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.

Continue reading ‘What Will the LHC Find?’

I had just stepped out of the shower yesterday (getting a bit of a late start, yes) when the building began to shake. We’re on the ninth floor of a twelve-story building in downtown Los Angeles, so it was quite exciting there for a while — the ground shook for maybe twenty seconds, the cat scampered under the bed, and an item or two had to be rescued from imminent spillage off of bookshelves. (Our cat has her own blog, so it usually takes quite a shock to drag her away from the internets.)

But a minor earthquake overall, just 5.4 on the Richter scale. No significant damage, even closer to the center (we were about 30 miles away). The interesting thing is that within seconds after the event you could hop to the US Geological Survey page to find a map of all the world’s recent earthquakes, and then home in on this one. Obviously most of the information is computer generated, although the main page for the earthquake does reassure you that “This event has been reviewed by a seismologist.”

So you can check out the Shake Map, of course:

We’re right on top of the dot labeled “Los Angeles.” But you can also find Google maps, travel times for the shocks,

and of course — waveforms!

Earthquakes are so much better with science. The only downside is that I spent the immediate aftermath looking for the kitty rather than drying my hair, so I went through the rest of the day with the dreaded “earthquake hair.”

In my last post, I discussed the puzzle posed for cosmologists and particle physicists by the observation of the baryon asymmetry of the universe (BAU) - the fact that the universe is composed almost entirely of matter, with a negligible amount of antimatter. In this post I’ll to go into a little more detail about one popular idea about how the BAU might be generated. Although I’ll be a little more technical here than usual, if people are interested in even more detail, they could read this review article, or this one.

The precise question that concerns us is; as the universe cooled from early times, at which one would expect equal amounts of matter and antimatter, to today, what processes, both particle physics and cosmological, were responsible for the generation of the BAU? In 1967, Andrei Sakharov established that any scenario for achieving this must satisfy the following three criteria;

• Violation of the baryon number (B) symmetry
• Violation of the discrete symmetries C (charge conjugation) and CP (the composition of parity and C)
• A departure from thermal equilibrium.

Continue reading ‘Matter v Antimatter II: Electroweak Baryogenesis’

Lenny Susskind has a new book out: The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. At first I was horrified by the title, but upon further reflection it’s grown on me quite a bit.

Some of you may know Susskind as a famous particle theorist, one of the early pioneers of string theory. Others may know his previous book: The Cosmic Landscape: String Theory and the Illusion of Intelligent Design. (Others may never have heard of him, although I’m sure Lenny doesn’t want to hear that.) I had mixed feelings about the first book; for one thing, I thought it was a mistake to put “Intelligent Design” there in the title, even if it were to be dubbed an “Illusion.” So when the Wall Street Journal asked me to review it, I was a little hesitant; I have enormous respect for Susskind as a physicist, but if I ended up not liking the book I would have to be honest about it. Still, I hadn’t ever written anything for the WSJ, and how often does one get the chance to stomp about in the corridors of capitalism like that?

The good news is that I liked the book a great deal, as the review shows. I won’t reprint the thing here, as you are all well-trained when it comes to clicking on links. But let me mention just a few words about information conservation and loss, which is the theme of the book. (See Backreaction for another account.)

It’s all really Isaac Newton’s fault, although people like Galileo and Laplace deserve some of the credit. The idea is straightforward: evolution through time, as described by the laws of physics, is simply a matter of re-arranging a fixed amount of information in different ways. The information itself is neither created nor destroyed. Put another way: to specify the state of the world requires a certain amount of data, for example the positions and velocities of each and every particle. According to classical mechanics, from that data (the “information”) and the laws of physics, we can reliably predict the precise state of the universe at every moment in the future — and retrodict the prior states of the universe at every moment in the past. Put yet another way, here is Thomasina Coverley in Tom Stoppard’s Arcadia:

If you could stop every atom in its position and direction, and if your mind could comprehend all the actions thus suspended, then if you were really, really good at algebra you could write the formula for all the future; and although nobody can be so clever as to do it, the formula must exist just as if one could.

This is the Clockwork Universe, and it is far from an obvious idea. Pre-Newton, in fact, it would have seemed crazy. In Aristotelian mechanics, if a moving object is not subject to a continuous impulse, it will eventually come to rest. So if we find an object at rest, we have no way of knowing whether until recently it was moving, or whether it’s been sitting there for a long time; that information is lost. Many different pasts could lead to precisely the same present; whereas, if information is conserved, each possible past leads to exactly one specific state of affairs at the present. The conservation of information — which also goes by the name of “determinism” — is a profound underpinning of the modern way we think about the universe.

Determinism came under a bit of stress in the early 20th century when quantum mechanics burst upon the scene. In QM, sadly, we can’t predict the future with precision, even if we know the current state to arbitrary accuracy. The process of making a measurement seems to be irreducibly unpredictable; we can predict the probability of getting a particular answer, but there will always be uncertainty if we try to make certain measurements. Nevertheless, when we are not making a measurement, information is perfectly conserved in quantum mechanics: Schrodinger’s Equation allows us to predict the future quantum state from the past with absolute fidelity. This makes many of us suspicious that this whole “collapse of the wave function” that leads to an apparent loss of determinism is really just an illusion, or an approximation to some more complete dynamics — that kind of thinking leads you directly to the Many Worlds Interpretation of quantum mechanics. (For more, tune into my Bloggingheads dialogue with David Albert this upcoming Saturday.)

In any event, aside from the measurement problem, quantum mechanics makes a firm prediction that information is conserved. Which is why it came as a shock when Stephen Hawking said that black holes could destroy information. Hawking, of course, had famously shown that black holes give off radiation, and if you wait long enough they will eventually evaporate away entirely. Few people (who are not trying to make money off of scaremongering about the LHC) doubt this story. But Hawking’s calculation, at first glance (and second), implies that the outgoing radiation into which the black hole evaporates is truly random, within the constraints of being a blackbody spectrum. Information is seemingly lost, in other words — there is no apparent way to determine what went into the black hole from what comes out.

This led to one of those intellectual scuffles between “the general relativists” (who tended to be sympathetic to the idea that information is indeed lost) and “the particle physicists” (who were reluctant to give up on the standard rules of quantum mechanics, and figured that Hawking’s calculation must somehow be incomplete). At the heart of the matter was locality — information can’t be in two places at once, and it has to travel from place to place no faster than the speed of light. A set of reasonable-looking arguments had established that, in order for information to escape in Hawking radiation, it would have to be encoded in the radiation while it was still inside the black hole, which seemed to be cheating. But if you press hard on this idea, you have to admit that the very idea of “locality” presumes that there is something called “location,” or more specifically that there is a classical spacetime on which fields are propagating. Which is a pretty good approximation, but deep down we’re eventually going to have to appeal to some sort of quantum gravity, and it’s likely that locality is just an approximation. The thing is, most everyone figured that this approximation would be extremely good when we were talking about huge astrophysical black holes, enormously larger than the Planck length where quantum gravity was supposed to kick in.

But apparently, no. Quantum gravity is more subtle than you might think, at least where black holes are concerned, and locality breaks down in tricky ways. Susskind himself played a central role in formulating two ideas that were crucial to the story — Black Hole Complementarity and the Holographic Principle. Which maybe I’ll write about some day, but at the moment it’s getting late. For a full account, buy the book.

Right now, the balance has tilted quite strongly in favor of the preservation of information; score one for the particle physicists. The best evidence on their side (keeping in mind that all of the “evidence” is in the form of theoretical arguments, not experimental data) comes from Maldacena’s discovery of duality between (certain kinds of) gravitational and non-gravitational theories, the AdS/CFT correspondence. According to Maldacena, we can have a perfect equivalence between two very different-looking theories, one with gravity and one without. In the theory without gravity, there is no question that information is conserved, and therefore (the argument goes) it must also be conserved when there is gravity. Just take whatever kind of system you care about, whether it’s an evaporating black hole or something else, translate it into the non-gravitational theory, find out what it evolves into, and then translate back, with no loss of information at any step. Long story short, we still don’t really know how the information gets out, but there is a good argument that it definitely does for certain kinds of black holes, so it seems a little perverse to doubt that we’ll eventually figure out how it works for all kinds of black holes. Not an airtight argument, but at least Hawking buys it; his concession speech was reported on an old blog of mine, lo these several years ago.

I’m in the middle of a couple of posts about the matter-antimatter asymmetry of the universe and have found that I keep referring to things I posted back on my old blog a long time ago. This became so frequent that I’ve decided to post a slightly edited version of these here, and in my next post, as preludes to some newer material that I’m getting to.

Antimatter is just like ordinary matter in every way, except that every quantity you can think of (apart from mass and spin), is reversed. As an example, the electron is a particle with a specific mass and carrying a specific amount of negative electric charge. The antiparticle of the electron is a positron, which has the identical mass to an electron, but precisely the opposite charge. The thing about particles and their antiparticles is that, if one puts them together, the net value of any quantity (called a quantum number by physicists) carried by the pair of them is zero. Therefore, a particle and an antiparticle together are merely mass which, thanks to Einstein’s E=mc², can be converted entirely into energy. As a result of this, when matter and antimatter come together, they annihilate, producing energy in the form of light (photons).

We know so much about antimatter for two reasons. The first is that it is a natural part of quantum field theories, which we use to describe matter, and which are among the best-tested theories in all of science. The second is that we can make and investigate antimatter in large amounts. For example, the purpose of the Fermi National Accelerator Laboratory near Chicago is to make vast numbers of antiprotons to study how they annihilate with protons.

Antimatter is important in cosmology because of the extreme temperatures and densities of the early universe. One consequence of such an extreme environment is that there is so much energy around that any kind of matter (including antimatter) can be created. Therefore, in the early universe, one expects there to have been equal amounts of both matter and antimatter and then, as the universe cooled, for these particles to find each other, annihilate, and leave our present universe with very little matter around (and an equally small amount of antimatter).

This is clearly at odds with what we observe in the universe, where we have relatively large amounts of matter and essentially no evidence of primordial antimatter. In fact, this asymmetry between matter and antimatter can be made quantitative (for baryons such as protons and neutrons) through observations of the abundances of light elements in the universe (Big Bang Nucleosynthesis - BBN) and also from the pattern of anisotropies in the cosmic microwave background radiation (CMB). Thus, there is clear quantitative evidence that the universe is composed of matter, with negligible antimatter.

This all constitutes a puzzle for cosmologists. How did the universe evolve from early times, in which there were equal numbers of baryons and antibaryons, to the present universe, in which there is a precisely measured baryon asymmetry of the universe (BAU)?

Potential solutions to this puzzle provide a wonderful example of the interplay between particle physics and cosmology. A beautiful feature of many theories beyond the standard model of particle physics is that, when considered in the context of the expanding universe, they automatically contain such a dynamical mechanism that can, in principle, explain the origin of the BAU. The generation of the BAU through one of these mechanisms is what is known as baryogenesis. This isn’t enough of course; we don’t yet know which, if any, of these theories might be the right one. However, upcoming experiments, such as those at the Large Hadron Collider (LHC), provide the exciting possibility of either ruling out some of them or providing significant evidence for one of them.

Over the course of my next few posts I’ll try to explain how some of these mechanisms work, and how they illustrate the particle-cosmology connection.

Fred Adams wonders whether we could still have stars if the constants of nature were very different. Answer: very possibly! It’s in arxiv:0807.3697:

Motivated by the possible existence of other universes, with possible variations in the laws of physics, this paper explores the parameter space of fundamental constants that allows for the existence of stars. To make this problem tractable, we develop a semi-analytical stellar structure model that allows for physical understanding of these stars with unconventional parameters, as well as a means to survey the relevant parameter space. In this work, the most important quantities that determine stellar properties — and are allowed to vary — are the gravitational constant $G$, the fine structure constant $\alpha$, and a composite parameter $C$ that determines nuclear reaction rates. Working within this model, we delineate the portion of parameter space that allows for the existence of stars. Our main finding is that a sizable fraction of the parameter space (roughly one fourth) provides the values necessary for stellar objects to operate through sustained nuclear fusion. As a result, the set of parameters necessary to support stars are not particularly rare. In addition, we briefly consider the possibility that unconventional stars (e.g., black holes, dark matter stars) play the role filled by stars in our universe and constrain the allowed parameter space.

I’ve never thought that our knowledge of what constituted “intelligent life” was anywhere near good enough to start making statements about the conditions under which it could form, apart from fairly weak stuff like “life probably can’t exist if the universe only lasts for a Planck time.” So when anthropic arguments start to hinge on thinking that fractional changes in the mass of this or that nucleus would result in a universe with no observers, it seems more prudent to admit that we just don’t know. But putting any anthropic considerations aside, it’s still interesting to ask what the universe would look like if the constants of nature were completely different. How robust are the starry skies?

One of the important features of the universe around us is that, on sufficiently large scales, it looks pretty much the same in every direction — “isotropy,” in cosmology lingo. There is no preferred direction to space, in which the universe would look different than in the perpendicular directions. The most compelling evidence for large-scale isotropy comes from the Cosmic Microwave Background (CMB), the leftover radiation from the Big Bang. It’s not perfectly isotropic, of course — there are tiny fluctuations in temperature, which are pretty important; they arise from fluctuations in the density, which grow under the influence of gravity into the galaxies and clusters we see today. Here they are, as measured by the WMAP satellite.

Nevertheless, there is a subtle way for the universe to break isotropy and have a preferred direction: if the tiny observed perturbations somehow have a different character in one direction than in others. The problem is, there are a lot of ways this could happen, and there is a huge amount of data involved with a map of the entire CMB sky. A tiny effect could be lurking there, and be hard to see; or we could see a hint of it, and it would be hard to be sure it wasn’t just a statistical fluke.

In fact, at least three such instances of apparent large-scale anisotropies have been claimed. One is the “axis of evil” — if you look at only the temperature fluctuations on the very largest scales, they seem to be concentrated in a certain plane on the sky. Another is the giant cold spot (or “non-Gaussianity,” if you want to sound like an expert) — the Southern hemisphere seems to have a suspiciously coherent blob of slightly lower than average CMB temperature. And then there is the lopsided universe — the total size of the fluctuations on one half of the sky seems to be slightly larger than on the other half.

All of these purported anomalies in the data, while interesting, are very far from being definitive. Although most people seem to agree that they are features of the data from WMAP, it’s hard to tell whether they are all just statistical flukes, or subtle imperfections in the satellite itself, or contamination by foregrounds (like our own galaxy), or real features of the universe.

Now we seem to have another such anomaly, in which the temperature fluctuations in the CMB aren’t distributed perfectly isotropically across the sky. It comes by way of a new paper by Nicolaas Groeneboom and Hans Kristian Eriksen:

Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data

Sexy title, eh? Here is the upshot: Groeneboom and Eriksen looked for what experts would call a “quadrupole pattern of statistical anisotropy.” Similar to the lopsided universe effect, where the fluctuations seem to be larger on one side of the sky than the other, this is an “elongated universe” effect — fluctuations are larger along one axis (in both directions) as compared to the perpendicular plane. Here is a representation of the kind of effect we are talking about — not easy to make out, but the fluctuations are supposed to be a bit stronger near the red dots than in the strip in between them.

It’s not a very large signal — “3.8 sigma,” in the jargon of the trade, where 3 sigma basically means “begin to take seriously,” but you might want to get as high as 5 sigma before you say “there definitely seems to be something there.” However, the WMAP data come in different frequencies (V-band and W-band), and the effect seems to be there in both bands. Furthermore, you can look for the effect separately at large angular scales and at small angular scales, and you find it in both cases (with somewhat lower statistical significance, as you might expect). So it’s far from being a gold-plated discovery, but it doesn’t seem to be a complete fluke, either.

Remember, looking for any specific effect is quite a project — there is a lot of data, and the analysis involves manipulating huge matrices, and you have to worry about foregrounds and instrumental effects. So why were these nice folks looking for a power asymmetry along a preferred axis in the sky? Well, you might recall my paper with Lotty Ackerman and Mark Wise, described in the “Anatomy of a Paper” series of blog posts (I, II, III). We were interested in whether the (hypothetical) period of inflation in the early universe might have been anisotropic — expanding just a bit faster in one direction than in the others — and if so, how it would show up in the CMB. What we found was that the natural expectation was a power asymmetry along the preferred axis, and gave a bunch of formulas by which observers could actually look for the effect. That is what Nicolaas and Hans Kristian did, with every expectation that they would establish an upper limit on the size of our predicted effect, which we had labelled g_*. But instead, they found it! The data are saying that

So naturally, Lotty and Mark and I are brushing up on our Swedish in preparation for our upcoming invitations to Stockholm. Okay, not quite. In fact, it’s useful to be very clear about this, given the lessons that were (one hopes) learned in John’s series of posts about Higgs hunting. Namely: small, provocative “signals” such as this happen all the time. It would be completely irresponsible just to take every one of them at face value as telling you something profound about the universe. And the more surprising the result — and this one would be pretty darned surprising — the more skeptical and cautious we have every right to be.

So what are we supposed to think? Certainly not that these guys are just jokers that don’t know how to analyze CMB data; the truth couldn’t be more different. But analyzing data like this is really hard, and other groups will doubtless jump in and do their own analyses, as it should be. It’s certainly possible that there is a small systematic effect in WMAP — “correlated noise” — rather than in the universe. The authors have considered this, of course, and it doesn’t seem to fit the finding very comfortably, but it’s a possibility. The very good news is that the kind of correlated noise one would expect from WMAP (given the pattern it used to scan across the sky) is completely different from that the we would worry about from the upcoming Planck mission, scheduled to launch next year.

Or, of course, we could be learning something deep about the universe. Maybe even that inflation was anisotropic, as Lotty and Mark and I contemplated. Or, perhaps more plausibly, there is some single real effect in the universe that is conspiring to give us all of the tantalizing hints contained in the various anomalies listed above. We don’t know yet. That’s what makes it fun.

I’m sure Ruben Bolling is making fun of people I disagree with, and not of me.

The underlying point is a good one, though, and one that is surprisingly hard for people thinking about cosmology to take to heart: without actually looking at it, there is no sensible a priori reasoning that can lead us to reliable knowledge about parts of the universe we haven’t observed. Einstein and Wheeler believed that the universe was closed and would someday recollapse, because a universe that was finite in time felt right to them. The universe doesn’t care what feels right, or what “we just can’t imagine”; so all possibilities should remain on the table.

On the other hand, that doesn’t mean we can’t draw reasonable a posteriori conclusions about the unobservable universe, if the stars align just right. That is, if we had a comprehensive theory of physics and cosmology that successfully passed a barrage of empirical tests here in the universe we do observe, and made unambiguous predictions for the universe that we don’t, it would not be crazy to take those predictions seriously.

We don’t have that theory yet, but we’re working on it. (Where “we” means an extremely tiny fraction of working scientists, who receive an extremely disproportionate amount of attention.)

Sorry, not in this post, but upcoming. I’m scheduled to do another episode of Bloggingheads.tv with David Albert, and we’ve decided to spend the whole hour talking about quantum mechanics. Start with the basics, try to explain this crazy theory and some of its outlandish consequences in ways that anyone can understand, and then dig into some of the mysteries of measurement, superposition, and reality.

So — what do you want to know? What are the really interesting questions about QM that we should be talking about?

One thing I don’t think we science-explainers get as clear as we could is the idea of the Wave Function of the Universe. It sounds scary and/or pretentious — an older colleague of mine at MIT once said “I’m too young to talk about the wave function of the universe.” But it’s a crucial fact of quantum mechanics (arguably the crucial fact) that, unlike in classical mechanics, when you consider two electrons you don’t just have a separate state for each electron. You have a single wave function that describes the two-electron system. And that’s true for any number of particles — when you consider a bigger system, you don’t “add more wavefunctions,” you beef up your single wave function so that it describes more particles. There is only ever one wave function, and you can call it “of the universe” if you like. Deep, man.

Here is another thing: in quantum mechanics, you can “add two states together,” or “take their average.” (Hilbert space is a vector space with an inner product.) In classical mechanics, you can’t. (Phase space is not a vector space at all.) How big a deal is that? Is there some nice way we can explain what that means in terms your grandmother could understand, even if your grandmother is not a physicist or a mathematician?

(See also Dave Bacon’s discussion of teaching quantum mechanics as a particular version of probability theory. There are many different ways of answering the question “What is quantum mechanics?”)

President Bush signed into law Monday a bill that will provide $62.5M for high energy physics. At Fermilab this morning director Pier Oddone announced the end of plans for involuntary layoffs of some 140 employees at the lab. Any remaining funds, according to the language of the bill, can be used to support new neutrino research projects; the Nova experiment was among the casualties of the omnibus appropriations in late December 2007.

This is fantastic news for Fermilab, where, with the LHC startup imminent, time is running out to make a dramatic new discovery. The Tevatron is running very well and the experiments are accumulating piles of high quality data. It’s make-or-break time.

The supplemental bill included $162 billion for funding the wars in Afghanistan and Iraq, and $3.6 billion of non-war-related funding. (So, somehow, this post I am writing here is reminding me of an old Monty Python skit, where a newscaster says “And now the news for Wombats. No wombats were killed today in an accident involving….”)

The supplemental bill failed to include the $160 million US contribution to ITER, and so leaves the US in default on our international agreement. This will compromise for years to come our ability to participate as a reliable partner in large international scientific projects.