Science

In the comments to Mark’s post about the embarassment being caused to the U.S. by the creationism trial in Dover, a scuffle has broken out over another deep question: does the Earth go around the Sun? See here and here and here.

It’s actually a more subtle question than you might think. The question is not “Was Ptolemy right after all?”, but rather “in the context of modern theories of spacetime, is it even sensible to say `X goes around Y,’ or is that kind of statement necessarily dependent on an (ultimately arbitrary) choice of coordinate system?”

You’ve come to the right place for this one; biologists can have their fun demolishing creationism, but we’re the experts on the whole geocentrism/heliocentrism thing. The answer, of course, does indeed depend on what one means by “move around,” and in particular the comments refer to the notion of a “reference frame.” I can think of at least three different things one might mean by that phrase. First there is the idea of a “global reference frame.” By this we mean, set up some perpendicular axes (some choice of coordinates x, y, and z) locally, right there in the room where you are sitting. Now extend these coordinates globally throughout space, by following straight lines and keeping everything appropriately perpendicular. That would be a global reference frame. (I am implicitly assuming that the coordinates are “Cartesian,” rather than using polar coordinates or some such thing — no reason to contemplate that particular complication.)

The second notion is that of an “inertial reference frame.” Inertial frames are actually a subset of all possible global frames; in particular, they are the global frames in which free (unaccelerated) particles appear to move on straight lines. Basically, this simply means that we allow the coordinate axes to float freely, as would gyroscopes in free-fall, rather than rotating them around. Newton figured out long ago that we could decide whether we were in an inertial frame or not by examining whether the water in a bucket that was stationary with respect to our frame began to creep up the sides (as it would if our bucket were rotating with respect to a really inertial frame).

Finally, we have the more flexible notion of a “coordinate system.” Unlike a global frame or the even-more-restrictive inertial frame, a coordinate system can be set down throughout space in any old way, so long as it assigns unique coordinates to each point. No mention is made of extending things along straight lines or keeping angles perpendicular; just put down your coordinates like a drunken sailor and be done with it.

Now what does all this pedantic geometry have to do with the Earth going around the Sun? Well, what Copernicus was really saying was that there is no inertial reference frame in which the Earth is stationary at the center and the Sun moves in a circle around it. Of course we could still imagine some global frame with the Earth stationary at the center; in fact, such geocentric reference frames are often quite useful. But it wouldn’t be inertial, as we could easily tell by the existence of Coriolis forces (as measured for example by Foucault’s pendulum). That is the sense in which it’s “really” the Earth that goes around the Sun, not vice-versa.

But now comes along Einstein and general relativity (GR). What’s the situation there? It actually cuts both ways. Most importantly, in GR the concept of a global reference frame and the more restrictive concept of an inertial frame simply do not exist. You cannot take your locally-defined axes and stretch them uniquely throughout space, there’s just no way to do it. (In particular, if you tried, you would find that the coordinates defined by traveling along two different paths gave you two different values for the same point in space.) Instead, all we have are coordinate systems of various types. Even in Newtonian absolute space (or for that matter in special relativity, which in this matter is just the same as Newtonian mechanics) we always have the freedom to choose elaborate coordinate systems, but in GR that’s all we have. And if we can choose all sorts of different coordinates, there is nothing to stop us from choosing one with the Earth at the center and the Sun moving around in circles (or ellipses) around it. It would be kind of perverse, but it is no less “natural” than anything else, since there is no notion of a globally inertial coordinate system that is somehow more natural. That is the sense in which, in GR, it is equally true to say that the Sun moves around the Earth as vice-versa.

On the other hand, sometimes one is able to make useful approximations, and there’s no reason to forget that. In particular, gravity in the Solar System is extremely well described as “flat spacetime (as in special relativity) plus a small perturbation.” From this perspective, we can very well define inertial frames in the flat background spacetime on top of which gravity is a tiny perturbation. And in those frames, it’s the Sun that is basically stationary and the Earth that is truly moving. So even the most highly sensitive general-relativists would not complain if you said that the Earth moved around the Sun, unless they hadn’t yet had their coffee that morning and were feeling especially confrontational.

Tune in tomorrow for a detailed examination of “what goes up, must come down.”

Brian Greene has an article in the New York Times about Einstein’s famous equation E=mc². The relation between mass and energy was really an afterthought, and isn’t as important to physics as what we now call “Einstein’s equation” — R_μν – (1/2)Rg_μν = 8πGT_μν, the relation between spacetime curvature and stress-energy. But it’s a good equation, and has certainly captured the popular imagination.

One way of reading E=mc² is “what we call the `mass’ of an object is the value of its energy when it’s just sitting there motionless.” The factor of the speed of light squared is a reflection of the unification of space and time in relativity. What we think of as space and time are really two aspects of a single four-dimensional spacetime, but measuring intervals in spacetime requires different procedures depending on whether the interval is “mostly space” or “mostly time.” In the former case we use meter sticks, in the latter we use clocks. The speed of light is the conversion factor between the two types of measurement. (Of course professionals usually imagine clocks that tick off in years and measuring rods that are ruled in light-years, so that we have nice units where c=1.)

Greene makes the important point that E=mc² isn’t just about nuclear energy; it’s about all sorts of energy, including when you burn gas in your car. At Crooked Timber, John Quiggin was wondering about that, since (like countless others) he was taught that only nuclear reactions are actually converting mass into energy; chemical reactions are a different kind of beast.

Greene is right, of course, but it does get taught badly all the time. The confusion stems from what you mean by “mass.” After Einstein’s insight, we understand that mass isn’t a once-and-for-all quantity that characterizes an object like an electron or an atom; the mass is simply the rest-energy of the body, and can be altered by changing the internal energies of the system. In other words, the mass is what you measure when you put the thing on a scale (given the gravitational field, so you can convert between mass and weight).

In particular, if you take some distinct particles with well-defined masses, and combine them together into a bound system, the mass of the resulting system will be the sums of the masses of the constituents plus the binding energy of the system (which is often negative, so the resulting mass is lower). This is exactly what is going on in nuclear reactions: in fission processes, you are taking a big nucleus and separating it into two smaller nuclei with a lower (more negative) binding energy, decreasing the total mass and releasing the extra energy as heat. Or, in fusion, taking two small nuclei and combining them into a larger nucleus with a lower binding energy. In either case, if you measured the masses of the individual particles before and after, it would have decreased by the amount of energy released (times c²).

But it is also precisely what happens in chemical reactions; you can, for example, take two hydrogen atoms and an oxygen atom and combine them into a water molecule, releasing some energy in the process. As commenter abb1 notes over at CT, this indeed means that the mass of a water molecule is less than the combined mass of two hydrogen atoms and an oxygen atom. The difference in mass is too tiny to typically measure, but it’s absolutely there. The lesson of relativity is that “mass” is one form energy can take, just like “binding energy” is, and we can convert between them no sweat.

So E=mc² is indeed everywhere, running your computer and your car just as much as nuclear reactors. Of course, the first ancient tribe to harness fire didn’t need to know about E=mc² in order to use this new technology to keep them warm; but the nice thing about the laws of physics is that they keep on working whether we understand them or not.

Could we just agree to tell the truth about this from now on? The New York Times has an interesting story by Cornelia Dean on the training that museums have started to give their docents and employees on how to deal with creationists. A sad commentary on our current state of affairs that such training is becoming necessary, but probably nobody reading this blog is surprised.

But as a supplement to the article, the Times reprints a FAQ from a pamphlet handed out by the Museum of the Earth in Ithaca, N.Y. It includes the following question:

Is evolution ‘just a theory’? A “theory” in science is a structure of related ideas that explains one or more natural phenomena and is supported by observations from the natural world; it is not something less than a “fact.” Theories actually occupy the highest, not the lowest, rank among scientific ideas. … Evolution is a “theory” in the same way that the idea that matter is made of atoms is a theory.

This is right in spirit, but the truth is not so very scary or technical that we can’t just fess up to it. The truth is that the hierarchy of “hypotheses” and “theories” and “laws” and “facts” that many people are taught in elementary school (or wherever) has absolutely no relationship to how real scientists use those words. Which is, that they are completely inconsistent and sloppy with their use. There is no procedure by which an ambitious young Hypothesis accumulates some promising support, and is brought up before the Most Supreme Council of Learned Scientists to be promoted to a Theory.

The reality of the situation is that it’s a mess. I can invent a half-baked idea tonight and call it a “model” or a “theory” and nobody cares, or would even notice. The Standard Model of Particle Physics is much closer to objective truth than Newton’s Law of Universal Gravitation, and the General Theory of Relativity is somewhere in between.

And “facts”? Eavesdrop on some scientists at work. You will go years without hearing any of them talk about “facts.” They’ll talk about data, and measurements, and observations, and experiments — those are things with identifiable meanings that we can work with. But call something a “fact” and you’re making some absolute metaphysical claim that isn’t the kind of thing scientists like to do. Likewise “proof.” Mathematicians and logicians, who deal with abstract symbols independent of any connection to nature, prove things. Scientists don’t. They figure out that certain beliefs should be held with greater and greater confidence, but proving something is simply outside the domain of science.

Which does bring us to the one almost-subtle point in this generally easy-to-understand business. Science never gets anything 100% right; it is always working on a better understanding, improving on the best current theory (or model, or whatever). But it does get some things right enough. The Big Bang, the round earth, Newton’s Laws, the Standard Model, natural selection — none of these is “proven” correct, but they are all correct, within certain domains of validity. There comes a point when, even though you can never (even in principle) prove an idea to be a fact, it becomes well-enough established that maintaining a skeptical attitude is a sign of crackpottery, not wisdom.

So let’s just quit the charade and let the unwashed masses in on the truth as far as “theory” is concerned. It’s a shorthand term for a model of some part of nature — but the label implies absolutely nothing about how true that model is. (The phlogiston theory didn’t stop being a theory once we knew it wasn’t true.) What matters isn’t whether we label something a “theory” or a “law” or a “fact,” it’s whether we label it “right” or “wrong.” As in, Darwin was “right,” the creationists are “wrong.”

Science magazine has a nice article about dark energy by Adrian Cho. But you can’t read it unless you subscribe. Except that the nice folks at UC Davis have decided that the article is nice publicity for Tony Tyson and the Large Synoptic Survey Telescope, so they’ve put the article online for free. See Mark’s post for some of the theoretical background.

The LSST is an ambitious project — a proposed giant telescope with a wide-field camera that scans the sky in real time. Every three nights it will complete a survey of the visible sky, providing unprecedented access to astrophysical phenomena in the time domain — supernovae, asteroids, variable stars, you name it. It will probe dark energy in at least two ways: using Type Ia supernovae as standard candles (which is how the acceleration of the universe was first discovered), and by measuring cosmic structure via weak gravitational lensing.

One of the great challenges of the project is the huge amount of data it will produce. We are talking about a petabyte of data per year (pdf) — about the size of the entire internet archive. To search such a database for some string of characters (say, using “grep”) would take several years! It’s a tremendous intellectual challenge just to design the ways that such data can be usefully arranged so that we can find what we’re looking for. As you might guess, expertise from people like Google is turning out to be very valuable. In fact, the value goes both ways. It turns out that computer companies love to play with astrophysical data, for simple reasons — it’s publicly available, and worth nothing on the open market. We like to think that the data has a loftier kind of worth.

Sad to hear that John Bahcall passed away on Tuesday. Here is an email from the Institute for Advanced Study.

From: Peter Goddard
Subject: Sad news

To the Institute Community,

It is with regret that I share the sad news of the passing yesterday evening of Professor John Bahcall.

John was the Richard Black Professor in the School of Natural Sciences, and had been with the Institute since 1968, when he arrived here as a Member. He was appointed to the Faculty in 1971.

Many of you are familiar with John and his distinguished career, which is marked by work on models of the Galaxy, dark matter, atomic and nuclear physics applied to astronomical systems, stellar evolution, and quasar emission and absorption lines. John was an expert on the elusive form of radiation known as neutrinos, and was involved for many years with NASA’s Hubble Telescope Working Group.

John was truly a pioneer, who made lasting contributions to the field of astrophysics. He will be greatly missed, and we extend our deep sympathy to his wife Dr. Neta Bahcall and their children Safi, Dan and Orli.

Peter Goddard

Bahcall was known primarily, of course, for his work on the solar neutrino problem. He was the theorist who calculated the expected number of neutrinos that the Sun should be emitting; he worked very closely with Ray Davis, the experimenter who first demonstrated a deficit of solar neutrinos reaching the earth. Davis was awarded the Nobel Prize in 2002, and many people (myself included) were very surprised that Bahcall didn’t share the award.