Miscellany

It’s not so hard to write down a model of phantom energy: just invent an ordinary scalar field, but with a negative kinetic energy. Left to its own devices, such a field will gradually increase its potential energy, leading to a net increase in the energy density, so cosmologists would measure the equation-of-state parameter w to be less than -1.

But just because you can write a model down doesn’t mean it makes sense. Remember that, in a model-independent sense, there was a good argument against w<-1: it violates the Dominant Energy Condition, which is the requirement that assures us that energy doesn't propagate faster than light. So could their be something fundamentally sick about theories of phantom energy? Well, yes. In particular, the energy density is not bounded below -- as the field vibrates more and more, you can create a negative energy that is as large as you like. This means that the theory is not stable. Ordinarily in field theory, we like to invent models that have a unique "vacuum state," the state of absolutely lowest energy; all other states are excitations of the vacuum, with an unambiguously larger energy. Then we can be assured that the dynamics don't go crazy; systems will tend to oscillate around the vacuum, or (in the presence of friction or other damping forces) gradually wind down to the vacuum. But if there is no vacuum, the system can simply run away, like a ball rolling down a hill with no bottom. This possibility is not so horrifying in principle, but conflicts with the apparent stability that we observe around us in Nature. Think of it in terms of particles. The world is made of fields, but quantum fields, not classical ones. When you quantize a field, and then observe it, you see particles. For a phantom field, the negative kinetic energy implies that the particle excitations have a negative mass. (In contrast to tachyons, which have an imaginary mass.) This helps us to see why there is an instability: starting from a purported “vacuum” state of completely empty space at zero energy, we can imagine processes that conserve energy while creating large numbers of positive-mass ordinary particles plus compensating numbers of negative-mass phantom particles. Empty space itself is liable to dissolve into a bath of billions of particles!

This is why most particle physicists just laugh at the idea of phantom energy: it seems ruled out before you even start. But because there is so little we know about dark energy, it’s a good idea to keep our options open. In collaboration with Mark Hoffman and Mark Trodden, I wrote a paper examining whether the idea of phantom energy could be part of a larger scheme that was not obviously ruled out. The idea is a very common one in field theory: you have some model (an “effective field theory“) that describes everything perfectly well, but only at energies below some cutoff where unknown physics kicks in. This is an interesting feature about quantum field theory; the effect of high-energy processes is to change the parameters (the coupling constants) of your low-energy theory, but not to produce qualitatively new phenomena. In other words, dramatic new physics at high energies is basically hidden from our sight, subsumed in the quantitative behavior of the low-energy physics we can actually observe. (That’s why the best way to learn new particle physics is to build particle accelerators of ever-higher energy, and also why it’s so damned difficult to get any direct experimental handle on string theory or other models of quantum gravity, which live way up at the Planck energy.)

So we asked the question: could phantom energy be right, if only as an effective field theory valid below certain energies? If the phantom theory were valid up to arbitrarily large energies, not only would the vacuum be unstable, the decay rate would be infinite! What we found is that you can indeed imagine that there is a cutoff beyond which the phantom description doesn’t apply, and if that cutoff is awfully low (about a milli-electron-volt) the field would be essentially stable over the lifetime of the universe. (Some of our numbers have been brought into question in a paper by Cline, Jeon, and Moore.) An explicit example of the kind of cutoff we were proposing was later investigated by Arkani-Hamed et al.

There’s an additional possibility, that I’ve investigated more recently with Trodden and Antonio DeFelice. This is that there is no phantom energy, and the real equation-of-state parameter w is -1 or larger, but that we can be tricked into thinking that we’ve measured w to be less than -1. That’s because we never really measure w; what we measure is the expansion of the universe, and use general relativity to infer the properties of the dark energy. But general relativity might not be right. We investigated the specific example of a scalar-tensor theory, where some scalar field was causing the value of Newton’s gravitational constant to gradually vary with time. Then what you’re measuring in cosmology isn’t simply the behavior of the dark energy, but some combination of the dark energy and the gravitational scalar field. We found that you can indeed be tricked into thinking that w is less than -1, but only with a very unnatural behavior for the scalar field; most of the time, we would have already detected the variation of Newton’s constant right here in the Solar System long before you would measure some unusual behavior of the expansion of the universe.

The lesson is simply this: don’t be too dogmatic, but do be honest, when you are inventing theories of something you are as clueless about as the dark energy. Theorists need to be quite careful; if they are going to propose models of phantom energy and so forth, they need to do the hard work of determining whether their models are stable and otherwise well-defined. But observers shouldn’t take too seriously the grandiose claims of theorists about what is and is not possible; they should do their experiments and see what the data imply. It would be a shame to miss out on a fantastic discovery because you believed some theorist who told you it couldn’t possibly be there.

Found at Arts and Letters Daily, an excerpt from an interview with Jürgen Habermas talking about his relationship with Jacques Derrida:

When he received the Adorno Prize, Derrida, for his part, gave a highly sensible speech in the Paulskirche in Frankfurt, in which the spiritual affinity of these two minds was impressively manifested. This kind of thing leaves one not unmoved. Actually, over and beyond all the politics, what connects me to Derrida is the philosophical reference to an author like Kant. Admittedly — and though we are roughly the same age, our life histories have been very different — what separates us is the later Heidegger. Derrida’s thinking has appropriated the Jewish-inspired perceptions of a Levinas. In Heidegger, I confront a philosopher who failed as a citizen — in 1933 and especially after 1945. But even as a philosopher, he is suspect to me because, in the 1930s, he received Nietzsche precisely as a neo-pagan, as it was then the fashion to do. Unlike Derrida, whose reading of “Andenken” accords with the spirit of monotheistic tradition, I take Heidegger’s botch-job “Seinsdenken” as a leveling of that epochal threshold in the history of consciousness that Jaspers had called the axial age. According to my understanding, Heidegger committed treason against that caesura which is marked, in various ways, by the prophetic-awakening Word from Mount Sinai, and by the Enlightenment of a Socrates.

I have no comment to add to this, except that I would love to be able to talk like that extemporaneously.

Last time we talked about dark energy and its equation-of-state parameter, w. This number tells you how quickly the dark energy density changes as the universe expands; if w=-1, the density is strictly constant, if w>-1, the density decreases, and if w<-1, the density actually increases with time. (In equations, if a is the scale factor describing the relative size of the universe as a function of time, then the density goes as a^-3(1+w).) For comparison purposes, cosmological “matter” (slowly-moving massive particles) has w=0, and “radiation” (relativistic particles, including photons) has w=1/3.

Einstein’s cosmological constant is just the idea that there is a fixed minimum energy density everywhere in the universe; this vacuum energy would correspond to w=-1. It’s easy enough to get an energy density that slowly diminishes, with w>-1; all you need to do is invent some scalar field slowly rolling down a very gentle potential, so that the energy is nearly constant but in fact gradually diminishes.

What about w<-1, corresponding to a gradually increasing energy density? It's not what you would typically expect; the expansion of the universe tends to dilute energy, not increase it. So for a some time cosmologists who put observational limits on the value of w would exclude w<-1 by hand. In fact, I am somewhat to blame for this custom. As far as I know, the first paper to constrain w using supernova data is the one by Garnavich et al., the High-Z Supernova Team. I am friends with these guys — Brian Schmidt, leader of the collaboration, was my officemate during grad school — and one day they called me up to ask whether there was a good reason why they could ignore w<-1. In general relativity, it often happens that we want to make some general statements about possible solutions without knowing exactly what the matter/energy sources are, so we invoke "energy conditions" that put some reasonable constraints on what the sources can do. The most physically reasonable condition is the Dominant Energy Condition (DEC), which is what allows you to prove that energy can’t propagate faster than the speed of light. So I pointed out that imposing the DEC would exclude the w<-1 possibility. I wrote a couple of paragraphs to this effect, and got included as a co-author on the paper; afterwards, people were happily ignoring w<-1 a priori. Most people, anyway. A notable exception was Robert Caldwell at Dartmouth, who wrote a paper suggesting that w could be less than -1, and built an explicit model. The idea was simple: have a scalar field rolling in a potential, but give it a negative kinetic energy. That means that the field tends to roll up the hill to the top of the potential, rather than rolling down to the bottom. The energy density thus tends to increase, implying w<-1. Caldwell called his idea "phantom energy," both because the Phantom Menace had just come out and also because negative-kinetic-energy fields also appear in the context of quantized gauge theories, where they are called "ghost" fields. More recently, Caldwell collaborated with Marc Kamionkowski and Nevin Weinberg on the idea of a “Big Rip.” If w is less than -1 and constant, the energy density grows without bound and everything in the universe is ripped to shreds at some finite point in the future. This is a fun idea to think about, but some observers took it too seriously, and began phrasing their limits in terms of how many years would have to pass before there would be a Big Rip. That is just silly; even if w<-1, there's certainly no good reason to think it's a constant. I’ve gone on too long again. Next time, I promise, I’ll talk about my own papers, which are what you really care about, I know. Maybe I’ll even talk about what w probably is, in addition to what it is allowed to be.

Sorry, this post isn’t about dark energy, it’s making fun of John Kerry. (We always taunt the ones we love.) So what is it with his policy of not talking to the media? Does he think this is a good way to get favorable press coverage? It’s gotten so bad that the pool reports are regularly making fun of him:

From: kerrypool

Sent: Friday, September 10, 2004 6:15 PM

Subject: Re: [Kerrypool]

The senator left hangar 7 at 6:10p ET and saw a group of seven people waiting in the parking lot. The senator took a picture with the group and upon leaving your pooler tried yet again to get the candidate we all cover as he runs for president of the united states to answer a question from his national press corps. Your pooler asked whether saddam hussein would be in power if he were president and then when if ever he would talk to the press.

He’s got to understand: the Saddam jibe is a softball question! He should have turned to the reporter and said this:

I’m sorry, but I couldn’t hear you very well. I think what you just asked was, “If you were president, would one thousand American servicemen and servicewomen still be alive? And would we be fighting the war on terror in places where actual terrorists are located, with the support of the world behind us?” Why, yes. Yes, those troops would still be alive, and we would be fighting a more effective war on terror. Very astute question.

As Preposterous readers know all too well, about seventy percent of the stuff in the universe is a mysterious substance called dark energy (unless general relativity is breaking down, which is interesting but less likely). We know only two things about the dark energy: it is spread nearly uniformly throughout space, and its density is nearly constant as a function of time. In other words, it doesn’t dilute as the universe expands, unlike the energy in ordinary matter and radiation. So as time goes by, the dark energy becomes more and more dominant, as ordinary stuff becomes increasingly rarefied. (Worried about conservation of energy? Don’t be.)

But we don’t understand the dark energy that well, so we want to measure its properties as precisely as possible to get clues as to exactly what it might be. The simplest possibility is that it’s vacuum energy, or the cosmological constant — a perfectly constant energy density inherent in the fabric of spacetime itself. But it could also be something dynamical, changing in density gradually as the universe expands. In that case, we can hope to measure how fast its changing by looking at the evolution of the expansion rate of the universe; according to Einstein, the expansion rate (the Hubble constant) is proportional to the square root of the total energy density. We can make this measurement using a variety of cosmological probes — supernovae, large-scale structure, the evolution of galaxies and clusters, the cosmic microwave background, gravitational lensing, gravitational waves, and more — and there is a grand multi-pronged program under way to do just that over the next decade or two.

There are an infinite number of ways that some quantity (the energy density of the dark energy, or equivalently the expansion rate of the universe) can change with time, but we don’t measure things with infinite precision. So we need to decide how to simply characterize the results of what we measure. Cosmologists have settled on quoting the equation-of-state parameter w, defined as the ratio of the pressure of the dark energy to its energy density. The interesting thing about dark energy is that it has a negative pressure, a/k/a a tension. This isn’t so surprising all by itself; a stretched rubber band has tension, too. It’s this tension that allows the density to persist as the universe expands. (Said another way, not necessarily more helpfully, the deceleration/acceleration of the universe depends on the energy density plus three times the pressure; so a large negative pressure induces acceleration, while a positive energy density without any accompanying pressure would cause the universe to decelerate.)

The equation-of-state parameter governs the rate at which the dark energy density evolves. For a perfect, unchanging vacuum energy, we have w=-1: the pressure is equal in magnitude and opposite in sign to the energy density. If w is a little bit greater than -1 (e.g., -0.9 or -0.8), the dark energy density will slowly decrease as the universe expands. This would be the case, for example, if the dark energy were the potential energy of some slowly-rolling scalar field (sometimes called “quintessence”). Current experimental bounds tell us that w=-1 is the central preferred value, but there is room for improvement; see the plot at the bottom of Licia Verde’s page for the latest results.

This is all preliminary to mentioning the most recent paper I’ve written, which I’ll do in the next post. (For a preview, see these slides from a recent talk [pdf].) If w is less than -1, the energy density of the dark energy is actually increasing as the universe expands. Is this okay? Have cosmologists gone crazy? Stay tuned for our exciting conclusion!

The latest Tangled Bank is now up at archy. I humbly submitted my Q&A about testing general relativity. Maybe some anti-evolutionists will read it and start wondering if perhaps GR is “just a theory.”

The next Tangled Bank will be hosted at Lean Left. As PZ Myers notes, there seems to be a general leftward tilt in the scientific slice of the blogosphere, at least that part which contributes to TB; this isn’t intentional, it just works out that way. Probably because liberals believe in objective truth, while conservatives have been forced by recent events to become shifty relativists.

The Genesis spacecraft, a NASA mission designed to collect particles from the solar wind and bring them back to Earth for study, has crashed into the Utah desert. Apparently there were at least two problems, likely to be related: the craft was not correctly rotating so as to maintain its attitude during descent, and the parachutes that were supposed to break its fall never opened. The original plan was for a daring rescue in which stunt pilots would snag the vehicle as it fell to Earth. It’s not clear at the moment whether the samples will be able to be recovered; scientists are examining the craft carefully, as the parachutes may still be explosively deployed.

From Crooked Timber, the local political news is fraught with religious significance: Alan Keyes says that Jesus wouldn’t vote for Barack Obama. (Presumably, He would vote for Alan Keyes, although Keyes is too humble to draw the obvious conclusion.)

For we non-believers, these esoteric theological discussions are all very confusing. I’ve gotten the wrong impression countless times by simply reading the Bible without an expert commentator at my elbow to help me along. Consider for example the famous passage in Matthew 19:24:

And again I say unto you, It is easier for a camel to go through the eye of a needle, than for a rich man to enter into the kingdom of God.

(The story is repeated in the other synoptic gospels, Mark and Luke.) Now, the meaning here seems pretty straightforward to the uneducated reader — rich people are going to have a really hard time getting into Heaven. An impossible time, actually; as Jesus surely knows, camels don’t fit through the eyes of needles. (Some weasels try to claim that the “eye” was really a gate outside Jerusalem, or the “camel” was really “rope,” but these ideas have been rightfully smacked down.) But that’s only because I’m a naive reader of the scriptures. At least I am quicker on the uptake than Jesus’ disciples, who dutifully play the straight man:

When his disciples heard it, they were exceedingly amazed, saying, Who then can be saved?

Here I would have expected Jesus to slap the disciples, aggravated at their cluelessness. If rich people won’t enter the kingdom of God, it seems pretty obvious that Heaven would be populated by (formerly) poor people. But that’s why I’m a physicist rather than the Messiah. Jesus explains:

But Jesus beheld them, and said unto them, With men this is impossible; but with God all things are possible.

So the point is not that rich people won’t enter Heaven; it that’s they can only enter with the help of God (just like everybody else)! All those parts of the Bible where Jesus appears to be saying disdainful things about wealth are really just a smokescreen — what’s important is not how much money you have, but how deeply you believe in Him. Otherwise how could our President stand a chance?

So I’m not going to offer an opinion about who Jesus would vote for. For all I know, He may think that the good citizens of Illinois should walk around carrying concealed machine guns. Sure would make the morning commute on the El more exciting!

Brian Leiter, prompted by Jessica Wilson, who was prompted by an essay at That Good Night, wonders whether recent events in the U.S. can usefully be thought of as proto-fascist. Specifically, are there interesting parallels between the U.S. today and Germany in the 1930’s? Let me go out on a limb here and provide a straightforward answer: yes and no.

“No”, in that I think there is essentially zero danger of the U.S. transforming into a fascist dictatorship any time in the foreseeable future. For one thing, as wrong-headed as they may be, nobody in the Bush administration actually wants to overthrow democracy. (Okay, maybe Ashcroft, but he’s only one guy.) It’s true that they want to paint everything in black and white and portray any kind of disagreement as treasonous, but that’s not enough to qualify as fascism. More importantly, democratic ideals are simply too deeply ingrained in U.S. society to allow any realistic chance of transforming into a dictatorship.

So, one’s first response is to think that even asking the question is somewhat alarmist, if not hysterical. But we should keep in mind that historical fascism was quite popular at certain times in certain places, and it’s perfectly reasonable to ask whether the impulses that led to some of the dramatic movements of the past are at work in our present situation. In a more recent post Leiter points to this short essay by Umberto Eco, discussing the universal characteristics of fascist societies. I have to say, some of the features Eco identifies are uncomfortably familiar. For a while now, like many other liberals, I’ve been trying to understand how any reasonable person could possibly support the current administration, which makes wrong choices nearly every time by any sensible criteria. Of course there are many answers to this question, but I think one huge factor (reflected quite explicitly in the campaign rhetoric) is the valorization of certainty (or “decisiveness”) over nuance or complexity (“flip-flopping”). There seems to be a strong feeling among Bush supporters that taking a definitive stand is more important that what that stand is. I don’t mean to be condescending, but this point of view is so alien to me that I can’t really do it justice. To these people, the war in Iraq was justified because Saddam was our enemy, regardless of the absence of weapons of mass destruction or any connection between Iraq and 9/11. It is taken as a sign of strength, rather than a bumbling approach to diplomacy, that our nominal allies are predominantly aligned against us across a range of foreign-policy questions. It is to these people that Dick Cheney’s smirks at Kerry’s “sensitive war on terror” are directed — in this view, the last thing you want to do in a war on terror is to understand the minds of the enemy.

To get back on track: Eco makes a strong case that a main theme of fascism is to establish a comfortable zone of certainty in which dissent, and even ambiguity, are considered traitorous. It is a feeling fed by resentment, both of ruling elites generally and of intellectuals in particular. You can see how such a stance might be compelling — it feels good to be a virtuous Everyman, defending one’s way of life against enemies at home and abroad. In a complicated world, there is comfort to be found in leaning on simple, strong, patriotic truths, whether decorating the town with American flags or lashing out with the armed forces. When Ann Coulter labels liberals as treasonous, or Zell Miller gives soldiers credit for freedom of speech, or Rick Santorum demonizes gays and atheists, they are appealing to exactly this feeling of unreflective anger.

After reading Eco’s essay, I am no more convinced than before that we are in any danger of becoming a fascist state, but I do think that the underlying principles of proto-fascism have something important in common with the motivating philosophies of the Bush administration. It explains much of what is otherwise confusing about Bush’s policies, especially to more libertarian-leaning conservatives. From the crusade against gay marriages, to the dramatic undermining of independent scientific advisory councils in policy making, to the cheerful disregard of judicial due process, to the sanguine acceptance of budget deficits and protectionist trade policies, we see a consistent appeal to a resentful and frustrated middle class.

There is a danger in throwing around scare words like “fascism”, that we will denigrate the level of political discourse even further. But we shouldn’t forget that historical fascism really was attractive to a large number of people, and for strong reasons; it’s not impermissible (yet) to think soberly about what those reasons were, and what relationship they have to political currents that still run strongly today.

A nice gesture from the director of Fermilab.

Date: Tue, 07 Sep 2004 09:31:35 -0500

From: FNAL Users Office

Subject: Fermilab Community – Three Minutes of Silence

To: usersorg@fnal.gov

September 7, 2004

To: The Fermilab Community

From: Michael Witherell, Director

Subject: Three Minutes of Silence at Noon Today

As children returned to classrooms around the US last week, a terrible tragedy unfolded at a school in Beslan, Russia. Violence claims lives every day, but when the victims are children we are even more deeply affected.

At Fermilab, it is both our privilege and our responsibility to carry forward the tradition of a field long known for its leadership in international collaboration. This tradition allows us to know one another as people as well as representatives of other nations. Fermilab has many close ties with Russia. Russian scientists and engineers are leading members of our staff, and many from Russian institutions participate in DZero, CDF, MINOS, BTeV, and CMS. To all of our Russian colleagues, we express our sorrow.

I ask you to observe three minutes of silence today, throughout the laboratory, beginning at 12:00 noon, in sympathy and solidarity with our Russian colleagues here at Fermilab and around the world.