Tuesday December 13 has been a very exciting day for particle physics. The ATLAS and CMS experiments at the Large Hadron Collider (LHC) announced today that they are both seeing hints of a Higgs boson with properties that are close to those expected for the Standard Model (SM) Higgs boson as originally proposed by Peter Higgs and others. While the “significance” of the signals has not yet reached “discovery level” (5 sigma in technical language) the two experiments both see signals that exceed 2 sigma so that there is less than a 5% chance that they are simply statistical fluctuations. Most persuasively, the signals in the channels with excellent mass determination (the photon-photon final decay state and the 4-lepton final state) are all consistent with a a Higgs boson mass of around 125 GeV IN BOTH EXPERIMENTS. This coincidence in mass between two totally independent experiments (as well as independent final states) is persuasive evidence that the photon-photon and 4-lepton excesses seen near 125 GeV are not mere statistical fluctuations.

Observation of the Higgs with approximately the SM-like rate suggests that to first approximation the Higgs is being produced as expected in the SM and that it also decays as predicted in the SM. Many theorists, including myself, have suggested that a Higgs might be produced as in the SM but might have extra decays that would have decreased the photon-photon and 4-lepton decay frequencies to an unobservable level, making the Higgs boson much harder to detect at the LHC. The level of the observed excesses argues against such extra decays being very important. The photon-photon and 4-lepton detection modes were originally proposed and shown to be viable for a SM-like Higgs boson by myself and collaborators (in particular, Gordy Kane and Jose Wudka) way back in 1986-1987. It has taken a long time (25 years) for the technology and funding to reach the point where these detection modes could be examined. I often joked that I was personally responsible for forcing each of the LHC collaborations to spend the 30 million dollars or so needed to build a photon detector with the energy resolution required. Fortunately, it seems that the money was well-spent and the ATLAS and CMS detectors both found ways to build the needed detectors, a real triumph of international collaboration and technical expertise. Also key is the very successful operation of the LHC that has produced the enormously large number of collision events needed to dig out the Higgs signal from uninteresting ‘background’ events. Until this summer produced the first very weak signs of the Higgs, I was beginning to wonder if the Higgs would be discovered during my lifetime. Fortunately, simplicity (i.e. a very conventional SM-like Higgs boson) seems to have prevailed and ended my wait.

Going forward, by the end of 2012 the levels of these excesses should reach the 5 sigma “discovery” level if the SM-like Higgs really does have the mass and decays indicated by current results. Further, we will begin to have some moderately precise (20%-30% or so?) measurements of the individual decay modes of the Higgs boson that might indicate just how precisely SM-like it is. Many theories beyond the Standard Model predict the possibility of deviations from the predictions of the purely SM Higgs boson. As data accumulate, looking for such deviations will be a major focus. Current data (weakly) hint at the possibility that the Higgs production rate might turn out to be modestly larger than predicted if the Higgs is that of the Standard Model and has mass of 125 GeV — the best-fit ATLAS cross section is about 1.5 times as large as the SM prediction, whereas the best-fit CMS cross section is very close to the SM prediction. Time (i.e. more accumulated data) will tell.

Of course, the current run of the LHC will be halted at the end of 2012, followed by a lengthy shut down for upgrades to the accelerator and to the detectors. After this upgrade, the LHC will operate at a much higher energy (14 TeV) compared to the current energy of 7 TeV, and, if all goes according to plan, have a much higher collision rate. At this point, precision studies of the Higgs boson will certainly be possible. If deviations are observed, then we will strongly suspect that the SM is incomplete. Even before that time, we are hoping that by the end of 2012 we will have seen new types of particles that do not fit into the Standard Model. This, for example, is predicted if the universe is supersymmetric. Supersymmetric models tend to predict a light Higgs boson that is fairly, but not completely, SM-like with mass in the range 110 GeV to 140 GeV and so are very consistent with what is being observed. If some supersymmetric particles (so called sparticles) are observed then their masses and properties constrain the Higgs mass in a given model and consistency of the entire theory can be nicely tested. Hopefully, some version of physics beyond the Standard Model will be directly observed at the LHC, in which case there will be at least a decade of exciting observations and analyses to determine the precise beyond-the-Standard-Model theory.

Still, the pure Standard Model with no new physics cannot be totally discarded. Although this would not allow a so-called “natural” explanation of the Z boson and Higgs boson masses, the pure SM is still internally consistent even at energies close to the Planck scale for a Higgs mass greater than or equal to about 125-130 GeV. In other words, the observed Higgs mass is on a borderline. Above 125-130 GeV, new physics below the Planck mass scale is not required for internal consistency of the SM. But, had the Higgs boson mass been significantly below this (the precise border being somewhat uncertain theoretically), the SM would necessarily break down at some energy scale below the Planck scale and at this lower energy scale new physics would have to enter. In short, a SM-like Higgs boson with mass near 125 GeV is maximally interesting from many theoretical perspectives.

In any case, theorists and experimentalists are all very relieved that the LHC appears to be observing a Higgs boson thereby ensuring an extremely interesting program of physics at the LHC for decades to come. Further, such a light SM-like Higgs boson provides strong motivation for a linear electron-positron collider of low center-of-mass energy. Studies suggest that only such a collider can easily measure the properties of such a light Higgs boson at the few percent level, although the LHC might not do that much worse depending upon future improvements and upgrades.

So we’re very happy to welcome a guest post by Matt Strassler, who is an expert particle theorist, to help explain what’s at stake and where the search for the Higgs might lead. Matt has made numerous important contributions, from phenomenology to string theory, and has recently launched the website Of Particular Significance, aimed at making modern particle physics accessible to a wide audience. Go there for a treasure trove of explanatory articles, growing at an impressive pace.

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After this year’s very successful run of the Large Hadron Collider (LHC), the world’s most powerful particle accelerator, a sense of great excitement is beginning to pervade the high-energy particle physics community. The search for the Higgs particle… or particles… or whatever appears in its place… has entered a crucial stage.

We’re now deep into Phase 1 of this search, in which the LHC experiments ATLAS and CMS are looking for the simplest possible Higgs particle. This unadorned version of the Higgs particle is usually called the Standard Model Higgs, or “SM Higgs” for short. The end of Phase 1 looks to be at most a year away, and possibly much sooner. Within that time, either the SM Higgs will show up, or it will be ruled out once and for all, forcing an experimental search for more exotic types of Higgs particles. Either way, it’s a turning point in the history of our efforts to understand nature’s elementary laws.

This moment has been a long time coming. I’ve been working as a scientist for over twenty years, and for a third decade before that I was reading layperson’s articles about particle physics, and attending public lectures by my predecessors. Even then, the Higgs particle was a profound mystery. Within the Standard Model (the equations that used at the LHC to describe all the particles and forces of nature we know about so far, along with the SM Higgs field and particle) it stood out as a bit different, a bit ad hoc, something not quite like the others. It has always been widely suspected that the full story might be more complicated. Already in the 1970s and 1980s there were speculative variants of the Standard Model’s equations containing several types of Higgs particles, and other versions with a more complicated Higgs field and no Higgs particle — with a key role of the Higgs particle being played by other new particles and forces.

But everyone also knew this: you could not simply take the equations of the Standard Model, strip the Higgs particle out, and put nothing back in its place. The resulting equations would not form a complete theory; they would be self-inconsistent. Though still effective in many contexts, they would become useless for predicting certain high-energy processes, including ones that the LHC, a few years from now, will directly study. So it was widely known, over thirty years ago, that something like a Higgs particle had to be in those equations to make them sensible. In fact, the condition is even stronger than that. The equations of the Standard Model will require significant and historic modifications unless the Standard Model Higgs particle is found with a mass below about 800 GeV/c². (For scale, the mass of a hydrogen atom is about 1 GeV/c².)

It’s this last point that explains why the current moment is such a critical one. Sure, previous experiments have looked for the Higgs particle too. And they were able to sweep some areas clean; we know, from these experiments, that the mass of the SM Higgs cannot lie below 115 GeV/c². But the LHC is special; it is the first accelerator capable of finding the SM Higgs over the entire allowed mass range still remaining, from 115 up to and beyond 800 GeV/c².

Phase 1, the search for the SM Higgs, is the easy part of the quest for the Higgs particle (or particles or whatever). What makes it easy? The Standard Model equations are so detailed and well-specified that everything about the SM Higgs particle is already known, except for one thing: its mass. More precisely, if you told me the SM Higgs particle’s mass, I could tell you how it is produced at the LHC and at what rate, and what it decays to, and how often it decays to one set of particles rather than another. This makes life relatively simple for the experimenters at ATLAS and CMS, because all they have to do is this: pick a mass in the allowed range, ask theorists to calculate the properties of an SM Higgs particle of that mass, figure out the best way to seek it in their data, and look at the data: is there evidence for or against its presence? They must then repeat this across the entire range of possible masses systematically, until they’ve covered all the allowed territory. (Actually they do all of these searches simultaneously, not sequentially.) When their coverage is complete — or when they find something — Phase 1 is over.

It is useful to think of Phase 1 as three subprojects, going on all at the same time but proceeding at different rates, involving the search strategies for a lightweight, middleweight and heavyweight SM Higgs. We’re almost done with the middleweight case, the easy one, in which one looks mainly for a Higgs decaying (i.e., disintegrating) to two W particles or two Z particles. The entire range from 141 to 470 GeV/c² is now excluded (according to the combination of the summer’s data from ATLAS and CMS that was announced a few weeks ago). The lightweight range, down to 115 GeV/c², is dominated by a search for a Higgs particle decaying to two photons. To observe this decay, a very rare process, requires a lot of data, so exploring this range fully will take another six months to a year. But we should already learn more about the lightweight Higgs on December 13th, when CERN will be providing an update on the Higgs search.

The heavyweight range — above 450 GeV/c² or so — is a little more subtle. Many theorists argue this window is already closed, by indirect experimental evidence. There are processes, carefully measured over the past 20 years, that are indirectly sensitive to the mass of the SM Higgs, and that strongly suggest it should be on the lighter side… below something like 300-400 GeV/c², though reasonable people might disagree on where exactly to set this bound. But even if you didn’t buy this powerful argument, it wouldn’t trouble the experiments. Depending upon exactly how much data the LHC takes in 2012, we should see most of the heavyweight range explored experimentally by late next year. The experimental results, combined with the theoretical arguments, should allow Phase 1 to conclude, to the satisfaction of almost all experts, once the 2012 data is fully analyzed.

So what are the possible outcomes of Phase 1?

1) The SM Higgs particle, already known with substantial confidence not to be in the middleweight range, might turn up in the lightweight or heavyweight range.
2) The SM Higgs particle might be entirely excluded, from 115 up to 800 GeV/c² or so. (Remember, though, that this would not mean there is no Higgs particle of any type — it would mean only that the simplest type is not found in nature.)
3) A Higgs-like particle that is clearly not a Standard Model Higgs particle (because it has the wrong production rates, or the wrong decay rates, given its mass) might be found instead.
3a) Some other great discovery at the LHC might move the SM Higgs search off the front pages for a while.

What would be the pros and cons of these different scenarios?

1) If the SM Higgs is found, that will be a historic discovery by the LHC, provisionally confirming the Standard Model’s simplest Higgs. That said, in some ways it will be a bit disappointing, since the Standard Model leaves many important questions in particle physics unanswered, and only by finding flaws in its equations do we have much hope of answering those questions.

2) If the SM Higgs is excluded, that will be an even more historic discovery, implying that the Standard Model’s equations are not the complete story at the LHC. For most particle physicists, this will be a much more exciting outcome! There will be a great opportunity for the LHC to teach us something profound about nature that we may not currently even suspect, although we’ll be on tenderhooks, potentially for quite a while, wondering whether the LHC’s data will provide clear guidance as to how to modify the Standard Model, or only give us some suggestive hints.

3) If a new non-SM Higgs particle is found, that will be the best possible outcome! Not only will we see the Standard Model’s equations fail, we’ll have a direct clue, in the form of the new particle, as to how to begin modifying them. In this case the LHC will immediately help us to start writing the new chapter in particle physics textbooks.

3a) And if something else unexpected is found in LHC data in the meantime, no one will complain! This of course would also mean the failure of the Standard Model’s equations, and new clues into nature’s mysteries.

You may have noticed that on this list there’s really no bad outcome. That’s right: as long as there are no technical problems at the LHC that limit the amount of data it collects in 2012, we are in a no-lose situation in the short term. This does not happen very often! And this is why there’s so much excitement right now in the field. We’re not wondering if we’ll get some historic information over the next year or so, or whether it will change the field of particle physics. We’re just wondering what it will be. (Needless to say, we’re all wishing the accelerator physicists and engineers over at the LHC, who keep the machine running efficiently, the very, very best — and while we’re at it, let’s hear a big round of applause for them right now, for what they’ve achieved in 2011!)

No matter what, there will be a very important Phase 2 to the Higgs search, which will extend for perhaps ten years beyond Phase 1. If Phase 1 finds something that looks like an SM Higgs particle, Phase 2 will be all about checking its details with high precision. The new particle may look at first as though it is just what the simplest version of the Higgs story would predict, but if even the slightest detail is out of place, it would show the Higgs is not so simple after all, which would be an exciting turn of events. If instead Phase 1 rules out the SM Higgs, then a great host of new search strategies will be brought to bear, and the experimentalists will (figuratively) fan out like a massive search party, looking for all varieties of exotic types of Higgs particles. Also — remembering that there may be no Higgs particle, but if so, the Standard Model’s equations can’t be entirely right — they’ll step up their efforts to look for the many other types of particles and forces that we might need to add to the Standard Model to make its equations sensible again, absent any type of Higgs particle in nature. And if a non-SM Higgs particle is found in Phase 1, Phase 2 will involve all of these strategies at once, producing the new Higgs particle in large quantities and studying it in detail, while looking for more clues as to what else is missing from the Standard Model’s equations.

It has been decades since a moment in particle physics looked as bright as do the next couple of years (healthy LHC operations permitting.) We’ve seen turning points in other fields: the human genome project was guaranteed to revolutionize genetics and genomics, and the study of the cosmic microwave background radiation was guaranteed to change our understanding of the early universe, as long as the experimental methods worked. These were great historic achievements that gave new life to those subjects; but we do not yet know whether the same is in store for particle physics. Will the flash of new understanding provided by Phase 1 quickly fade, or will it brighten into a dawn of a new age? Will the Standard Model’s equations work perfectly at the LHC, giving us a sense of satisfaction but no clues for future understanding? Will the equations fail, but in an obscure fashion, leaving us uncertain as to how to fix them? Or will their failure be clear and instructive, as has been the case for so many sets of equations before them, allowing the LHC, along perhaps with other experiments, to provide us with the insights we need to proceed to a more profound understanding of nature?

There is only one way to find out: run the experiment, and let nature speak.

So keep your eyes on Phase 1 of the Higgs search as it progresses toward a conclusion over the coming weeks and months. If the LHC works as hoped, the year ahead will be a memorable one.

To help understand the lay of the land, we’re very happy to host this guest post by David Wallace, a philosopher of science at Oxford. David has been one of the leaders in trying to make sense of the many-worlds interpretation of quantum mechanics, in particular the knotty problem of how to get the Born rule (“the wave function squared is the probability”) out of the this formalism. He was also a participant at our recent time conference, and the co-star of one of the videos I posted. He’s a very clear writer, and I think interested parties will get a lot out of reading this.

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Why the quantum state isn’t (straightforwardly) probabilistic

In quantum mechanics, we routinely talk about so-called “superposition states” – both at the microscopic level (“the state of the electron is a superposition of spin-up and spin-down”) and, at least in foundations of physics, at the macroscopic level (“the state of Schrodinger’s cat is a superposition of alive and dead”). Rather a large fraction of the “problem of measurement” is the problem of making sense of these superposition states, and there are basically two views. On the first (“state as physical”), the state of a physical system tells us what that system is actually, physically, like, and from that point of view, Schrodinger’s cat is seriously weird. What does it even mean to say that the cat is both alive and dead? And, if cats can be alive and dead at the same time, how come when we look at them we only see definitely-alive cats or definitely-dead cats? We can try to answer the second question by invoking some mysterious new dynamical process – a “collapse of the wave function” whereby the act of looking at half-alive, half-dead cats magically causes them to jump into alive-cat or dead-cat states – but a physical process which depends for its action on “observations”, “measurements”, even “consciousness”, doesn’t seem scientifically reputable. So people who accept the “state-as-physical” view are generally led either to try to make sense of quantum theory without collapses (that leads you to something like Everett’s many-worlds theory), or to modify or augment quantum theory so as to replace it with something scientifically less problematic.

On the second view, (“state as probability”), Schrodinger’s cat is totally unmysterious. When we say “the state of the cat is half alive, half dead”, on this view we just mean “it has a 50% probability of being alive and a 50% probability of being dead”. And the so-called collapse of the wavefunction just corresponds to us looking and finding out which it is. From this point of view, to say that the cat is in a superposition of alive and dead is no more mysterious than to say that Sean is 50% likely to be in his office and 50% likely to be at a conference.

Now, to be sure, probability is a bit philosophically mysterious. It’s not uncontroversial what it means to say that something is 50% likely to be the case. But we have a number of ways of making sense of it, and for all of them, the cat stays unmysterious. For instance, perhaps we mean that if we run the experiment many times (good luck getting that one past PETA), we’ll find that half the cats live, and half of them die. (This is the Frequentist view.) Or perhaps we mean that we, personally, know that that the cat is alive or dead but we don’t know which, and the 50% is a way of quantifying our lack of knowledge. (This is the Bayesian view.) But on either view, the weirdness of the cat still goes away.

So, it’s awfully tempting to say that we should just adopt the “state-as-probability” view, and thus get rid of the quantum weirdness. But This doesn’t work, for just as the “state-as-physical” view struggles to make sense of macroscopic superpositions, so the “state-as-probability” view founders on microscopic superpositions.

Consider, for instance, a very simple interference experiment. We split a laser beam into two beams (Beam 1 and Beam 2, say) with a half-silvered mirror. We bring the beams back together at another such mirror and allow them to interfere. The resultant light ends up being split between (say) Output Path A and Output Path B, and we see how much light ends up at each. It’s well known that we can tune the two beams to get any result we like – all the light at A, all of it at B, or anything in between. It’s also well known that if we block one of the beams, we always get the same result – half the light at A, half the light at B. And finally, it’s well known that these results persist even if we turn the laser so far down that only one photon passes through at a time.

According to quantum mechanics, we should represent the state of each photon, as it passes through the system, as a superposition of “photon in Beam 1″ and “Photon in Beam 2″. According to the “state as physical” view, this is just a strange kind of non-local state a photon is. But on the “state as probability” view, it seems to be shorthand for “the photon is either in beam 1 or beam 2, with equal probability of each”. And that can’t be correct. For if the photon is in beam 1 (and so, according to quantum physics, described by a non-superposition state, or at least not by a superposition of beam states) we know we get result A half the time, result B half the time. And if the photon is in beam 2, we also know that we get result A half the time, result B half the time. So whichever beam it’s in, we should get result A half the time and result B half the time. And of course, we don’t. So, just by elementary reasoning – I haven’t even had to talk about probabilities – we seem to rule out the “state-as-probability” rule.

Indeed, we seem to be able to see, pretty directly, that something goes down each beam. If I insert an appropriate phase factor into one of the beams – either one of the beams – I can change things from “every photon ends up at A” to “every photon ends up at B”. In other words, things happening to either beam affect physical outcomes. It’s hard at best to see how to make sense of this unless both beams are being probed by physical “stuff” on every run of the experiment. That seems pretty definitively to support the idea that the superposition is somehow physical.

There’s an interesting way of getting around the problem. We could just say that my “elementary reasoning” doesn’t actually apply to quantum theory – it’s a holdover of old, bad, classical ways of thinking about the world. We might, for instance, say that the kind of either-this-thing-happens-or-that-thing-does reasoning I was using above isn’t applicable to quantum systems. (Tom Banks, in his post, says pretty much exactly this.)

There are various ways of saying what’s problematic with this, but here’s a simple one. To make this kind of claim is to say that the “probabilities” of quantum theory don’t obey all of the rules of probability. But in that case, what makes us think that they are probabilities? They can’t be relative frequencies, for instance: it can’t be that 50% of the photons go down the left branch and 50% go down the right branch. Nor can they quantify our ignorance of which branch it goes down – because we don’t need to know which branch it goes down to know what it will do next. So to call the numbers in the superposition “probabilities” is question-begging. Better to give them their own name, and fortunately, quantum mechanics has already given us a name: amplitudes.

But once we make this move, we’ve lost everything distinctive about the “state-as-probability” view. Everyone agrees that according to quantum theory, the photon has some amplitude of being in beam A and some amplitude of being in beam B (and, indeed, that the cat has some amplitude of being alive and some amplitude of being dead); the question is, what does that mean? The “state-as-probability” view was supposed to answer, simply: it means that we don’t know everything about the photon’s (or the cat’s) state; but that now seems to have been lost. And the earlier argument that something goes down both beams remains unscathed.

Now, I’ve considered only the most straightforward kind of state-as-probability view you can think of – a view which I think is pretty decisively refuted by the facts. It’s possible to imagine subtler probabilistic theories – maybe the quantum state isn’t about the probabilities of each term in the superposition, but it’s still about the probabilities of something. But people’s expectations have generally been that the ubiquity of interference effects makes that hard to sustain, and a succession of mathematical results – from classic results like the Bell-Kochen-Specker theorem, to cutting-edge results like the recent theorem by Pusey, Barrett and Rudolph – have supported that expectation.

In fact, only one currently-discussed state-as-probability theory seems even half-way viable: the probabilities aren’t the probability of anything objective, they’re just the probabilities of measurement outcomes. Quantum theory, in other words, isn’t a theory that tells us about the world: it’s just a tool to predict the results of experiment. Views like this – which philosophers call instrumentalist – are often adopted as fall-back positions by physicists defending state-as-probability takes on quantum mechanics: Tom Banks, for instance, does exactly this in the last paragraph of his blog entry.

There’s nothing particularly quantum-mechanical about instrumentalism. It has a long and rather sorry philosophical history: most contemporary philosophers of science regard it as fairly conclusively refuted. But I think it’s easier to see what’s wrong with it just by noticing that real science just isn’t like this. According to instrumentalism, palaeontologists talk about dinosaurs so they can understand fossils, astrophysicists talk about stars so they can understand photoplates, virologists talk about viruses so they can understand NMR instruments, and particle physicists talk about the Higgs Boson so they can understand the LHC. In each case, it’s quite clear that instrumentalism is the wrong way around. Science is not “about” experiments; science is about the world, and experiments are part of its toolkit.

Tom’s last post was “technical” in the sense that it dug deeply into speculative ideas at the cutting edge of research. This one is technical in a different sense: the concepts are presented at a level that second-year undergraduate physics majors should have no trouble following, but there are explicit equations that might make it rough going for anyone without at least that much background. The translation from LaTeX to WordPress is a bit kludgy; here is a more elegant-looking pdf version if you’d prefer to read that.

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Rabbi Eliezer ben Yaakov of Nahariya said in the 6th century, “He who has not said three things to his students, has not conveyed the true essence of quantum mechanics. And these are Probability, Intrinsic Probability, and Peculiar Probability”.

Probability first entered the teachings of men through the work of that dissolute gambler Pascal, who was willing to make a bet on his salvation. It was a way of quantifying our risk of uncertainty. Implicit in Pascal’s thinking, and all who came after him was the idea that there was a certainty, even a predictability, but that we fallible humans may not always have enough data to make the correct predictions. This implicit assumption is completely unnecessary and the mathematical theory of probability makes use of it only through one crucial assumption, which turns out to be wrong in principle but right in practice for many actual events in the real world.

For simplicity, assume that there are only a finite number of things that one can measure, in order to avoid too much math. List the possible measurements as a sequence

The a_N are the quantities being measured and each could have a finite number of values. Then a probability distribution assigns a number P(A) between zero and one to each possible outcome. The sum of the numbers has to add up to one. The so called frequentist interpretation of these numbers is that if we did the same measurement a large number of times, then the fraction of times or frequency with which we’d find a particular result would approach the probability of that result in the limit of an infinite number of trials. It is mathematically rigorous, but only a fantasy in the real world, where we have no idea whether we have an infinite amount of time to do the experiments. The other interpretation, often called Bayesian, is that probability gives a best guess at what the answer will be in any given trial. It tells you how to bet. This is how the concept is used by most working scientists. You do a few experiments and see how the finite distribution of results compares to the probabilities, and then assign a confidence level to the conclusion that a particular theory of the data is correct. Even in flipping a completely fair coin, it’s possible to get a million heads in a row. If that happens, you’re pretty sure the coin is weighted but you can’t know for sure.

Physical theories are often couched in the form of equations for the time evolution of the probability distribution, even in classical physics. One introduces “random forces” into Newton’s equations to “approximate the effect of the deterministic motion of parts of the system we don’t observe”. The classic example is the Brownian motion of particles we see under the microscopic, where we think of the random forces in the equations as coming from collisions with the atoms in the fluid in which the particles are suspended. However, there’s no a priori reason why these equations couldn’t be the fundamental laws of nature. Determinism is a philosophical stance, an hypothesis about the way the world works, which has to be subjected to experiment just like anything else. Anyone who’s listened to a geiger counter will recognize that the microscopic process of decay of radioactive nuclei doesn’t seem very deterministic.

The place where the deterministic hypothesis and the laws of classical logic are put into the theory of probability is through the rule for combining probabilities of independent alternatives. A classic example is shooting particles through a pair of slits. One says, “the particle had to go through slit A or slit B and the probabilities are independent of each other, so,

It seems so obvious, but it’s wrong, as we’ll see below. The probability sum rule, as the previous equation is called, allows us to define conditional probabilities. This is best understood through the example of hurricane Katrina. The equations used by weather forecasters are probabilistic in nature. Long before Katrina made landfall, they predicted a probability that it would hit either New Orleans or Galveston. These are, more or less, mutually exclusive alternatives. Because these weather probabilities, at least approximately, obey the sum rule, we can conclude that the prediction for what happens after we make the observation of people suffering in the Superdome, doesn’t depend on the fact that Katrina could have hit Galveston. That is, that observation allows us to set the probability that it could have hit Galveston to zero, and re-scale all other probabilities by a common factor so that the probability of hitting New Orleans was one.

Note that if we think of the probability function P(x,t) for the hurricane to hit a point x and time t to be a physical field, then this procedure seems non-local or a-causal. The field changes instantaneously to zero at Galveston as soon as we make a measurement in New Orleans. Furthermore, our procedure “violates the weather equations”. Weather evolution seems to have two kinds of dynamics. The deterministic, local, evolution of P(x,t) given by the equation, and the causality violating projection of the probability of Galveston to zero and rescaling of the probability of New Orleans to one, which is mysteriously caused by the measurement process. Recognizing P to be a probability, rather than a physical field, shows that these objections are silly.

Nothing in this discussion depends on whether we assume the weather equations are the fundamental laws of physics of an intrinsically uncertain world, or come from neglecting certain unmeasured degrees of freedom in a completely deterministic system.

The essence of QM is that it forces us to take an intrinsically probabilistic view of the world, and that it does so by discovering an unavoidable probability theory underlying the mathematics of classical logic. In order to describe this in the simplest possible way, I want to follow Feynman and ask you to think about a single ammonia molecule, NH₃. A classical picture of this molecule is a pyramid with the nitrogen at the apex and the three hydrogens forming an equilateral triangle at the base. Let’s imagine a situation in which the only relevant measurement we could make was whether the pyramid was pointing up or down along the z axis. We can ask one question Q, “Is the pyramid pointing up?” and the molecule has two states in which the answer is either yes or no. Following Boole, we can assign these two states the numerical values 1 and 0 for Q, and then the “contrary question” 1 − Q has the opposite truth values. Boole showed that all of the rules of classical logic could be encoded in an algebra of independent questions, satisfying

where the Kronecker symbol δ_ij = 1 if i = j and 0 otherwise. i,j run from 1 to N, the number of independent questions. We also have ∑Q_i = 1, meaning that one and only one of the questions has the answer yes in any state of the system. Our ammonia molecule has only two independent questions, Q and 1 − Q. Let me also define s_z = 2Q − 1 = ±1, in the two different states. Computer aficionadas will recognize our two question system as a bit.

We can relate this discussion of logic to our discussion of probability of measurements by introducing observables A = ∑a_i Q_i , where the a_i are real numbers, specifying the value of some measurable quantity in the state where only Q_i has the answer yes. A probability distribution is then just a special case ρ = ∑p_i Q_i, where p_i is non-negative for each i and ∑p_i = 1.

Restricting attention to our ammonia molecule, we denote the two states as | ±_z 〉 and summarize the algebra of questions by the equation

We say that ” the operator s_z acting on the states | ±_z 〉 just multiplies them by (the appropriate ) number”. Similarly, if A = a₊ Q + a₋ (1 − Q) then

The expected value of the observable Aⁿ in the probability distribution ρ is

In the last equation we have used the fact that all of our “operators” can be thought of as two by two matrices acting on a two dimensional space of vectors whose basis elements are |±_z 〉. The matrices can be multiplied by the usual rules and the trace of a matrix is just the sum of its diagonal elements. Our matrices are

They’re all diagonal, so it’s easy to multiply them.

So far all we’ve done is rewrite the simple logic of a single bit as a complicated set of matrix equations, but consider the operation of flipping the orientation of the molecule, which for nefarious purposes we’ll call s_x,

This has matrix

Note that s_z² = s_x² = 1, and s_x s_z = − s_z s_x = − i s_y , where the last equality is just a definition. This definition implies that s_y s_a = − s_a s_y, for a = x or a = z, and it follows that s_y² = 1. You can verify these equations by using matrix multiplication, or by thinking about how the various operations operate on the states (which I think is easier). Now consider for example the quantity B ≡ b_x s_x + b_z s_z . Then B² = b_x² + b_z² , which suggests that B is a quantity which takes on the possible values ±√{b₊² + b₋²}. We can calculate

for any choice of probability distribution. If n = 2k it’s just

whereas if n = 2k + 1 it’s

This is exactly the same result we would get if we said that there was a probability P₊ (B) for B to take on the value √{b_z² + b_x²} and probability P₋ (B) = 1 − P₊ (B), to take on the opposite value, if we choose

The most remarkable thing about this formula is that even when we know the answer to Q with certainty (p₊ = 1 or 0), B is still uncertain.

We can repeat this exercise with any linear combination b_x s_x + b_y s_y + b_z s_z. We find that in general, if we force one linear combination to be known with certainty, that all linear combinations where the vector (c_x, c_y, c_z) is not parallel to (b_x , b_y, b_z) are uncertain. This is the same as the condition guaranteeing that the two linear combinations commute as matrices.

Pursuing the mathematics of this further would lead us into the realm of eigenvalues of Hermitian matrices, complete ortho-normal bases and other esoterica. But the main point to remember is that any system we can think about in terms of classical logic inevitably contains in it an infinite set of variables in addition to the ones we initially thought about as the maximum set of things we thought could be measured. When our original variables are known with certainty, these other variables are uncertain but the mathematics gives us completely determined formulas for their probability distributions.

Another disturbing fact about the mathematical probability theory for non-compatible observables that we’ve discovered, is that it does NOT satisfy the probability sum rule. This is because, once we start thinking about incompatible observables, the notion of either this or that is not well defined. In fact we’ve seen that when we know “definitely for sure” that s_z is 1, the probability for B to take on its positive value could be any number between zero and one, depending on the ratio of b_z and b_x.

Thus QM contains questions that are neither independent nor dependent and the probability sum rule P(s_z or B ) = P(s_z) + P(B) does not make sense because the word or is undefined for non-commuting operators. As a consequence we cannot apply the conditional probability rule to general QM probability predictions. This appears to cause a problem when we make a measurement that seems to give a definite answer. We’ll explain below that the issue here is the meaning of the word measurement. It means the interaction of the system with macroscopic objects containing many atoms. One can show that conditional probability is a sensible notion, with incredible accuracy, for such objects, and this means that we can interpret QM for such objects as if it were a classical probability theory. The famous “collapse of the wave function” is nothing more than an application of the rules of conditional probability, to macroscopic objects, for which they apply.

The double slit experiment famously discussed in the first chapter of Feynman’s lectures on quantum mechanics, is another example of the failure of the probability sum rule. The question of which slit the particle goes through is one of two alternative histories. In Newton’s equations, a history is determined by an initial position and velocity, but Heisenberg’s famous uncertainty relation is simply the statement that position and velocity are incompatible observables, which don’t commute as matrices, just like s_z and s_x. So the statement that either one history or another happened does not make sense, because the two histories interfere.

Before leaving our little ammonia molecule, I want to tell you about one more remarkable fact, which has no bearing on the rest of the discussion, but shows the remarkable power of quantum mechanics. Way back at the top of this post, you could have asked me, “what if I wanted to orient the ammonia along the x axis or some other direction”. The answer is that the operator n_x s_x + n_y s_y + n_z s_z, where (n_x , n_y, n_z) is a unit vector, has definite values in precisely those states where the molecule is oriented along this unit vector. The whole quantum formalism of a single bit, is invariant under 3 dimensional rotations. And who would have ever thought of that? (Pauli, that’s who).

The fact that QM was implicit in classical physics was realized a few years after the invention of QM, in the 1930s, by Koopman. Koopman formulated ordinary classical mechanics as a special case of quantum mechanics, and in doing so introduced a whole set of new observables, which do not commute with the (commuting) position and momentum of a particle and are uncertain when the particle’s position and momentum are definitely known. The laws of classical mechanics give rise to equations for the probability distributions for all these other observables. So quantum mechanics is inescapable. The only question is whether nature is described by an evolution equation which leaves a certain complete set of observables certain for all time, and what those observables are in terms of things we actually measure. The answer is that ordinary positions and momenta are NOT simultaneously determined with certainty.

Which raises the question of why it took us so long to notice this, and why it’s so hard for us to think about and accept. The answers to these questions also resolve “the problem of quantum measurement theory”. The answer lies essentially in the definition of a macroscopic object. First of all it means something containing a large number N of microscopic constituents. Let me call them atoms, because that’s what’s relevant for most everyday objects. For even a very tiny piece of matter weighing about a thousandth of a gram, the number N  ∼ 10²⁰. There are a few quantum states of the system per atom, let’s say 10 to keep the numbers round. So the system has 10¹⁰²⁰ states. Now consider the motion of the center of mass of the system. The mass of the system is proportional to N, so Heisenberg’s uncertainty relation tells us that the mutual uncertainty of the position and velocity of the system is of order [1/N]. Most textbooks stop at this point and say this is small and so the center of mass behaves in a classical manner to a good approximation.

In fact, this misses the central point, which is that under most conditions, the system has of order 10^N different states, all of which have the same center of mass position and velocity (within the prescribed uncertainty). Furthermore the internal state of the system is changing rapidly on the time scale of the center of mass motion. When we compute the quantum interference terms between two approximately classical states of the center of mass coordinate, we have to take into account that the internal time evolution for those two states is likely to be completely different. The chance that it’s the same is roughly 10^−N, the chance that two states picked at random from the huge collection, will be the same. It’s fairly simple to show that the quantum interference terms, which violate the classical probability sum rule for the probabilities of different classical trajectories, are of order 10^−N. This means that even if we could see the [1/N] effects of uncertainty in the classical trajectory, we could model them by ordinary classical statistical mechanics, up to corrections of order 10^−N.

It’s pretty hard to comprehend how small a number this is. As a decimal, it’s a decimal point followed by 100 billion billion zeros and then a one. The current age of the universe is less than a billion billion seconds. So if you wrote one zero every hundredth of a second you couldn’t write this number in the entire age of the universe. More relevant is the fact that in order to observe the quantum interference effects on the center of mass motion, we would have to do an experiment over a time period of order 10^N. I haven’t written the units of time. The smallest unit of time is defined by Newton’s constant, Planck’s constant and the speed of light. It’s 10^{− 44} seconds. The age of the universe is about 10⁶¹ of these Planck units. The difference between measuring the time in Planck times or ages of the universe is a shift from N = 10²⁰ to N = 10²⁰ − 60, and is completely in the noise of these estimates. Moreover, the quantum interference experiment we’re proposing would have to keep the system completely isolated from the rest of the universe for these incredible lengths of time. Any coupling to the outside effectively increases the size of N by huge amounts.

Thus, for all purposes, even those of principle, we can treat quantum probabilities for even mildly macroscopic variables, as if they were classical, and apply the rules of conditional probability. This is all we are doing when we “collapse the wave function” in a way that seems (to the untutored) to violate causality and the Schrodinger equation. The general line of reasoning outlined above is called the theory of decoherence. All physicists find it acceptable as an explanation of the reason for the practical success of classical mechanics for macroscopic objects. Some physicists find it inadequate as an explanation of the philosophical “paradoxes” of QM. I believe this is mostly due to their desire to avoid the notion of intrinsic probability, and attribute physical reality to the Schrodinger wave function. Curiously many of these people think that they are following in the footsteps of Einstein’s objections to QM. I am not a historian of science but my cursory reading of the evidence suggests that Einstein understood completely that there were no paradoxes in QM if the wave function was thought of merely as a device for computing probability. He objected to the contention of some in the Copehagen crowd that the wave function was real and satisfied a deterministic equation and tried to show that that interpretation violated the principles of causality. It does, but the statistical treatment is the right one. Einstein was wrong only in insisting that God doesn’t play dice.

Once we have understood these general arguments, both quantum measurement theory and our intuitive unease with QM are clarified. A measurement in QM is, as first proposed by von Neumann, simply the correlation of some microscopic observable, like the orientation of an ammonia molecule, with a macro-observable like a pointer on a dial. This can easily be achieved by normal unitary evolution. Once this correlation is made, quantum interference effects in further observation of the dial are exponentially suppressed, we can use the conditional probability rule, and all the mystery is removed.

It’s even easier to understand why humans don’t “get” QM. Our brains evolved according to selection pressures that involved only macroscopic objects like fruit, tigers and trees. We didn’t have to develop neural circuitry that had an intuitive feel for quantum interference phenomena, because there was no evolutionary advantage to doing so. Freeman Dyson once said that the book of the world might be written in Jabberwocky, a language that human beings were incapable of understanding. QM is not as bad as that. We CAN understand the language if we’re willing to do the math, and if we’re willing to put aside our intuitions about how the world must be, in the same way that we understand that our intuitions about how velocities add are only an approximation to the correct rules given by the Lorentz group. QM is worse, I think, because it says that logic, which our minds grasp as the basic, correct formulation of rules of thought, is wrong. This is why I’ve emphasized that once you formulate logic mathematically, QM is an obvious and inevitable consequence. Systems that obey the rules of ordinary logic are special QM systems where a particular choice among the infinite number of complementary QM observables remains sharp for all times, and we insist that those are the only variables we can measure. Viewed in this way, classical physics looks like a sleazy way of dodging the general rules. It achieves a more profound status only because it also emerges as an exponentially good approximation to the behavior of systems with a large number of constituents.

To summarize: All of the so-called non-locality and philosophical mystery of QM is really shared with any probabilistic system of equations and collapse of the wave function is nothing more than application of the conventional rule of conditional probabilities. It is a mistake to think of the wave function as a physical field, like the electromagnetic field. The peculiarity of QM lies in the fact that QM probabilities are intrinsic and not attributable to insufficiently precise measurement, and the fact that they do not obey the law of conditional probabilities. That law is based on the classical logical postulate of the law of the excluded middle. If something is definitely true, then all other independent questions are definitely false. We’ve seen that the mathematical framework for classical logic shows this principle to be erroneous. Even when we’ve specified the state of a system completely, by answering yes or no to every possible question in a compatible set, there are an infinite number of other questions one can ask of the same system, whose answer is only known probabilistically. The formalism predicts a very definite probability distribution for all of these other questions.

Many colleagues who understand everything I’ve said at least as well as I do, are still uncomfortable with the use of probability in fundamental equations. As far as I can tell, this unease comes from two different sources. The first is that the notion of “expectation” seems to imply an expecter, and most physicists are reluctant to put intelligent life forms into the definition of the basic laws of physics. We think of life as an emergent phenomenon, which can’t exist at the level of the microscopic equations. Certainly, our current picture of the very early universe precludes the existence of any form of organized life at that time, simply from considerations of thermodynamic equilibrium.

The frequentist approach to probability is an attempt to get around this. However, its insistence on infinite limits makes it vulnerable to the question about what one concludes about a coin that’s come up heads a million times. We know that’s a possible outcome even if the coin and the flipper are completely honest. Modern experimental physics deals with this problem every day both for intrinsically QM probabilities and those that arise from ordinary random and systematic fluctuations in the detector. The solution is not to claim that any result of measurement is definitely conclusive, but merely to assign a confidence level to each result. Human beings decide when the confidence level is high enough that we “believe” the result, and we keep an open mind about the possibility of coming to a different conclusion with more work. It may not be completely satisfactory from a philosophical point of view, but it seems to work pretty well.

The other kind of professional dissatisfaction with probability is, I think, rooted in Einstein’s prejudice that God doesn’t play dice. With all due respect, I think this is just a prejudice. In the 18th century, certain theoretical physicists conceived the idea that one could, in principle, measure everything there was to know about the universe at some fixed time, and then predict the future. This was wild hubris. Why should it be true? It’s remarkable that this idea worked as well as it did. When certain phenomena appeared to be random, we attributed that to the failure to make measurements that were complete and precise enough at the initial time. This led to the development of statistical mechanics, which was also wildly successful. Nonetheless, there was no real verification of the Laplacian principle of complete predictability. Indeed, when one enquires into the basic physics behind much of classical statistical mechanics one finds that some of the randomness invoked in that theory has a quantum mechanical origin. It arises after all from the motion of individual atoms. It’s no surprise that the first hints that classical mechanics was wrong came from failures of classical statistical mechanics like the Gibbs paradox of the entropy of mixing, and the black body radiation laws.

It seems to me that the introduction of basic randomness into the equations of physics is philosophically unobjectionable, especially once one has understood the inevitability of QM. And to those who find it objectionable all I can say is “It is what it is”. There isn’t anymore. All one must do is account for the successes of the apparently deterministic formalism of classical mechanics when applied to macroscopic bodies, and the theory of decoherence supplies that account.

Perhaps the most important lesson for physicists in all of this is not to mistake our equations for the world. Our equations are an algorithm for making predictions about the world and it turns out that those predictions can only be statistical. That this is so is demonstrated by the simple observation of a
Geiger counter and by the demonstration by Bell and others that the statistical predictions of QM cannot be reproduced by a more classical statistical theory with hidden variables, unless we allow for grossly non-local interactions. Some investigators into the foundations of QM have concluded that we should expect to find evidence for this non-locality, or that QM has to be modified in some fundamental way. I think the evidence all goes in the other direction: QM is exactly correct and inevitable and “there are more things in heaven and earth than are conceived of in our naive classical philosophy”. Of course, Hamlet was talking about ghosts…

Don’s reply focuses less on details of eternal inflation and more on the general issue of how we should think about quantum gravity in a cosmological context, especially when it comes to counting the number of states. Don is (as he mentions below) an Evangelical Christian, but by no means a Young Earth Creationist!

Same rules apply as before: this is a technical discussion, which you are welcome to skip if it’s not your cup of tea.

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I tend to agree with Tom’s point that “it is extremely plausible, given the Bekenstein Hawking entropy formula for black holes, that the quantum theory of a space-time , which is dS in both the remote past and remote future, has a finite dimensional Hilbert space,” at least for four-dimensional spacetimes (excluding issues raised by Raphael Bousso, Oliver DeWolfe, and Robert Myers for higher dimensions in Unbounded entropy in space-times with positive cosmological constant) if the cosmological constant has a fixed finite value, or if there are a finite number of possible values that are all positive. The “conceptual error … that de Sitter (dS) space is a system with an ever increasing number of quantum degrees of freedom” seems to me to arise from considering perturbations of de Sitter when it is large (on a large compact Cauchy surface) that would evolve to a big bang or big crunch when the Cauchy surface gets small and hence would prevent the spacetime from having both a remote past and a remote future. As Tom nicely puts it, “In the remote past or future we can look at small amplitude wave packets. However, as we approach the neck of dS space, the wave packets are pushed together. If we put too much information into the space in the remote past, then the packets will collide and form a black hole whose horizon is larger than the neck. The actual solution is singular and does not resemble dS space in the future.”

So it seems to me that, for fixed positive cosmological constant, we can have an arbitrarily large number of quantum states if we allow big bangs or big crunches, but if we restrict to nonsingular spacetimes that expand forever in both the past and future, then the number of states may be limited by the value of the cosmological constant.

This reminds me of the 1995 paper by Gary Horowitz and Robert Myers, The value of singularities, which argued that the timelike naked singularity of the negative-mass Schwarzschild solution is important to be excluded in order to eliminate such states which would lead to energy unbounded below and instabilities from the presumably possible production (conserving energy) of arbitrarily many possible combinations of positive and negative energy. Perhaps in a similar way, big bang and big crunch singularities are important to be excluded, as they also would seem to allow infinitely many states with positive cosmological constant.

Now presumably we would want quantum gravity states to include the formation and evaporation of black holes (or of what phenomenologically appear similar to black holes, whether or not they actually have the causal structure of classical black holes), which in a classical approximation have singularities inside them, so presumably such `singularities’ should be allowed, even if timelike naked singularities and, I would suggest, big bang and big crunch singularities should be excluded. Perhaps one can postulate that one should restrict to states of immortal de Sitter spacetime, which has no timelike naked singularities anywhere, and which is asymptotically a single region in the very distant past that is locally de Sitter (though globally it can be highly distorted) and which is also asymptotically a single region in the very distant future that is likewise locally de Sitter, without any big crunch or big bang singularities in between, or between more than one asymptotic region (as one would expect to get from perturbations of the Nariai metric that lead to asymptotic de Sitter regions separated by big bang and big crunch singularities). Such singularities might be considered mortal wounds for de Sitter, allowing an infinite number of states to fester up from such wounds, killing the hope for a finite number of states and for unitarity. On the other hand, a localized black hole that forms within de Sitter could be considered a wound that is not mortal and which can be healed by Hawking evaporation without going outside the assumed finite number of quantum states for immortal de Sitter with a strictly positive cosmological constant. I have considered such a possibility in my paper No-Bang Quantum State of the Cosmos.

On the other hand, even if we find such a restriction for positive cosmological constant to a finite set of states, the number of such states for the observed tiny value of the cosmological constant seems so huge that it would seem surprising to me if most of them can explain our observations, so I now am skeptical of the maximally mixed state I proposed in No-Bang Quantum State of the Cosmos and now tend to prefer a pure state like what I proposed in Symmetric-Bounce Quantum State of the Universe. When coupled with a solution to the measure problem, such as what I proposed in Agnesi Weighting for the Measure Problem of Cosmology, this pure state seems to be consistent with all our observations, though of course these are highly preliminary proposals and are not yet fully precisely specified, nor are they nearly so simple and esthetically pleasing as I would hope for in a final complete theory of the universe. We would like a simple quantum state for the universe and simple rules for extracting the probabilities of observations from it. (In The Born Rule Dies and in related papers, I showed that the Born rule, interpreted mathematically in the form that probabilities of observations are expectation values of projection operators, does not work in a universe large enough for multiple copies of an observation, but the probabilities still could be expectation values of other quantum operators, though it is so far unknown what they should be; this knowledge would be a solution of the measure problem if the quantum state were also known.)

Some people seem to prefer the simple state that is the maximally mixed state out of a finite-dimensional Hilbert space, but if this does not explain our observations, I see no objection to postulating that the state is some other simple state, perhaps (but not necessarily) a pure state. By Occam’s razor, we scientists tend to ascribe higher prior probabilities to simpler theories, so we would tend to prefer a simpler quantum state, but I don’t think we should take so narrow a view that such a simple state has to be a thermal state, or a maximally mixed state.

Now even if the quantum state of the universe is chosen (perhaps as a simple mixed state, perhaps as a simple pure state) from a finite set of states, or even if it is a particular pure state, I’m agnostic as to whether or not this could be a state with eternal inflation. Eternal inflation may lead to a huge universe in which there are an arbitrarily large number of nearby states, but those may be states with mortal perturbations (evolving forward and/or backward in time to mortal singularities in a classical description) that would be excluded from the allowed states. So I don’t see that there is any problem with having disallowed states that at some time look nearby to the allowed states. Our universe looks very much as if it could have had a big bang in its past (which would allow an infinite number of states), and presumably a generic quasiclassical perturbation of the present state would evolve back to such a mortal singularity, but the actual state of our universe might have been one of the very large but finite number of states that did not have such a mortal singularity but instead had a bounce. If it did have a bounce, the size at the bounce seems that it might have been much smaller than the throat of de Sitter with the observed value of the cosmological constant, which suggests to me that the quantum state is much more restricted than just the restriction to the large but finite number of states that have bounces rather than mortal singularities.

The question seems to be open, even if the state is immortal de Sitter (by which I mean having a positive cosmological constant but no mortal singularities, not that it is metrically de Sitter or even close to de Sitter), whether this state consists of a superposition of quasiclassical spacetimes with most of them with significant amplitudes having a huge or infinite number of bubbles that keep forming and branching off (and presumably attaching on as well). Even from the considerations of Tom Banks and of my discussion above, I don’t see any obvious reason why it might not. One could presumably have a single simple pure state such that, if it were decomposed into quasiclassical components, would have components that are individually very complex, rather as the binary representation of the Bible, or of the Library of Congress, or of the eprint arXiv, or the entire Internet, or of all the words that have ever been written on earth, is each a very large and presumably very complex integer but is just one component of the set of all integers, which is a simple whole, of which almost all of the separate parts are individually much more complex.

I would guess that presumably at least some quasiclassical components of any simple quantum state that could describe our universe would be very complex and perhaps have a huge number of bubble or pocket subuniverses that could be described as having eternal inflation. Perhaps a more relevant question is whether the probabilities of our observations are given by something like a path integral that is dominated by such eternal inflating spacetimes, or whether the path integral (or whatever procedure gives the quantum probabilities) is dominated by simpler spacetimes, such as ones with only one region and a single bounce. For thermodynamic reasons I presently have some slight personal inclination toward the latter view, that for the dominant contribution it is sufficient to consider only one bounce in the past, at roughly five trillion days ago (an easily memorized value for the age of the universe that fits to four digits the middle of the range of the current measurements of 13.69(13) Gyr), rather than an infinite sequence of bubble formations in my past. Though I am not a Young Earth Creationist as some of my fellow Evangelical Christians are, perhaps I am still a Young Universe Creationist (for thermodynamic reasons rather than for theological reasons, since I personally do not see any theological reason that God could not have created an infinite eternally inflating universe) in the sense that I suspect that most of the quantum amplitude for our observations can be ascribed to quasiclassical universes (or spacetimes in a path integral) that each had its smallest spatial size (say in a foliation of Cauchy surfaces that are closed hypersurfaces of constant extrinsic curvature, to exclude nearly null hypersurfaces of arbitrarily tiny three-volume) not much more than about five trillion days ago. But so far as I can see, this question of whether or not eternally inflating spacetimes are important for the quantum probabilities of our observations is very much an open question, even if the set of quantum states is restricted to be finite or to be a single pure state.

Tom is a professor at Rutgers and UC Santa Cruz, an extremely accomplished researcher in field theory and string theory, and the author of a textbook on quantum field theory. In collaboration with Fischler, Shenker, and Susskind, he proposed the (M)atrix Theory non-perturbative formulation of string theory. Most recently, he (often working with Willy Fischler) has been exploring the connections between holography and cosmology, developing a detailed model of the evolution of the universe that is compatible with the holographic principle. Here is video of a lecture Tom recently gave on holographic cosmology.

This post is at a more technical level than most of our entries here at CV, and we’re going to try to keep the discussion useful for workers in the field. Sincere questions are welcome, but we’ll be deleting any unproductive philosophical gripes or advertisements for anyone’s personal outsider theories.

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Why I Don’t Believe in Eternal Inflation

A lot of research in high energy theory has been devoted to the topic of eternal inflation. More and more, over the last few years, I’ve come to regard this as an enormous waste of intellectual resources and I’ve chosen Cosmic Variance as a very public way to make my objections to this theoretical mistake clear. The theory was developed in the 1980s, when it seemed plausible that quantum field theory in curved space-time was a good approximation to a real theory of quantum gravity whenever the energy densities and curvatures of the background geometry were small in Planck units. This idea is simply wrong. The fact that its falsification came through a back door, the rather philosophical discussion of whether black hole evaporation violates the rules of quantum mechanics, has led to a widespread but unfortunate tendency to ignore this FACT.

There are two other psychological reasons for the widespread interest in Eternal Inflation, which I will discuss below. They have led even the inventors of the resolution of the black hole information paradox through the notion of holography, to try to find a sensible holographic theory which incorporates the notion of EI. While this attempt itself is subject to a number of objections, I will not go into them here. Instead, I’ll concentrate on evidence from the seminal Coleman-De Luccia (CDL) theory of tunneling in quantum gravity, which is one of the two biggest clues to what the theory of quantum gravity really is.

There are, in my opinion, two serious conceptual errors behind the theory of EI. The first is the notion that space-time geometry is a fluctuating quantum variable. The second is that de Sitter (dS) space is a system with an ever increasing number of quantum degrees of freedom. The increase is supposed to take place as the global dS time coordinate, or the time coordinate in flat coordinates, goes to future infinity. I’ll end this post with a brief discussion of the formalism of Holographic Space Time (HST), in which both of these ideas are seen to be false, in a very explicit manner. The fact that the HST formalism is able to give an approximate description of particle physics in a curved space-time background is by itself enough to falsify any claim that the semi-classical ideas that lead to EI are inevitable consequences of ANY sensible theory of quantum gravity. For this purpose, it’s not even necessary that HST be right, only that it have a limit in which it reduces to QFT in curved space-time.

There are two flavors of EI. The first comes from applying the theory of vacuum tunneling in QFT to individual horizon volumes at late times in an exponentially expanding space-time. In QFT, tunneling proceeds, like the boiling of water, via the formation of bubbles. It is argued that as long as the bubble radius is much smaller than the horizon scale, then bubbles will form independently in each horizon volume, since these are causally separated regions. This is true in QFT is a fixed background dS space , but the question is which background dS space are we talking about. The whole formalism of QFT in curved space-time is predicated on the notion that fluctuations of space-time geometry are negligible and small, and can be treated as gravitons propagating in a fixed space-time background. This is true even when we “derive” QFT in curved space-time from a formalism in which space-time geometry is assumed to be a fluctuating quantum variable (the Wheeler-DeWitt (WD) equation). In other words, the formalism of QFT in curved space-time is not the proper tool for evaluating the validity of EI, whose fundamental premise is that tunneling events change the asymptotic structure of space-time by changing the cosmological constant (c.c.).

The purpose of the CDL theory is precisely to deal with tunneling events that change the c.c., and the fact that in every case its results are drastically different from those of tunneling in QFT in a fixed space-time background are universally ignored by proponents of EI. Let us begin with the case of a potential on field space, all of whose minima have positive c.c. If there are many minima, there are many instantons (imaginary time classical solutions describing tunneling events from one minimum to another), but they all share several characteristics. They are all compact Euclidean manifolds with negative Euclidean action, I < 0. The compactness means that there are no collective coordinates for translation invariance, and the dilute instanton gas approximation (DGA), which is the mathematical basis for the claim that there are multiple bubbles in disjoint space-like regions of the real space-time does not work. Even when the bubble size is much less than the dS radius, one finds fewer than (R_dS/R_bubble)³ bubbles. This estimate is based on sticking instantons into a fixed dS background, but in fact in the CDL instanton, the geometry responds to the instanton and the fixed background approximation breaks down for multiple instantons. Furthermore, there are important interactions between the bubbles, which are neglected in the DGA. I suspect that they correspond to attractive forces (in the DGA sense) between instanton centers, which means that no multi-instanton solutions exist. The standard theory of EI has well known problems with infinities (THE MEASURE PROBLEM) and one might have thought that these observations about CDL instantons would be relevant to regulating the infinite numbers of bubbles encountered in the conventional treatment. In fact, these obvious facts about CDL instantons are mentioned nowhere in that literature. The upshot of this is that there is really no theoretical basis for a picture of bubbles nucleating independently in causally disconnected patches of an exponentially expanding universe.

The problem with negative action is well known, and has a very illuminating solution. As in any tunneling problem, one must subtract the action of the meta-stable configuration. In this case this is dS space, whose imaginary time version is just a sphere. The sphere is a compact Euclidean manifold with negative action, and the difference I_inst − I_F is positive so the the reciprocal of its exponential can be a decay probability. Here we’ve subtracted the action of the higher or false dS minimum, but the action of the lower minimum is even larger so exp(I_T −I_inst) can be interpreted as the probability of transition between the lower and upper state. The thermal nature of dS space leads us to expect such upward fluctuations. The ratio of forward to backward rates is given by exp(I_T −I_F) , and this is rather miraculous, because the absolute value of the Euclidean action for dS space is precisely the Bekenstein- Gibbons-Hawking entropy of the state. This entropy, like that of black holes, was initially rather mysterious, but black hole entropy counting in string theory has given us confidence in the idea that it really does come from a counting of quantum states. In the black hole context we already knew from the thermodynamics of Hawking radiation that black hole entropy was necessary in order to obey the laws of thermodynamics. The CDL instanton formula is the analogous statement for dS space. In the dS case, there is no process which continuously varies the c.c., but the CDL process tells us how to change it in discrete jumps. The formula for the ratio of forward and backward rates is simply the principle of detailed balance for a system at infinite temperature. There is a matrix element for transitions between the states represented by the two dS minima of the potential. Fermi’s golden rule tells us that the ratio of forward to backward transitions is just the ratio of the number of available quantum microstates corresponding to each macrostate. The fact that entropies, rather than free energies, enter the rate equations, tells us that the system is at infinite temperature, and that the total number of quantum states is finite. This bolsters two other arguments that dS space has a finite number of states.

The first is simply that the Covariant Entropy Bound tells us that no observer in dS space can ever probe more than a finite number of states. The Observer Complementarity Principle tells us that different observers in dS space simply use different non-commuting Hamiltonians. Each explores the same finite space of states in a different manner. Taken together these two principles imply that the quantum theory of all possible observers in dS space is finite dimensional. A less abstract argument for the same point comes from examining ”scattering” in dS space. Consider incoming small perturbations of the dS solution of any Lagrangian. In global coordinates this solution looks like a sphere which contracts down from infinite radius to some finite radius and then re-expands to infinite radius. In the remote past or future we can look at small amplitude wave packets. However, as we approach the neck of dS space, the wave packets are pushed together. If we put too much information into the space in the remote past, then the packets will collide and form a black hole whose horizon is larger than the neck. The actual solution is singular and does not resemble dS space in the future. Thus, it is extremely plausible, given the Bekenstein Hawking entropy formula for black holes, that the quantum theory of a space-time , which is dS in both the remote past and remote future, has a finite dimensional Hilbert space.

Readers used to the statement that the inverse dS temperature is the circumference of the sphere may be puzzled by the statement that the temperature is infinite. This is, quite literally, a question of point of view. One can look at the Hamiltonian corresponding to an observer following a trajectory of fixed distance from the origin of the static coordinates, which cover a single horizon volume of dS space. The trajectory at the origin is a geodesic, but the others are all accelerated and see an Unruh temperature different from the conventional dS temperature. As the radius approaches the horizon the temperature goes to infinity. The Hamiltonian P₀ describing the geodesic observer approximately decouples the particle degrees of freedom of the system from those on the horizon. The usual dS temperature is a reflection of the degeneracy of P₀ eigenstates in the dS vacuum ensemble. This will all be discussed in some detail in a forthcoming paper on the Unruh effect in Holographic Space-time.

This interpretation of the CDL instanton can be generalized to a large class of potentials which have both positive and negative energy densities at their minima. Given such a potential, one can add a negative constant so that the lowest positive c.c. minimum is brought down to zero. We can then ask if there is a positive energy theorem for the resulting Minkowski space solution. There obviously is if all the other minima are still positive. The results of the CDL paper show us that this persists for SOME potentials with negative minima. We say that potentials with a positive energy theorem when the lowest positive c.c. is translated to zero energy are Above the Great Divide. It is easy to see that one can move a potential from below to above the Great Divide by tuning a single parameter. Let f be any smooth non-negative function on the space of fields, which vanishes exponentially rapidly when one moves away from those minima of the potential V, which have negative energy density. Then for sufficiently large ε, V + εf is above the Great Divide. It is easy to show, for potentials above the great divide, that CDL transitions from the lowest dS minimum to the negative region of the potential (which, as shown by CDL always leads to a Big Crunch solution in which the field is driven out of the negative region as one approaches the singularity), are suppressed by an entropy factor. That is to say: just like the upward transitions to high positive c.c., for these potentials the downward jumps to Big Crunches are low entropy transitions of a finite system, analogous to all of the air in a room gathering into one cubic centimeter. In fact, when the covariant entropy bound is applied to the crunching region of space-time, one finds that no observer in that region can observe an entropy comparable to that of the minimal c.c. dS space.

To summarize: for potentials above the great divide, all of the evidence from CDL instantons points to a quantum theory with a finite number of states, most of which resemble the empty dS vacuum with the lowest c.c. All CDL transitions away from this state have an entropic suppression, and the principle of detailed balance assures us that the inverse transition will occur much more rapidly. In the case of upward transitions the CDL formula confirms this, but reverse transitions from the Big Crunch to dS space are not amenable to purely semi-classical analysis. For these potentials, if we accept this evidence, the entire formalism of conventional EI is invalid. Indeed, in that formalism, the difference between a potential above and below the divide is merely quantitative, so potentials above the divide have the same issues with infinite numbers of bubbles as potentials below the divide. The standard discussion of EI uses a treatment appropriate for field theory instantons in a fixed space-time background, to discuss CDL transitions in which the final state has a radically different space-time geometry than the initial state. For potentials above the great divide, EI gets the physics infinitely wrong.

I think that CDL transitions for potentials below the divide are unlikely to have a sensible interpretation in quantum theory. They are like quantum Hamiltonians for systems that do not have energy bounded from below. This leaves the question of whether there is a sensible quantum interpretation of low energy Lagrangians which allow a meta-stable dS space to decay to a region of the potential with vanishing energy density. These transitions are central to the FRW/CFT program of the Stanford group. As I said above, there are numerous issues with the attempts to make a theory of these transitions, but I won’t discuss them here. I should note that for “phenomenological” reasons (see the discussion of Boltzmann Brains below) these authors often insist that dS solutions in their models be below the great divide for transitions to negative c.c. Crunches in addition to being unstable to decay into the vanishing energy density region.

Before going on to the second class of EI models I want to mention the only response I got from EI theorists to my complaint that the multi-instanton solutions they are positing simply don’t exist in the CDL formalism. This response was that the same issue exists for quantum field theory in a fixed dS background, where we ”know” the EI discussion is correct. This is simply not correct. QFT on a large sphere has the symmetries of the sphere. Every point-like instanton configuration will have rotational collective coordinates, which approach the translational collective coordinates of flat Euclidean space in the large radius limit. If the size of the instanton is much smaller than the radius of the sphere then there are approximate solutions which are just superpositions of solutions with a rotated center and large distances between the centers. That is to say, the DGA configurations are approximately correct. By contrast, the CDL instanton for decay of dS space has no exact collective coordinates. When the instanton size is much smaller than the dS radius, then the single instanton solution looks like a small cap cut out of the dS sphere. But when we put in another instanton, the geometry changes in response to its matter content. Once one starts thinking about solutions with many instantons one loses all control over the shape of the solution or whether it exists. Above I gave the bound (R_dS/R_inst)³ as an upper bound on the number of instantons, based on the field theory in a fixed dS background. My guess is that the actual number is much smaller than this, and that inter-instanton forces may preclude the existence of any multi-instanton CDL solutions at all. At any rate, without a thorough investigation of this question it seems to me that the standard discussion of EI is simply wild conjecture. The alternative interpretation of CDL transitions above the great divide, in terms of a system with a finite number of states, suggests strongly that EI is a wrong conjecture for those potentials.

The second flavor of EI is called chaotic eternal inflation or the self-reproducing inflationary universe. In these models, the formalism for calculating small fluctuations around a slow roll inflation model is extended to the regime of large fluctuations. In particular, Starobinsky’s proposal that one view the fluctuations in each independent horizon volume as a stochastic force added to the classical slow roll equations leads, for a certain range of values of the parameters in the potential, to a regime in which the stochastic kicks up the potential are more important than the force coming from the slope of the potential. Any given point will eventually roll down and inflation will end, but there are “always” (The Starobinsky equations have a global time for all points. One has to ask how this time is defined in a global picture of the space-time geometry. This leads to one aspect of the dreaded Measure Problem) points which are still inflating. This formalism takes for granted that the global picture of the inflationary space-time, with independent degrees of freedom in an infinite number of horizon volumes in the flat slicing of dS space, is valid. It also ignores the ultimate fate of the post-inflationary regimes. Indeed, in the eternal inflation regime of parameters, it is guaranteed that fluctuations on large enough scales become of order one, and there is probability one that every post-inflationary regime will be crunched inside a black hole. It is argued that those crunches occur on a time scale much longer than the age of our universe, so we can ignore them. However, if one is looking for a mathematical definition of the theory one cannot be so cavalier.

Advocates of this point of view will counter that the formalism has been validated by its application to the calculation of observable fluctuations in the Cosmic Microwave Background. I don’t think this argument is correct. The CMB fluctuations can be equally well accounted for by slow roll inflation models in the self reproducing regime, and by models without self reproduction. The CMB fluctuations are very small and extend over a range of scales that is at most 10⁵ in size (if one includes the fluctuations that form galaxies). The fact that a set of equations works over this limited regime says nothing about the validity of its use in a much more ambitious context. There have, for example, been suggestions that “string theory may never give rise to potentials in the self-reproducing regime”. I no longer think that that is the correct way to think about the problem, but it seems to me to be an indicator that this version of EI is on no firmer footing than that based on tunneling.

The Psychology of EI

I believe that there are two rather different psychological arguments that are driving the renewed interest in EI and the rejection of a more holographic point of view (or the attempt to shoehorn EI into a holographic theory via FRW/CFT). These are the success of the calculation of inflationary fluctuations, and that of Weinberg’s anthropic estimate of the c.c. Andrei Linde and I independently invented the first inflationary models which led to a mechanism for anthropic determination of the c.c. Subsequently, Weinberg estimated an upper bound on the c.c. from the requirement that galaxies form, assuming the size of primordial fluctuations and the dark matter density at the beginning of matter domination were fixed. Many of the proponents of the String Landscape and EI view it as the only framework which will give rise to a distribution of universes, with varying c.c., on which one can do anthropic selection. This is incorrect and the HST formalism I will describe below is an explicit counterexample. The string landscape version of anthropic selection seems to point to the likelihood that all of the parameters in low energy effective field theory are random variables constrained only by anthropic selection. Such a proposal has enormous phenomenological problems, which to my knowledge have only been addressed by recourse to our ignorance about the nature of the (so far entirely hypothetical) String Landscape. I think it is likely that only a very small number of parameters in low energy physics are random numbers fixed by selection effects.

The success of the inflationary predictions for CMB fluctuations points to the reality of independent degrees of freedom in different inflationary horizon volumes. However, as I emphasized above, there is nothing in the data that attests to more than about 25 e-foldings of inflation and a finite number of horizon volumes. It’s been evident since Bousso’s first papers on the covariant entropy bound that inflationary cosmology is not dS space. Indeed, it’s precisely the observability of the CMB fluctuations that shows us the difference. The maximal causal diamond of an observer in an inflationary universe is determined not be the inflationary c.c. but by the value of the c.c., which dominates the asymptotic future. Using the covariant entropy bound to estimate the number of allowed degrees of freedom we find that about 85 e-folds of GUT scale inflation are compatible with the covariant entropy bound and the value of the c.c. suggested by cosmological data. Thus, the success of the CMB calculations gives us no reason to believe the hyperbolic claims of EI theorists.

Holographic Space Time

I want to outline the theory of Holographic Space Time (HST) and how it addresses the problems of dS space and inflation. HST is an infinite collection of quantum systems, each of which describes the entire universe as seen from the perspective of a different time-like trajectory in space-time. A segment of such a trajectory, with finite proper time defines a causal diamond – the region in space-time that can be probed by a detector following that trajectory. The diamond is the intersection of the interior of the backward light cone emanating from the future end of the trajectory and that of the forward light cone of its past endpoint. Alternatively, we can think of the trajectory as being defined by a nested sequence of causal diamonds, each one larger than the former. The Holographic Principle tells us that the Hilbert space corresponding to all observations in the diamond is finite dimensional. When the dimension is large, it defines the largest area 2-surface on the boundary of the diamond (this surface is called the holographic screen of the diamond), via the asymptotic formula D → e^A/4, where the area is measured in Planck units (10⁻⁶⁶cm²). Using this formula we say that a time-like trajectory is equivalent to a sequence of nested Hilbert spaces, each containing the previous one as a tensor factor. The maximal dimension Hilbert space, for infinite proper time along the trajectory, has dimension D_max, which might be infinite. The time evolution operator must be time dependent, since causality tells us that for proper time T it must factor into an operator acting only on the Hilbert space of measurements that could have been done during that time, and one which acts on degrees of freedom that could not yet have been measured at that time, because they are at space-like separation. Mathematically, the latter space is the tensor complement of the Hilbert space accessible at time T in the Hilbert space at infinite proper time.

Now consider another time-like trajectory, which doesn’t intersect the first. It consists of a sequence of Hilbert spaces and evolution operators, as above. HST also specifies, at each time, an overlap Hilbert space, which corresponds geometrically to the Hilbert space associated with the maximal area causal diamond in the intersection between the causal diamonds of the individual trajectories. Thus, for any pair of trajectories there is a sequence of overlap Hilbert spaces. The dynamics associated with each individual trajectory, plus a choice of initial state, determines a sequence of density matrices in this sequence of overlap spaces. The basic dynamical constraint of the theory is that the two different sequences of density matrices, be unitarily equivalent to each other. Finally, we put a topology on the space of trajectories, which we can think about as defining the topology of a Cauchy surface in space-time. In the limit of large areas, each HST quantum system defines a Lorentzian metric. The space-time metric is not a fluctuating quantum variable, but is implicit in the dynamics of the individual quantum systems and their relations. We have found several solutions of the consistency conditions, and each corresponds to a simple space-time geometry, satisfying Einstein’s equations with a simple stress tensor.

The fluctuating quantum variables of HST are related to the holographic screen of the diamond they describe. They define a non-commutative approximation to the algebra of functions on the screen, which becomes commutative as the screen gets large. If we insist on Lorentz invariance for large spherical screens (the Lorentz group is the conformal group of a sphere, and we need some kind of conformal invariance to control the large sphere limit), then we can show that the degrees of freedom describe (in the limit) an infinite number of massless supersymmetric particles, plus a set of “horizon degrees of freedom”. The horizon degrees of freedom saturate the covariant entropy bound, but to get a sensible large time (which means large area causal diamond) limit, the particles must decouple from the horizon variables. This leads to a scattering matrix for particle states. The particle interactions are mediated by the much more numerous horizon degrees of freedom.

The HST formalism is also capable of describing situations in which particles do not decouple from the horizon, which occur in the presence of black holes and in the very early universe. Fischler and I are in the midst of working out a model for inflationary dynamics in the HST formalism, and we can already see how to get small (approximately) Gaussian fluctuations from a manifestly finite system with none of the paradoxes of EI. The dS invariance of the fluctuation spectrum, which gives the correct answer for the CMB, can be at best approximate. We do not yet understand how to parametrize the deviations from dS invariance and whether our models can reproduce the “red tilted, approximately scale invariant” spectrum, which is seen in the data.

The HST formalism has much to say about numerous other problems in string theory and particle physics. Here I will only outline it’s version of a “multiverse”. The original solution of the HST constraints has a coarse grained description as a homogeneous isotropic spatially flat cosmology, with equation of state that pressure equals energy density. This is what one would expect heuristically for a universe in which every horizon volume is filled with a maximal size black hole, and these black holes merge as the horizon expands, so that the horizon filling black hole condition is satisfied at every moment. We called this solution the D(ense) B(lack) H(ole) F(luid). We also discussed a solution to Einstein’s equations which was a black hole with de Sitter interior embedded in this homogeneous isotropic cosmology. In the paper referred to above, we have found an exact quantum model, satisfying all the consistency conditions of HST, which corresponds to that solution. There is a one parameter family of models corresponding to the choice of dS c.c. We can also find approximate solutions of the consistency conditions corresponding to two or more such black holes, separated by a large distance. Using the Einstein equations as a guide, we surmise that these multi black hole solutions will evolve in a way that depends on the initial positions and velocities of the black holes in the underlying cosmological space-time. The black holes will be stable, except for collisions, when we expect them to merge to form a black hole with larger area. So we can construct models in which there are many values of the c.c. depending on which black hole interior one resides in. Each mini dS universe will be stable, unless it collides with another. Such a model is ripe for anthropic selection arguments, but the parameters of low energy physics that get anthropically selected may be few. In the paper referred to above, Fischler and I conjecture that only the inflationary and asymptotic values of the c.c. vary among these models, with all other parameters determined in terms of them. The basis of this conjecture is that the limiting theory for small asymptotic c.c. is a super-Poincare invariant theory of gravity, with no moduli, and a discrete R symmetry. There are no known theories of this type coming from string theory, and the conditions that define them in low energy supergravity are non-generic (N+1 equations for N unknowns). The fact that the theory becomes supersymmetric for vanishing c.c. puts a strong lower bound, and probably also an upper bound on the c.c. The scales of SUSY breaking and electroweak physics depend strongly on the c.c., and the QCD scale does also, but in a different way. So having stable atoms and stars requires a special value of the c.c. . The inflationary c.c. determines the size of primordial fluctuations in the universe, and for fixed asymptotic c.c., Weinberg’s galaxy formation bound constrains this to be roughly its observed value.

This version of the multi-verse also resolves the Boltzmann Brain problem, which has been claimed to invalidate any theory of stable dS space. In fact the argument is that Boltzmann’s Brains rule out any theory in which the universe eventually comes to thermodynamic equilibrium. This is an extreme version of anthropic reasoning. Once one has bought into trying to explain a lot of the physical world by anthropic arguments, one tends to be forced to start trying to estimate the number of observers that can exist under various hypotheses and saying that, since we could be any one of those observers, we must be a typical one. In a universe that comes to thermodynamic equilbrium, with finite entropy, the most typical observer is a brain with all of YOUR memories, which spontaneously pops from the vacuum by a thermal fluctuation. This happens an infinite number of times, and with much higher probability than a rerun of the history of the universe as it really happened. The BB quickly dies, and according to this way of thinking, we’re constantly doing the experiment that shows we’re not Boltzmann Brains, and so falsifying a theory which predicts that typical observers are BBs.

I think this argument is silly, and mistakes our theory of the universe for the universe itself. Given the dS temperature corresponding to the observed c.c., the probability of fluctuating even the most modest sized BB is of order exp(−10⁶⁶). This number is so small that the time we would have to wait to see it happen is so long that it’s essentially the same number measured in Planck times as it is in units of the age of the universe. Thus, this theoretical event is not a part of real physics. We can modify our theory in an infinite number of ways (with a time dependent Hamiltonian) which will make identical predictions for everything we or anyone else will measure over the entire history of the universe (including the events which have not yet happened when our local group of galaxies collapses into a black hole, which then evaporates back to the dS vacuum), but change what happens over the time scales on which BB’s are nucleated, and makes the probability of a BB exactly zero. The HST multiverse has an explicit mechanism for making this happen. In order to make a model which explains the history of the universe up to some point in time, it is only necessary that our particular dS black hole interior last for that period of time. Depending on the initial conditions for black hole positions and velocities defining the HST model, we can make one in which our black hole suffers a collision after that point in time. The result of that collision will be catastrophic, and will result in a new equilibrium state with a substantially smaller value of the c.c.. Given the connection between the c.c. and particle physics, it is likely that atoms are no longer meta-stable excitations of this system and so there are no BB’s after that point. The proponents of EI, fixated on CDL instantons as the only mechanism for making a dS space decay, instead argue that the low energy effective field theory MUST be below the Great Divide, in order to eliminate BBs. There are more things in heaven and earth than are dreamed of in their philosophy.

The Takeway

The brevity of a blog post prevents me from expanding on the manifold virtues of the HST approach to quantum gravity. No matter. You can read about them in hep-th 1109.2435 and references therein. Within the next year, I’ll also put out a long review article on HST. What you should take away from this post is the following message: the very popular idea of Eternal Inflation is built on a foundation of sand. One version of it applies intuition about field theory instantons in a fixed space-time to transitions in which the shape of space-time changes dramatically. The actual theory of such transitions, adumbrated by Coleman and De Lucia in 1981, does not support that intuition. The analysis of CDL instantons for roughly half the potentials one can write on the space of scalar fields instead supports a picture of dS space as a quantum system with a finite dimensional Hilbert space, most of whose states resemble the dS vacuum. All CDL transitions are short lived excursions into a low entropy state of the system. Most other CDL transitions are likely to be fictitious. There is no real theory of quantum gravity in which these transitions occur (for example, almost all instabilities of Anti-de Sitter space are of this type). Transitions to a state with zero c.c. are still not well understood.

The other flavor of eternal inflation is based on extrapolating a theory of small fluctuations, without modification, to a regime where the fluctuations are large. It’s really rather hard to check its consistency since the evident disasters caused by the large fluctuations are always ignored by arguing that they will only occur much later in the history of the universe. This sort of phenomenological attitude prevents one from discussing the mathematical meaning of the formalism.

Both types of EI lead to infinities, and I have argued that there is nothing in either theory or observation which should lead us to believe that these infinities are part of a well defined model. I gave the example of HST as a formalism that can probably explain the data within the context of a manifestly finite model of the entire universe we can observe. HST also provides a new venue for applying anthropic reasoning to the determination of the c.c. and many ways to resolve the putative Boltzmann Brain problem of an asymptotically dS universe.

So we’re very happy to welcome Lisa aboard to guest blog about her new book, just out today: Knocking on Heaven’s Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World. (Among other virtues, this book has the single most impressive collection of blurbers of any book ever written, from Bill Clinton to Carlton Cuse.) From personal experience I can verify that writing a book doesn’t just happen; it’s a tremendous commitment over an extended period of time, and once it’s done there’s not much chance to go back and change it. So deciding to write a book at all, and more importantly how exactly to target the writing, is a delicate and critical process.

While Lisa hasn’t yet become a regular blogger, she is active on Twitter, where you can follow her at @lirarandall.

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In conjunction with the publication of Knocking on Heaven’s Door, I thought I’d take advantage of Sean’s kind invitation to post on Cosmic Variance to explain my motivations in writing my book. I haven’t done a lot of blogging myself but I am impressed at the care and interest that go into science blogs. They are a way of sharing developments as they happen and an opportunity to have meaningful discussion of results.

I talk about a lot of science in my book. So I thought rather than summarizing it all—at least in this post—I’d focus on the question of why I wrote this particular book. I waited several years before even considering embarking on a second book project. I certainly didn’t want to simply repeat the content of my previous book, and my own personal goal is always to branch out into new arenas—in this case into new types of writing–while still remaining true to my physics roots. I didn’t know the exact book I was after but I did know some of the topics I considered important and timely.

These topics fell into several categories. First, I wanted to give an accurate picture of what is happening in particle physics and cosmology today—both with experiments and with theory. Particle physicists know this to be the era of the Large Hadron Collider (LHC), the machine that is colliding together protons at unprecedented energies to test the nature of matter and forces at smaller distances than ever explored. The interactions between theorists and experimenters is more intense than it has been during the time I’ve been actively pursuing physics. That is because everyone realizes this interactions are essential with these challenging experiments to get to the right answers. I wanted to convey the excitement and implications of the research taking place there, so when discoveries are made, anyone interested can understand what was found and what it could mean.

Cosmologists too find this is an important time and I wanted to share some of the interest in that major topic as well. One arena that both particle physicists and cosmologists are excited about are experimental studies of the nature of dark matter. Many find this topic perplexing, whereas even if difficult to tackle experimentally, the underlying idea really is not. I wanted to explain a bit how I think about dark matter and how experiments are searching for its feeble and elusive effects.

But I wanted to do more than just summarize the physics. The second important category of ideas I wanted to address has to do with the nature of science itself, and how active scientists go about advancing their field. After writing my first book, I was struck by how we take for granted the key underlying principles in our research, and don’t always remember to share these basic, sometimes subtle, and critical ideas.

Although perhaps I shouldn’t admit this, I had an even more ambitious agenda in mind. The ideas that underlie science are critical to rational thinking in general and should be widely known, even by those silly few who don’t care about any specific science research topic. These ideas are broad and deep, and it would make a difference in many of today’s debates if they were more widely understood and applied.

So interwoven with the physics story I wanted another story about the way science works. At this point, you might have surmised that the book I ended up writing included these topics, so rather than talk about what I wanted to write, I’ll just tell about a few of the topics I cover in the book I eventually settled on.

I begin with some key ideas–frequently introduced through anecdotes. One such concept that is essential to the way physicists in particular go about their work is an “effective theory,” which tells us to focus on what is measurable when making predictions. The underlying ideas here are the notions of “scale” such as energy or distance scales, and what it means to be right and wrong—both themes that resonate in other topics I’ll later address. I’ll later use scale to categorize what we know about matter— from the interior of an atom to the remote edges of the cosmos–and how the LHC and other particle accelerators, as well as various astrophysical probes, help us access successfully more remote scales.

The first section also expands on the nature of science, taking Galileo, whose work recently held its four hundredth birthday, as a departure point. Given my book’s title, I figured I also had to address the relation of religion and science (though that is not what the title really refers to). Aside from the obvious historical relevance, what I was really interested in were the questions of why we have this debate, as well as how thinking about scale as a way of categorizing what science really tells us helps us understand and clarify some of the confusions

There are many other ideas about science including risk and uncertainty that are woven into chapters with more detail than you might even want about the actual physics. General discussions of truth and beauty and how physicists suggest models of matter or the universe, as well as top-down versus bottom-up physics and how model building contrasts with string theory are used to frame discussions of how we theorists go about our business. The book also delves into the role of creativity in science and the relation between science and technology–both important topics I enjoy thinking about.

Yes Knocking on Heaven’s Door covers a lot of territory. But it’s a big story, and one well worth telling And in case you were wondering, the title refers to accessing the edges of knowledge—a worthy goal for all of us.

More recently Jim has written another book, The Amazing Story of Quantum Mechanics. But even without superheroes in the title, everything Jim thinks about ends up being relevant to movies before too long. The new movie Source Code features a twist at the end that involves — you guessed it — quantum mechanics. Jim has applied his physicist super-powers to unraveling what it all means, and was kind enough to share his thoughts with us in this guest post.

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There is an interesting discussion taking place on the internets concerning the ending of the newly released film SOURCE CODE, that suggests that the film concludes with a paradox. I believe that any such paradox can be resolved – with Physics!

This entire post is one big honkin’ SPOILER, so if you want to read about the final twist ending of a film without having seen said film – by all means, read on, MacDuff!

In SOURCE CODE, Jake Gyllenhaal plays US helicopter pilot Colter Stevens, whose consciousness is inserted into another man’s body (Sean Fentress, a school teacher in Chicago) through a procedure that requires a miracle exception from the laws of nature (involving quantum mechanics and “parabolic calculus” – by the way, there is no such thing as parabolic calculus). Thanks to some technobabble (or as Q-Bert on Futurama would describe it – weapons grade bolognium) Colter’s mind can only enter Sean’s body in the last eight minutes of Sean’s life. As Sean is sitting on a city bound Chicago commuter train, on which a bomb will explode at 7:58 AM, killing everyone aboard, the goal is for Colter to ascertain who planted the bomb. He cannot stop it from exploding, he is told, because that has already happened. He cannot affect the past, but he can bring information obtained in the past back to his present time. Learning the identity of the bomber would enable the authorities to prevent the detonation of a threatened second “dirty atomic” bomb is downtown Chicago.

While the above can be discerned from the movie trailer, what I am going to discuss next involves the actual ending of the film, and if you do not want this ending spoiled, you should stop reading now.

Colter learns that the reason his last memory is being attacked in his helicopter in Afghanistan is that he in fact died in the crash. His mangled body is kept artificially alive, and his brain can be activated, and sent to inhabit the body of Sean Fentress (who happens to be a neurological match). At the end of the film, after multiple failed attempts, Colter manages to identify the bomber. Providing this information to Col. Goodwin (a military officer played by Vera Farmiga) and Prof. Rutlidge (the great Jeffrey Wright), the scientist who designed the Source Code project, the terrorist is caught before he can set off the second bomb, but after, of course, the first bomb on the Chicago train explodes.

It is left somewhat vague as to whether Colter is going to parallel realities, a la the Many World’s interpretation of Quantum Mechanics, or whether he is engaging in a quantum/ neurological simulation. If the former (which seems to be borne out by the ending) then this would tie into notions of time travel being explored in the context of quantum gravity. That is, if one could time travel into the past, you need not fear any Grandfather paradox (what if you killed your ancestor – preventing your birth, but then you would not be able to travel back in time to ice Grandpa). Some physicists argue that time travel is only possible via parallel realities. You do not go back in time in your own reality, but to an alternate Earth’s past. You can thus kill as many grandparents as you have bullets, remaining safe in your own timeline. In any event it is assumed that the bomber is the same person every time Colter enters the Source Code.

While everyone is celebrating the capture of the bomber, the first successful trial of the Source Code project, Colter convinces Goodwin to send him back one last time, to try to save the passengers on the train. At the end of the eight minutes, he convinces Goodwin to terminate his life support, allowing him to die in actuality, as the world and his father believe happened months ago in Afghanistan. Needless to say, he manages to stop the first bomb from exploding on the train, hands the bomber to the authorities, and kisses his love interest just as the eight minute mark is reached. We see Goodwin make good on her promise and end his life support at that moment, at which point she is arrested my the military police for acting against Rutlidge’s instructions.

On the train however, Sean/Colter is still alive after the kiss. The film implies that he goes on to live happily ever after in Sean’s body, with Colter’s mind, while Colter’s deformed body remains at the Nellis laboratory on life support. As the bomb never went off on the Chicago train – there was no reason to activate Coulter and send him into the Source Code, and the project awaits its first true trial by fire. Thus it is indicated that we are witnessing two alternate realities – one where Goodwin is arrested after pulling the plug on Colter following the successful application of the Source Code, and the other where Sean/Colter is still alive, where the Source Code project has not been activated.

Among the many discussions I’ve noted on the web about the ending of this film, I wish to address two particular issues that are being debated by the Hive Mind. In the film’s final reality, where the bomb does not explode on the train – does Colter’s consciousness reside in two places at once? And, what happens to Sean Fentriss’ consciousness in this final reality?

Reasonable people may reach different conclusions concerning these two points. As I am a physics professor – I will tell you the RIGHT answers!

(1) In the final reality – Colter is NOT consciousness in two places at once. He is awake and aware in Sean’s body and at the same time his damaged body is in the Nellis lab – IN A NON-CONSCIOUS STATE. He is not awake and aware in the lab at Nellis, he can not initiate motion or form an independent coherent thought. He is in essence brain dead, kept artificially alive until there is a time and need for him to be activated (if there is a terrorist attack).

Even if he is activated – this would NOT influence or affect Colter in Sean’s body, as it would take place in Sean/Colter’s FUTURE. Remember he was sent back to Chicago at 7:50 AM – the bomb exploded at 7:58. Time progresses forward for both Sean/Colter and Nellis/Colter at the same rate. This was why Goodwin and Rutlidge were upset about how many trials it was taking – for each trial burned up a minimum of eight minutes, and brought the second explosion closer to happening.

What you are doing and thinking now is not affected by what you will be doing and thinking several hours from now. Do you know what you will be thinking about several hours from now (ok – for the guys this is an easy one). Nellis/Colter may not be activated for weeks/months/years later. But even if he is – Sean/Coulter can live his life, unaffected by what is happening in his future. There is no paradox, for Colter in Sean’s body is only awake and conscious at one point in time. Colter is NOT like Schrodinger’s cat, in two different conscious states simultaneously, as they are separated in time.

(2) What happened to Sean’s consciousness? Here there is a potential problem. Basically I believe Sean is dead. When Colter’s mind jumps into his body, it over-writes Sean’s consciousness. Rutlidge probably knows this, and ignores the ethical issues. Sean will be dead when the bomb explodes after all, and Rutlidge believes that cannot be changed. By sending Colter into Sean’s body, he robs Sean of the last eight minutes of his life. As Sean is unaware that a bomb will explode, killing him and everyone on board, he would not do anything extraordinary in those eight minutes. Rutlidge probably believes that it is acceptable to sacrifice the last eight minutes of one man’s life in order to save millions of lives if they can prevent the second bomb blast in downtown Chicago. Every time Coulter enters the Source Code at 7:50 AM, he essentially kills Sean. Sean will die in every reality where Colter does not enter the code, and he will also die in all N – 1 realities where he does – so this is an ethical problem of order 1/N where N goes to infinity.

Alternatively, Sean may be alive in Colter’s damaged body – but there was no suggestion that something like that was happening. Here I’m taking the Quantum Leap analogy too literally. (There is a wonderful tip of the hat to Quantum Leap – listen carefully to Coulter’s Dad).

Sorry this is so long. Never ask a professor a simple question – you always get a lecture in reply!

We’re very happy to have a guest post from Neal Weiner, one of the leading theorists working in the fast-moving area. (Don’t forget our previous guest post from one of the leading experimentalists.) Neal is responsible for some of the most imaginative models for what’s going on in the dark sector, and is excited about the upcoming experimental prospects. If you want to know what particle physicists are thinking about dark matter these days, you’ve come to the right place.

For anyone in the New York area, Neal is giving a public lecture on dark matter at AMNH on Friday the 4th (tomorrow). If you have a chance to go, I’d recommend not missing it.

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The Era of Dark Matter Direct Detection

Commonly, when I speak to my friends who don’t spend their time obsessing about the prospects for dark matter discovery, I am confronted by indifference, or worse, pessimism, when I mention the next few years of dark matter experiment. The history of dark matter direct detection has largely been a string of experiments, increasingly able to better find nothing, interrupted by occasional unverified claims, they point out. Why should this era be any different?

In contrast, I remain incredibly optimistic about the coming era. I feel this level of sensitivity is special, and that if we are to discover WIMP scattering, it should be in the next few years.

Why am I so optimistic?

1)This level of sensitivity is special

When we talk about discovering dark matter through direct detection, we are typically referring to discovering WIMPs, or Weakly Interacting Massive Particles (although a variety of searches for axions are ongoing). These are particles with masses ranging from roughly the proton mass, to 1000 x the proton mass. The hope is that by putting large (~100 kg or larger) experiments underground, where cosmic rays are shielded, experiments can detect the rare scattering of one of these WIMPs as they pass through the detector. (Estimates of the local density suggest that for WIMPs 300 x the proton mass, there should be about 1000 of them in a cubic meter of space near Earth.)

For dark matter to scatter off of the nucleus, it must interact with it. In the standard model, there are only a limited number of possibilities, and for “renormalizable” interactions, there are only two. It can scatter by exchanging a Z-boson, or by exchanging a Higgs boson.

If the interaction is through a Z-boson, the strength is completely calculable. While a “weak” interaction, the Z-boson provides a relatively strong interaction as far as weak interactions go. Indeed, a WIMP exchanging a Z-boson to elastically scatter off a nucleus would have been seen already about a decade ago, and is excluded by about four orders of magnitude by present experiments (i.e., current experiments would have seen roughly 10^4 events, instead of few or none).

However there is a second possibility – that the WIMP interacts through a Higgs boson. The coupling of the Higgs to ordinary matter is orders of magnitude weaker, with a strength 10 – 100 times weaker than the current generation of experiments, but within reach of the next decade’s experiments. This is not something just pointed out now – Burgess, Pospelov and ter Veldhuis pointed this out a decade ago.

While other force carriers appear in new physics models, such as supersymmetry, even there, the Higgs is often the dominant one. Thus, if you had asked me twenty years ago* what the most interesting levels of sensitivity to think about were, I’d have told you to look for the Z and the Higgs exchange. We know it’s not the Z, and we’re about to know about the Higgs.

*OK, twenty years ago I’d actually have said “huh?”, but that misses the point.

2) If anomalies mean anything, we should find out soon

A great deal of thinking and excitement on the theoretical side has come from considering dark matter anomalies. The DAMA collaboration has reported an annual modulation in the flashes of light in a NaI(Tl) experiment for a decade. This modulation signature was pointed out by Drukier, Freese and Spergel in 1986. When the Earth orbits the sun, sometimes we move with the galactic rotation and sometimes we move against it, consequently the flux of WIMPs should change seasonally, and events in the detector should as well. This is precisely what the DAMA collaboration has observed.

Competing experiments, such as XENON, CDMS, Edelweiss, ZEPLIN and others have seen no such evidence, however, excluding the most conventional scenarios. This has prompted a variety of new ideas: light dark matter, inelastic dark matter, resonant dark matter, luminous dark matter… All of these allow a signal at DAMA consistent with other searches. When compelled by a novel result, theorists begin to see a wider range of possibilities. But even these possibilities make predictions.

More recently, the CoGeNT experiment has seen event rates in their detector above what is expected from background. While no claim has been made of discovery, it is in a range where light dark matter should be expected to be found. XENON and CDMS (and in particular a recent low-energy analysis of the CDMS data, who use the same target) do not see what would have been expected, but a clear background explanation is lacking.

These may be signs of dark matter, and they may not be. If they are, we may already have guessed the correct model, or we may not have, but enough upcoming experiments have sensitivity that almost any scenario should be tested.

What should we be looking for this year?

• CoGeNT will update its data: with more exposure time, their radioactive backgrounds should decay, allowing the signal to be extracted more clearly. Does it modulate as expected? If so, theorists will have to go back to the drawing board.
• KIMS should report soon: the KIMS experiment (Korea Invisible Mass Search) is a CsI(Tl) experiment, with a 100kg target. DAMA began as a 100kg, and grew to 250 kg target of NaI(Tl). KIMS will not test WIMP-sodium scattering explanations of DAMA, but will test WIMP-iodine explanations, and even scenarios where the tiny amount of thallium is what the dark matter interacts with.
• COUPP: the Chicagoland Observatory for Underground Particle Physics is now operating a 4kg target of CF3I at SNOLAB in Canada. With both fluorine (which is light) and iodine (which is heavy and present in DAMA), it should have the ability to test most interpretations of DAMA as well as CoGeNT.
• XENON100: the gorilla in the room is the XENON100 experiment. With already a large exposure on a 30kg target of XENON recorded, the community is eagerly awaiting their results. They could come early in 2011 and may shake up the field.

Going forward, improvements to established detector technologies (such as CDMS) and the maturation of the liquid nobles (such as XENON, but also LUX, DEAP/CLEAN, WARP, DarkSide and more) promise an era of rapid progress, with sensitivity improving by orders of magnitude over the next decade. If WIMPs are there, this coming era is our best opportunity to see them. When coupled with the LHC and new data from astrophysics experiments (Fermi, and PLANCK among others), our attitudes of what dark matter is – or at least what it is not – will soon be entirely different.

We’re very happy to have a guest post from one of the people who is doing exactly that hard work — Matt Johnson, who guest-blogged for us before. He and his collaborators just come out two papers that examine the cosmic microwave background, looking for evidence of “bubble collisions.”

First Observational Tests of Eternal Inflation
Stephen M. Feeney (UCL), Matthew C. Johnson (Perimeter Institute), Daniel J. Mortlock (Imperial College London), Hiranya V. Peiris (UCL)
arXiv:11012.1995

First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results
Stephen M. Feeney (UCL), Matthew C. Johnson (Perimeter Institute), Daniel J. Mortlock (Imperial College London), Hiranya V. Peiris (UCL)
arXiv:1012.3667

The hope is that these other “universes” might not be completely separate from our own — maybe we collided in the past. They’ve done a very careful job going through the data, with intriguing but inconclusive results. (See also Backreaction.)

Looking for this kind of signature in the CMB is certainly reminiscent of the concentric circles predicted by Gurzadyan and Penrose. But despite the similarities, it’s different in crucial ways — different theory, different phenomenon leading to the signal, different analysis, different conclusions. The road to sorting out this multiverse stuff is long and treacherous, but our brave cosmological explorers will eventually guide us through.

Here’s Matt.

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Observing other universes: is this science fiction?

Perhaps not. Stephen Feeney, Daniel Mortlock, Hiranya Peiris and I recently performed an observational search for the signatures of colliding bubble universes in the cosmic microwave background. Before getting to our results, let me explain some of the back-story.

The idea that there might be other universes is taken quite seriously in high energy physics and cosmology these days. This is mainly due to the fact that the laws of physics, and the various “fundamental” constants appearing in them, could have been otherwise. More technically worded, there is no unique vacuum in theories of high energy physics that involve spontaneous symmetry breaking, extra dimensions, or supersymmetry. Having a bunch of vacua around is interesting, but to what extent are they actually realized in nature? Surprisingly, when a spacetime region undergoing inflation is metastable, there are cases when all of the vacua in a theory can be realized in different places and at different times. This phenomenon is known as eternal inflation. In an inflating universe, if a region is in a metastable vacuum, bubbles containing different vacua will form. These bubbles then expand, and eat into the original vacuum. However, if the space between bubbles is expanding fast enough, they never merge completely. There is always more volume to convert into different vacua through bubble formation, and the original vacuum never disappears: inflation becomes eternal. In the theory of eternal inflation, our entire observable universe resides inside one of these bubbles. Other bubbles will contain other universes. In this precise sense, many theories of high energy physics seem to predict the existence of other universes.

In the past four years, a few groups have tried to understand if it is possible to confront this radical picture of a “multiverse” with observation. The idea is to look for signatures of a collision between another bubble universe and our own. Even though the outside eternally inflating spacetime prevents all bubbles from merging, there will be many collisions between bubbles. How many we are even in principle able to see depends in detail on the underlying theory, and given the proliferation of theories, there is no concrete prediction.

Currently, the best information about the primordial universe comes from the cosmic microwave background (CMB). A collision will produce inhomogeneities in the early stages of cosmology inside our bubble, which are then imprinted as temperature and polarization fluctuations of the CMB. One can look for these fingerprints of a bubble collision in data from the WMAP or Planck satellites.

Most of the previous work has been to establish a proof of concept that observable bubble collisions can exist, and that there are theories which predict that we expect to see them; many of the details remain to be worked out. There are however a number of generic signatures of bubble collisions that we used to guide our search. Since a collision affects only a portion of our bubble interior, and because the colliding bubbles are nearly spherical, the signal is confined to a disc on the CMB sky (imagine two merging soap bubbles; the intersection is a ring). The effect of the collision inside the disc is very broad because it has been stretched by inflation. In addition, there might be a jump in the temperature at the boundary of the disc (although the magnitude and sharpness of such a jump has yet to be worked out in detail).

In a pair of papers (summary: arXiv:1012.1995 , details: arXiv:1012.3667) with Stephen Feeney, Daniel Mortlock, and Hiranya Peiris, we performed a search for these types of generic signatures in CMB data from the WMAP satellite. Our philosophy was to define a phenomenological model that encompasses the generic signatures of bubble collisions, and use the data to constrain the free parameters in the model. See the picture shown below, which is a simulated CMB sky containing a bubble collision, for an example of what a very clear signal might look like.

Predicted signal on the cosmic microwave background from a simulated collision with a bubble from another “universe.”

Zoomed in on the simulated bubble from above.

Cutting to the chase, we were first able to use simulated CMB data containing bubble collisions to rule out a range of parameter space as inconsistent with WMAP data. As it turned out, the existence of a temperature discontinuity at the boundary of the disc greatly increases our ability to make a detection. We did not find any circular temperature discontinuities in the WMAP data.

While we didn’t make any clear detections of bubble collisions, we did find four features in the WMAP data that are better explained by the bubble collision hypothesis than by the standard hypothesis of fluctuations in a nearly Gaussian field. We assess which of the two models better explain the data by evaluating the Bayesian evidence for each. The evidence correctly accounts for the fact that a more complex model (the bubble collisions, in this case) will generally fit the data better simply because it has more free parameters. This is the self-consistent statistical equivalent of applying Ockham’s Razor. In addition, using information from multiple frequencies measured by the WMAP satellite and a simulation of the WMAP experiment, we didn’t find any evidence that these features can be attributed to astrophysical foregrounds or experimental systematics.

One of the features we identified is the famous Cold Spot, which has been claimed as evidence for a number of theories including textures, voids, primordial inhomogeneities, and various other candidates. A nice aspect of our approach is that it can be used to compare these hypotheses, without making arbitrary choices about which features in the CMB need explaining (focusing on the Cold Spot is an a posteriori choice). We haven’t done this yet, but plan to soon.

While identifying the four features consistent with being bubble collisions was an exciting result, these features are on the edge of our sensitivity thresholds, and so should be considered only as a hint that there might be bubble collisions to find in future data. The good news is that we can do much more with data from the Planck satellite, which has better resolution and lower noise than the WMAP experiment. There is also much better polarization information, which provides a complementary signal of bubble collisions (found by Czech et. al. – arXiv:1006.0832). We’ll be gearing up to analyze this data, and hopefully there will be more to the story then.

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I noticed a puzzled look on Vicky’s face — she was squinting at the blackboard filled with equations describing how the subtitution rule in integral calculus works. She is one of my better students whom I know to be following my lectures well. I took it as a cue that I have not made a point clear, and I knew I must fallen back into speaking as though as my students are native English speakers. They are not — they speak Haitian Creole, and I was trying to teach them basic intro to mathematics in English and and a smattering of Creole.

Hello from Fondwa, Haiti, elevation 850m, Population 8000. For the past twenty days, I have been teaching a group of enthusiastic Haitian university students at the University of Fondwa. As I mentioned in my previous post, the university lost all its buildings during the Jan 12 quake. At the moment, we are using an abandoned warehouse as a temporary campus. It has no roof, so we put a tin roof over to keep the rain out. We use tarps (thank you USAID) for our windows to keep the rain out. There are 3 classrooms and an office. Some of the students have lost their homes in the Jan 12 earthquake, so the university allowed them to stay inside the warehouse.

We have no running water and a few solar panels for power. Water is obtained from wells, from a spring (about 15 minutes walk up hill), and from the regular rain showers we have been getting — hurricane season is upon us after all. This often led to me wondering whether I should be wishing for rain so we can fill up our water tank, or for the sun so we can charge up our batteries.

Many of the students are extremely enthusiastic. In my first full day, when I was just waiting for a teaching assignment, Deb, Vicky and Everest approached me and asked me in halting English what I would be teaching. I told them I would probably be teaching them math, and they said they have not had a math professor for the entire semester, and oh would you help us with some of these problems. So I ended up working with them right there and then. Turns out that these vanguard of students have been trying to teach themselves math from some books. They have had some confusion with concepts that one would expect from being self-taught, but they were sharp and intelligent. I found it a joy to work with them. Deb in particular, is especially strong and spoke some English, so I hired him as my Teaching Assistant who can also translate for me. Given his mathematical acumen, I started teaching him more advanced topics in a special class.

I was assigned to teach two classes in four weeks — an Intro to mathematics (for first years) and the vaguely titled “Business Mathematics” class to the 4th years. After a quick evaluation of the students’ ability, I ended up deciding that I am going to teach the first years differential and integral calculus — useful things to know whether you are going to be an agronomist or a manager. For the “business math” class, I chose to teach them some basic statistics — with the goal that they should be able to deal with frequency and probability distribution functions when completed.

English is not a widely spoken language in Haiti, so it was a challenge to teach the classes. However, I find that we can make a lot of headway with a mixture of my rudimentary Creole and the combined English knowledge of my students, assisted by a dictionary. The classes understandably proceed slower than usual, but that is not always a bad thing in pedagogy. After a hesitant start, we settled on a good system where some of the more capable English speakers would translate for the other students in real time. Sometimes, some of the more advanced students would volunteer to teach a difficult concept which they have grasped to the class in Creole. The students are generally attentive, and eager — I am often asked to teach extra classes.

When classes are not in session, I am kept busy with students who wanted to learn more, or have questions about math or English. I find these impromptu discussion sessions the most rewarding — I can teach the students at the pace at which they are learning. As a personal bonus, I have the luxury of having the students teach *me* Creole. Although I am assigned a very good Creole teacher, I learned most of my Creole from such constant interaction with the students.

Living conditions in Fondwa are rough. I am staying in a semi-collapsed building with a couple of volunteers from the US (Rohan Mahy and Reuben Grandon), and a rotating roster of Haitian teachers, most who live outside Fondwa : unfortunately qualified teachers and lecturers are extremely scarce in Haiti. Our quake damaged building has no running water, no power, and red “X” marks on parts of the buildings that are unstable — a non-trivial indicator since we are still experiencing aftershocks (I personally felt three so far). On the other hand, we have a great view — on a clear day, we can see distant Leogane northward and the Gulf of Mexico, 80 km away.

Nevertheless, our humble abode is a palace compared to the conditions that most Haitians live in. Many of them have lost homes in the quake; some of hem are still living in tents. Ironically, many of the stone buildings collapsed, while the wooden ones survived. I visited one of the tent cities of Port-au-Prince — they are hot, dusty, crowded and so incredibly unsanitary that they seems like epidemic timebombs waiting to go off. Every single building left standing suffered some form of damage from the quake — sometimes looking past the intact facade will reveal a completely collapsed back portion of the house. This does not stop Haitians from living in them. There is a strong sense of communal spirit among rural Haitians, more than once, I was told by the tenants that their house was “kraze” (destroyed) in the gudu-gudu (quake) and they are living in that “kind madame’s” house. Our neighbouring house, a wooden structure no bigger than the size of a school bus, is home to thirty men, women and children.

The Haitians are very friendly. After getting past the initial bemusement (and amusement) of being called “blan” (white man) in the first few days, I find the Haitians incredibly hospitable, and resilient in the face of such hardship. Wherever I go, it is easy to smile and call out a “bonjou” or “bonswa”, or “komen ou ye” (how are you?) to people passing me or just doing chores in front of their houses. I have a special love for the Haitian children — they are the most energetic and playful bunch of kids I have ever met. A group of them would show up at our house from time to time, screaming the names of us *blan* volunteers, and we would end up playing with them until we are exhausted. It is poignant for me to know that some of them have lost siblings and parents in the quake.

I will be leaving Haiti in a few days. Personally, I found the teaching experience and my interactions with the Haitians incredibly fulfilling and rewarding. But it was also very sobering to see the damage, destruction and human misery caused by the quake. There is a lingering sense of not having done enough, and that there is so much more left to be done. I do plan to come back again, and perhaps learn enough Creole to teach in it next time.

But Eugene always cared about other things in addition to physics, and today he’s bringing us a guest post about a heart-wrenching topic: education in Haiti in the aftermath of their devastating earthquake. Not content to agitate for support from the comfort of his computer, Eugene is actually hopping on a plane this weekend to spend a month teaching math at a poor rural university. Here’s his introduction, and we hope to have a follow-up post after he returns from his travels.

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On Tuesday, January 12, 2010 at 4:53pm, a massive quake hit Haiti, killing an approximate quarter of a million people, injuring another quarter of a million, and causing massive infrastructure damage. Today, more than five months later, as the news cycle has moved on, Haitians are still pulling themselves out of the disaster, with 1.5 million people still homeless.

Fondwa is the 10th Communal Section of Leogane situated about 60 km south of the Haitian capital, Port-au-Prince, near the epicenter of the quake. It is a rural community with big dreams, the peasants banded together in 1988 to form the APF (Association of Peasants of Fondwa) to create a model community, not just with the aim of providing basic services but to empower the people of Haiti by providing them with the education and knowledge to improve their own lives.

One of their amazing achievement is the founding of a university, the University of Fondwa (UNIF) in 2004 in the mountains of Haiti, offering majors in Management, Agricultural Engineering and Veterinary Science — skills necessary for a rural community to survive and thrive — with about 40 students from all over Haiti. They graduated their first class last year.

The quake destroyed all the buildings of UNIF : the main building, the dorms and the lecture halls. Remarkably, classes continued after the quake, first in tents, and hopefully soon in temporary shelters. Final exams were given and graded, and the new semester began on schedule, May 5.

I met the founder of the University, Fr. Joseph Phillipe in New York a few weeks ago (he also founded Haiti’s biggest microfinance bank, FONKOZE, but that’s another story) — a series of hopeful email inquiries inspired by the watching a documentary about Fondwa led to having coffee with him in uptown New York City. Despite the challenges that his community is facing, he was full of energy, focusing on what to do for the future. I was impressed. I told him I want to help out.

I told him I wanted to volunteer to teach in UNIF, but I was not sure what I need to do. He said “We are waiting for you in Fondwa.”

This week, I am headed down to Fondwa to teach math for a month. I was told to be prepared to be caught unprepared. Internet permitting, I hope to post a follow-up to this when I get to Fondwa with more pictures from the ground.

A month is not exactly a long time. But I hope that any help is better than no help at all — they are short on teaching staff after the quake. Personally, I have been inspired by humanitarian groups like Doctors without Borders and Paul Farmer’s Partners in Health. I can’t save lives as a doctor, but I can teach! A long term hope is to be able to build ties in Fondwa, and perhaps do this on a yearly basis. I believe that academics have a lot to contribute in making this world a better place beyond hanging out in our ivory towers.

I asked Fr. Joseph what else I can do to help, he said “Tell your friends about us, and ask your friends to come too”.

Sean has kindly allowed me to use this blog to publicize the plight of the community at Fondwa. They are still trying to get basic services in. Their main needs are monetary donations, temporary housing, clean water and volunteers! They are especially looking for long term volunteers for six months of longer. They are also looking for a President for UNIF — I am serious — if you are interested or know anybody who might be interested, email APF below.

If you like want to volunteer, the best way is to contact APF directly at apf222@aol.com or go to the APF homepage. If you like to donate directly to APF click on the link to my blog for the bank information. If you want help out Haitians to help themselves : support Fonkoze’s microfinancing efforts by helping out here.

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It’s a real privilege to be able to write a guest blog for Cosmic Variance and to take a little side trip from my regular postings to Life, Unbounded – the science of origins.

The modern search for life in the universe encompasses everything from exoplanets and astrochemistry to geophysics and paleontology. Underlying and motivating the investigations in these fields – collectively labeled astrobiology – there are some fundamental assumptions, but do they make sense?

In recent weeks one might be forgiven for thinking that a shadowy biosphere surrounds us, aliens are poised to dismantle civilization, and that time traveling species are flitting in and out of view like barflies on a Saturday night. It’s a little disconcerting, does the Kool Aid have something special in it this Spring?

Unfortunately I think that all of these headline grabbing items miss the real story of what life is, here on Earth and potentially further afield. The idea of ‘shadow biospheres’ or multiple origins of terrestrial life sounds intriguing, and certainly helps bring focus to the fact that we can be very blinkered in our outlook. It also steers attention away from a more interesting and demonstrably real point.

In the past couple of decades we have found a shadow biosphere, except that far from lurking in the cracks it turns out to be the biggest, most critical, biosphere on the planet. An astonishing 99.9% of life on Earth cannot be coerced to grow in a lab, and so we have overlooked it. Microbial life – single-celled bacteria and our ancient cousins the Archaea – is not just the stuff under your fingernails, it is what makes multi-cellular life like us function, and it helps govern the grand chemical cycles of our planet, from the continents to the oceans to the atmosphere. Such organisms have, over three to four billion years, evolved into an eye popping array of microscopic machines, the ultimate nano-bots. They can extract energy and raw materials from, it seems, almost any environment. A particularly good example is Desulforudis audaxviator – discovered 2.8 km down in a South African gold mine in a pocket of isolated water. Little audaxviator lives all alone when the vast majority of microbial life is utterly reliant on colonial symbiosis. It earns a living by mopping up the molecular detritus left after radioactive decay in the uranium rich rocks dissociates water and bicarbonates. That’s a very, very neat trick.

Twenty or thirty years ago we barely understood that such life existed on this planet. Now we are beginning to see that the longevity of our biosphere owes itself to precisely this crowd of ‘shadowy’ organisms. A truly wonderful paper was published a couple of years ago in which Falkowski, Fenchel and Delong laid out the big picture for life on Earth. In essence, they argue that single-celled microbial life is the manifestation of an even deeper truth; the core planetary gene set. This is the set of recipes for metabolism, or how to harvest a planet for energy, and we all rely on them. The result of billions of years of natural selection, these genes are widely dispersed across the microbial biosphere. This is true to such an extent that should 99% of life be wiped out by an asteroid collision, supervolcano, or dirty telephone receiver, the information for the molecular machinery that drives all organisms will be safely preserved in the surviving 1%. The living world does not end, it just reboots. Because of this, carbon-based life is a far more robust phenomenon than we could have ever imagined. It is the ultimate, Google-like, cloud computer.

Still though, isn’t this also a blinkered view of what might constitute life? Well, sure, but there’s another fact to consider. When we look out into the universe we find that the chemistry of our life – carbon based molecular structures – is not just occasional, it’s ubiquitous. Carbon is a fabulous player; simple molecules, rings, chains, polymers, sheets, crystals, and great clumps of sooty particles abound. Some is produced directly from the huge outflows of cooling gas from old stars, much forms in the thick nebulae and proto-stellar cocoons that eventually give rise to planets. Thousands of recognizable organic molecules, including amino acids, are found in the treacly mix of some meteorites – the remains of our own ancient solar system. This is a chemical bonanza that must have played a role in setting the stage on the young planet Earth. If this is blinkered then stick a blindfold on me.

So life on Earth is tough and tenacious, and the building blocks are everywhere. Is this enough reason to think that a similar blueprint exists in other places across the universe? Well, it’s definitely motivation to go looking, and to go looking for the kind of exotica that we already know, rather than inventing new ones. Is this reason enough to think that ‘intelligent’ life exists somewhere else? That’s a tough call. Life on Earth did remarkably well for the past 3.5 billion years without us around, I don’t think there is anything that indicates we are more than an evolutionary oddity (albeit an incredible one). It’s a big universe though, with plenty of room for oddities, even if they turn out to be extremely familiar.

With this varied background, Malcolm studies connections between biomechanics and neuroscience — how do brains and bodies interact? This unique expertise helped land him a gig as the science advisor on Caprica, the SyFy Channel’s prequel show to Battlestar Galactica. He also blogs at Northwestern’s Science and Society blog. It’s a pleasure to welcome him to Cosmic Variance, where he’ll tell us about robots, artificial intelligence, and war.

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It’s a pleasure to guest blog for CV and Sean Carroll, a friend of some years now. In my last posting back at Northwestern University’s Science and Society Blog, I introduced some issues at the intersection of robotics, artificial intelligence (AI), and morality. While I’ve long been interested in this nexus, the most immediate impetus for the posting was meeting Peter Singer, author of the excellent book ‘Wired for War’ about the rise of unmanned warfare, while simultaneously working for the TV show Caprica and a U.S. military research agency that funds some of the work in my laboratory on bio-inspired robotics. Caprica, for those who don’t know it, is a show about a time when humans invent sentient robotic warriors. Caprica is a prequel to Battlestar Galactica, and as we know from that show, these warriors rise up against humans and nearly drive them to extinction.

Here, I’d like to push the idea that as interesting as the technical challenges in making sentient robots like those on Caprica are, an equally interesting area is the moral challenges of making such machines. But “interesting” is too dispassionate—I believe that we need to begin the conversation on these moral challenges. Roboticist Ron Arkin has been making this point for some time, and has written a book on how we may integrate ethical decision making into autonomous robots.

Given that we are hardly at the threshold of building sentient robots, it may seem overly dramatic to characterize this as an urgent concern, but new developments in the way we wage war should make you think otherwise. I heard a telling sign of how things are changing when I recently tuned in to the live feed of the most popular radio station in Washington DC, WTOP. The station had commercial after commercial from iRobot (of Roomba fame), a leading builder of unmanned military robots, clearly targeting military listeners. These commercials reflect how the use of unmanned robots in the military has gone from close to zero in 2001 to over ten thousand now, with the pace of acquisition still accelerating. For more details on this, see Peter Singer’s ‘Wired for War’, or the March 23 2010 congressional hearing on The Rise of the Drones here.

While we are all aware of these trends to some extent, it’s hardly become a significant issue of concern. We are comforted by the knowledge that the final kill decision is still made by a human. But is this comfort warranted? The importance of such a decision changes as the way in which war is conducted, and the highly processed information supporting the decision, becomes mediated by unmanned military robots. Some of these trends have been helpful to our security. For example, the drones have been effective against the Taliban and Al-Qaeda because they can do long-duration monitoring and attacks of sparsely distributed non-state actors. However, in a military context, unmanned robots are clearly the gateway technology to autonomous robots, where machines can eventually be in the position to make decisions that have moral weight.

“But wait!” many will say, “Isn’t this the business-as-usual-robotics-and-AI-are-just-around-the-corner argument we’ve heard for decades?” Robotics and AI have long been criticized as promising more than they could deliver. Are there signs that this could be changing? While an enormous amount could be said about the reasons for the past difficulties of AI, it is clear that some of its past difficulties stem from having too narrow a conception of what constitutes intelligence, a topic I’ve touched on for the recent Cambridge Handbook of Situated Cognition. This narrow conception revolved around what might loosely be described as cognitive processing or reasoning. Newer types of AI and robotics, such as embodied AI and probabilistic robotics, tries to integrate some of the aspects of what being more than a symbol processor involves: for example, sensing the outside world and dealing with the uncertainty in those signals in order to be highly responsive, and emotional processing. Advanced multi-sensory signal processing techniques such as Bayesian filtering were in fact integral to the success of Stanley, the autonomous robot that won DARPA’s Grand Challenge to drive without human intervention across a challenging desert course.

As these prior technical problems are overcome, autonomous decision making will become more common. Eventually, this will raise moral challenges. One area of challenge will be how we should behave towards artifacts, be they virtual or robotic, which are endowed with such a level of AI that how we treat them becomes an issue. On the other side, how they treat us becomes a problem, most especially in military or police contexts. What happens when an autonomous or semi-autonomous war robot makes an error and kills an innocent? Do we place responsibility on the designers of the decision making systems, the military strategists who placed machines with known limitations into contexts they were not designed for, or some other entity?

Both of these challenges are about morality and ethics. But it is not clear whether our current moral framework, which is a hodgepodge of religious values, moral philosophies, and secular humanist values, is up to responding to these challenges. It is for this reason that the future of AI and robotics will be as much a moral challenge as a technical challenge. But while we have many smart people working on the technical challenges, very few are working on the moral challenges.

How do we meet the moral challenge? One possibility is to look toward science for guidance. In my next posting I’ll discuss some of the efforts in this direction, pushed most recently by a new activist form of atheism which holds that it is incorrect to think that we need religion to ground morality, and even dangerous. We can instead, they claim, look to the new sciences of happiness, empathy, and cooperation for guiding our value system.

This is a hot topic, as we all know, and I’m hoping we get a thoughtful and respectful discussion in the comments. Nevertheless, this might be a good place to remind people that we’ll generally delete comments that are off topic or offensive.

Now, here’s Faye.

There must be some redeeming lesson to come from covering the so-called climate gate scandal that’s dragged on over the last two months. Member of the public actually care about science. They’re even passionate about it. But when that happens it’s not always pretty.

Never in my 14 years as a newspaper science writer have I found myself on the receiving end of such a powerful stream of hate mail – searing bombs of name-calling that get fired into my personal and work inboxes, as well as screaming, profanity-laced screeds landing in my voice mail. There’s much gloating about the downfall of newspapers and speculation that soon I’ll perish on the streets, begging for pennies.

I even got my first death threat following this story. It was the first of three stories I wrote on this topic for the Philadelphia Inquirer after a cache of e-mail messages were stolen from some prominent climate scientists and picked over by their worst enemies for signs of malfeasance.

Many member of the public are raging at me for failing to point out what they see as an inexcusable case of scientific fraud. For them, there’s no distinction between committing fraud and being wrong. That might worry some members of the scientific community.

I wasn’t ordered to write anything on this issue. During the same period I also wrote a nice story about the Hubble Telescope, and one about heroic cancer researchers. I could easily have skipped this whole mess and written other nice stories – on Kepler, or maybe LHC. People always like stories about planets and particles.

But instead, I returned from Thanksgiving vacation to write this quick overview, followed by the more offbeat Q and A story linked above.

Then, in a fit of masochism, I decided to profile one of the scientists involved – Michael Mann – because he works nearby at Penn State University. That gave the whole thing a local angle.

Mann’s work has been scrutinized for years, after a researcher in Canada pointed out a possible statistical flaw in some climate reconstructions done in the 1990s. That eventually led to an investigation by a National Academy panel. They concluded that Mann’s initial papers weren’t perfect but the general conclusions held up, and there was no evidence of fraud.

In other areas of science, the public can be more tolerant. Back in the 1990s, people were in some disagreement about the age of the universe. When new information came in, some were shown to be off be a few billions years, give or take, but they didn’t get carted off to Siberia.

Others had wrong ideas about the shape and fate of the universe, since nobody back then thought it was accelerating. That’s the beauty of science. It’s self-correcting – though sometimes the corrections can take a while.

The other lesson here is that many people don’t understand the role of uncertainty in science. There is uncertainty over the way water vapor changes the situation, for example, with most experts saying it will create a positive feedback but a few arguing for a negative one.

And still, some people write to inform me that the science is “settled.” These critics are not sure what’s settled but they’ve heard this and seem to think it’s important to repeat.

Others recognize the uncertainty in climate science and find it appalling. That’s particularly true of engineers, who seem pretty well-represented among self-proclaimed global warming skeptics. It’s a level of uncertainty that would never fly in modeling systems for chemical refineries, or so they tell me.

One MIT-trained engineer said his own calculations prove that the climate models can’t work because, in short: “junk in equals junk out”. It would make for a great story if a local guy who worked for a chemical refinery took down the whole climate science establishment on the back of an envelope. Unfortunately, I have to consider the possibility that he hasn’t.

The global warming skeptics also love to use the term “AGW theory”. This proved a great strategy for debating because the scientists don’t really refer to anthropogenic global warming as a theory, and many aren’t sure what AGW theory means. That gives the critics the freedom to say it means that only humans can influence the climate – and that the climate never changed at all before humans hit the scene. Then they can point to this untenable position and say, “ha ha – aren’t these scientists dumb!”

Coming from the more liberal side of things, a reader suggested that even if some fatal flaw crops up in both the climate models and the climate reconstructions, and the world does plunge into a protracted global cold spell, the scientists who had done the original work shouldn’t necessarily be thrown in prison or burned at the stake.

It might seem strange, even insane, for the public to base views of the carbon cycle and water vapor feedbacks on politics. Is it a problem of science illiteracy? I don’t think so. We could all be better educated about basic physics and chemistry and this debate would still play out the same way.

It all makes more sense, though, in light of the way differing political philosophies tolerate uncertainty – whether they’re considering government-funded scientists delivering uncertainty or the prospect of policy changes based on uncertain science. How much should we know before we start conserving energy? Classify CO2 as a pollutant? Submitting to international regulations? The best we can do as scientists and science writers is respect those political differences, state what’s known as clearly as possible, and be honest about what’s not known. People will still hate us, of course. There’s no way to escape that.

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I had the pleasure of meeting up with Sean and some other old friends at the World Science Festival in NYC last month, and over champagne at the opening night reception (science has its benefits) Sean graciously invited me to write a guest post on gravitational lensing. It’s a broad topic, mainly because lensing is proving to be such an incredibly useful tool for many areas of cosmology and astronomy, but I have to admit that the visual beauty of the images produced by lensing is part of the appeal for me.
I’m also enamored of the visceral connection between these images and lensing phenomena that all of us encounter in daily life – and the access into a complex theory that this connection affords. The giant arcs, Einstein Rings, and multiple copies of a single distant galaxy or quasar that have now been observed in hundreds of images are concrete visualizations of otherwise abstract concepts of general relativity – they effectively trace out the warps in spacetime created by massive objects, revealing the outline of the cosmos much as the technique of “rubbing” can reveal the writing on an ancient gravestone.

This image, from a recent paper by Adi Zitrin and Tom Broadhurst is both scientifically and visually irresistible:

First, the image itself is really cool. The bright white/yellow galaxies are members of a cluster known as MACS J1149.5+2223, while the blue amoeba-like objects that appear to be invading the cluster are actually five images of a single distant (z ~ 1) spiral galaxy.

This galaxy has been lensed by the warp in spacetime created by the cluster. Light from the galaxy, which lies almost directly behind the center of the cluster but much farther away from us, travels along several curved paths through the cluster lens, producing multiple magnified images of the galaxy. The inset box shows a computer generated model of the unlensed source galaxy, enlarged by a factor of four so that the details, including the spiral arm structure, are visible. Without the lensing power of the cluster, we would see this galaxy as a single small blue smudge.

In general, lensing will both magnify and distort (shear) images of a background source. This lens is fairly unique in that we see large but relatively intact images of the spiral galaxy, which implies that the mass distribution in the central region of the cluster must be nearly uniform. The images in the upper left (#1) and lower right (#2) are especially striking. #1 is magnified but very minimally distorted, while #2, the largest image with a magnification of over 80, seems to be curling its tentacles about one of the galaxies in the cluster.

A close look also reveals the negative parity (mirror symmetry) of the remaining three images – the spiral arms appear to circle in the opposite direction – as expected from lensing. The total magnification of the distant galaxy (the sum of all five images) is about 200, the largest known to date – supporting the authors’s claim that this is “the more powerful lens yet discovered.”

This is not just a pretty picture, however – the image packs a lot of scientific information. The authors extract the mass distribution in the cluster (which has implications for cosmological models), measure the mass-to-light ratio of the bright galaxy in the center of the cluster, and use the magnifying power of the lens to search for even more distant galaxies.

The basic idea is to construct a model of the lens, starting with the cluster galaxies and a dark matter halo; then refine the model to reproduce the multiple images that are seen. Using this refined model it’s possible to predict the location of additional images of a given source, and to identify regions of high magnification that can then be examined for multiple images of other sources. Any additional images that are found can be used to further refine the model and so on.

For example in this system, image #1 is “delensed” to obtain an image of the source galaxy; this model source image is then relensed and the resulting multiple images are compared (size, shape and location) with the observed images. The agreement between observed and modeled images is excellent. Using this lens model nine additional multiply-lensed galaxies (all fainter and at a higher redshift than the spiral galaxy) were found. In total there are 33 images of 10 background source galaxies.

So what does this tell us? The model of the lens outlines the (projected 2D) mass profile of the cluster – which doesn’t seem to agree with numerical simulations for clusters, assuming a standard ΛCDM cosmology. The mass concentration in the center of the cluster is higher than predicted, a result that has also been found for other massive clusters studied with gravitational lensing. This implies that we’re either missing some physics in our simulations, or we may need to modify our cosmological model.

And I suspect that we will hear from this lens again. The most distant galaxy discovered to date, at a redshift of z ~ 7.6, was found courtesy of the cluster lens A1689, and MACS J1149 offers another powerful magnifying glass through which to search for the earliest galaxies in the universe.

Matt Johnson, Lisa Randall and I just came out with a paper that takes a partial stab at this question: Dynamical Compactification from de Sitter Space. (And a similar-sounding paper came out the same day from Jose Blanco-Pillado, Delia Schwartz-Perlov, and Alex Vilenkin.) It’s an intriguing idea, if I do say so myself: starting with nothing more complicated than a higher-dimensional spacetime with a positive vacuum energy and an electromagnetic field (or a higher-dimensional generalization thereof), you will automatically get quantum fluctuations into lower-dimensional spacetimes! If we really believe in extra dimensions, we need to understand how regions with different effective dimensionalities are cosmologically related, and this is a step in that direction.

Normally I’d blog all about it, but on this occasion we’re outsourcing to a guest blogger. My collaborator Matt Johnson is a postdoc at Caltech, and before that was a grad student at UC Santa Cruz, where he worked with Anthony Aguirre — a previous guest-blogger of ours! We like to keep things in the family.

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Extra dimensions. Sounds preposterous at first. Well, perhaps more accurately, it sounds preposterous to most people who don’t do high-energy theory. But, really I assure you, there are many well-motivated reasons why us wacky theorists like to ponder the existence of extra dimensions.

For one, as shown long ago by Kaluza and Klein, it is possible to get Maxwell’s equations of electromagnetism in four dimensions by taking 5 dimensional General Relativity and wrapping one of the spatial dimensions up in a circle too small to see. The smaller the circle is, the harder it is to move in this “other direction,” and so there is no danger in getting lost on the way home. In this way, Maxwell’s equations have an elegant geometrical origin and gravity and electricity & magnatism are combined into one force (5 dimensional gravity).

Another strong motivation comes from string theory, which is only a consistent quantum theory of gravity if there are 10 or 11 dimensions in total. Again, since we don’t see them, it is necessary to hide the existence of the extra dimensions. Inspired by the fact that it was possible to hide one extra dimension by wrapping it up in a circle, generally the extra 6 or 7 dimensions are thought to be “compactified” into a very small compact geometry like a sphere or a torus.

At this point, the five-year-old in the audience is insistently asking, “If you have all these extra dimensions, and you are telling me that they are wrapped up into this tiny ball, how did they get wrapped up in the first place? Why are the four dimensions we see so large, and the others so small?”

After nearly a century of thinking about the existence of extra dimensions, there are surprisingly few plausible answers to this very simple question. One of the few answers was proposed by Brandenberger and Vafa. They studied the thermodynamics of strings in a torus-shaped hot early-universe, and found that miraculously it is favorable for only four of the dimensions to become large. Pretty nice, if the universe is a torus and all the dimensions started out small and compact. But, it would be nice to have some alternatives in case this turns out not to be viable.

Sean Carroll, Lisa Randall, and I recently wrote a paper that revisits the five-year-old’s question. We wanted to start with the very simplest model that has extra dimensions and solutions in which some of them can be compactified. A minimal set of ingredients needed to accomplish this includes 1) D-dimensional gravity, 2) a positive D-dimensional cosmological constant, and 3) a (D-4)-form gauge field (think E&M, but with more indices). This theory has long been known to have solutions where 4 of the dimensions are non-compact and (D-4) of them correspond to directions on a sphere, whose size is stabilized by the energetics of curvature and a background Electric or Magnetic field.

More interestingly, we showed that some of the spacetimes that are solutions to this theory contain a four-dimensional universe that lives behind the event horizon of an extended object, a “p-brane” or “black brane,” that is embedded in a background D-dimensional spacetime. Moreover, there are mechanisms that dynamically give rise to such objects, thanks to the magic of quantum mechanics, and this leads to an explanation for why some number of extra dimensions became compact!

Sounds complicated, but you can actually go a long way towards understanding what we did by considering plain-old four dimensional black holes. If you are falling into a black hole, eventually you cross the event horizon, a spherical surface that denotes the point-of-no-return: once you get in, you can’t get out. Sadly for you, everyone knows that lurking in the interior of the black hole is a singularity, and your fate will be spaghettification or worse.

What if there was no singularity? By this, I don’t necessarily mean some quantum gravity resolution, but rather, what if the geometry was such that the radius of spheres became frozen at some value close to the value on the event horizon. In this case, you don’t die, but you are still suck inside of the black hole due to the event horizon. You also notice that It is not very spacious in there, because the black hole is of finite size. Effectively, two of the original four dimensions have become compactified on a sphere. Therefore, falling into this made-up black hole, you would experience two of the four dimensions compactifying!

Upping the number of dimensions to D, it is possible to find black branes that do exactly this – when you cross an event horizon, you enter a region in which some number of the extra dimensions have become compact. The number of compact dimensions is determined by the symmetry of the event horizon. If the event horizon has (D-4)-dimensional spherical symmetry, then the region inside of the black brane is effectively four dimensional. Further, the 4 dimensional region has a natural “slicing” into space and time, that yields a cosmology. The big-bang in this 4-dimensional cosmology corresponds to the event horizon of the black brane.

These black branes can be embedded in a D-dimensional de Sitter space, which has some very interesting properties itself. Most relevant for us is that energy conservation does not work in de Sitter space, since it has a finite temperature. This means that every once in a while, a fluctuation will occur that produces one of the black brane solutions, and therefore a 4-dimensional universe. This is a mechanism of dynamical compactification.

The devil is now in the details. First off, the brane needs to be charged under the gauge field for there to be one of these interesting solutions. For each value that the charge can take, a slightly different lower-dimensional universe will be produced, and if there are different types of gauge fields, then universes with different numbers of dimensions will be produced as well. There is a “landscape” of many possible lower-dimensional vacua, just like in string theory. Dynamical compactification will be happening all over the place in the D-dimensional de Sitter space, realizing all of these possibilities in different spacetime regions, and yielding what is referred to as a “multiverse.”

The zeroth order question is if any of these universes look like ours. This involves having an early time epoch of inflation and late-time evolution towards a universe dominated by a small cosmological constant. We found that the answer can be yes on both counts for the models we studied.

A more ambitious goal is then to ask if there is any reason that picks out the universe we observe. This is of course a scary path to walk down, fraught with numerous incarnations of the Anthropic monster, but is a necessary demon to face in a theory where the fundamental parameters vary in different spatiotemporal regions of the multiverse. Although we did not explore this question in depth, there are some suggestive hints. First of all, it is easier to get into a vacuum with a small positive cosmological constant than it is to get out. It is also easier to produce universes with a smaller value for the late-time cosmological constant, although it is much more likely to get a negative vacuum energy solution, which undergoes a crunch. Depending on the total number of dimensions, we also found some cases where the rates to produce four dimensional universes was highest. These questions will be interesting to address in the future.

So, next time you go falling into an event horizon, you can hold out the hope that you will simply be banished to a lower-dimensional universe!

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Here are some thoughts on something that has been bothering me for a while. How do we know the world is the way it is? Easy, a pragmatic person would say, just look and measure. We see a tree, a chair, a table; we hear the wind, music, people talking. We feel heat and cold against our skin. Once our brains integrate this sensorial information, we have a conception of what is real that allows us to function in the world. We know where to go, what to eat, what not to touch; we enjoy a good meal, a nice hug. But what happens when we go beyond our senses, using tools to extend our conception of reality? We don’t see galaxies with the naked eye (well, maybe Andromeda on a moonless, dry night) and much less a carbon atom. How do we know they are there, that they exist?

When Galileo showed his telescope to the Venetian senators in 1609, some refused to accept that what they saw was real. More recently, late in the 19th century, physicist and philosopher Ernst Mach refused to accept the existence of atoms, claiming they would never be seen and hence couldn’t be proven to exist. Mach and the Venetian senators were wrong. What we see through telescopes is, of course, perfectly real; we capture photons—particles of light—that a celestial body emits (or reflects, for planets and moons). If the source doesn’t emit in the visible and is so dim that we can’t capture photons between red and violet, we capture photons from radio or infrared radiation, no less real even though our eyes can’t see them. When atomic electrons jump from orbit to orbit, they also emit (or absorb) photons that can be detected by instruments or, in the case of certain transitions, by our eyes. The instruments we use in the study of natural phenomena are an extension of our senses. This amplification of reality is one of the most spectacular feats of science, allowing us to see beyond the visible. So far, so good.

The situation gets complicated when the complexity of the phenomenon forces us to filter the data, and we select to study only part of what is happening. Our brains, of course, do this all the time, what we call “focus”; otherwise, we would be flooded with such an absurd amount of sounds and images that we wouldn’t be able to do anything. When we look at a star with the naked eye or with an optical telescope, we only see part of it, what it emits in the visible. A complete view of the star would incorporate all of its emissions, in the infrared, ultraviolet, x rays, etc. This fact has a simple but, to my mind, profound consequence: our construction of reality, being necessarily filtered, is incomplete. We only know what we can measure.

In the case of elementary particle physics the situation is even more alarming. The Large Hadron Collider, for example, should start working this coming summer or early fall. In its full capacity, it should produce around 600 million collisions per second. This translates to about 700 megabytes per second of data, more than 10 petabytes (1015) per year. That’s more than a million hard drives, each with a gigabyte. To make sense of this flood of information, physicists have to filter the data, selecting events deemed “interesting.” This selection, in turn, is based on our current theories that speculate on what’s beyond the standard model of particle physics, that is, theories that speculate on stuff we don’t know is there. Although these theories are mostly pretty solid (the Higgs particle as universal giver of mass; extensions of the standard model using more than one Higgs, supersymmetry or/and more than three spatial dimensions…) they can only be confirmed through the very same experiments whose outcome they are trying to predict. Given this mechanism, there is a risk that unexpected phenomena, not predicted by any current theory and hence not included in the subset of collisions deemed interesting, will be eliminated by the data filtering process. In this case, and in a paradoxical way, the theories that we construct to amplify our view of physical reality will actually limit what we can know about nature.

And if you dropped the delimiter “American” from the question above, the winner would undoubtedly be Stephen Hawking. So we’re very happy to have a guest post from Kip, announcing an upcoming talk by Hawking.

Left to right: John Preskill, Kip Thorne, and Stephen Hawking.

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Stephen Hawking is coming to town – to Pasadena, that is.

Caltech, in Pasadena, California, is Hawking’s home away from home. Since 1991 he has spent roughly a month a year here as our Sherman Fairchild Distinguished Scholar. This year he flies in from his English home at the end of February, then heads off to Texas in early April.

He arrives with an entourage of five care givers to tend to his physical needs, one or two family members, several graduate students, and a “graduate assistant” who handles logistics and serves as general fixit-person for his computer system and mechanized wheel chair. His current chair is new and sophisticated. At the flick of a switch, its hydraulics can lift him up to a standing person’s eye level or slide him down near ground level for high-speed chases — he has been known to take pleasure from running over the toes of university presidents.

Hawking’s Pasadena sojourns are rather like Einstein’s in the 1930s. Caltech is an intellectual magnet – a crossroad for ideas about the cosmos and the fundamental laws of nature, which are Hawking’s passion. He contributes mightily to the ferment, and partakes. Our California night life (LA, not Caltech!) is also pretty good; and Hawking, like Einstein, is a party animal, only more so. During his annual month here, my own social life intensifies five-fold just from being his closest California friend. He loves opera, theater, jazz clubs, barbecues that he hosts in the patio of his Pasadena home, and dinners with fine wine – especially an Indian Feast prepared for him by Caltech undergraduates. Yes, we geeks can cook up a storm – well, not me, but the younger generation.

Conversation with Stephen is slow, about 3 words a minute, produced by Stephen moving a muscle in his face (imaged by a lens and photodetector) to control a cursor on his computer screen. It’s slow, but rewarding. You never know, until his sentence is complete, whether it will be a pearl of wisdom or an off-the-wall joke. Faster speeds are on the horizon: computer control via brane waves, without drilling a hole in his head (he’s opposed to that). But he resists changing technology, even without drilling, until forced to. “I can’t believe it’s as good as what I have.” (It actually is; my wife has a friend with ALS who proves it so.)

Most of Hawking’s Pasadena time is spent thinking, conversing, and working on projects. Jim Hartle drives down from Santa Barbara to continue their decades-long research collaboration on the birth of the Universe. Leonard Mlodinow, a Pasadena-based free-lance writer, toils with him on a book: in the past, A Briefer History of Time; now, their forthcoming The Grand Design. And there are drives to Hollywood to film for Star Trek or the Simpsons or the forthcoming Stephen Hawking’s Beyond the Horizon.

On each Pasadena visit, Hawking gives a lecture for the general public – always before in Caltech’s limited-seating Beckman Auditorium, but this year in the newly renovated Pasadena Convention Center, at 8PM, Monday March 9. “Why We [the human race] Should Go into Space” is his title. It’s an opportunity to see him in action, be immersed in his mind’s world, and – if last year’s lecture is any indication – participate in a happening. Tickets are available from the Caltech ticket office, (626) 395-4652, at $10 each.

The last time I saw Hawking speak to such a large audience, thousands, was in a converted railway station in Santiago Chile, soon after General Pinochet’s regime gave way to civilian rule. It was quite a show. Hawking made a grand entrance to rock music and charmed the crowd. The President of Chile and other civilian officials sat on one side of the giant stage, the military brass on the other, with enormous tension between them; they were hardly speaking to each other in those days. Only Hawking could bring them into the same room. His aura works magic. The next day the military flew us to Antarctica: a C130 cargo plane filled with TV cameras, journalists and physicists. It was August, the Antarctic winter, the first flight to Antarctica in more than a month due to winter storms. It was a Hawking Adventure, one among many. He lives life to the fullest. He will fly on a rocket into space soon.

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John Updike (1932-2009)

John Updike, one of the great American writers, died on Tuesday. The Cosmic Variance bloggers might seem to write incessantly, but they had nothing on him. Updike produced 26 novels, 9 poetry collections, and, it seemed, a short story in the New Yorker every other week. There was no aspect of culture that he did not know. Yesterday, I saw him celebrated on the sports page of the San Francisco Chronicle for his classic on Ted Williams’ last at bat, “Hub Fans Bid Kid Adieu”. We scientists should also acknowledge our gratitude and send our friends out to read his work.

Every particle physicist knows Updike’s poem “Cosmic Gall,” the number one popularization of neutrinos:

At night, they enter at Nepal
and pierce the lover and his lass
From underneath the bed …

Readers of Cosmic Variance will find much more interesting his 1986 novel Roger’s Version. In Chapter One, the scruffy fundamentalist computer science graduate student Dale Kohler walks into the office of the comfortably middle-aged Harvard professor of divinity Roger Lambert and shatters his worldview by explaining that new discoveries in physics and cosmology require intelligent design. The characters in the story that follows personify all points of view in the science versus religion debate, until — but I shouldn’t ruin the surprise.

People who are serious about literature claim that these works have merely intellectual interest. If you are in that group, there are also Updike novels that will move you with the depth of his empathy. His masterwork is the set of four Rabbit Angstrom novels, a thousand pages in all, one novel every ten years from 1960 to 1990. The greatest moments of Harry “Rabbit” Angstrom’s life came in high school, when he was a star basketball player in his small town in upstate Pennsylvania. When the first novel opens, that part of his life is already over. He has an uninspiring job, a tiny apartment, and a baby who dies in the first few pages. Harry has no introspection. The glow that surrounded him on the basketball court brings him women, and, one after another, they push him into all varieties of trouble. Harry’s wife Janice is tougher and recognizes that the two are stronger together than apart, but she cannot control his whims. In Rabbit, Run, he wanders in and out of his new marriage and an affair with a girl from the town. In Rabbit, Redux, he takes in a runaway teen and her drug habit. In Rabbit is Rich, he inherits his father-in-law’s Toyota dealership and samples the country-club life. In Rabbit at Rest, he tries to retire to Florida, but the bad choices of the past three books — and one astonishing new one — follow him. Harry also seduces his readers. We stay one step ahead of him in anticipating the next catastrophe, but we also watch through his eyes the panorama of America in Updike’s era.

If this is too heavy to carry, you could pick up the short, early novel The Centaur. A father, a high school science teacher, sacrifices himself for his son. It is a brief story, told with great pathos. But also, magically, just under the surface, the story unfolds as a Greek myth, and, in the end, the father, Updike’s father, ascends to the heavens.

It may not be true for those who blog, but those who put pen to paper will always be with us. Enjoy!

John Updike Image (c) Michael Mundy