Scientific American on energy & cosmology

Tamara Davis’s cover article (paywall) in the latest issue of Scientific American is about the old puzzle of whether it makes sense to talk about energy conservation in the expanding Universe.  It has the good taste to refer to my work with David Hogg on the nature of the redshift, which is at the heart of this question.   In fact, one of the figures in the article is essentially a slick, nice-looking version of something from our paper:


I think the article’s very good.  I think it gets the science right and emphasizes pretty much the right things.

Andrew Hearin ’03

Like most academics, I obsessively keep track of who’s citing my work.  As a result, this paper caught my eye today.  (If that link doesn’t work, try this one.)  The lead author is a UR alumnus and winner of both of the physics departments main awards in his senior year.  During my first year here, I taught him in an independent study course on relativity.  He went off to graduate school in mathematics, but he later saw the light and came back to physics.

I haven’t read the paper in detail yet, but from the abstract it looks like a very nice piece of work (in addition to having the good taste to cite me). Congratulations, Andrew!


Two papers I submitted a while ago were accepted for publication by the American Journal of Physics this week, within minutes of each other as a matter of fact.  To be precise, they were “conditionally accepted,” meaning that they’ve successfully passed the review by external referees and the science content been deemed acceptable.  There’s a further review by the editors for style, clarity, etc., before they’re  finally accepted.  Because AJP is a journal with a pedagogical slant, they place a heavy emphasis on clarity, which is probably why they have this “conditional acceptance” stage.

Both of these are less technical than the usual research paper: they’re intended for readers who know some physics but are not necessarily specialists in any particular field.  The first one requires a bit of knowledge of relativity (students who took my Physics 479 course should be fine) , and the second one requires just undergraduate-level thermodynamics and statistical mechanics.

The first article is on the correct interpretation to place on the observed redshifts of galaxies in the expanding Universe.  I blogged about it when we originally submitted it.  These redshifts are usually described as being due to the “stretching of space,” but David Hogg and I argue that this conceptual model is misleading.  We claim that, contrary to what you often see in introductory textbooks,  it’s correct to think of the redshift as being due to a plain old Doppler shift.

Here’s the revised version of the paper.  It  doesn’t differ all that much from the one we originally submitted, although some aspects of the argument are expanded and clarified a bit in response to the referees’ comments.

The second article is on the relationship between entropy and the second law of thermodynamics.  It’s a response to a very nice paper by Daniel Styer, which attempts to show quantitatively that the entropy production due to sunlight is more than enough to account for the entropy reduction required for biological evolution (contrary to claims often made by creationists).  The original article had a serious gap in it: it depended on an assumption that was unjustified and, I argue, almost certainly wrong.  My paper presents an argument that doesn’t depend on that assumption.  The new argument shows quite rigorously that there is no conflict between evolution and the second law.

I blogged about the original Styer article and about my response a while back.  Here’s the revised version of the paper.  Thanks to the referees, I think the new version is much clearer than the original.  It’s also much longer.  I was thinking of the original as just a comment on Styer’s earlier paper, but the new version reads more like a stand-alone article.

Down with the rubber sheet

People like to visualize the expanding Universe as a sort of a stretching rubber sheet. Textbooks and popular cosmology books play up this analogy in a big way. Like most analogies, it’s useful in some ways, but taken too far it can lead to misconceptions. David Hogg and I have written an article in which we try to fight back against some of these mistakes.

The article is about how we should interpret the redshifts of distant objects. Most of the time, redshifts are Doppler shifts, indicating that something is moving away from you. In the cosmological context, though, a lot of people think that you’re not allowed to interpret the redshift in this way. The idea is that galaxies are “really” at rest with respect to the stretching rubber sheet. Since they’re not “really” moving, what we see is something different from a Doppler shift. The point of our article is to rehabilitate the Doppler shift interpretation.

The real reason I care about this is not that I think it matters much what we call the redshift, but because I think that this is a good example of the muddled thinking that the rubber sheet analogy causes. In particular, the analogy provides precisely the wrong intuitions about the nature of space and time in the theory of relativity. If you want to know more specifically what we mean by this, you’ll have to read the article!

To understand the guts of the article, you really need to have studied relativity a fair bit. (Students who took my Physics 479 course should be able to handle it.) Even if you don’t know enough relativity to understand all the technical details, the beginning and end might be interesting and accessible. (Certainly, this paper should be more accessible to non-specialists than the last one I wrote about, which is pretty technical.)


Apparently there’s a tradition here at the University of Richmond: when a faculty member gets tenured, he or she chooses a book for the library and writes a description of the importance of the book. The library inserts that description into the catalog, or into the book, or something like that.

Since I just got tenure, I had to choose a book to write about. After thinking about it for a while, I decided to go with Galileo’s Dialogue concerning the two chief world systems. Here’s the description I’m sending off to the library.

By the way, I really mean it when I say in here that the book is extremely readable. I can’t think of any other book that’s (a) anywhere near as important as this one and (b) actually fun to read. If you haven’t read it, check it out! (Although if you’re at UR, you’ll have to wait a week or so to get it out of the library, because I’ve got it at the moment.)

Anyway, here’s what I wrote:

The central idea of astrophysics is that the same laws of nature we discover in labs on Earth can be used throughout the Universe: there are not separate laws for heavenly bodies. It would be hard to overstate the importance of this insight to the emergence of modern science. Galileo did not invent this idea – like most really big ideas, this one cannot be attributed to any one person. But he deserves a large share of the credit for developing the idea and for persuasively and cogently championing it. Galileo is an all-too-rare figure among the giants of science: he wrote with clarity and even wit for an audience of non-specialists. He wrote in the common language, not in Latin, in a style that makes his work still readable and even enjoyable today.

Galileo has a lot in common with Einstein, so it is fitting that Einstein wrote the foreword to this English translation. In particular, Galileo's description of experiments performed below decks on a moving ship is the direct ancestor of Einstein's discovery of relativity, both in the scientific content of the ideas and in the ingenious use of thought experiments.

Einstein and me

I never met Einstein, which is not surprising, since he died over 20 years before I was born. [Update: Make that 12 years.  See Matt Trawick’s comment below.]  (The most famous physicists I have ever met, I think, are Eugene Wigner and John Wheeler, who are not exactly household names to non-scientists.) But back when I was in college I did get to know an old friend of Einstein’s pretty well.

Her name was Gabrielle Oppenheim, and she was about 95 when I knew her in the summer of 1988. Because her eyesight was very poor, she hired students to read the newspaper to her. This was a great job, which was passed on from student to student. I don’t remember how much it paid; I would have done it for nothing.

Mrs. Oppenheim told me lots of stories about Einstein. She first met him at a party in Brussels in 1911. Her husband pointed Einstein out and said, “That man will be one of the greatest physicists.” Mrs. Oppenheim’s response: “So I gave him one sandwich more.” (She later told this story to F. Murray Abraham in a Nova documentary, but I heard it first.)

She also said she was with Einstein in 1919 when he got the telegram from Sir Arthur Eddington, announcing that his observations of the bending of starlight had confirmed Einstein’s theory of general relativity. This was the event that made Einstein world-famous. But according to Mrs. Oppenheim, Einstein was much less excited about the result than the other people who were there at the time, because he had never doubted what the result would be.

She knew Einstein in Europe, but she spent much more time with him later in the U.S., when she and her husband had come to Princeton. (Her husband, Paul Oppenheim, was a philosopher.) Once, she and her husband were sailing with Einstein when the boat capsized. Her husband said, “Well, at least if we die with Einstein, we’ll be famous.”

She told me lots of other good stories. Once, she said, she was at a dinner party somewhere in Europe during World War I. A German army officer asked where she was from, and she told him she was Belgian. He replied that Germany would be invading Belgium soon. Mrs. Oppenheim said, “I was so offended by that, that I turned away and didn’t speak to him for the rest of the dinner.”

Mrs. Oppenheim told me way back then that I was “the scientist type”. Given that she hobnobbed with some of the greatest physicists of the 20th century (Bohr and others as well as Einstein), I figured she must know what she was talking about.