracy here, or are there really 4 pillars to the Multiverse ? Four would seem to be a slam-dunk !

  • Shantanu

    Sean, what do you think about
    this
    which appeared yesterday. (given that you have also worked
    on torsion). also what as happened to your co-bloggers?
    shantanu

  • Sam

    Sean,
    I can normally follow your clear writing. But this post I found very confusing. Could you perhaps elaborate more on each of the points here to make it easier to understand?
    Thanks

  • http://broadspeculations.com Jim Cross

    The idea of the multiverse really doesn’t solve the problem of why there is something instead of nothing. It just pushes the problem out of this universe to another level – why is there a multiverse?

    If the universe reached a state of maximum entropy, through random fluctuations, isn’t it 100% probable that over infinite time the universe would convert to the opposite state of minimum entropy?

  • s johnson

    What justifies the concern with the appearance of observers? Initial conditions must be compatible with the emergence of observers (us,) but wouldn’t eternal inflation of any sort say observer-compatible sets of boundaries conditions may indeed be infinitesimal? Meaning that there is no meaningful measure applicable to both observer-compatible and generic sets of boundary conditions? The only marker I could think of would be total mass/energy, each universe having a unique value for each. Then the multiverse might be ordered into a cosmos by this single parameter. Except of course it appears that infinite inflation doesn’t just mean an infinite multiverse but an infinite universe, although I confess I’ve never understood the logic there. (To be embarrassingly honest I’ve never quite understood why violation of mass/energy conservation was no big deal for infinite inflation.)

    Perhaps the problem is that in every multiverse scenario, our universe is radically contingent.
    But is that a real problem? An actual infinite does not have to be an infinite Person after all. If eternal inflation seems to admit of such a thing, might it not be a strong indicator there is something fundamentally wrong with the concept?

  • jim

    Re: What Jimbo (and B. Greene) said:

    But are all 4 the same multiverse? Or is it just that 4 different lines of thought lead to some concept of a multiverse – but not the same concept.

    Now, what if they actually were the same? For example, if the many worlds multiverse was the same as a bubble universes multiverse, would that mean quantum states could interact gravitationally with each other? So when a single particle passes through a double slit it’s 2 states have some gravitational interaction with each other?

  • Christian Takacs

    I am repeating what I said on the blog Not Even Wrong about this same, “Why is there something?” question.

    When someone studies or examines “Why not something instead of nothing?” it is called Existential Angst, and can be cured by growing up and getting a good job, raising a family and living a good life. When someone studies or examines “Why not nothing instead of something?” it is called Nihlism, and can’t really lead to anything (by its own definition), except perhaps a fatal overdose of drugs or self inflicted gunshot to the head (or foot). If a contemporary Mathematician wanted to model either of these “Why not” scenarios, all they would need to do is take the possible number of speculations in this universe and multiply by the number of multiverses, then multiply by (n+1) dimensions in an infinite series, divide by the number of papers that could be produced with “X” amount of funding in “T” amound of time, then multiply by zero. This formula should provide an extremely predictive and accurate answer.

    I must disclose that this experiment has actually already been performed by the very well funded “Deep Thought” Project. Unfortunatly, their results diverge from mine by exactly 42, and took… slightly longer to calculate. It has already been proposed that with even greater government funding and resources a third research venture might take place that will settle the discrepency between the two answers and maybe snag a nobel prize in the process!

    P.S.
    It saddens me that physics has come to the point where Douglas Adams begins to sound more visionary and less absurd than current theory. Ad Absurdum speculation on the nature of creatio ex nihlo came about only because certain Christian philosophers and scholars were ‘offended’ by the creation story of genesis which orginally had been philosophically creatio ex materia. The original story spoke of God using the waters of chaos as his base material to form the world from. Theologians did not like the inference that the ‘waters of chaos’ might have prexisted before the creator, or have been required since it would imply God was not absolute, and not the source of the stuff of creation. Instead of wasting time on pondering why aren’t we not here, why not take note of the fact that we are here, and study existence, not it’s lack thereof.

  • martenvandijk

    There is no distinction between the directions of time and the directions in space.

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    I think someone in another thread asked Sean’s opinion on http://arxiv.org/abs/1108.3080 so I’ll ask again here as it is relevant to this thread as well. The teeming millions want to know.

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    RE: #3: Just to be clear, the papers from viXra are not by Milgrom. They are, however, typical of viXra fare.

  • http://broadspeculations.com Jim Cross

    #13 Christian

    I agree with the absurdity of the “something not nothing” speculation but point to a different reason than Existential Angst.

    When we talk of “something” and “nothing” in ordinary language, we talk in reference to something. For example, there is an orange on the table so I can say there is “something on the table”. If the table is bare, I can say there is “nothing on the table”. The “something” and “nothing” are in reference to the table. “Nothing” in this context is a useful placeholder, like the number zero in mathematics, that allows us to say the opposite of “something is on the table”.

    We tend to think in a binary fashion. Something is a generalization of objects. Nothing, therefore, must be the absence of objects. This works fine in ordinary language. When we try to extrapolate this to the universe, however, it becomes meaningless. The something/nothing argument is really a misapplication of ordinary language to a sphere where it is inappropriate to be used.

    However, where much of the multiverse speculation is going is to try to find an answer to “intelligent design”, in other words to find a compelling argument to explain why we live in an universe friendly to life and with conscious observers. The best they can come up with is we just got lucky.

    This is not to say I buy into “intelligent design” either but any speculation about multiverse is ultimately bound to be as unable to be proved as the existence of God and effectively is little different from it.

  • http://dispatchesfromturtleisland.blogspot.com ohwilleke

    @3 Milgrom is probably more like one of the guys who discover one of the predecessors to the ideal gas law, or Tully and Fischer, or maybe even Linnaeas. In other words, somebody who comes up with a widely applicable and important empirical relationship that probably ends up not being fundamental or complete. In other words, a good guy who makes important contributions but not a Hall of Famer that will become a household name, like Milgram the social psychologist who did the abuse of authority experiments.

    FWIW, my instincts are a bit in tune with @5. I’m just not feeling the love for baby universes and multiverses, let alone the anthropic principle. Do we really need to “go cosmic” to get an arrow of time? Given the way CP violation manifests, the arrow of time seems like more of a grass roots pheneomena than something emergent from or even deeply tied to some kind of big picture.

    The more removed one’s theorizing gets from what we know, the more vulnerable one is at missing some big obvious point even as one gets all the details just right.

    I’m reminded of how I felt when I put a huge amount of research in a comparative law class into the details of the judicial system and private law of Singapore only to realize a few days after I’d turned it in that I’m missed the big picture: the flog people for petty offenses and execute people for middling ones and its pretty much a beneficient police state.

    Physicists are vulnerable to the same kind of miss the big picture thinking (and unlike mathematicians can’t pretend that the weird irrelevant theory they’ve come up with was what they were after all along), with a healthy heaping of group think thrown in. They tend to be hedgehogs not foxes.

  • Daniel Harlow

    Hi Sean,
    You didn’t mention it in this post, but there was recently an excellent paper by Bousso putting together a lot of the arguments about why eternal inflation & the landscape allow for a solution of the arrow of time problem. A particularly interesting point is that the presence of terminal (ie negative or zero cc) vacua is crucial in making it work. Also (shameless self-promotion) we recently added (3rd version) a discussion of this to our Eternal Symmetree paper which illustrates the mechanism in our simple toy model. You are right that assumptions about the measure are necessary for any such argument, but I’m not sure why you think Guth/Farhi needs to be figured out. The basic principle is more general than any witchcraft about Euclidean gravity…
    Daniel

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

    Daniel– Thanks for chiming in. Personally, I think Raphael is cheating just a bit, in treating past and future differently. (Note that none of his diagrams representing jumps between vacua look the same in the past as the future…) I hope to discuss this in more detail in the paper I’m supposedly working on.

  • Daniel Harlow

    I think that is the point though; decays of dS vacua to terminals never happen the other way. Think of it as a finite sized box with some gas in it, with a hole leaking out into infinite space, and with the boundary conditions at spatial infinity that nothing is coming in. This is a well-defined dynamical system, and it has an arrow of time because the gas gradually leaks out of the box until nothing is left. No matter how long you wait, the gas never comes back from spatial infinity. Of course in this system you just run out of gas, which is rather boring, but in eternal inflation (as well as we understand it) more gas keeps appearing in the box and you have an infinite directed flow…

  • Christian Takacs

    @Jim Cross,
    Thank you for addressing some of what I said in my earlier reply. I am coming from a slightly different perspective I think on the “Meaning of life” in this universe question however.

    I am first of all positing that all science and especially physics is supposed to be based on a mechanical causality that requires certain methods to be employed for it’s practice and comprehension to be possible. As far as science is concerned, Time is the rate of change of something compared against the relatively uniform rate of change of something else, usually a clock (Ticks per minute, cycles of the moon, miles per hour, ocillations per second, etc.). This means we do not actually measure time, we measure change in relation to some interval of something else and euphemistically call the interval “time”. That’s all time is or can be in regards to science, and it always has to be one second per second, or all bets are off as all measurements are dependent upon time being used to calculate rate and distance (Do not bring up Einstein’s twin pardoxes and contradictions, they are paradoxes and contradictions because Einstein made many mistakes in interpreting relativity, he even admitted as much). In any logical debate, a contradiction is not a ‘feature’, its a boo-boo. A paradox is not cosmically clever nor profound, it’s a logical error, ask any logician. To avoid such sillyness, time is one second per second, at any velocity. Everyone is travelling at some rate, if you are going to claim time moves at different speeds at every persons’ location, science and physics is not possible. No accurate rate of velocity or distance in calculation is possible at any location if every locations’ time moves at a different rate, everyone would get different asnwers if it was so, no science or measurement would be consistent…think about it. The only thing relativity does is act as a transform for ‘data’ being sent from distant moving sources. Relativity basically takes the distortion out of the funhouse mirror you are looking into, it doesn’t change the way you actually appear in any way, nor make you age faster or slower… Planet of the Apes be damned.

    Because all physical measurement and movement depends upon the use of time, you can not ‘do’ anything without it, much less science, physics, or logic. All science requires causality, all causality requires change. Any change you wish to monitor or observe, test or verify, requires the use of ‘time’ in making any kind of calculation possible. You want to discuss probability? statistics? You also require time. Mathematicians do not often like this fact. Not too surprising, since mathematics IS NOT reality, at best it is a language that may describe or model aspects of reality in abstraction. In any form Mathematics takes, it still requries Calculation, which is a process, and thus requires time in order to operate. Even Mathematicians in their ‘purity’ of the abstract do their work in time, good grief, they certainly want to get paid for it and fill out their time cards like anyone else in any other lowly profession.

    I have taken this rant up in the attempt to dispel any romanticized or abstracted consideration of time or “it’s arrow” in relation to science. If you are going to approach the universe with science to understand it, You are going to have to get used to the idea that if there is measurement of change, there is a before and an after. Always, no exceptions, no contradictions, no paradoxes. There is no “And then a miracle occurred” followed by very inexplicable large Kablooeys. You don’t get to start or stop time like a stopwatch. There most assuredly is no “rewind button” or Do-Over Mulligan switch ( Do not make me drag Minkowski or Einstein-Rosen into this) . You don’t have any scientific way to measure without or ‘outside’ of time, it isn’t logically possible, no argument can progress or emerge without time. You also do not have any way to scientifically theorize outside of time, how could you measure or test such theory? Virtual time, Meta Time? bunch of hooey, you can’t, not with science anyway. If anyone finds the stringent requirement of time in the very nature of science too confining for their speculations, They should stop pretending to do science or physics and look elsewhere for their answers where actual measurements are not required nor needed.

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

    Daniel– if it can happen one way, it can happen the other way. Just change coordinates by sending t -> -t. It might be unlikely, even “infinitely unlikely” in some way of calculating things, but in any fair accounting it would therefore be infinitely unlikely to find yourself in a dS vacuum in the first place.

    Or said another way: your boundary condition “nothing is coming in from spatial infinity” is clearly time-asymmetric (since you’re allowing things to escape to spatial infinity). So it’s no wonder you get an arrow of time — but you’re cheating by putting it in by hand, not deriving it from the dynamics.

  • Daniel Harlow

    “It would be infinitely unlikely to find yourself in a dS vacuum in the first place” – I agree, although I’d just say that it is infinitely unlikely to find a dS vacuum anywhere. The claim is that one needs to condition on there being a dS region someplace. The rough idea is that if you do this, then any initial state that satisfies this restriction gives rise to an arrow of time for the observers it produces via eternal inflation.

    I wouldn’t call this cheating however, conditioning on initial states that give rise to observers is allowed. The “problem” of the arrow of time is that “most” initial states that give rise to observers might give rise to `Boltzmann” observers rather than “ordinary” observers. But if we are able to argue that the presence of dS vacua someplace is necessary to have any observers, then at least in some measures with terminals present all initial states which produce any dS vacua produce “ordinary” observers more than “Boltzmann” observers. Technically “dS vacua” here means things that are long lived enough that they don’t globally exit.

    This probably isn’t the best way to discuss this…

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

    Conditioning on *states* that give rise to observers is allowed, but forcing them to be “initial” is cheating. If some particular terminal vacuum (e.g. Minkowski) is the most likely place to end, it’s also the most likely place to begin. So a non-cheating trajectory would begin in a terminal vacuum, hop up somehow to an anthropically-allowed vacuum, then exit to a terminal vacuum again. Generically such a trajectory would either (1) not involve inflation from a high-energy metastable vacuum, and therefore not create a large number of ordinary observers, or (2) probably go through such a vacuum, but also probably come out via that vacuum, in which case the anthropic vacuum will be very long-lived and be dominated by Boltzmann brains. (Always easier to make brains than to up-tunnel to a metastable vacuum.)

  • Daniel Harlow

    I think I’m claiming something weaker than what you want. You seem to want to have a way to compare the relative probabilities of completely different initial states, for example of being in AdS5xS5 vs being in 11 dimensional flat space, so that you can put a completely unconditioned probability distribution on the “space of all states” of whatever unknown completion of string theory is supposed to have all those things unified together. Personally I have no idea if concepts like phase space and Hamiltonian evolution make sense in such a general context.

    What Bousso etc. are saying is that there is a well-defined arrow of time problem that doesn’t require going so far beyond what we know. Consider a theory of stable dS space (which probably doesn’t exist but let’s ignore that). There is an arrow of time problem – even if you start in an initial state where there are observers who see entropy production for a while, eventually the thing equilibrates and crazy fluctuations happen, so most observers are Boltzmann. The claim is that this is not true once decays to terminal vacua are included. It seems that any state which leads to eternal inflation in the “future ”, with future being an arbitrary choice of the direction to evolve in, can lead predominantly to observers who see entropy production and are not Boltzmann. Since this is NOT true without terminals, I think something has been gained, even though it might not be a sufficiently broad set of initial states to make you happy.

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig
  • steven johnson

    This has got to be the most cryptic Carroll blog ever. It doesn’t even seem to be aimed at public outreach. Why such concern with observers, with or without Boltzmann brains?

  • Hephaestus

    I always wanted to be a cosmologist. When you do solid state or surface physics, you’re pretty well constrained by reality. In cosmology, you start at bat-guano crazy and extrapolate from there.

  • http://juanrga.com Juan Ramón González Álvarez

    Sean writes:

    The most important point of my paper with Jennie was to argue that a dynamical origin of the arrow of time is possible if and only if the space of states is infinitely big

    This idea has been known and explored since the 60s by very-well prepared people. It gives to fundamental difficulties. That is the reason for which, the Brussels School (leaded by the last Nobel laureate Ilya Prigogine) moved beyond the Hilbert space. Unfortunately, there are technical difficulties with such abandon (the precise mathematical nature of the space needed to deal with an infinite number of degrees of freedom is not known). Moreover, its can be shown that the assumption of an infinite number of degrees of freedom does not introduce any arrow of time (it is not a surprise that the Brussels School obtains *two* semigroups).

    There are many more reasons for the which your preprint do not hold up on close inspection. At first I would recommend you a look to the section 8 in the paper Non-redundant and natural variables definition of heat valid for open systems where several misunderstandings of the so-named “Generalized Second Law” (you allude to in your paper with Chen) and other mistaken topics in the gravitational thermodynamics literature are corrected.

  • rickflick

    Templeton? Tell me it ain’t so Sean. Tell me it ain’t so!

  • pakri

    Maybe a quote (Aristotle ?) could be a guide to us : Asking the right question is to know half
    the answer. Our present observation is that the universe is expanding with increasing acceleration.
    Beyond that we could be just speculating with or without maths.
    Similar questions were posed 2500 years ago, for example “Is the universe finite or infinite?”
    The unequivocal answer was : It is a profitless question.

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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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