Science

The arrow of time wasn’t the only big science problem garnering media attention last week: there was also a claim that dark energy doesn’t exist. See Space.com (really just a press release), USA Today, and a bizarre op-ed in the Telegraph saying that maybe this means global warming isn’t real either, so there.

The reports are referring to a paper by mathematicians Blake Temple and Joel Smoller, which is behind a paywall at PNAS but publicly available on the arxiv. (And folks wonder why journals are dying.) Now, some of my best friends are mathematicians, and in this paper they do the kind of thing that mathematicians are trained to do: they solve some equations. In particular, they solve Einstein’s equation of general relativity, for the particular case of a giant spherical “wave” in the universe. So instead of a universe that looks basically the same (on large scales) throughout space, they consider a universe with a special point, so that the density changes as you move away from that point.

Then — here’s the important part — they put the Earth right at that point, or close enough. And then they say, “Hey! In a universe like that, if we look at how fast distant galaxies and supernovae are receding from us, we can fit the data without any dark energy!” That is, they can cook up a result for distance vs. redshift in this model that looks like it would in a smooth model with dark energy, even though there’s nothing but ordinary (and dark) matter in their cosmology.

There are three things to note about this result. First, it’s already known; see e.g. Kolb, Marra, and Matarrese, or Clifton, Ferreira, and Land. In fact, I would argue that it’s kind of obvious. When we observe distant galaxies, we don’t see the full three dimensions of space at every moment in time; we can only look back along our own light cone. If the universe isn’t homogeneous, but is only spherically symmetric around our location, I can arrange the velocities of galaxies along that past light cone to do whatever I want. We could have them spell out “Cosmic Variance” in Morse code if we so desired. So it’s not very surprising we could reconstruct the observed distance vs. redshift curve of an accelerating universe; you don’t have to solve Einstein’s equation to do that.

Second, do you really want to put us right at the center of the universe? That’s hard to rule out on the basis of data — although people are working on it. So it’s definitely a possibility to keep in mind. But it seems a bit of a backwards step from Copernicus and all that. Most of us would like to save this as a move of last resort, at least while there are alternatives available.

Third, there are perfectly decent alternatives available! Namely, dark energy, and in particular the cosmological constant. This idea not only fits the data from supernovae concerning the distance vs. redshift relation, but a bunch of other data as well (cosmic microwave background, cluster abundances, baryon acoustic oscillations, etc.), which this new paper doesn’t bother with. People should not be afraid of dark energy. Remember that the problem with the cosmological constant isn’t that it’s mysterious and ill-motivated — it’s that it’s too small! The naive theoretical prediction is larger than what’s required by observation by a factor of 10¹²⁰. That’s a puzzle, no doubt, but setting it equal to zero doesn’t make the puzzle go away — then it’s smaller than the theoretical prediction by a factor of infinity.

The cosmological constant should exist, and it fits the data. It might not be the right answer, and we should certainly keep looking for alternatives. But my money is on Λ.

We’re all waiting for the LHC to restart. Current plans call for collisions later this year, but at lower energies than originally hoped.

Why is it so hard to say for sure? Here’s a nice article in the CERN Bulletin that lays out some of the difficulties.

Due to the huge amount of inter-dependency between different areas of work in the LHC, even a small change can necessitate a complete overhaul of the schedule. For example, something as simple as cleaning a water cooling tower – required regularly by Swiss law to prevent Legionella – has a huge impact on the planning: “When you clean the water tanks it means we don’t have water-cooling for the compressors, that means we can’t run the cryogenics, so the temperature starts to go up,” explains Myers. “If a sector gets above 100 K, then the expansion effects of heating can cause problems, and we could have to replace parts.”

That may be cold comfort (get it? cold comfort!), but it’s the real world. I have no strong opinions about the job CERN is doing, except to recognize that this is the most complicated machine ever built, so patience is probably called for. The particles and interactions are going to be the same next year as they were last year. (Or if they’re not, that would be even more interesting.)

The purpose of the LIGO experiment is to search for gravitational waves in the universe. They haven’t found any yet, but no good big-science experiment would be complete without a few cool spinoffs. They LIGO folks have an especially cool one: they’ve put a kilogram-sized pendulum and “cooled” it so effectively that it’s almost in its quantum-mechanical ground state. To be honest, I’m not exactly sure what this is good for, but it’s really cool. Ha ha, little physics humor there, get it? “Cool.”

LIGO works by bouncing lasers down a pair of evacuated tubes four kilometers in length. The laser beams bounce off a mirror suspended from a pendulum, and then recombine back at the source, where you look for tiny changes in the phase of the light wave. If a gravitational wave passes by, it will gently disturb the pendulums, and the length the laser has to travel down one or the other tube will be slightly changed, leading to a detectable shift in the phase. But obviously they’re looking for an extremely tiny shift, so it’s important that those mirrors not be jiggling around just due to random noise. Thus, they need to be kept cool; a warm mirror will be jiggling just from its thermal motion, even before we start worrying about noisy trucks passing by the observatory.

Physicists are pretty good at getting things to be cold; they can cool down collections of atoms to under a billionth of a Kelvin (room temperature is about 300 Kelvin). But there we’re talking about relatively small collections of atoms, maybe a million at a time. Here we’re talking about a kilogram, which is a honking big number of atoms, something like 10²⁵. And the LIGO folks have cooled the oscillator down to about a millionth of a Kelvin, which is pretty cold.

The secret is that they don’t cool the entire mirror down to that low temperature. That would mean taking all of those 10²⁵ atoms and putting them close to their quantum-mechanical ground state. But instead of thinking of the mirror as a collection of individual atoms, you can think of it as a single “center of mass,” plus a bunch of individual displacements from that center for each of the atoms. Then forget about the individual atoms, and just worry about that center of mass. That’s what we do all the time in the real world; when you tell someone where you are, you give them a single position — you don’t individually specify the location of every atom in your body.

We can think of the center of mass as an isolated “degree of freedom,” and talk about its quantum state apart from that of all the other atoms. Ordinarily, if a big collection of atoms is in thermal equilibrium, each of its degrees of freedom is “excited” above its ground state by a similar amount. Every physicist learns about the simple harmonic oscillator, which is one of the most basic physical systems we can study — it’s just a pendulum. In quantum mechanics, the nice thing about such an oscillator is that it has discrete energy levels, equally spaced, that depend only on the frequency of the pendulum. There is a ground state with just a tiny bit of energy (the “zero-point energy”), then a bunch of higher energy levels, from the first excited state all the way up to infinity. The energy of the Nth excited state is just (N+1/2) times Planck’s constant, times the frequency of the oscillator.

What the LIGO folks have done is to isolate that single degree of freedom, the center of mass of the oscillator, and gently coax it into a very low quantum state: N is about 200, whereas at room temperature N would be about 40 billion. An amazing feat, for a collection of that many atoms.

So what can you do with it? Don’t ask me. But the LIGO scientists know they have something interesting on their hands, and are thinking of ways they can take advantage of this approach to the quantum realm. It’s different, but complementary, to the strategy of putting entire macroscopic objects in a coherent quantum state. (Notice that the linked article is still talking about 10¹⁰ atoms, not 10²⁵ atoms.) The LIGO mirror as a whole is still resolutely classical, even if the center-of-mass degree of freedom is near its quantum ground state. But taking big things and pushing them toward the quantum realm is a growth industry these days, and I’m sure we’ll be hearing more about clever applications of the process.

Everyone and their niece is emailing me that I should post these. (And Aatish in comments.) And a good thing, too, because it usually takes at least half a dozen emails before I will do anything at all.

In 1964, Richard Feynman gave the Messenger Lectures at Cornell, aimed at a general audience. They were later collected into The Character of Physical Law, a great little book with a depressingly boring cover. Feynman-worship is often overdone, but man, the guy could lecture. And he knew a lot about physics!

The good news is that Bill Gates has now put the full video of the lectures online, as part of Project Tuva. I had to update some software to view them on my Mac, but it seems to be working now.

Lecture Five is about the arrow of time. If you skip ahead to the 18th minute or so, you’ll hear Feynman explain the Boltzmann Brain argument.