Guest Post

The lure of blogging is strong. Having guest-posted about problems with eternal inflation, Tom Banks couldn’t resist coming back for more punishment. Here he tackles a venerable problem: the interpretation of quantum mechanics. Tom argues that the measurement problem in QM becomes a lot easier to understand once we appreciate that even classical mechanics allows for non-commuting observables. In that sense, quantum mechanics is “inevitable”; it’s actually classical physics that is somewhat unusual. If we just take QM seriously as a theory that predicts the probability of different measurement outcomes, all is well.

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. …

Guest Post: Tom Banks on Probability and Quantum MechanicsRead More »

Following the guest post from Tom Banks on challenges to eternal inflation, we’re happy to post a follow-up to this discussion by Don Page. Don was a graduate student of Stephen Hawking’s, and is now a professor at the University of Alberta. We have even collaborated in the past, but don’t hold that against him.

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. …

Guest Post: Don Page on Quantum CosmologyRead More »

Now that we’ve softened you up by explaining a bit about eternal inflation and its puzzles, we’re very happy to host a guest post by Tom Banks in which he really hits on some of these problems hard.

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. …

Guest Post: Tom Banks Contra Eternal InflationRead More »

I tell everyone I meet that we are at the dawn of the Dark Matter Decade. Usually they slowly back away, but I’m pretty persistent. Our technology has reached the point that we have an excellent chance of actually detecting most of the matter in the universe for the first time.

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’ve been talking about life quite a bit here recently at Cosmic Variance, and it’s always fun to talk about areas in which one has absolutely no professional expertise. But it’s also fun to bring in experts, which is why we’re happy to welcome Caleb Scharf as a guest blogger. Caleb is Director of Astrobiology at Columbia University, author of a textbook on the subject, an recently jumped into blogging. In this post he reminds us that we’re still learning a lot about the forms of life right here on Earth — knowledge that will be invaluable as we search for it elsewhere.

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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.