We’re a little bit late here, but I wanted to note that Chinese physicist Fang Lizhi died on Friday in Arizona at the age of 76.

Fang’s research area was quantum cosmology, but he was most well-known for his political activism, fighting against repression in China. Originally a member of the Communist Party, he was expelled for protesting some of the government’s policies. The NYT obituary relates an amusing/horrifying story, according to which Fang attracted the government’s censure by co-authoring a paper entitled “A Solution of the Cosmological Equations in Scalar-Tensor Theory, with Mass and Blackbody Radiation.” Seems pretty innocuous from where we are sitting, but in Communist China the Big Bang model was considered to be a challenge to Engels’s idea that that the universe was infinite, and therefore was deemed heresy. Googling around brought me to this 1988 article in Contemporary Chinese Thought, which shows what Fang was up against. The abstract quotes Lenin, and says in all seriousness “with every new advance in science the idealists distort and take advantage of the latest results of physics to “prove” with varying sleights of hand that the universe is finite, serving the reactionary rule of the moribund exploiting classes.”

In the late 1980′s Fang helped organize resistance to China’s authoritarian regime, in the lead-up to the Tiananmen Square protests. He was fired from his job as a professor, and sought refuge in the American embassy. He was finally permitted to leave the country and emigrate to America in 1990. He finally settled down at the University of Arizona, but continued his work campaigning for human rights.

I’ve reached the cosmology part of my General Relativity (GR) course, and one of the early points that comes up is my traditional rant against confusing three very distinct concepts when thinking about the universe. Roughly stated, these are; What is the shape of the universe? Is the universe finite or infinite? and Will the universe expand forever or recollapse.

When we apply GR to cosmology, we make use of the simplifying assumptions, backed up by observations, that there exists a definition of time such that at a fixed value of time, the universe is spatially homogeneous (looks the same wherever the observer is) and isotropic (looks the same in all directions around a point). We then specialize to the most general metric compatible with these assumptions, and write down the resulting Einstein equations with appropriate sources (regular matter, dark matter, radiation, a cosmological constant, etc.). The solutions to these equations are the famous Friedmann, Robertson-Walker spacetimes, describing the expansion (or contraction) of the universe.

It is important to take a moment to emphasize what we have done here. GR is indeed a beautiful geometric theory describing curved spacetime. But practically, we are solving differential equations, subject to (in this case) the condition that the universe look the way it does today. Differential equations describe the local behavior of a system and so, in GR, they describe the local geometry in the neighborhood of a spacetime point.

Because homogeneity and isotropy are quite restrictive assumptions, there are only three possible answers for the local geometry of space at any fixed point in time – it can be spatially positively curved (locally like a 3-dimensional sphere), flat (locally like a 3-dimensional version of a flat plane) or negatively spatially curved (locally like a 3-dimensional hyperboloid). A given cosmological solution to GR tells you one of these answers around a spacetime point, and homogeneity then tells you that this is the same answer around every spacetime point. This is what we mean when we say that GR tells us about geometry – the shape of the universe – as depicted in the NASA graphic below.

This raises a very different question that is often confused with the one above. If our solution tells us that the universe is locally a 3-sphere (or flat space, or a hyperboloid) around every point, then does that mean it is a 3-sphere, or an infinite flat 3-dimensional space, or an infinite hyperboloid. This is really a question of topology – how is it connected up – which also answers the question of whether the universe is finite or infinite. To illustrate the point, suppose we have solved the cosmological equations of GR, and discovered that at every spacetime point, the universe is locally a flat 3-dimensional space. This is, by the way, what observations actually indicate our universe is like. Then, just off the top of your head, you can think of many different spaces with precisely this same property. One example is, of course, that the universe is indeed a flat, infinite 3-dimensional space. Another is that the universe is a 3-torus, in which if you were to fix time and trace out a line away from any point along the x, y or z-axis, you traverse a circle and come right back to where you started. This is a finite volume space, that is connected up in a very specific way, but which is everywhere flat, just like the infinite example. In two dimensions, one might visualize it as

Of course, I could have only made one or two directions into circles (leaving it still infinite in some directions), or made the space into a finite one with more than one hole, or any number of other possibilities.

This is the beauty of topology, but it is not something that solving the equations of GR tells us. Rather it is an extra input into our solutions. It is, however, something we can test, most precisely through measurements of the Cosmic Microwave Background radiation, as I may discuss in a later post.

Completely independent of questions of topology, the geometry of a given cosmological solution raises another issue that is often mixed up with those of geometry and topology. Suppose that the universe contains only conventional matter sources (regular matter, dark matter and radiation, say), and suppose you know (you might question whether this is truly possible) that this is all it will ever contain. Then the equations easily predict that, in the case of positive spatial curvature, an expanding universe will ultimately reach a maximum size and recollapse in a big crunch, whereas flat or negatively curved universes will expand forever. These are predictions of the destiny of the universe, and often lead to the following connection

However, as I made clear, there are some assumptions that go into the connection between geometry and destiny, and although these may have seemed reasonable ones at one time, we know today that the accelerated expansion of the universe seems to point to the existence of some kind of dark energy (a cosmological constant, for example), that behaves in a way quite different from conventional mass-energy sources. In fact, we know that for sources like this, once acceleration begins, it is easily possible for a positively curved universe, for example, to expand forever. Indeed, in the case of a cosmological constant, this is precisely what happens.

So the universe may be positively or negatively curved, or flat, and our solutions to GR tell us this. They may be finite or infinite, and connected up in interesting ways, but GR does not tell us why this is the case. And the universe may expand forever or recollapse, but this depends on detailed properties of the cosmic energy budget, and not just on geometry. Cosmological spacetimes are some of the simplest solutions to GR that we know, and even they admit all kinds of potential complexities, beyond the most obvious possibilities. Wonderful, isn’t it?

Driving to work yesterday, my local public radio station was talking about a recent incident in which a student at Fullerton Union High School was disqualified from a competition by an assistant principal. The student, asked onstage where he’d like to be in ten years, said he hoped that gay marriage would become legal and he could be married to someone he loved. The assistant principle thought this was outrageous and immediately pulled him from the competition. Most interesting to me were the uniformly astonished reactions from the radio voices — how could it be, in this age of anti-bullying efforts and growing acceptance of homosexuality, that an authority figure could act so callously? You mean to say that there are still grownups out there who are willing to say out loud that homosexuality is immoral?

There are. And if you want to know why, at least part of the answer can be found in several discussions popping up in my newsreader about what Jesus thought about homosexuality. Here’s a Christian mother who travels the difficult road from hatred to acceptance once she learns that her own son is gay. Here’s a theological debate between Ron Dreher and Andrew Sullivan on the precise degree to which sexuality should be considered sinful. And here’s a moving speech by Matthew Vines, a 21-year-old man who tries his best to argue that the traditional understanding of the Bible as strongly anti-homosexuality is mistaken (essentially because that would condemn gay people to being tortured and unloved, and surely the Bible wouldn’t be in favor of that). Personally I think Jesus probably didn’t approve of homosexuality, but since the Gospels were written decades after Jesus died, by people who probably had never met him, I admit the historical record is not exactly definitive. Maybe Jesus was extremely compassionate toward gay people, although that would have been quite out of character for messianic figures from first century A.D. Palestine, so had that been true it would have been worth an explicit mention. It’s an inevitable problem when you are committed to taking your moral cues from two-thousand-year-old semi-mythical stories about a charismatic preacher, rather than trying to found them on reason and reflection.

Which brings me to the Problem of Instructions. This is a challenge to the idea that belief in God is a plausible hypothesis to help us account for the world, much like the Problem of Evil but much less well known, possibly because (as far as I know) I made it up. I mentioned the Problem of Instructions in our recent debate, but I’ve never written it down, so here you go. (I have no doubt that analogous issues have been discussed by real theologians.)

Read the rest of this entry »

The LHC just saw its first collisions at 8 TeV, and all seems well. This should be an exciting year for the accelerator, and a film crew is documenting the action as part of a project called CERNPeople. It consists of a YouTube channel and a Google+ page, worth checking out. Throughout the year they’ll be putting up short videos in which they talk to the scientists and technicians about this and that. Here they ask about a perennial topic: competition between the experiments.

Via JenLuc Piquant’s twitter feed, here’s one time I’m not going to stick up for my colleagues in the social sciences: a misguided attempt to cast the search for empirical support as “physics envy.” It’s a New York Times Op-Ed by Kevin Clarke and David Primo, political scientists at the University of Rochester.

There is something rightly labeled “physics envy,” and it is a temptation justly to be resisted: the preference for reducing everything to simple and clean quantitative models whether or not they provide accurate representations of the phenomena under study. The great thing about physics is that we study systems that are so simple that it’s quite useful to invoke highly idealized models, from which fairly accurate quantitative predictions can be extracted. The messy real world of the social sciences doesn’t always give us that luxury. The envy becomes pernicious when we attack a social-science problem by picking a few simple assumptions, and then acting like those assumptions are reality just because the model is so pretty.

However, that’s not what Clarke and Primo are warning against. Their aim is at something altogether different: the idea that theories should be tested empirically! They write,

Many social scientists contend that science has a method, and if you want to be scientific, you should adopt it. The method requires you to devise a theoretical model, deduce a testable hypothesis from the model and then test the hypothesis against the world…

But we believe that this way of thinking is badly mistaken and detrimental to social research. For the sake of everyone who stands to gain from a better knowledge of politics, economics and society, the social sciences need to overcome their inferiority complex, reject hypothetico-deductivism and embrace the fact that they are mature disciplines with no need to emulate other sciences…

Unfortunately, the belief that every theory must have its empirical support (and vice versa) now constrains the kinds of social science projects that are undertaken, alters the trajectory of academic careers and drives graduate training. Rather than attempt to imitate the hard sciences, social scientists would be better off doing what they do best: thinking deeply about what prompts human beings to behave the way they do.

Sorry, but “thinking deeply” doesn’t cut it. People are not especially logical creatures, and we’re just not smart enough to gain true knowledge about the world by the power of reason alone. That’s why empiricism was invented in the first place, and why it’s been so spectacularly successful over the last few centuries.

Clarke and Primo seem to confuse “the need for empirical testing” with “the need for every model proposed to be backed up by data before it gets published.” If they had stuck to rejecting the latter narrow idea, they would have had a decent case. Certainly we physicists don’t require that every model be supported by data before it is published — otherwise my CV (and those of most of my friends) would be a lot shorter! But we all agree that the ultimate test of an idea is a confrontation with data, even if a theory might be too immature for that confrontation to take place just yet.

Zooming around the LHC, colliding at unprecedentedly high energies: 8 trillion electron volts total, in comparison with last year’s 7 TeV. The ultimate goal is to reach an amazing 14 TeV, although that won’t happen soon — the plan is to shut down for quite a while after the end of this year’s run, tighten the gaskets and so forth, and then resume the march to higher and higher energies.

This year’s run is all about luminosity, i.e. getting as many collisions in the can as they can. Last year they reached about 5 inverse femtobarns, while this year they’re shooting for 15 inverse femtobarns. Yes, those are the goofiest units in all of physics. Think of it this way: imagine the protons entering a detector are shooting at a tiny target with some fixed size, measured in units of area. Then we can measure the luminosity by counting the number of protons passing through that area in a fixed moment of time: i.e., the number of protons per square centimeter per second. That’s at any one moment; if we integrate up over the course of a year, the “per second” disappears and leaves us with the total number of protons that have passed through the target area, i.e. a certain number of protons per square centimeter. But that number would be enormously huge, so rather than using square centimeters, particle physicists like to use “barns,” defined as 10^-24 cm². (Broad side of a barn, get it?) But even measuring the luminosity in inverse barns would be really big, so they go for inverse femtobarns (1 fb = 10^-39 cm²). Long story short: 10 inverse femtobarns is equivalent to 10⁴⁰ protons passing through a 1 cm target area. (That’s much larger than the number of collisions — to get the number of collisions for any particular process, you need to multiply by the cross-section for that process, which is often quite tiny. That’s why particle physics is hard! Still, there will be a buttload of collisions.)

Anyway, I’m pretty sure the LHC is back to colliding protons after this year’s winter shutdown, and they’re smashing together at 8 TeV. But to be honest my only hard evidence is from Twitter, where the ATLAS collaboration has tweeted this image.

Meanwhile, results are still coming out from last year’s run. Sadly, they’re doing a great job at constraining possible new physics, but no convincing discoveries as yet. Here’s a recent result from LHCb, the experiment that looks at decays of mesons containing b quarks. This plot is from David Straub, from a talk at Moriond, based on this paper.

Horizontal axis is the fraction of time (the branching ratio) bottom/strange mesons decay into two muons, while the vertical axis is the fraction of time bottom/down mesons do the same thing. These numbers have specific predictions within the good old Standard Model, but it’s very easy for new physics such as supersymmetry to enhance the numbers quite a bit. LHCb has put an upper limit on both quantities, which rules out all the gray area of the plot, leaving only the colorful part at the bottom left. The colors correspond to possible predictions in different versions of supersymmetry. As you see, it would have been very easy to have detected a substantial deviation from the Standard Model by now, but no such luck. This doesn’t mean some other version of supersymmetry isn’t right, just that we’ll have to try harder. No question that a proper update of our likelihood functions will have to decrease the chance that we expect fo find SUSY at the LHC compared to what we would have thought a few years ago, however. This is why the march to higher energies will be so important.

If you want to ask some detailed questions about the accelerator and the experiment, the CMS and ATLAS collaborations are having a Google+ hangout this Wednesday that you are welcome to join. It starts at 7 am Los Angeles time, so I’m unlikely to make it, but let us know if anyone here participates.

This semester I’m teaching General Relativity, and as part of discussing gravitational waves, this week I briefly discussed pulsars. It was quite timely therefore when I learned of a new proposal that pulsars may ultimately provide a perfect navigation system for spacecraft far from Earth.

Here on Earth, the Global Positioning System (GPS) gives us a highly accurate way of determining position, and many of us now use hand-held devices every day to help with directions. These work because GPS satellites provide a set of clocks, the relative timings of the signals from which can be translated into positions. This is, by the way, another place where both special and general relativity are crucial to how the system works. Out in deep space, of course, our clocks are unfortunately useless for this purpose, and the best we currently can do is by comparing the timing of signals as they are measured back on Earth by different detectors. But the accuracy of this method is limited, since the Earth is a finite size, and our terrestrial detectors can therefore only be separated by a relatively small amount. The further away a spacecraft is, the worse this method is.

What Werner Becker of the Max-Planck Institute for Extraterrestrial Physics in Garching has realized (and announced yesterday at the UK-Germany National Astronomy Meeting in Manchester), is that the universe comes equipped with its own set of exquisite clocks – pulsars – the timing of which can, in principle, be used to guide spacecraft in a similar way to how GPS is used here on Earth. Of course, it isn’t quite as simple as all that.

A significant obstacle to making this work today is that detecting signals from the pulsars requires X-ray detectors that are compact enough to be easily carried on spacecraft. However, it turns out the relevant technology is also needed by the next generation of X-ray telescopes, and should be ready in twenty years or so. Perhaps one day our spacecraft will map their routes through the cosmos thanks to yet another spinoff from basic research.

Adrienne Rich, one of the leading American poets of the 20th century, died on Tuesday at the age of 82. Anything you read about her will emphasize her identity as a feminist and a lesbian, which is perfectly appropriate, but don’t let it get in the way of the fact that she was an amazingly inventive and affecting poet. She was also widely admired as a lecturer and essayist. (And I can only imagine she would have cringed at the line in the NYT obit where it says she “burst genteelly onto the scene as a Radcliffe senior in the early 1950s.” Is bursting something one can do genteelly?)

This is the ending of “Planetarium,” about Caroline Herschel; the entire poem is here.

I have been standing all my life in the
direct path of a battery of signals
the most accurately transmitted most
untranslatable language in the universe
I am a galactic cloud so deep           so invo-
luted that a light wave could take 15
years to travel through me            And has
taken           I am an instrument in the shape
of a woman trying to translate pulsations
into images            for the relief of the body
and the reconstruction of the mind.

How best to represent data is a question that physicists spend a lot of time thinking about. While theorists like myself are not the primary examples of this, I do find it striking when I stumble upon an example of data visualization that gets the pertinent facts across in a significantly clearer way than I’ve seen before.

For a terrific example of this, see the Carbon Map. The idea of Cartograms has been around for a while, of course, and in particular, I recall them being used extensively here in the US to represent the voting tendencies of regions of the country in the lead up to the 2008 presidential election. For example, here’s one in which the sizes of counties have been rescaled according to their population.

What is nice about the Carbon Map is that it is an animated cartogram, in which one can choose different datasets and have the world map dynamically rescale to represent the new data. The screen shot below is of the scaling of areas by population, but as you can see there are other possibilities.

Obviously, this example (the first I’ve seen) is meant to get across a particular point, but that isn’t what I’m discussing here. What impressed me is the clarity and power of representing the data in this way. I’m sure there are many other ways in which this technique would be useful, some of them in physics and astronomy.

Took a little work, but the spark of human willpower was ultimately able to overcome the stubborn resistance of technology, and the video from our science/religion debate at Caltech on Sunday is finally up. Michael Shermer and I took on Dinesh D’Souza and Ian Hutchinson. Short version: we won, but judge for yourself if you want to sit through all two hours.

YouTube comments — always an enlightening read — seem to be mostly about Dawkins and Hitchens, although I don’t remember either of them being there.