The First Quantum Cosmologist

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Many of you scoffed last week when I mentioned that Lucretius had been a pioneer in statistical mechanics. (Not out loud, but inwardly, there was scoffing.) But it’s true. Check out this passage from De Rerum Natura, in which Lucretius proposes that the universe arises as a quantum fluctuation:

For surely the atoms did not hold council, assigning order to each, flexing their keen minds with questions of place and motion and who goes where.

But shuffled and jumbled in many ways, in the course of endless time they are buffeted, driven along, chancing upon all motions, combinations.

At last they fall into such an arrangement as would create this universe…

Lucretius, along with Democritus and Epicurus, was an early champion of atomism — the idea that the tremendous variety of substances we see around us arise from different combinations of a few kinds of underlying particles. He was also a materialist, believing that the atoms obeyed laws, not that they received external guidance. So a problem arose: how could all of that regular atomic motion give rise to the complexity we see around us? In response, Lucretius (actually Epicurus — see below) invented the “swerve” — an occasional, unpredictable deviation from regular atomic behavior. And then, he points out, if you wait long enough you will swerve your way into the universe.

It’s a good idea, and one that has been re-invented since then. Boltzmann, another famous atomist, hit upon the same basic scenario. Here is Boltzmann in 1897:

There must then be in the universe, which is in thermal equilibrium as a whole and therefore dead, here and there relatively small regions of the size of our galaxy (which we call worlds), which during the relatively short time of eons deviate significantly from thermal equilibrium. Among these worlds the state probability increases as often as it decreases. For the universe as a whole the two directions of time are indistinguishable, just as in space there is no up or down.

However, just as at a certain place on the earth’s surface we can call “down” the direction toward the centre of the earth, so a living being that finds itself in such a world at a certain period of time can define the time direction as going from less probable to more probable states (the former will be the “past” and the latter the “future”) and by virtue of this definition he will find that this small region, isolated from the rest of the universe, is “initially” always in an improbable state.

Boltzmann imagines the universe as a whole (or what we would call the “multiverse”) is in thermal equilibrium, about which he knew a lot more than Lucretius. But he also understood that the Second Law was only statistical, not absolute. Eventually there would be statistical fluctuations that took the thermal gas and turned them into something that looks like our universe (which, as far as Boltzmann knew, was just the galaxy).

We are now smart enough to know that this kind of scenario doesn’t work, at least in its unmodified form. The problem is that fluctuations are rare, and large fluctuations are much more rare; a universe-size fluctuation would be rare indeed. Who needs 100 billion galaxies when one will do? Or even just one observer? This objection was forcefully put forward by none other than Sir Arthur Eddington in 1931:

A universe containing mathematical physicists [which is obviously the correct anthropic criterion — ed.] will at any assigned date be in the state of maximum disorganization which is not inconsistent with the existence of such creatures.

These days, we throw away the rest of the mathematical physicist and focus exclusively on the cognitive capacities thereof, and call the resulting thermodynamic monstrosity a Boltzmann Brain. The conclusion of this argument is: the universe we see around us is not eternal in time and bounded in phase space. Because if it is, over the long term we really would just see statistical fluctuations, and we would most likely be lonely brains. So either the universe is not eternal — so that it doesn’t have time to fluctuate ergodically throughout phase space — or its set of states is not bounded — so that it evolves forever, but doesn’t sample every possible configuration.

Sorry about that, Lucretius. You’ll be happy to know that we’re still struggling with these same issues. Except that you’re dead and famously railed against the irrationality of belief in life after death. So probably you don’t care.

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The Hidden Complexity of the Olympics

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Chad laments that we don’t hear that much about the decathlon any more, because Americans aren’t really competitive. I also think it’s a shame, because any sport in which your score can be a complex number deserves more attention.

Yes, it’s true. The decathlon combines ten different track and field events, so to come up with a final score we need some way to tally up all of the individual scores so that each event is of approximately equal importance. You know what that means: an equation. Let’s imagine that you finish the 100 meter dash in 9.9 seconds. Then your score in that event, call it x, is x = 9.9. This corresponds to a number of points, calculated according to the following formulas:

points = α(x0–x)β   for track events,

points = α(x–x0)β   for field events.

That’s right — power laws! With rather finely-tuned coefficients, although it’s unclear whether they occur naturally in any compactification of string theory. The values of the parameters α, x0 and β are different for each of the ten events, as this helpful table lifted from Wikipedia shows:

Event α x0 β Units
100 m 25.437 18 1.81 seconds
Long Jump 0.14354 220 1.4 centimeters
Shot Put 51.39 1.5 1.05 meters
High Jump 0.8465 75 1.42 centimeters
400 m 1.53775 82 1.81 seconds
110 m Hurdles     5.74352    28.5    1.92    seconds
Discus Throw 12.91 4 1.1 meters
Pole Vault 0.2797 100 1.35 centimeters
Javelin Throw 10.14 7 1.08 meters
1500 m 0.03768 480 1.85 seconds

The goal, of course, is to get the most points. Note that for track events, your goal is to get a low score x (running fast), so the formula involves (x0–x); in field events you want a high score (throwing far), so the formula is reversed, (x–x0). Don’t ask me how they came up with those exponents β.

You might think the mathematics consultants at the International Olympic Committee could tidy things up by just using an absolute value, |x–x0|β. But those athletes are no dummies. If you did that, you could start getting great scores by doing really badly! Running the 100 meter dash in 100 seconds would give you 74,000 points, which is kind of unfair. (The world record is 8847.)

However, there remains a lurking danger. What if I did run a 100-second 100 meter dash? Under the current system, my score would be an imaginary number! 61237.4 – 41616.9i, to be precise. I could then argue with perfect justification that the magnitude of my score, |61237.4 – 41616.9i |, is 74,000, and I should win. Even if we just took the real part, I come out ahead. And if those arguments didn’t fly, I could fall back on the perfectly true claim that the complex plane is not uniquely ordered, and I at least deserve a tie.

Don’t be surprised if you see this strategy deployed, if not now, then certainly in 2012.

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Blogoplexus

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Apparently this is some newfangled technology by which pajamas-wearing loners can share their deep thoughts with strangers. New examples keep appearing, as if the existing blogs don’t already say more or less everything worth saying. Here is a long-overdue blogroll update, conveniently sorted into categories:

Physics-y Blogs

Yes, Leonard Susskind has a blog. No, he doesn’t update it. But he was answering questions in comments there for a while.

Blogs Not … Physics. Some Not Even Blogs.

No, I don’t read all of these blogs, not to mention all of the others on the blogroll; it’s more fun to rotate through different ones occasionally. And it’s absolutely crucial to use a newsreader, either Bloglines or Google Reader (or whatever). Infinitely easier. In the future, sleazy guys in bars will be asking not for your number, but for your RSS feed.

Nevertheless, there remain people out there who pine for the days of paper cuts and text you can underline. Female Science Professor has noted this proclivity, and turned some of her greatest blog hits into a book. Maybe we should do that someday?

And remember, if you have a blog that you would like to see on our blogroll, just let us know. We’ll forward the suggestion to our crack team of blog critics and reviewers, who will subject the blog to a rigorous screening program, after which we will forget about it for six months and perhaps update the blogroll.

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Superhorizon Perturbations and the Cosmic Microwave Background

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And another paper! Will the science never end?

Superhorizon Perturbations and the Cosmic Microwave Background
Adrienne L. Erickcek, Sean M. Carroll, Marc Kamionkowski (Caltech)

Abstract: Superhorizon perturbations induce large-scale temperature anisotropies in the cosmic microwave background (CMB) via the Grishchuk-Zel’dovich effect. We analyze the CMB temperature anisotropies generated by a single-mode adiabatic superhorizon perturbation. We show that an adiabatic superhorizon perturbation in a LCDM universe does not generate a CMB temperature dipole, and we derive constraints to the amplitude and wavelength of a superhorizon potential perturbation from measurements of the CMB quadrupole and octupole. We also consider constraints to a superhorizon fluctuation in the curvaton field, which was recently proposed as a source of the hemispherical power asymmetry in the CMB.

This is a followup to our paper on the lopsided universe, although the question we’re tackling is a little different. Remember that the point there was that we imagined some sort of ultra-long-wavelength perturbation, much larger than the size of the visible universe, and we asked how that would change the amplitude of small-scale perturbations in one direction of the sky as compared to the other.

In the new paper, we actually address a more basic question: what about the induced temperature anisotropy itself? So instead of looking at the power asymmetry (how does the amplitude of fluctuations in one direction compare to that in the opposite direction), we’re looking at the temperature asymmetry (how does the temperature in one direction compare to the temperature in the other). In fact, we’re looking at the “dipole” asymmetry — not small-scale fluctuations, but the large-scale hemispherical pattern.

Ordinarily, we simply ignore the dipole asymmetry, for a good reason: you get a dipole just from the ordinary Doppler effect, even if there are no intrinsic fluctuations in the CMB. If you have both, it’s hard to disentangle one from the other. But we were considering a supermode that was pretty substantial, and it became an issue — if the predicted dipole was much larger than what we actually observe, it would be hard to wriggle out of.

Except — it exactly cancels. That’s what the new paper shows. (And another paper the next day, by Zibin and Scott, comes to the same conclusion.) We were surprised by the result. There are clearly competing effects: we do have a peculiar velocity, so there is a Doppler effect, and there is an intrinsic anisotropy from the primordial density perturbation (the Sachs-Wolfe effect), and there is also something called the “integrated Sachs-Wolfe effect” from the evolution of the gravitational field between us and the CMB. And they all delicately cancel. We came up with a plausible hand-waving explanation after the fact, but it was the grungy calculations that were more convincing.

Nevertheless, the supermode idea is still constrained — the dipole cancels, but there are higher-order effects (quadrupole and octupole) that are observable. Karl Popper would be proud.

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Dark Matter and Fifth Forces

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I promised (myself) that I would post something every time I submitted a paper, but have been falling behind. An exciting glimpse into How Science Is Done!

So here is arxiv:0807.4363:

Dark-Matter-Induced Weak Equivalence Principle Violation
Sean M. Carroll, Sonny Mantry, Michael J. Ramsey-Musolf, Christopher W. Stubbs

A long-range fifth force coupled to dark matter can induce a coupling to ordinary matter if the dark matter interacts with Standard Model fields. We consider constraints on such a scenario from both astrophysical observations and laboratory experiments. We also examine the case where the dark matter is a weakly interacting massive particle, and derive relations between the coupling to dark matter and the coupling to ordinary matter for different models. Currently, this scenario is most tightly constrained by galactic dynamics, but improvements in Eotvos experiments can probe unconstrained regions of parameter space.

The idea of a long-range “fifth force” is a popular one, although it’s hard to make compelling models that work. In this paper we focused in on one particular idea: imagine that there were a new long-range force that directly coupled only to dark matter. (An old idea: see Frieman and Gradwohl, 1993.) After all, there is a lot more dark matter than ordinary matter, and we don’t know much about the physics in the dark sector, so why not? But then we can also imagine that the dark matter itself interacts, via the weak interactions of the Standard Model, with ordinary matter — i.e., that the dark matter is a Weakly Interacting Massive Particle (WIMP). Then, through the magic of quantum field theory, the fifth force would automatically interact with ordinary matter, as well.

So we scoped out the possibilities and wrote a short paper; a longer one that goes into more details about the field theory is forthcoming. The punchline is this graph:

You can think of the horizontal axis as “strength with which the new force couples to ordinary matter,” and the vertical axis as “strength with which the new force couples to dark matter.” Then you have various experimental constraints, and a band representing a range of theoretical predictions. The excluded blue region to the right, labeled ηOM, comes from direct searches for fifth forces coupled to ordinary matter, by measuring tiny composition-dependent accelerations of test bodies in the lab. The excluded red region on top, labeled β and involving only dark matter, comes from purely astrophysics, namely the fact that dark matter and ordinary matter seem to move in concert in the Sagittarius tidal stream. The diagonal green region at top right which doesn’t actually independently exclude anything, labeled ηDM, comes from searching for anomalous accelerations in the direction of the galactic center, where the source would mostly be dark matter. If the experimental sensitivity improves by enough, that constraint will become independently useful. The yellow diagonal band is the prediction of our models, in which the fifth force only interacts with ordinary matter via its coupling to WIMP’s. The length comes from the fact that the direct coupling of the new force to WIMP’s is a completely free parameter, and the thickness comes from the fact that the WIMP’s can couple to ordinary matter in different ways, depending on things like hypercharge, squarks, etc.

It was a fun paper to write — a true collaboration, in that none of the authors would ever have written a paper like this all by themselves. Part of our goal was to use particle physicist’s techniques on a problem that gets more attention from astrophysicists and GR types.

[Update: this part of the post is edited from the original, as will become clear.] Amusing technical sidelight: the way that you actually get a coupling between the fifth force and Standard Model particles can depend on details, as we show in the paper. For example, if there are “sfermions” (scalar partners with the same quantum numbers as SM fermions) in the theory, you can induce a coupling at one loop. But if you stick just to the WIMP’s themselves, the coupling first appears at two loops:

You certainly need at least one WIMP loop (that’s χ), by hypothesis. You might think that you could just have a single SU(2)L or U(1) hypercharge gauge boson connect that loop to the Standard Model fermion ψ, but that vanishes by gauge invariance; you need two gauge bosons, and thus two loops. But the the interaction you are looking for couples left- and right-handed fermions, so you need to insert a Higgs coupling. At low energies the Higgs gets a vacuum expectation value, and acts like a mass term, converting the left-handed fermion into a right-handed fermion, which is what you want.

In the original version of this post (and in the original version of our paper), I claimed that you would need a three loop diagram in the case where the dark matter had zero hypercharge (so you had to use SU(2)L gauge bosons, which couple only to the left-handed fermions). It was just the diagram shown above, with an extra gauge boson connecting the final leg to the segment between the existing gauge bosons. Fortunately, Tim Tait and Jacques Distler convinced us otherwise, in the comments of this very blog. (Fortunately for the integrity of the scientific method, anyway; for us personally, we would rather have figured it out ourselves.) You can read my version of an explanation here. The internet works!

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Great Moments in Framing

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Via Sociological Images.

That’s why you should become scientists, kids! (Because engineers don’t have sex. You want me to spell it out for you?)

I really should just leave it at that, but the sprawling, multifaceted stupidity of this public service announcement — apparently having sex, like smoking the wacky weed, kills brain cells and will cripple your SAT scores, or something — is difficult to let pass without comment. The immaturity of our cultural attitudes toward sex is flat-out embarrassing. There are real concerns that adolescents should be taught about — disease and the risk of unwanted pregnancy being the obvious ones. But they should also be taught that, as long as you are careful about such things, there is nothing wrong with having sex. Done correctly, it can be fun! Sure, there can be emotional trauma, awkward moments, broken hearts, impetuous late-night phone calls that you wish you could take back the next day. But these are downsides associated with life, not with sex per se.

But as a society, we’re too uptight and hypocritical to say these things. Instead, we get stuff like abstinence-only sex ed, with predictable results. And adolescence, which isn’t going to be an easy time of life for most people no matter how much sensible advice they are given, becomes just that much more agonizing and uncertain.

Except for engineers, of course! They have it figured out.

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Spiritual Menu

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Currently reporting from a tiny, hip hotel at an undisclosed location on the West Coast. Of the various ways in which this establishment brands itself as edgy and unconventional, there is no standard-issue Gideon Bible tucked in a drawer somewhere in each room. Instead, one is presented with a small laminated Spiritual Menu — a list of texts that can be fetched up to your room by a quick call to the front desk. Options include:

  • Bhagavad Gita: A New Translation
  • Book of Mormon
  • Buddhist Bible
  • KJV Gift and Award Bible: Revised Edition, King James Version
  • The Koran
  • New American Bible
  • Tao Te Ching
  • The Torah: The Five Books of Moses, Standard Edition
  • Book on Scientology

Probably, like me, you are wondering why there aren’t any options available for atheists. (Tedious explanatory note, since this is the internet: I am not really serious. Therefore, please to not respond with a lecture on why, when faced with a “Spiritual Menu,” the proper response for an atheist is simply to fast.) I mean, there have to be more of us than Scientologists, right? Although perhaps not among people who matter.

On the other hand, it’s not clear what would constitute an appropriate choice, as atheists have never been very big on sacred texts. I can think of a few possibilities. Something like The God Delusion wouldn’t be right, regardless of its various warts and charms, as it’s essentially reactive in nature — talking about why one shouldn’t believe in God, rather than celebrating or elaborating how to live as a cheerful materialist. Something like On the Origin of Species or Galileo’s Dialogue Concerning the Two Chief World Systems would be interesting choices, although they are too specialized to really fit the bill. You could make a very good case for a modern post-Enlightenment book like Richard Rorty’s Contingency, Irony, and Solidarity, as a serious (if not especially systematic) attempt to figure out how we should deal with a contingent world free of any guidance from outside.

But I would probably vote for Lucretius‘s De Rerum Natura (On the Nature of Things). As good empiricists, we should recognize that a classic text doesn’t have to get everything right, as our understanding continues to be revised and improved. So why not go for a true classic? Writing in the first century BCE, Lucretius (a Roman admirer of the Greek philosopher Epicurus) took materialism seriously, and thought deeply about the place of human beings in a world governed by the laws of nature. He advocated skepticism, dismissed the idea that life continued after death in any form, preached personal responsibility, and thought hard about science, especially the role of atoms and statistical mechanics. (Slightly ahead of his time.) And the book itself comes in the form of an occasionally-inscrutable poem, originally in Latin. Which adds a certain gravitas, if you know what I mean.

And, verily, those tortures said to be
In Acheron, the deep, they all are ours
Here in this life. No Tantalus, benumbed
With baseless terror, as the fables tell,
Fears the huge boulder hanging in the air:
But, rather, in life an empty dread of Gods
Urges mortality, and each one fears
Such fall of fortune as may chance to him.

It’s far from a perfect book — when it comes to sexuality, in particular, Lucretius stumbles a bit. But I’ll take it over any of the Spiritual Menu offerings, any day.

Shall we take up a collection to leave copies of Lucretius in hotel rooms around the world?

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Quantum Diavlog

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Remember when I asked for suggested topics for an upcoming Bloggingheads discussion with David Albert about quantum mechanics? The finished dialogue is up and available here:

I would estimate that we covered about, say, three percent of the suggested topics. Sorry about that. But perhaps it’s better to speak carefully about a small number of subject than to rush through a larger number.

And I think the dialogue came out pretty well, if I do say so myself. (And if not me, who?) We started out by laying out our respective definitions of what quantum mechanics “is,” in terms that should be accessible to non-experts. (One user-friendly answer to that question is here.) Happily, that didn’t take up the whole dialogue, and we had the chance to home in on the real sticky issue in the field: what really happens when we observe something? This is known as the “measurement problem” — it is unique to quantum mechanics, and there is no consensus as to what the right answer is.

In classical mechanics, there is no problem at all; you can observe anything you like, and if you are careful you can observe to any precision you wish. But in quantum mechanics there is no option of “being careful”; a physical system can exist in a state that you can never observe it to be in. The famous example is Schrodinger’s cat, trapped in a box with some quantum-mechanical killing device. (Someone must write a thesis on the ease with which scientists turn to bloodthirsty examples to illustrate their theories.) After a certain time has passed, the cat exists in a superposition of states: half alive, half dead. It’s not that we don’t know; it is really in a superposition of both possibilities at once. But when you open the box and take a look, you never see that superposition; you see the cat alive or dead. The wave function, we say, has collapsed.

This raises all sorts of questions, the most basic of which are: “What counts as `looking’ vs. `not looking’?” and “Do we really need a separate law of physics to describe the evolution of systems that are being looked at?”

In our dialogue, David does a good job at laying out the three major schools of thought. One, following Niels Bohr, says “Yes, you really do need a new law, the wave function really does collapse.” Another, following David Bohm, says “Actually, the wave function doesn’t tell the whole story; you need extra (`hidden’) variables.” And the final one, following Hugh Everett, says “You don’t need a new law, and in fact the wave function never really collapses; it just appears that way to you.” This last one is the “Many Worlds Interpretation.”

I want to actually talk about the pros and cons of the MWI, but reality intervenes, so hopefully some time soon. Enjoy the dialogue.

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Chatting Theology with Robert Novak

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Robert Novak, conservative pundit/journalist and TV personality, is retiring after being diagnosed with a brain tumor. Novak and I probably don’t agree on many things, and he isn’t called “The Prince of Darkness” for nothing (nor does he seem to especially mind). But brain tumors shouldn’t happen to anyone, so perhaps this is the place to share my Novak story.

Last September I gave a talk at a somewhat unusual venue: a conference at the University of Illinois on “Plato’s Timaeus Today.” Most of the speakers and attendees, as you might expect, were philosophers or classicists interested in this particular Platonic dialogue — which, apparently, used to be one of his most popular back in the Middle Ages, although it’s fallen a bit out of favor since then. But one of the central purposes of the Timaeus (full text here) was to explain Plato’s theory of the origin of the universe. (Briefly: the demiurge did it, not from scratch, but by imposing order on chaos.) (Also! This dialogue is the origin of the myth of Atlantis. It was not, as far as anyone can tell, a pre-existing story; Plato just made it up.) So the organizers thought it would be fun to invite a physicist or two, to talk about how we think about the universe these days. Sir Tony Leggett gave a keynote address, and I gave a talk during the regular sessions.

The point of my talk was: Plato was wrong. In particular, you don’t need an external agent to create the universe, nor to impose order on the chaos. These days we are reaching toward an understanding of the entire history of the universe in which there is nothing other than the laws of physics working themselves out — a self-contained, complete, purely materialist conception of the cosmos. Not to say that we have such a theory in its full glory, obviously, but we see no obstacles and are making interesting progress. See here and here for more physics background.

And there, during my talk, sitting in the audience, was none other than Robert Novak. This was a slight surprise, although not completely so; Novak was a UIUC alumnus, and was listed as a donor to the conference. But he hadn’t attended most of the other talks, as far as I could tell. In any event, he sat there quietly in his orange and navy blue rep tie, and I gave my talk. Which people seemed to like, although by dint of unfortunate scheduling it was at the very end of the conference and I had a plane to catch so had to run away.

And there, as I was waiting at the gate in the tiny local airport, up walks Robert Novak. He introduced himself, and mentioned that he had heard my talk, and had a question that he was reluctant to ask during the conference — he didn’t want to be a disruption among the assembled academics who were trying to have a scholarly conversation. And I think he meant that sincerely, for which I give him a lot of credit. And I give him even more credit for taking time on a weekend to zip down to Urbana (from Chicago, I presume) to listen to some talks on Plato. Overall, the world would be a better place if more people went to philosophy talks in their spare time.

Novak’s question was this: had I discussed the ideas I had talked about in my presentation with any Catholic theologians? The simple answer was “not very much”; I have talked to various theologians, many of them Catholic, about all sorts of things, but not usually specifically about the possibility of an eternally-existing law-abiding materialist universe. The connection is clear, of course; one traditional role of religion has been to help explain where the world came from, and one traditional justification for the necessity of God has been the need for a Creator. (Not the only one, in either case.) So if science can handle that task all by itself, it certainly has implications for a certain strand of natural theology.

Understanding that it was not an idle question (and that Novak is a Catholic), I added my standard admonition when asked about the theological implications of cosmology by people who don’t really want to be subjected to a full-blown argument for atheism: whether you want to believe in God or not, it’s a bad idea to base your belief in God on an urge to explain features of the natural world, including its creation and existence. Because eventually, science will get there and take care of that stuff, and then where are you?

And, once again to his credit, Novak seemed to appreciate my point, whether or not he actually agreed. He nodded in comprehension, thanked me again for the talk, and settled down to wait for his flight.

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What Will the LHC Find?

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With the Large Hadron Collider almost ready to turn on, it’s time to prepare ourselves for what it might find. (The real experts, of course, have been preparing themselves for this for many years!) Chad Orzel was asked what we should expect from the LHC, and I thought it would be fun to give my own take. So here are my judgments for the likelihoods that we will discover various different things at the LHC — to be more precise, let’s say “the chance that, five years after the first physics data are taken, most particle physicists will agree that the LHC has discovered this particular thing.” (Percentages do not add up to 100%, as they are in no way exclusive; there’s nothing wrong with discovering both supersymmetry and the Higgs boson.) I’m pretty sure that I’ve never proposed a new theory that could be directly tested at the LHC, so I can be completely unbiased, as there’s no way that this experiment is winning any Nobels for me. On the other hand, honest particle phenomenologists might be aware of pro- or con- arguments for various of these scenarios that I’m not familiar with, so feel free to chime in in the comments. (Other predictions are easy enough to come by, but none with our trademark penchant for unrealistically precise quantification.)

  • The Higgs Boson: 95%. The Higgs is the only particle in the Standard Model of Particle Physics which hasn’t yet been detected, so it’s certainly a prime target for the LHC (if the Tevatron doesn’t sneak in and find it first). And it’s a boson, which improves CERN’s chances. There is almost a guarantee that the Higgs exists, or at least some sort of Higgs-like particle that plays that role; there is an electroweak symmetry, and it is broken by something, and that something should be associated with particle-like excitations. But there’s not really a guarantee that the LHC will find it. It should find it, at least in the simplest models; but the simplest models aren’t always right. If the LHC doesn’t find the Higgs in five years, it will place very strong constraints on model building, but I doubt that it will be too hard to come up with models that are still consistent. (The Superconducting Super Collider, on the other hand, almost certainly would have found the Higgs by now.)
  • Supersymmetry: 60%. Of all the proposals for physics beyond the Standard Model, supersymmetry is the most popular, and the most likely to show up at the LHC. But that doesn’t make it really likely. We’ve been theorizing about SUSY for so long that a lot of people tend to act like it’s already been discovered — but it hasn’t. On the contrary, the allowed parameter space has been considerably whittled down by a variety of experiments. String theory predicts SUSY, but from that point of view there’s no reason why it shouldn’t be hidden up at the Planck scale, which is 1015 times higher in energy than what the LHC will reach. On the other hand, SUSY can help explain why the Higgs scale is so much lower than the Planck scale — the hierarchy problem — if and only if it is broken at a low enough scale to be detectable at the LHC. But there are no guarantees, so I’m remaining cautious.
  • Large Extra Dimensions: 1%. The idea of extra dimensions of space was re-invigorated in the 1990’s by the discovery by Arkani-Hamed, Dimopolous and Dvali that hidden dimensions could be as large as a millimeter across, if the ordinary particles we know and love were confined to a three-dimensional brane. It’s a fantastic idea, with definite experimental consequences: for one thing, you could be making gravitons at the LHC, which would escape into the extra dimensions. But it’s a long shot; the models are already quite constrained, and seem to require a good amount of fine-tuning to hold together.
  • Warped Extra Dimensions: 10%. Soon after branes became popular, Randall and Sundrum put a crucial new spin on the idea: by letting the extra dimensions have a substantial spatial curvature, you could actually explain fine-tunings rather than simply converting them into different fine-tunings. This model has intriguing connections with string theory, and its own set of experimental predictions (one of the world’s experts is a co-blogger). I would not be terribly surprised if some version of the Randall-Sundrum proposal turned out to be relevant at the LHC.
  • Black Holes: 0.1%. One of the intriguing aspect of brane-world models is that gravity can become strong well below the Planck scale — even at LHC energies. Which means that if you collide particles together in just the right way, you could make a black hole! Sadly, “just the right way” seems to be asking for a lot — it seems unlikely that black holes will be produced, even if gravity does become strong. (And if you do produce them, they will quickly evaporate away.) Fortunately, the relevant models make plenty of other predictions; the black-hole business was always an amusing sidelight, never the best way to test any particular theory.
  • Stable Black Holes That Eat Up the Earth, Destroying All Living Organisms in the Process: 10-25%. So you’re saying there’s a chance?
  • Evidence for or against String Theory: 0.5%. Our current understanding of string theory doesn’t tell us which LHC-accessible models are or are not compatible with the theory; it may very well be true that they all are. But sometimes a surprising experimental result will put theorists on the right track, so who knows?
  • Dark Matter: 15%. A remarkable feature of dark matter is that you can relate the strength of its interactions to the abundance it has today — and to get the right abundance, the interaction strength should be right there at the electroweak scale, where the LHC will be looking. (At least, if the dark matter is thermally produced, and a dozen other caveats.) But even if it’s there, it might not be easy to find — by construction, the dark matter is electrically neutral and doesn’t interact very much. So we have a chance, but it will be difficult to say for sure that we’ve discovered dark matter at the LHC even if the accelerator produces it.
  • Dark Energy: 0.1%. In contrast to dark matter, none of the energy scales characteristic of dark energy have anything to do with the LHC. There’s no reason to expect that we will learn anything about it. But again, maybe that’s because we haven’t hit upon the right model. It’s certainly possible that we will learn something about fundamental physics (e.g. supersymmetry or extra dimensions) that eventually leads to a breakthrough in our understanding of dark energy.

    • …

    What Will the LHC Find?Read More »

What Will the LHC Find? Read More »

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