An infinitely good read

Via CP at the Knight Science Journalism Tracker (a highly recommended site for general science news) comes the suggestion for this excellent article by Science News editor Tom Siegfried: Success in coping with infinity could strengthen case for multiple universes.

Despite the strangeness and fanciful-seemingness of some of the ideas suggested in the title and the article itself, it's a pretty good summary of some current thinking about life, the universe, and everything. It's even understandable on one level – as long as you don't insist on knowing the mathematical details of things like string theory and cosmic inflation.

In outline, some reputable physicists, including some of the originators of inflationary cosmology, are arguing that they may have mathematical "proof" that there must exist multiple universes. The argument is based on the idea that without an infinite number of existing universes, similar in some respects to ours, yet possibly different in radical ways, the probability is nil that all the characteristics of our universe could be so precisely tuned as to allow the existence of sentient life.

While some may question whether sentient life does in fact exist in our universe, just take that as an assumption for the present. The idea just described is sometimes known as the Anthropic Principle. There are several forms of this principle, and all are rather controversial, in some degree or another, in the minds of people (such as physicists and philosophers) who think about such things.

Tom Siegfried is reporting (among other things) that physicists like Alan Guth and Andre Linde think they may have found a way to prove mathematically that an infinity of multiple universes must exist in order to explain the highly unlikely existence of sentient life in the one universe we know about.

Using the word "unlikely" here means that what's involved in a rigorous argument has to use the mathematical theory of probability. And to employ that theory, it is necessary to define what's called a "measure", which is a way of assigning a specific number to the relative size of a subset of a larger set. What has to be done, to support a mathematical argument for some validity in an application of the Anthropic Principle for deducing the necessity of multiple universes, is to find a suitable measure that makes it exceedingly unlikely that the universe we are aware of, with its particular forms of life as we know them, could exist if there were only one universe (or a finite number of them).

There are certain unobvious problems that have to be dealt with, for example the problem of "Boltzmann brains". That refers to something exactly like a human brain that could arise purely by chance in a universe that's infinitely large and infinitely old.

There are physicists who object violently to the idea of the Anthropic Principle, in any form, as an explanation for why the universe we can perceive seems to have the properties which allow the existence of sentient life. An alternative that many of these physicists prefer is the existence of mathematical principles that uniquely determine the properties of our universe – rather than have it all be a matter of chance, which leads to an infinite number of universes, each with very different characteristics and physical laws. Einstein, too, was a believer in the existence of deterministic principles, long before inflation was even thought of, but also before it was recognized just how finely-tuned a universe has to be to support life.

Unfortunately, a huge problem remains with this deterministic view, that our universe, if it's one of at most a finite number of other possible universes, can have the life-friendly properties we (think we) observe. Namely, why should mathematical principles dictate exactly this kind – and only this kind – of universe? Yet if such principles could allow more than a finite number of other universes, we'd be back in the multiple universe scenario, whether or not it's the scenario string theory seems to call for.

Further reading

Boltzmann brains and the scale-factor cutoff measure of the multiverse – August 2008 arXiv paper by Alan H. Guth, Andrei Linde, Alexander Vilenkin, and others

Life, the Universe, and Everything: A Conference Looks to Ultimate Origins – Sky and Telescope report on the conference

Searching for dark energy... at the South Pole

Not all experimental astrophysical studies require elaborate, incredibly expensive equipment deployed at the L2 Sun-Earth Lagrangian point, like WMAP. A lot can be done with a microwave antenna just 10 meters across... if it's located at the South Pole.

Cosmologists Probe Mystery Of Dark Energy With South Pole Telescope

What can the SPT tell us about the past and future of dark energy? John E. Carlstrom, director of KICP and the S. Chandrasekhar Distinguished Professor in Astronomy and Astrophysics at the University of Chicago, says the telescope is examining clusters of galaxies to learn what role dark energy played in their evolution. “One of the important things we need to learn about dark energy is what influence it has had on structure,” Carlstrom says. If scientists can learn how the density of clusters changed over time, he says they can determine “constraints on the equation of state of dark energy.” That is, they can get a more precise idea of whether dark energy is taking us toward a big rip, a big crunch or something in between.

The telescope is looking specifically for the Sunyaev-Zel’dovich (SZ) effect, a distortion of the CMB radiation caused by the highly energized gas of galaxy clusters. When photons originating from the CMB traverse the clusters, they interact with electrons and tend to scatter, creating slight variations in temperature -- shadows against the microwave background – that the SPT detects with a battery of 1,000 sensors chilled to near absolute zero.

The SPT will survey about a fifth of the entire southern sky and is expected to detect thousands of clusters. Analyzing follow-up data from optical telescopes, the scientists will determine the mass, distance and age of the clusters. They will then map the clusters in space and time to see how their density and structure evolved over billions of years under the competing pulls of gravity and dark energy. They hope to learn how much power dark energy exerted in the early universe, how it evolved to dominate the universe now, and by extension, how much power it may wield in the future.

But the SPT isn't adapted only for studies of dark energy. As a sensitive microwave telescope, it can also make detailed observations of the cosmic microwave background, much as WMAP does.

The SPT’s activity will not end with this survey of galaxy clusters. Another project in the works will use the telescope to scan the CMB for tiny fluctuations in its polarization. Like visible light, the microwave radiation from the Big Bang has waves moving in electromagnetic fields at different angles, some up-and-down and other side-to-side. Observations with another South Pole instrument, the degree angular scale interferometer (DASI), have confirmed that the CMB is polarized as expected from prevailing theories about the physics of the Big Bang. Researchers now want to use the more sensitive SPT to look for minute variations in the CMB polarization that mark the presence of huge gravity waves.

Stephan Meyer, associate director of KICP and Professor in Astronomy and Astrophysics at the University of Chicago, says these waves are “a reasonable fraction of the size of the universe” in length and would have been generated in the “inflationary epoch” of the Big Bang. This was the time when the universe was just 10^-50 seconds old and matter had not yet coalesced into neutrons and protons. “We don’t really understand the physics of that era,” Meyer says. A new set of sensors, able to detect polarization as well as heat, is being built by the University of Chicago and should be ready for installation on the SPT by the austral summer (the northern winter) of 2009-10.

Tags: dark energy, cosmic inflation

Inflation and the cosmic microwave background

About three weeks ago I wrote a little about the cosmic microwave background (CMB), and talked about writing more. So here's a little more. The CMB is microwave radiation we can (almost) literally "see" even though it originated only about 350,000 years after the big bang. (I'll explain more in a minute about what "originated" means in this context.)

There are a number of things very wonderful and remarkable about the CMB. Not only is it one of the major pieces of evidence supporting the big bang theory in general, but it also gives us much information about things as diverse as the relative proportions of ordinary matter and dark matter in the universe, the overall curvature of the universe ("flat", "convex", or "concave"), and the ratio of the number of baryons (protons and neutrons) to photons in the universe.

Further, of particular concern here, the CMB provides a means of testing a theory – the theory of cosmic inflation – that describes a much different period of time than that of the CMB itself, a period of time that began only about 10^-35 seconds after the big bang itself. The theory of inflation comprises a range of models describing what may have happened at that time. If there is any truth at all to the theory, the CMB can help narrow the range of acceptable models.

I have a couple of older articles on this from back in March/April here and here. These deal with the announcement back then of analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP) that, among several other things, gave the first reasonable evidence for inflation.

Rather than dive right away into further explanation of that, I'm going to refer you first to this excellent recent article on the subject by Sean Carroll: Reconstructing Inflation.

What's that, you say? It sounds impressive, but you don't quite follow the details? OK, let's step back for a moment and review the basics. The picture below is a graphical representation of the main data obtained from WMAP:

This picture shows slight variations in temperature across the entire sky, at microwave frequencies, where blue represents coolest and red represents warmest. The variations are actually very small: the whole range is ± 200 microKelvins (millionths of a degree K).

Temperature differences correspond directly to differences in matter density – because a gas under higher pressure is warmer and denser than the same gas under lower pressure (the "combined gas law"). So what we see here are minute ripples of higher and lower pressure in the matter of the universe at roughly 350,000 years after the big bang. What has caused these pressure waves? Carroll's article explains

The same basic mechanism works in both cases — quantum fluctuations (due ultimately to Heisenberg’s uncertainty principle) at very small wavelengths are amplified by the process of inflation to macroscopic scales, where they are temporarily frozen-in until the expansion of the universe relaxes sufficiently to allow them to dynamically evolve.

The spots and blotches you see in this picture are shadows on the wall, as it were, of quantum fluctuations that actually occurred 10^-35 seconds after the big bang. At first, in a period that lasted perhaps only 10^-33 seconds, these fluctuations were inflated at an incredible rate. Thereafter, they continued to expand along with the rest of spacetime itself, until we see them projected on the CMB wall 350,000 years later.

To be more precise, we should note that this metaphorical CMB "wall" did not form at some single precise time. Instead, the CMB itself is a result of most of the hydrogen and helium matter in the early universe making the transition from an ionised plasma to an ordinary gas of neutral atoms, as free electrons were "captured" by the hydrogen and helium ions. Consider, for simplicity, just the hydrogen. It takes 13.6 eV (electron volts) of energy to separate an electron from a hydrogen atom. In the early universe when the typical photon had much more than this energy, atomic hydrogen could not exist for long, as most passing photons could "liberate" the electrons. But when the energy of the typical photon dropped, as the universe expanded, to the equivalent of around 13.6 eV, hydrogen atoms became stable for longer periods of time. This is known as the period of "recombination" (even though prior to this, protons and electrons had never been in a "combined" state). Once there was a lot of atomic hydrogen, photons of the most common energy levels "scattered" from the atomic hydrogen, and the universe was somewhat opaque to those photons.

But as the temperature dropped further, most photons did not have enough energy to liberate electrons from hydrogen atoms. So most photons ceased to scatter from atomic hydrogen, and the universe effectively became transparent again. Although this happened over a relatively short period of time, it was not instantaneous. By the time that most hydrogen was in an unionized state, a typical photon never again scattered off a hydrogen atom. So around any present observer, there is a "surface of last scattering". Assuming what are currently considered the most likely cosmological parameters, this corresponds to a time about 13.3 billion years ago (equivalent to a red shift of about 1100), about 350,000 years after the big bang. This surface of last scattering is what we see today as the CMB. The temperature of the universe at this time of last scattering was about 3000° Kelvin, but due to the subsequent expansion of the universe, the CMB photons now have an energy that peaks around 2.725° K, in the microwave part of the spectrum.

There is another way to represent the WMAP data for the CMB. You've probably seen it in some form. (It's in Carroll's article, if you read that.)

The vertical scale on the left is a measure of the amplitude of temperature fluctuations. The top and bottom scales are measures of angular size. 90°, for instance, is one fourth of the whole sky. The "multipole moment" (l) is an integer that corresponds to an angular measure of 180°/l. So, for instance, the peak on the above graph occurs around l=200, which is slightly less than 1°. For comparison, the angular size of the full moon viewed from earth is about .5°. What the graph is saying, roughly, is that strongest temperature fluctuations (spots in the picture above the graph), if you could see them with your naked eyes, are almost twice the angular size of a full moon. (Astrophysicists use multipole moments, since they are the relevant identifiers of "spherical harmonic" functions that are used to construct a series representation of the function which describes theoretical temperature variations, similar to the way that a Fourier series can represent a function of one real variable.)

The small dots on the graph are WMAP measurements for various values of l. They come with error bars, which are mostly too small to see, because the WMAP measurements were mostly pretty precise. The red line through the measured values is the theoretically predicted values, assuming that the temperature variations are actually the result of quantum fluctuations that occurred in the inflationary period. The locations of the two peaks to the right of the main peak are especially important, and they correspond fairly well to theoretical predictions.

Carroll's article explains how there are actually two kinds of perturbations we might potentially observe in measured quantities: "scalar" and "tensor", reflecting the fact that Einstein's equation describing gravity waves (which result from the inflation-era quantum fluctuations) is a tensor differential equation. Further, all that we can readily measure from the WMAP data are scalar perturbations:

To date, we are quite sure that we have detected the influence of scalar perturbations; they are responsible for most, if not all, of the temperature fluctuations we observe in the Cosmic Microwave Background. We’re still looking for the gravity-wave/tensor perturbations. It may someday be possible to detect them directly as gravitational waves, with an ultra-sensitive dedicated satellite; at the moment, though, that’s still pie-in-the-sky (as it were). More optimistically, the stretching caused by the gravity waves can leave a distinctive imprint on the polarization of the CMB — in particular, in the type of polarization known as the B-modes. These haven’t been detected yet, but we’re trying.

Problem is, even if the tensor modes are there, they are probably quite tiny. Whether or not they are substantial enough to produce observable B-mode polarization in the CMB is a huge question, and one that theorists are presently unable to answer with any confidence.

The WMAP experiment was capable of studying polarization of CMB microwaves only rather crudely. But a new experiment is due for launch very soon (early 2007) in the form of the European Space Agency's Planck mission. Considering that it took several years to analyze WMAP data, we may not have better information right away – but it won't be too long, if everything goes reasonably well.

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Further information about CMB:

Wilkinson Microwave Anisotropy Probe

NASA web site of WMAP, containing background information, images, and graphs.

Wayne Hu's Home Page

One of the best collections of CMB information, including an introduction, explanation of the physics, and discussion of CMB polarization.

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Tags: astrophysics, cosmology, cosmic microwave background, CMB, Microwave Anisotropy Probe, WMAP, cosmic inflation