Blogs / Cosmic Variance

As I advertised, the bloggingheads.tv discussion that Sean and I recorded on Wednesday is now posted

following on from on our first effort, and covering different, and somewhat more controversial topics.

Hope you enjoy it.

On Wednesday Sean and I recorded another episode of bloggingheads.tv. In our last outing we discussed the standard cosmology, dark matter, cosmic acceleration, and a number of other issues concerning the observed matter-energy content of today’s universe. This time, we thought we’d go all early universe on you and discuss the problems of the standard cosmology, inflation, its shortcomings, and ultimately the initial conditions of the universe. Some of these topics, such as inflation, have a rather tight connection to current observations, while others are more speculative and some are touching on the philosophical, at least at this stage in our understanding.

We’ll post a link to the new episode when it comes out tomorrow. At one stage Sean and I discuss the initial conditions for inflation, and in doing so we were led into the issues of eternal inflation, entropy and the arrow of time (I guess he’s written some sort of extended blog post about it). Leading up to this, however, I brought up the question of what it means to require a sufficiently large, smooth, potential energy dominated patch of the universe in order for inflation to begin. I referred to a paper I wrote many years ago with Tanmay Vachaspati and I thought that it might be useful to describe that work here. I’ve done this before, over at Orange Quark, but it can’t hurt to have a version here also. This will be a little more technical than usual, but far less technical than the actual paper (hopefully).

As I first learned about inflation, the idea can be summarized as the following: the universe is born and one can say very little about it since quantum gravity (whatever that is) is undoubtedly important at extremely early times. However, after some time (approximately the Planck time), the semi-classical universe emerges, and we can begin to analyze meaningfully such things as the dynamics of field theories, and the response of gravity to them. There is no a priori reason for the universe to be homogeneous at this epoch. However, local, causal particle dynamics can act to homogenize patches of the universe. After some time, a small patch becomes homogeneous and dominated by the vacuum energy of a scalar field. This patch then undergoes inflation – a quasi-exponential period of expansion in which the original small patch expands to a size many orders of magnitude larger than the observable universe today. This expansion explains the flatness of the universe, and its homogeneity on large scales today.

Now, there are a number of models of inflation in which the above story is modified (in particular, chaotic inflation), and I’ll get back to them later. For now let me focus on this claim of homogeneity in the theories I described above.

Why does inflation, as described, “solve” the homogeneity (or horizon) problem? Clearly, the idea is that the homogeneity of the initial pre-inflationary patch, explained by causal physics, is translated into the homogeneity of the larger space after the exponential expansion. At the risk of being pedantic, this can only be true if the original patch is made homogeneous by causal processes, otherwise homogeneity would once again be an assumption, albeit a less severe one.

What did we do in our paper? We first imagined that the early universe, emerging from the Planck epoch, was not inflating. To make progress we’ll need a few definitions, which I’ll define below in a more blog-friendly way than in the paper.

Let’s focus on spherically symmetric space-times and pick an origin. Then examine spherical surfaces centered on this origin. Such surfaces can be divided into three categories in the following way. Imagine sitting on such a surface with two flashlights, both pointing radially and close together. The flashlights can both be pointing outwards (away from the origin), or both pointing inwards (towards the origin). The categories are then:

1. NORMAL: When the flashlights point inwards, the rays converge to the origin. When they point outwards, the rays diverge away from the origin. This is how regular parts of space-time behave; for example, points in our universe closer to us than the horizon.
2. TRAPPED: When the flashlights point inwards, the rays converge to the origin. When they point outwards, the rays still converge to the origin. Such surfaces can be found inside the horizon of a black hole.
3. ANTI-TRAPPED: When the flashlights point inwards, the rays nevertheless diverge away from the origin. When they point outwards, the rays diverge away from the origin. Such surfaces can be found, for example, beyond the horizon in our universe.

Now, back to what our paper showed. If the universe is not born inflating, then we want to imagine that, at some later time, local, causal particle dynamics yield a patch that is homogeneous and vacuum-dominated, and thus begins to inflate. The fundamental question for us was; how small can this patch be?

The main tool we used is called the Raychaudhuri equation. It describes the rate of change of divergence of close by pairs of light rays, as I described above. The equation is a little complicated but, by considering the types of light rays I mentioned above (perpendicular to spherical surfaces), and by making two further assumptions: that the Einstein equations are satisfied, and that the weak energy condition holds (matter isn’t too weird), the most important consequence of the Raychaudhuri equation can be stated as: Light rays pointing inwards cannot emanate from a normal surface and cross an anti-trapped one.

What does this mean? Well, if the original inflating patch is smaller than the Hubble size of the background space-time, then, it can be shown that light rays violating the above statement must exist. Thus, we conclude that the size of the initial inflating patch is at least as large as the Hubble size of the background space-time. But this size is large compared to typical particle physics processes that can act to homogenize a region (actually, if the background space-time is radiation-dominated FRW, the Hubble size IS the causal horizon). Thus, in this simple context it is hard to see how such an initially homogeneous inflating patch might form. This was our main result.

However, one of the things Sean and I discussed on blogginheads.tv was eternal inflation – the idea, supported by careful calculations in some models, that it is possible that inflation, if it begins in one patch of the universe, gives rise to an infinite expanding space, which produces an infinite number of regions of the universe that look like ours. This provides a very different was to think about the probability for inflation beginning, and seems to provide a possible way around the problem we pointed out. Furthermore, it may provide a way to seek answers to some of the other big questions of the earliest times in the universe – many of which depend on a full understanding of the issue of initial conditions.

I’m sure you’ll be able to find a relevant book if you’re interested in learning more.

A question that we have all been asking has been answered today: What will be the LHC run energy?  A press release has just been issued from CERN Director General, Rolf Heuer, following the completion of tests on the LHC magnets and splices.  Here are the excepts which just beeped into my inbox:

The LHC will run for the first part of the 2009-2010 run at 3.5 TeV per beam, with the energy rising later in the run. That’s the conclusion that we’ve just arrived at in a meeting involving the experiments, the machine people and the CERN management. We’ve selected 3.5 TeV because it allows the LHC operators to gain experience of running the machine safely while opening up a new discovery region for the experiments.

The developments that have allowed us to get to this point are good progress in repairing the damage in sector 3-4 and the related consolidation work, and the conclusion of testing on the 10000 high-current electrical connections last week. With that milestone, every one of the connections has been tested and we now know exactly where we stand.

The procedure for the 2009 start-up will be to inject and capture beams in each direction, take collision data for a few shifts at the injection energy, and then commission the ramp to higher energy. The first high-energy data should be collected a few weeks after the first beam of 2009 is injected. The LHC will run at 3.5 TeV per beam until a significant data sample has been collected and the operations team has gained experience in running the machine. Thereafter, with the benefit of that experience, we’ll take the energy up towards 5 TeV per beam. At the end of 2010, we’ll run the LHC with lead-ions for the first time. After that, the LHC will shut down and we’ll get to work on moving the machine towards 7 TeV per beam.

This is welcome news.  Starting at injection energy (450 GeV/beam) for a few shifts is safe and smart.  Experimenters will be guaranteed to record some data which will be used to calibrate the detectors.  Detectors must be properly aligned and calibrated before we can have discoveries!  Then they will ramp up and run awhile at 3.5 TeV/beam, giving the LHC its long-awaited status of being the highest energy accelerator in the world.  A short run at this energy does not have much discovery room given the strong constraints on new physics from the Tevatron, but will mainly serve to further calibrate the detectors and build up experience running the machine.  Finally, a slow ramp up to 5 TeV/beam seems like a safe option for the machine, and allows for the possibility of discovery by the end of 2010!

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.

We’ve gotten a little bent out of shape over gravitational lensing recently (see here and here). But the fun doesn’t stop: gravitational lensing has now officially come into the 21st Century with the release of Eli Rykoff’s GravLens. (Not to be confused with GRAVLENS, Chuck Keeton’s immensely useful and powerful gravitational lensing modeling software). You can now lens a star, a galaxy, or an image of whatever or whomever you want (e.g., your favorite blogger), right in the comfort and safety of your own palm. GravLens is freely available at the iPhone application store. Go download it, and make yourself a beautiful Einstein Ring. This is your chance to support the fledgling “Physics applications for the iPhone” industry!

Children of light and children of darkness is the vision of physics that emerges from this chapter, as from other branches of physics. The children of light are the differential equations that predict the future from the present. The children of darkness are the factors that fix these initial conditions.

– Misner, Thorne, and Wheeler, Gravitation (1973), p. 555.

I’m spending most of this week at the 2009 meeting of the Division of Particle and Fields of the American Physical Society (DPF2009), which is being held at Wayne State University in Detroit. I’m here giving a talk, and convening, with Corbin Covault from Case Western, a couple of sessions on particle astrophysics and cosmology.

I’m enjoying the conference, and have managed to fit in a number of very illuminating discussions with colleagues from other institutions, which is really the most useful part of conferences anyway, as everyone knows. Plus, I finally got to meet the only one of my co-bloggers that I’d never met before. Furthermore, the talks have generally been good – well thought through, and eloquently presented – and we had a lovely reception last evening at the beautiful Detroit public library, where I snapped the mural, which seemed appropriate (except for the pecs). Nevertheless, the overwhelming vibe that I’m getting here is one of extreme impatience and anticipation. This, of course, is all about the Large Hadron Collider (LHC).

There have been talks presenting rather recent and significant results, of course – for example Angela Olinto’s talk about high energy cosmic rays and gamma rays was a lovely survey of the combined data from Fermi, Auger, PAMELA, ATIC, and other experiments; Josh Frieman’s talk on cosmology, and particularly cosmic acceleration, provided a clear picture of the vibrancy of the field and the great progress that has been made over the last decade; and there are numerous other interesting talks coming up on QCD, heavy ion physics, neutrinos, etc.. But in high-energy particle physics I think we’re mostly seeing talks, albeit good talks, summarizing things we’ve seen again and again for a long time. The details of the LHC detectors (ATLAS, CMS, LHCb and ALICE); how one hopes to tease out evidence for the Higgs from the data; ditto for supersymmetric particles, and those arising from large extra dimensions; and a talk by Lyn Evans summarizing the progress towards getting the LHC back online after last year’s calamity.

Particle physics is screaming out for a new result pointing the way to the physics that we know must lie beyond the unreasonably successful standard model. We know this physics should be there because of purely particle physics problems, such as the hierarchy problem – why is the weak scale so much lower than the Planck scale, and stable against quantum corrections – but also because cosmological observations such as the matter antimatter asymmetry of the universe and dark matter tell us that new particles and interactions must be out there, perhaps at the energy scale of the LHC.

People aren’t sitting around twiddling their thumbs and just waiting for the machine to turn back on, of course. And none of what I’ve written above is in any way intended as a criticism. Ongoing work at existing experiments (such as those at the Tevatron, for example) is placing new limits (for example the recent claimed exclusion of a Higgs mass between 160 and 170 GeV), and experimentalists are busy refining their techniques for extracting the maximum amount of information from the upcoming LHC data. This is all extremely important work, and certainly very interesting. But it doesn’t change the fact that people really want the LHC.

And it isn’t just pure particle physicists who feel this way. Those of us in particle cosmology have been getting a wealth of data from cosmology for a while now. But this has left us in a position where dark matter and cosmic acceleration are on such a firm footing that more than ever we desperately need to understand how these phenomena fit into our understanding of fundamental physics. The LHC is the next essential tool in this quest. New physics discovered there may have direct implications for cosmology. And if it doesn’t, then proposed theoretical explanations will be constrained by, and may well open up new vistas for, cosmology.

So we’re all, particle physicists and cosmologists, keeping our fingers tightly crossed for the planned turn on later this year.

A few hours ago the longest total solar eclipse of the Century swept across Asia. And a few days ago Evalyn Gates provided a wonderful guest post on gravitational lensing. This seems like an opportune time to note that gravitational lensing and total solar eclipses are inextricably linked.

One of the most interesting predictions of Einstein’s new theory of relativity was that gravity would cause light to bend. Imagine you are looking at a distant source of light, for example a star, or a faraway galaxy, or a quasar at the edge of the Universe. And let’s assume that, along the line-of-sight to the distant source there’s a massive object, for example the Sun, or a black hole, or a galaxy, or a cluster of galaxies. The gravity from the massive object will “pull” on the photons as they pass, shifting their paths, and thereby affecting the image that we see in our telescopes. In the simple case of a distant point source of light (e.g., a far away star), and a compact spherically symmetric lens (e.g., a black hole), the bending angle is given by

In this equation M is the mass of the lens, r is the minimum distance between the (unperturbed) line-of-sight to the source and the lens, G is the gravitational constant, and c is the speed of light. This was a crucial prediction of Einstein’s new theory, and one way to test it was to see if the stars on the sky “jump” as the Sun (which is quite massive, and traverses the sky quite briskly) comes nearby on the sky. If you plug in the appropriate numbers above ((G/c^2)*M_sun = 1.5 km [geometric units], R_sun = 700,000 km), you find that a star should shift on the sky by 1.75 arcseconds (8.57e-6 radians) as the Sun approaches. There’s one slight snag in measuring this effect: the Sun is sort of bright. When it’s up in the sky it can be a little hard to see what the stars are doing. By the time it’s dark and you can see stars, the Sun is far away on the sky (e.g., below the horizon), and there’s no longer a measurable effect. But nature conveniently provides a very elegant solution to this problem: the total Solar eclipse. In one of the more mysterious coincidences (or is it an argument for “intelligent design”?), it turns out that the Moon and the Sun have very similar angular sizes, when seen from Earth. So every now and then the Moon crosses right in front of the Sun and blocks it out. The sky goes dark. The stars come out in the middle of the day. It even becomes possible to see stars near the very edge of the Sun. Nature conveniently provides the perfect system in which to validate the general relativity prediction of gravitational lensing.

We have a habit in science of simplifying the historical progression. Einstein’s initial 1911 prediction was off by a factor of two (giving hope to us mere mortals). Over the next few years a number of expeditions were mounted to test his prediction, but all of them failed (e.g., bad weather, World War I). This gave Einstein time to discover his error, and in 1915 he fixed his result, arriving at the equation above. The definitive (though subsequently controversial) measurement was performed by Sir Arthur Eddington in 1919. He observed the positions of stars during a total eclipse, claimed to confirm Einstein’s prediction, and vaulted Einstein to fame. In one of the best newspaper headlines ever, the New York Times front page page 17 announced: “LIGHTS ALL ASKEW IN THE HEAVENS; Men of Science More or Less Agog Over Results of Eclipse Observations”.

We’ve come a long way. Gravitational lensing is now one of our best probes of the Universe, revealing the presence of dark matter, and maybe eventually becoming a sensitive probe of dark energy. I’m super bummed I didn’t get to see the total eclipse a few hours ago. But I have every confidence that the stars were all appropriately askew, and that people were appropriately agog.

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.

One frustrating aspect of our discussion about the compatibility of science and religion was the amount of effort expended arguing about definitions, rather than substance. When I use words like “God” or “religion,” I try to use them in senses that are consistent with how they have been understood (at least in the Western world) through history, by the large majority of contemporary believers, and according to definitions as you would encounter them in a dictionary. It seems clear to me that, by those standards, religious belief typically involves various claims about things that happen in the world — for example, the virgin birth or ultimate resurrection of Jesus. Those claims can be judged by science, and are found wanting.

Some people would prefer to define “religion” so that religious beliefs entail nothing whatsoever about what happens in the world. And that’s fine; definitions are not correct or incorrect, they are simply useful or useless, where usefulness is judged by the clarity of one’s attempts at communication. Personally, I think using “religion” in that way is not very clear. Most Christians would disagree with the claim that Jesus came about because Joseph and Mary had sex and his sperm fertilized her ovum and things proceeded conventionally from there, or that Jesus didn’t really rise from the dead, or that God did not create the universe. The Congregation for the Causes of Saints, whose job it is to judge whether a candidate for canonization has really performed the required number of miracles and so forth, would probably not agree that miracles don’t occur. Francis Collins, recently nominated to direct the NIH, argues that some sort of God hypothesis helps explain the values of the fundamental constants of nature, just like a good Grand Unified Theory would. These views are by no means outliers, even without delving into the more extreme varieties of Biblical literalism.

Furthermore, if a religious person really did believe that nothing ever happened in the world that couldn’t be perfectly well explained by ordinary non-religious means, I would think they would expend their argument-energy engaging with the many millions of people who believe that the virgin birth and the resurrection and the promise of an eternal afterlife and the efficacy of intercessory prayer are all actually literally true, rather than with a handful of atheist bloggers with whom they agree about everything that happens in the world. But it’s a free country, and people are welcome to define words as they like, and argue with whom they wish.

But there was also a more interesting and substantive issue lurking below the surface. I focused in that post on the meaning of “religion,” but did allude to the fact that defenders of Non-Overlapping Magisteria often misrepresent “science” as well. And this, I think, is not just a matter of definitions: we can more or less agree on what “science” means, and still disagree on what questions it has the power to answer. So that’s an issue worth examining more carefully: what does science actually have the power to do?

I can think of one popular but very bad strategy for answering this question: first, attempt to distill the essence of “science” down to some punchy motto, and then ask what questions fall under the purview of that motto. At various points throughout history, popular mottos of choice might have been “the Baconian scientific method” or “logical positivism” or “Popperian falsificationism” or “methodological naturalism.” But this tactic always leads to trouble. Science is a messy human endeavor, notoriously hard to boil down to cut-and-dried procedures. A much better strategy, I think, is to consider specific examples, figure out what kinds of questions science can reasonably address, and compare those to the questions in which we’re interested.

Here is my favorite example question. Alpha Centauri A is a G-type star a little over four light years away. Now pick some very particular moment one billion years ago, and zoom in to the precise center of the star. Protons and electrons are colliding with each other all the time. Consider the collision of two electrons nearest to that exact time and that precise point in space. Now let’s ask: was momentum conserved in that collision? Or, to make it slightly more empirical, was the magnitude of the total momentum after the collision within one percent of the magnitude of the total momentum before the collision?

This isn’t supposed to be a trick question; I don’t have any special knowledge or theories about the interior of Alpha Centauri that you don’t have. The scientific answer to this question is: of course, the momentum was conserved. Conservation of momentum is a principle of science that has been tested to very high accuracy by all sorts of experiments, we have every reason to believe it held true in that particular collision, and absolutely no reason to doubt it; therefore, it’s perfectly reasonable to say that momentum was conserved.

A stickler might argue, well, you shouldn’t be so sure. You didn’t observe that particular event, after all, and more importantly there’s no conceivable way that you could collect data at the present time that would answer the question one way or the other. Science is an empirical endeavor, and should remain silent about things for which no empirical adjudication is possible.

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