Hard to believe it’s been 15 years since the publication of Spacetime and Geometry: An Introduction to General Relativity, my graduate-level textbook on everyone’s favorite theory of gravititation. The book has become quite popular, being used as a text in courses around the world. There are a lot of great GR books out there, but I felt another one was needed that focused solely on the idea of “teach students general relativity.” That might seem like an obvious goal, but many books also try to serve as reference books, or to put forward a particular idiosyncratic take on the subject. All I want to do is to teach you GR.

And now I’m pleased to announce that the book is changing publishers, from Pearson to Cambridge University Press. Even with a new cover, shown above.

I must rush to note that it’s exactly the same book, just with a different publisher. Pearson was always good to me, I have no complaints there, but they are moving away from graduate physics texts, so it made sense to try to find S&G a safe permanent home.

Well, there is one change: it’s cheaper! You can order the book either from CUP directly, or from other outlets such as Amazon. Copies had been going for roughly $100, but the new version lists for only $65 — and if the Amazon page is to be believed, it’s currently on sale for an amazing $46. That’s a lot of knowledge for a minuscule price. I’d rush to snap up copies for you and your friends, if I were you.

My understanding is that copies of the new version are not quite in stores yet, but they’re being printed and should be there momentarily. Plenty of time for courses being taught this Fall. (Apologies to anyone who has been looking for the book over the past couple of months, when it’s been stuck between publishers while we did the handover.)

Again: it’s precisely the same book. I have thought about doing revisions to produce an actually new edition, but I think about many things, and that’s not a super-high priority right now. Maybe some day.

Thanks to everyone who has purchased Spacetime and Geometry over the years, and said such nice things about it. Here’s to the next generation!

I talked a bit on Twitter last night about the Past Hypothesis and the low entropy of the early universe. Responses reminded me that there are still some significant misconceptions about the universe (and the state of our knowledge thereof) lurking out there. So I’ve decided to quickly list, in Tweet-length form, some true facts about cosmology that might serve as a useful corrective. I’m also putting the list on Twitter itself, and you can see comments there as well.

1. The Big Bang model is simply the idea that our universe expanded and cooled from a hot, dense, earlier state. We have overwhelming evidence that it is true.
2. The Big Bang event is not a point in space, but a moment in time: a singularity of infinite density and curvature. It is completely hypothetical, and probably not even strictly true. (It’s a classical prediction, ignoring quantum mechanics.)
3. People sometimes also use “the Big Bang” as shorthand for “the hot, dense state approximately 14 billion years ago.” I do that all the time. That’s fine, as long as it’s clear what you’re referring to.
4. The Big Bang might have been the beginning of the universe. Or it might not have been; there could have been space and time before the Big Bang. We don’t really know.
5. Even if the BB was the beginning, the universe didn’t “pop into existence.” You can’t “pop” before time itself exists. It’s better to simply say “the Big Bang was the first moment of time.” (If it was, which we don’t know for sure.)
6. The Borde-Guth-Vilenkin theorem says that, under some assumptions, spacetime had a singularity in the past. But it only refers to classical spacetime, so says nothing definitive about the real world.
7. The universe did not come into existence “because the quantum vacuum is unstable.” It’s not clear that this particular “Why?” question has any answer, but that’s not it.
8. If the universe did have an earliest moment, it doesn’t violate conservation of energy. When you take gravity into account, the total energy of any closed universe is exactly zero.
9. The energy of non-gravitational “stuff” (particles, fields, etc.) is not conserved as the universe expands. You can try to balance the books by including gravity, but it’s not straightforward.
10. The universe isn’t expanding “into” anything, as far as we know. General relativity describes the intrinsic geometry of spacetime, which can get bigger without anything outside.
11. Inflation, the idea that the universe underwent super-accelerated expansion at early times, may or may not be correct; we don’t know. I’d give it a 50% chance, lower than many cosmologists but higher than some.
12. The early universe had a low entropy. It looks like a thermal gas, but that’s only high-entropy if we ignore gravity. A truly high-entropy Big Bang would have been extremely lumpy, not smooth.
13. Dark matter exists. Anisotropies in the cosmic microwave background establish beyond reasonable doubt the existence of a gravitational pull in a direction other than where ordinary matter is located.
14. We haven’t directly detected dark matter yet, but most of our efforts have been focused on Weakly Interacting Massive Particles. There are many other candidates we don’t yet have the technology to look for. Patience.
15. Dark energy may not exist; it’s conceivable that the acceleration of the universe is caused by modified gravity instead. But the dark-energy idea is simpler and a more natural fit to the data.
16. Dark energy is not a new force; it’s a new substance. The force causing the universe to accelerate is gravity.
17. We have a perfectly good, and likely correct, idea of what dark energy might be: vacuum energy, a.k.a. the cosmological constant. An energy inherent in space itself. But we’re not sure.
18. We don’t know why the vacuum energy is much smaller than naive estimates would predict. That’s a real puzzle.
19. Neither dark matter nor dark energy are anything like the nineteenth-century idea of the aether.

Feel free to leave suggestions for more misconceptions. If they’re ones that I think many people actually have, I might add them to the list.

In completely separate video news, here are videos of lectures I gave at CERN several years ago: “Cosmology for Particle Physicists” (May 2005). These are slightly technical — at the very least they presume you know calculus and basic physics — but are still basically accurate despite their age.

1. Introduction to Cosmology
2. Dark Matter
3. Dark Energy
4. Thermodynamics and the Early Universe
5. Inflation and Beyond

Update: I originally linked these from YouTube, but apparently they were swiped from this page at CERN, and have been taken down from YouTube. So now I’m linking directly to the CERN copies. Thanks to commenters Bill Schempp and Matt Wright.

Stephen Hawking died Wednesday morning, age 76. Plenty of memories and tributes have been written, including these by me:

• “Stephen Hawking’s Most Profound Gift to Physics,” in The New York Times — a piece concentrating on black hole evaporation and the information-loss puzzle.
• “Stephen Hawking Was Very Particular About His Tea,” in The Atlantic — more focused on our personal interactions and Hawking’s human side.

I can also point to my Story Collider story from a few years ago, about how I turned down a job offer from Hawking, and eventually took lessons from his way of dealing with the world.

• “What Would Stephen Hawking Do?“

Of course Hawking has been mentioned on this blog many times.

When I started writing the above pieces (mostly yesterday, in a bit of a rush), I stumbled across this article I had written several years ago about Hawking’s scientific legacy. It was solicited by a magazine at a time when Hawking was very ill and people thought he would die relatively quickly — it wasn’t the only time people thought that, only to be proven wrong. I’m pretty sure the article was never printed, and I never got paid for it; so here it is!

(If you’re interested in a much better description of Hawking’s scientific legacy by someone who should know, see this article in The Guardian by Roger Penrose.)

Stephen Hawking’s Scientific Legacy

Stephen Hawking is the rare scientist who is also a celebrity and cultural phenomenon. But he is also the rare cultural phenomenon whose celebrity is entirely deserved. His contributions can be characterized very simply: Hawking contributed more to our understanding of gravity than any physicist since Albert Einstein.

“Gravity” is an important word here. For much of Hawking’s career, theoretical physicists as a community were more interested in particle physics and the other forces of nature — electromagnetism and the strong and weak nuclear forces. “Classical” gravity (ignoring the complications of quantum mechanics) had been figured out by Einstein in his theory of general relativity, and “quantum” gravity (creating a quantum version of general relativity) seemed too hard. By applying his prodigious intellect to the most well-known force of nature, Hawking was able to come up with several results that took the wider community completely by surprise.

By acclimation, Hawking’s most important result is the realization that black holes are not completely black — they give off radiation, just like ordinary objects. Before that famous paper, he proved important theorems about black holes and singularities, and afterward studied the universe as a whole. In each phase of his career, his contributions were central.

…

Stephen Hawking’s Scientific LegacyRead More »

So here’s something intriguing: an observational signature from the very first stars in the universe, which formed about 180 million years after the Big Bang (a little over one percent of the current age of the universe). This is exciting all by itself, and well worthy of our attention; getting data about the earliest generation of stars is notoriously difficult, and any morsel of information we can scrounge up is very helpful in putting together a picture of how the universe evolved from a relatively smooth plasma to the lumpy riot of stars and galaxies we see today. (Pop-level writeups at The Guardian and Science News, plus a helpful Twitter thread from Emma Chapman.)

But the intrigue gets kicked up a notch by an additional feature of the new results: the data imply that the cosmic gas surrounding these early stars is quite a bit cooler than we expected. What’s more, there’s a provocative explanation for why this might be the case: the gas might be cooled by interacting with dark matter. That’s quite a bit more speculative, of course, but sensible enough (and grounded in data) that it’s worth taking the possibility seriously.

[Update: skepticism has already been raised about the result. See this comment by Tim Brandt below.]

Let’s think about the stars first. We’re not seeing them directly; what we’re actually looking at is the cosmic microwave background (CMB) radiation, from about 380,000 years after the Big Bang. That radiation passes through the cosmic gas spread throughout the universe, occasionally getting absorbed. But when stars first start shining, they can very gently excite the gas around them (the 21cm hyperfine transition, for you experts), which in turn can affect the wavelength of radiation that gets absorbed. This shows up as a tiny distortion in the spectrum of the CMB itself. It’s that distortion which has now been observed, and the exact wavelength at which the distortion appears lets us work out the time at which those earliest stars began to shine.

Two cool things about this. First, it’s a tour de force bit of observational cosmology by Judd Bowman and collaborators. Not that collecting the data is hard by modern standards (observing the CMB is something we’re good at), but that the researchers were able to account for all of the different ways such a distortion could be produced other than by the first stars. (Contamination by such “foregrounds” is a notoriously tricky problem in CMB observations…) Second, the experiment itself is totally charming. EDGES (Experiment to Detect Global EoR [Epoch of Reionization] Signature) is a small-table-sized gizmo surrounded by a metal mesh, plopped down in a desert in Western Australia. Three cheers for small science!

But we all knew that the first stars had to be somewhen, it was just a matter of when. The surprise is that the spectral distortion is larger than expected (at 3.8 sigma), a sign that the cosmic gas surrounding the stars is colder than expected (and can therefore absorb more radiation). Why would that be the case? It’s not easy to come up with explanations — there are plenty of ways to heat up gas, but it’s not easy to cool it down.

One bold hypothesis is put forward by Rennan Barkana in a companion paper. One way to cool down gas is to have it interact with something even colder. So maybe — cold dark matter? Barkana runs the numbers, given what we know about the density of dark matter, and finds that we could get the requisite amount of cooling with a relatively light dark-matter particle — less than five times the mass of the proton, well less than expected in typical models of Weakly Interacting Massive Particles. But not completely crazy. And not really constrained by current detection limits from underground experiments, which are generally sensitive to higher masses.

The tricky part is figuring out how the dark matter could interact with the ordinary matter to cool it down. Barkana doesn’t propose any specific model, but looks at interactions that depend sharply on the relative velocity of the particles, as . You might get that, for example, if there was an extremely light (perhaps massless) boson mediating the interaction between dark and ordinary matter. There are already tight limits on such things, but not enough to completely squelch the idea.

This is all extraordinarily speculative, but worth keeping an eye on. It will be full employment for particle-physics model-builders, who will be tasked with coming up with full theories that predict the right relic abundance of dark matter, have the right velocity-dependent force between dark and ordinary matter, and are compatible with all other known experimental constraints. It’s worth doing, as currently all of our information about dark matter comes from its gravitational interactions, not its interactions directly with ordinary matter. Any tiny hint of that is worth taking very seriously.

But of course it might all go away. More work will be necessary to verify the observations, and to work out the possible theoretical implications. Such is life at the cutting edge of science!