An Astronomy Math Puzzle

It's pretty easy to measure the radial velocities of distant stars or galaxies. (The "radial" velocity is the motion of an object directly toward or directly away from us). Astronomers use the Doppler shift, the stretching or compression of light from the moving object. Light from stars or galaxies moving toward us gets "bunched up," and the wavelength shrinks, making the light bluer, while light from objects moving away from us gets stretched out and becomes redder. The Doppler effect works so well that we can pin down the radial velocities of the most distant galaxies in the universe -- these observations provided the first evidence for the expanding universe.

But it's a lot harder to measure the sideways, or "transverse" velocity. The only way to measure a transverse velocity is to keep careful watch on an object and wait... and wait... and wait... We've been able to measure the transverse motions of stars for a long time -- the star with the fastest transverse motion is Barnard's Star, named after Vanderbilt's E.E. Barnard. But even Barnard's star is moving at a glacial rate across the sky -- 10 arcseconds a year.  At that rate, it will take almost 200 years to move the width of a full moon.

Galaxies are much farther away than stars, so their transverse motions are minuscule in comparison and have never been observed. But recently the Gaia satellite has allowed astronomers to pinpoint the locations of distant objects with unprecedented accuracy. So there's speculation that if we could monitor distant galaxies for a long enough time (10 years? 20 years?) we might be able to measure their transverse motions.

All of which leads to a puzzle. We don't want to sit around for 10 years, only to discover that we've been watching a slowpoke galaxy that's hardly moving sideways at all. If we could monitor only a handful of distant galaxies, which ones are likely to have the biggest transverse velocities? Are they the galaxies with the largest radial velocities? That makes sense -- a galaxy with a large radial velocity is more likely to have a large total velocity, so the component of its velocity in the transverse direction is also likely to be large. But here's an argument in the opposite direction: if all the galaxies are moving at about the same speed, then a large radial velocity means that the galaxy is likely to be moving almost directly toward or away from us, so it will have a small transverse velocity, while a galaxy with almost no radial motion is likely to be moving perpendicular to our viewing direction and will have a very large transverse velocity. In that case, we should monitor the galaxies with the smallest radial velocities.

So what's the answer?

Time Travel Stinks

Time travel is one of the most enduring themes in science fiction, as well as one of the most implausible -- I've discussed the science of time travel here. But there's one piece missing from almost all fictional discussions of time travel: the smell.

Dark Energy: The Final Exam

Where do theoretical physicists get their ideas? That's a hard question to answer. But in the case of my most recent paper, which just appeared in Physical Review D (the preprint version is available here), I can tell you exactly where the idea came from: a final exam.

What is the Universe Made Of?

Good question.  I gave a public lecture (more specifically, the Lois McGlothlin Donaldson Endowed Lecture in Physics) on this subject at the University of Memphis last week -- if you are interested you can watch it here.

How Did We Survive the 1980s?

I just finished writing a short story that had to be set, for various reasons, in the early 1980s.  And I could feel my characters' pain.  How does one character find out about another one when there's no internet??  I couldn't have anyone type into a computer, call each other on cellphones, or look up facts on Wikipedia.

Stephen Hawking 1942-2018

I met Stephen Hawking a few times over the years -- the most memorable was in the early 1980s when I was a grad student at the University of Chicago. Stephen was visiting the university, but he also wanted to take a side trip out to Fermilab -- a one-hour drive outside of Chicago. This being the days before GPS (back when we had to navigate by the stars) I was assigned by my Ph.D. adviser to ride along with Stephen and his driver and direct them to Fermilab.

I showed up at the hotel in Hyde Park at the appointed hour and went to the lobby, but Stephen was nowhere to be seen. What to do? Had this been an ordinary theoretical physicist, I would simply have asked the hotel clerk to phone his room. But this was Stephen Hawking -- one does not simply go and knock on his door. So I just waited in the lobby, assuming that Stephen would make his appearance when he wished. After quite a bit of time had passed, Stephen's assistant/driver popped into the lobby and asked, "Why didn't you call up to our room? We've been waiting up there for you!"

Meanwhile (I learned later) one of the senior scientists in the astrophysics group at Fermilab was pacing back and forth, muttering that if anything happened to Hawking, he would "send Scherrer to Tuscaloosa" -- presumably a form of internal exile. But Stephen Hawking, his driver, and I finally did make it out to Fermilab (late) and all was forgiven.

Many years later, I finally got a chance to visit Tuscaloosa to speak at the University of Alabama. It's really a very nice town.

Was the Early Universe Lumpy?

When the universe was only a few minutes old, was it smooth, like Cream of Wheat (yum!), or was it lumpy, like oatmeal? (Yuk!)  British cosmologist John Barrow and I explored this question in this paper, posted yesterday. Most cosmologists think that the matter in the early universe was smooth, not lumpy, and there's no compelling reason to believe otherwise, but it's always important to look at alternatives.

How can we even say anything intelligent about the universe when it was only a few minutes old? Our best probe is the production of elements in the early universe, which goes under the tongue-twisting name of "primordial nucleosynthesis." Most of the atomic nuclei on Earth were made in stars, but a small number, including helium, deuterium, and lithium, were manufactured in the first few minutes of the universe. And the amount of each element produced is exquisitely sensitive to the density of protons and neutrons when the universe was just a few minutes old. If the universe were lumpy rather than smooth, then the element abundances would fluctuate up and down in a predictable way, and we can average these out to get a prediction for what we would see today.

A Bayesian Coin Flip

Anyone who's spent any time at all with the scientific literature has encountered the phrase "Bayesian statistics." What's that all about?  How can there be more than one kind of statistics? Isn't statistics just a branch of mathematics, where everything is cut and dried? Alas, no. In his book Numerical Recipes, Bill Press describes statistics as "that gray area which is as surely not a branch of mathematics as it is neither a branch of science." Statistics is all about using data to derive conclusions, but there's no single "right" way to do this. So the world of statistics resembles Europe during the Reformation, divided into various factions and sects, one of these being the Cult of the Bayesians. The key idea of Bayesian statistics is that one needs to incorporate prior assumptions about reality into any modeling of data.

Here's an example.  Suppose that Alfred flips a coin 20 times, and he gets 20 heads in a row (this is very unlikely -- the probability of 20 heads in a row is less than one in two million).

Now Alfred flips the coin one more time. What is the probability that this coin flip will come up heads?  Is it

(A) Less than 1/2?  Alfred has used up all the heads.
(B) Exactly 1/2?  Past performance tells you nothing about future returns.
(C) Greater than 1/2?  Alfred is on a roll!

Why I am not a Biologist

I diligently avoided biology throughout my high school and college years. Why? Well, for starters biology is the smelly science. Also wet, sticky, and generally disturbing. Contrast that with the clean, crystalline clarity of physics. But I've also come to understand that there's a fundamental difference between the way that biologists and physicists think about the world. Maybe you've seen this famous poster of "metabolic pathways":

I have to admit that the first time I encountered it in the hallway of my university, I thought it was some sort of a joke. What kind of Rube Goldberg machine is this anyway? Of course, it's very real, but my reaction shows the gulf between the way that physicists and biologists think.

Interstate Traffic Jams and Galactic Structure

Last fall I drove up to Williamsburg and Washington with a couple of my kids. It was a pleasant trip, except for the stretch of I-95 between Richmond and Washington. There, on a sunny Sunday afternoon, we encountered a series of sporadic traffic jams. Each time we hit a slowdown, I expected to see an accident by the side of the road, but no such accident ever appeared. Instead, the traffic simply speeded up again a few miles down the road for no apparent reason. So what was the origin of this mysterious roving I-95 traffic jam? I suspect it's the very same thing that produces these beautiful structures in spiral galaxies:

Is Dark Matter Hiding Right Under our Noses?

Consider the lowly neutron. Neutrons make up about half the mass in your body, but they contribute nothing to chemistry. They just lounge quietly inside the atomic nuclei and get carried along for the ride. But this past week, two physicists at the University of California, San Diego, suggested that the neutron might be the key to unlocking the mystery of dark matter in the universe.