A lot of us have been waiting for a long time to hear this news! The NANOGrav collaboration has announced strong evidence of a background of low frequency gravitational waves emitted from supermassive black hole mergers. Their detection methods are pulsar timing arrays (still one of those fantastically simple, cool … Click to continue reading this post
About two years ago I wrote a post entitled “A Return”, upon moving to Princeton for a year (I was a Presidential Visiting Scholar at the Physics department). I reflected upon the fact that it was a return to a significant place from my past, where I’d been transformed in so many ways. Princeton was the first place I visited (not counting airports) in the USA, the location of my first postdoctoral appointment (at the Institute for Advanced Study (IAS)), and its was there that I did a deep enriching dive into the hubbub of Theoretical Physics, at one of the very top places in the world to do so.
After that, I moved West, to Santa Barbara, where my next postdoc position was at the Institute for Theoretical Physics at the University of California Santa Barbara (UCSB), now called the KITP. I was very lucky to be able to go from one top place to another, and (as I’ve recently talked about in a BBC interview here) additionally, my field was in a delicious turmoil of activity and discovery. I was able to be a part of the maelstrom (the “Second Superstring Revolution”, and all the gifts it gave us, including better understanding of the role in quantum gravity of extended objects beyond strings (such as D-branes), the physics of quantum black holes, the tools to unlock the holographic nature of quantum gravity more generally (through AdS/CFT), and so on. (I’ve blogged about many of these topics here, so use the search tool for more.)
I’ve been known to say that Princeton was the place where I found my physics voice (Edward Witten was a key guide at that time). Well, to continue the theme, Santa Barbara (with its wonderful research group made up of people from both the KITP and the wider Physics Department) was the place where I started to learn how to use that voice to sing (with the guidance of Joe Polchinski (who sadly passed away a few years ago)).
Well, as you may be guessing after that long introduction, I’m doing “A Return” again, but this time not with some boxes and suitcases of things for a year’s stay: I can now announce that I’ll be leaving the University of Southern California (USC) and (as of 1st July 2023) joining […] Click to continue reading this post
After doing a night bottle feed of our youngest in the wee hours of the morning some nights earlier this week, in order to help me get back to sleep I decided to turn on BBC Sounds to find a programme to listen to… and lo and behold, look what had just aired live! The programme that I’d recorded at Broadcasting House a few weeks ago in London.
So it is out now. It is an episode of Jim Al-Khalili’s excellent BBC Radio 4 programme “The Life Scientific”. The show is very much in the spirit of what (as you know) I strive to do in my work in the public sphere (including this blog): discuss the science an individual does right alongside aspects of the broader life of that individual. I recommend listening to […] Click to continue reading this post
I’m sitting, for the second night in a row, in a rather pleasant restaurant in Oxford, somewhere on the walk between the physics department and my hotel. They pour a pretty good Malbec, and tonight I’ve had the wood-fired Guinea Fowl. I can hear snippets of conversation in the distance, telling me that many people who come here are regulars, and that correlates well with the fact that I liked the place immediately last night and decided I’d come back. The friendly staff remembered me and greeted me like a regular upon my return, which I liked. Gee’s is spacious with a high ceiling, and so I can sit away from everyone in a time where I’d still rather not be too cavalier with regards covid. On another occasion I might have sought out a famous pub with some good pub food and be elbow-to-elbow with students and tourists, but the phrase “too soon” came to mind when I walked by such establishments and glanced into the windows.
However, I am not here to do a restaurant review, although you might have thought that from the previous paragraph (the guinea fowl was excellent though, and the risotto last night was tasty, if a tiny bit over-salted for my tastes). Instead I find myself reflecting on […] Click to continue reading this post
As I mentioned in the previous post, I had business at BBC Broadcasting House this week. I was recording an interview that I’ll fill you in on later on, closer to release of the finished programme. Recall that in the post I mentioned how amusing it would be for me … Click to continue reading this post
[caption id="attachment_20038" align="aligncenter" width="499"]
Brompton bicycle rental lockers.[/caption]
I’ll be visiting Broadcasting House during my time here in London this week, for reasons I’ll mention later. Needless to say (almost), as a Brompton rider, and fan of the wonderful show W1A, I feel a sense of regret that I don’t have my bike here so that I can ride up to the front of the building on it. you won’t know what I’m talking about if you don’t know the show. Well, last night I was a-wandering and saw the rental option shown in the photo. It is very tempting…
[I was originally going to use the title “Back Home”, but then somehow this choice had a resonance to it that I liked. (Also reminds me of a lovely Joshua Redman album…)] So I am back in London, my home town. And since I’ve got 8 hour jet lag, I’m … Click to continue reading this post
Happy New Year!
I was greeted by great deal of green in Griffith Park today, and it was particularly lovely to look out over the whole park when I’d reached higher elevation, as the greens of various kinds stretched off in all directions, and even into the city. You’ve likely seen recent photos from me from a similar vantage point, where the dominant colours are brown and grey, so you can probably appreciate the contrast. The speed with which the green can come back in full strength never ceases to amaze me.
I’ve not done a run in this part of the park for a few weeks, for one reason or another, and so that made it all the more stark a contrast, I imagine, since there’s been a lot of rain here and there (and a lot over the last few days) and that has no doubt helped the transformation.
I’m going to take the green as an encouraging sign to press ahead (“green for go”) with this new year. There’s a great deal on my […] Click to continue reading this post
The red curve in this figure is the probability distribution of the ground state energy [latex]E=s[/latex] of the microstate spectra of quantum completions of JT gravity. Put differently (the way Wigner might have) if you ask what are all the discrete spectra that are compatible with the leading semi-classical result for quantizing JT gravity (the famous Schwarzian result for the density of states: [latex]\rho(E)=e^{S_0}(4\pi^2)^{-1}\sinh(2\pi\sqrt{E})[/latex]), this curve gives the shape of the distribution of ground states. (The blue curve is simply the associated CDF.) I first uncovered this distribution in a paper last year, with further insights and generalizations in a paper earlier this year, along with the distributions for higher energy levels that follow from it. But the exciting new result of my paper from a few weeks ago is that I have now shown that it is a solution of an ordinary differential equation (or a family of them). This allows for some powerful universal things to be said analytically about the properties of the distribution!
This is fully analogous to what happened for the well-known Tracy-Widom distribution for the largest (or smallest) energy of Gaussian random hermitian matrices. While many workers (such as Forrester) had uncovered important aspects of the distribution, and while it was known that it can be expressed as a particular Fredholm determinant, Tracy and Widom broke new ground in 1994 by showing that the distribution was governed by a well known ODE – the Painleve II equation – and in particular can be given in terms of a special solution of it studied earlier by Hastings and McLeod. The result helped forge further connections between properties of random matrix theory and several interesting areas of mathematics and mathematical physics. Furthermore, […] Click to continue reading this post
A major part of the reason I’ve been very quiet here since the last post is because I was working on a different kind of project that has in fact taken up much of my bandwidth during the last many months. This has been very welcome, as there is a … Click to continue reading this post
That Feeling
Several weeks ago, while writing up a nice set of results that extended some work I did last year, I found that I was stuck finding the right wording for how I should nuance a (seemingly minor) matter in the introductory remarks. It was partly because, frankly, I’d got bored of the standard introduction I usually make to papers on this particular subject (matrix models and 2D gravity), because I’ve written quite a few in the last two years (10-Yikes!). But I’d found a new feature that warranted a more careful way of saying the usual things, and I wanted to incorporate that aspect, and also get the Reader interested in why this aspect was interesting and worth unpacking. I played around with better ways of saying it, and still was not entirely happy. I chipped away for a bit more over a few days, and kept coming up with something less than satisfactory. I’d carry on with things in the body of the paper that would be there whatever the introduction said. Then, after coming back to the introduction and trying again, I had to stop and explore the consequences of some of the rephrasing I was doing – to make sense of the new way I was trying to say what I wanted to say.
And then it happened…
You might know that feeling: A sort of pop goes off in your head and a tingle through the whole body, and then everything looks different all of a sudden, because you realize that you’ve found a completely new way of looking at things. A way that fits *so* well and incorporates so many of the facts that it just. feels. inevitable.
That’s what happened. And then I tried to see what it would say about the larger picture of physics this all fits in, looking for a way to make it fit, or to challenge the idea to see if it breaks. Not only did not not break, it just kept making sense, and (almost like the idea itself took charge of the process) immediately offered solutions to the problems I threw at it, and readily gobbled up existing challenges that the community has been facing for a while, and explained certain things that have been a puzzle for a long time.
For the next few days I actually could not write properly at the keyboard any more. My hands were trembling every time as I utterly rebuilt the entire paper and my world view, and I could barely sit still at times.
I know this sounds like a lot, and you should know that I am open to the possibility that it is somehow wrong, but it is too compelling not to share, so that’s what my paper that came out earlier this week is all about. I am not going to repeat the paper here, but will try to highlight some features of it that form a foundation for why this changes a lot about how we think about things in this corner of physics.
Random Stuff
Let me start in the simplest way possible, as I have done in the past, with a model that is well known to many different physics communities. The Gaussian random matrix model. Random matrix models have a very long history in trying to understand complicated systems (going back to Wishart (1928), and then Wigner (1955) – physicists seem to always forget to mention Wishart, and I’m sure I’m forgetting someone else too), and they show up in all kinds for systems. There are a lot of powerful results that have been developed, and you’ve read my writings about them here to do with how they get used for understanding aspects of string theory and quantum gravity in 2D, and also in higher dimensions. The “double scaling limit” is something I’ve talked about a lot here in particular. I won’t repeat all of it here, but invite you to go and look at other posts.
[…] Click to continue reading this post
[A rather technical post follows.]
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This figure will make more sense later in the post. It is here for decoration. Sit tight.[/caption]
For curious physicists following certain developments over the last two years, I’ll put below one or two thoughts about the new paper I posted on the arXiv a few days ago. It is called “Consistency Conditions for Non-Perturbartive Completions of JT Gravity”. (Actually, I was writing a different paper, but a glorious idea popped into my head and took over, so this one emerged and jumped out in front of the other. A nice aspect of this story is that I get to wave back at myself from almost 30 years ago, writing my first paper in Princeton, waving to myself 30 years in the future. See my last post about where I happen to be visiting now.) Anyway here are the thoughts:
Almost exactly two years ago I wrote a paper that explained how to define and construct a non-perturbatively stable completion of JT gravity. It had been defined earlier that year as a perturbative […] Click to continue reading this post
Well, I’m back.
It has been very quiet on the blog recently because I’ve been largely occupied with the business of moving. Where have I moved to? For the next academic year I’ll be on the faculty at Princeton University (as a Presidential Visiting Scholar) in the Physics department. It’s sort of funny because, as part of the business of moving forward in my research, I’ve been looking back a lot on earlier eras of my work recently (as you know from my last two year’s exciting activity in non-perturbative matrix models), and rediscovering and re-appreciating (and then enhancing and building on) a lot of the things I was doing decades ago… So now it seems that I’m physically following myself back in time too.
Princeton was in a sense my true physical first point of entry into the USA: My first postdoc was here (at the Institute for Advanced Study, nearby), and I really began […] Click to continue reading this post
For your weekend listening: Recently, I chatted with Maiken Scott, the host of the podcast The Pulse (WHYY) about many everyday aspects of energy. It was a delightful conversation and episode. Listen and share with friends! Link is here. Enjoy! -cvj
So I have a confession to make. I started working on random matrix models (the large $latex N$, double-scaled variety) in 1990 or 1991, so about 30 years ago, give or take. I’ve written many papers on the topic, some of which people have even read. A subset of those have even been cited from time to time. So I’m supposed to be some kind of expert. I’ve written extensively about them here (search for matrix models and see what comes up), including posts on how exciting they are for understanding aspects of quantum gravity and black holes. So you’d think that I’d actually done the obvious thing right? Actually taken a bunch of random matrices and played with them directly. I don’t mean the fancy path integral formulation we all learn, where you take N large, find saddle points, solve for the Wigner semi-circle law that the Dyson gas of eigenvalues forms, and so forth. I don’t mean the Feynman expansion of that same path integral, and identify (following ‘t Hooft) their topology with a tessellation of random 2D surfaces. I don’t mean the decomposition into orthogonal polynomials, the rewriting of the whole problem at large $latex N$ as a theory of quantum mechanics, and so forth. No, those things I know well. I just mean do what it says on the packet: close your eyes, grab a matrix out of the bag at random, compute its eigenvalues. Then do it again. Repeat a few thousand times and see that all those things in the data that we compute those fancy ways really are true. I realized the other day that in 30 years I’d never actually done that, and (motivated by the desire to make a simple visual illustration of a point) I decided to do it, and it opened up some wonderful vistas.
Let me tell you a little more. […] Click to continue reading this post
