Author Archives: Clifford

Custard

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When looking for an excuse to have some custard, simply whip up an upside down cake built on a bit of fruit, spices, and whatnot you might have (here: apples cooked in butter, basking on caramel, with toasted walnuts, cinnamon…etc). –cvj

Black Holes and a Return to 2D Gravity! – Part II

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(A somewhat more technical post follows.)

Continuing from part I: Well, I set the scene there, and so after that, a number of different ideas come together nicely. Let me list them:

[caption id="attachment_19442" align="alignright" width="250"]illustration of JT gravity background What “nearly” AdS_2 looks like via JT gravity. The boundary wiggles, but has fixed length 1/T.[/caption]
  • Exact solution of the SYK model (or dual JT model) in that low temperature limit I mentioned before gave an answer for the partition function $latex Z(\beta)$, by solving the Schwarzian dynamics for the wiggling boundary that I mentioned earlier. (The interior has a model of gravity on $latex AdS_2$, as I mentioned before, but as we’re in 2D, there’s no local dynamics associated with that part. But we’ll see in a moment that there’s very interesting stuff to take into account there too.) Anyway, the result for the Schwarzian dynamics can be written (see Stanford and Witten) in a way familiar from standard, say, statistical mechanics: $latex Z_0(\beta)=\int dE \rho_0(E) \exp(-\beta E)$, where $latex \rho_0(E)\sim\sinh(2\pi\sqrt{E})$ is the spectral density of the model. I now need to explain why everything has a subscript 0 in it in the last sentence.
  • On the other hand, the JT gravity model organises itself as a very interesting topological sum that is important if we are doing quantum gravity. First, recall that we’re working in the “Euclidean” manner discussed before (i.e., time is a spatial parameter, and so 2D space can be tessellated in that nice Escher way). The point is that the Einstein-Hilbert action in 2D is a topological counting parameter (as mentioned before, there’s no dynamics!). The thing that is being counted is the Euler characteristic of the space: $latex \chi=2-2g-b-c$, where $latex g,b,c$ are the number of handles, boundaries, and crosscaps the surface has, characterising its topology. Forget about crosscaps for now (that has to do with unorientable surfaces like a möbius strip $latex (g=0,b=1,c=1)$ – we’ll stick with orientable surfaces here). The full JT gravity action therefore has just the thing one needs to keep track of the dynamics of the quantum theory, and the partition function (or other quantities that you might wish to compute) can be written as a sum of contributions from every possible topology. So one can write the JT partition function as $latex Z(\beta)=\sum_{g=0}^\infty\hbar^{-(1-2g)}Z_g(\beta)$ where the parameter $latex \hbar$ weights different genus surfaces. In that sum the weight of a surface is $latex \hbar^{-\chi}$ and $latex b=1$ since there’s a boundary of length $latex \beta$, you may recall.

    The basic Schwarzian computation mentioned above therefore gives the leading piece of the partition function, i.e., $latex g=0$, and so that’s why I put the subscript 0 on it at the outset. A big question then is what is the result for JT gravity computed on all those other topologies?!

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Black Holes and a Return to 2D Gravity! – Part I

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(A somewhat more technical post follows.) Well, I think I promised to say a bit more about what I’ve been up to in that work that resulted in the paper I talked about in an earlier post. The title of my paper, “Non-perturbative JT gravity” has JT (Jackiw-Teitelbiom) gravity in … Click to continue reading this post →

More Pie

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Well, you know the saying: When life hands you several apples, some blackberries, and a chunk of pastry left over from your last pie-making… you make another apple-blackberry pie, taking the opportunity to make it even better! (No? Never heard that saying? Huh.) -cvj

Chalky

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I realized recently that I’ve forgotten a great deal of my drawing skills, settling back into some clunky habits, due to zero practice. But I’m going to need them back for a project, and so will start teaching myself again. Above is a (digital) chalk doodle I did yesterday. –cvj

Rolling…

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And so it began… All this butter had to end up inside this little bit of flour/water mix. But in lots of tasty layers of deliciousness! (And I’ll do this four times, and so that’s my morning.) More later. I love puff pastry! –cvj

Two Days at San Diego Comic-Con 2019

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[caption id="attachment_19354" align="aligncenter" width="499"] Avengers cosplayers in the audience of my Friday panel.[/caption]It might surprise you to know just how much science gets into the mix at Comic-Con. This never makes it to the news of course – instead its all stories about people dressing up in costumes, and of course features about big movie and TV announcements. Somewhere inside this legendary pop culture maelstrom there’s something for nearly everyone, and that includes science. Which is as it should be. Here’s a look at two days I spent there. [I took some photos! (All except two here – You can click on any photo to enlarge it.]

Day 1 – Friday

I finalized my schedule rather late, and so wasn’t sure of my hotel needs until it was far too late to find two nights in a decent hotel within walking distance of the San Diego Convention Center — well, not for prices that would fit with a typical scientist’s budget. So, I’m staying in a motel that’s about 20 minutes away from the venue if I jump into a Lyft.

My first meeting is over brunch at the Broken Yolk at 10:30am, with my fellow panellists for the panel at noon, “Entertaining Science: The Real, Fake, and Sometimes Ridiculous Ways Science Is Used in Film and TV”. They are Donna J. Nelson, chemist and science advisor for the TV show Breaking Bad (she has a book about it), Rebecca Thompson, Physicist and author of a new book about the science of Game of Thrones, and our moderator Rick Loverd, the director of the Science and Entertainment Exchange, an organization set up by the National Academy of Sciences. I’m on the panel also as an author (I wrote and drew a non-fiction graphic novel about science called The Dialogues). My book isn’t connected to a TV show, but I’ve worked on many TV shows and movies as a science advisor, and so this rounds out the panel. All our books are from […] Click to continue reading this post →

News from the Front XIX: A-Masing de Sitter

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[caption id="attachment_19335" align="alignright" width="215"] Diamond maser. Image from Jonathan Breeze, Imperial College[/caption]This is part 2 of a chat about some recent thoughts and results I had about de Sitter black holes, reported in this arxiv preprint. Part 1 is here, so maybe best to read that first.

Now let us turn to de Sitter black holes. I mean here any black hole for which the asymptotic spacetime is de Sitter spacetime, which is to say it has positive cosmological constant. This is of course also interesting since one of the most natural (to some minds) possible explanations for the accelerating expansion of our universe is a cosmological constant, so maybe all black holes in our universe are de Sitter black holes in some sense. This is also interesting because you often read here about explorations of physics involving negative cosmological constant, so this is a big change!

One of the things people find puzzling about applying the standard black hole thermodynamics is that there are two places where the standard techniques tell you there should be a temperature associated with them. There’s the black hole horizon itself, and there’s also the cosmological horizon. These each have temperature, and they are not necessarily the same. For the Schwarzschild-de Sitter black hole, for example, (so, no spins or charges… just a mass with an horizon associated with it, like in flat space), the black hole’s temperature is always larger than that of the cosmological horizon. In fact, it runs from very large (where the black hole is small) all the way (as the black hole grows) to zero, where the two horizons coincide.

You might wonder, as many have, how to make sense of the two temperatures. This cannot, for a start, be an equilibrium thermodynamics system. Should there be dynamics where the two temperatures try to equalise? Is there heat flow from one horizon to another, perhaps? Maybe there’s some missing ingredient needed to make sense of this – do we have any right to be writing down temperatures (an equilibrium thermodynamics concept, really) when the system is not in equilibrium? (Actually, you could ask that about Schwarzschild in flat space – you compute the temperature and then discover that it depends upon the mass in such a way that the system wants to move to a different temperature. But I digress.)

The point of my recent work is that it is entirely within the realm of physics we have to hand to make sense of this. The simple system described in the previous post – the three level maser – has certain key interconnected features that seem relevant:

  • admits two distinct temperatures and
  • a maximum energy, and
  • a natural instability (population inversion) and a channel for doing work – the maser output.

My point is that these features are all present for de Sitter black holes too, starting with the two temperatures. But you won’t see the rest by staring at just the Schwarzschild case, you need to add rotation, or charge (or both). As we shall see, the ability to reduce angular momentum, or to reduce charge, will be the work channel. I’ll come back to the maximum […] Click to continue reading this post →