A newly computed spectral density function for a new example…
Oh, this? I’m very pleased with it. I’ll tell you more about what it is at a later point, but this is mostly for my own entertainment. It’s a sort of big brother to the spectral curve shown in the
previous post. I’d been thinking about how to get this curve (those plus marks) to come out right for a few days, and repeatedly getting it not quite right*, with puzzlement and frustration. And then while out on a run it came to me how to do it right…. Then after writing the
matlab routines to make my solution happen, out it popped! Hurrah. (Update: The inset was added to show more detail. Now it is in the paper as an added extra.)
(* Update: “not quite right” means, for example, that the large E behaviour should have been E^(3/2), generalising the E^(1/2) of the previous example, but it wasn’t for a bit, because of a normalization issue. All fixed now!)
To (most of) you it’s just a bunch of dots and wiggles and that’s ok. To me is some very nice physics that connects things I’d been thinking about back some 30 years ago with things I’m thinking about now. More later. Sorry if this is annoying, I’m just very pleased with the result.
-cvj
Like this:
Like Loading...
Related
Pingback: Black Holes and a Return to 2D Gravity! - Part I | Asymptotia
In my opinion, all black holes are quantum black holes. Quantum black holes for me and many means “the quantum physics of black holes”. In other words, trying to understand black holes in regimes where quantum physics is important, and indeed cannot be ignored. For some of us, there are signs that black holes simply don’t make complete sense unless you understand the quantum physics. The fact that black holes have a horizon (which in some sense defines them) inevitably bumps you up against their quantum nature. What lies behind the horizon? What is the full description of things falling behind the horizon and re-emerging as (apparent) radiation? What is the spectrum of a black hole – discrete? – continuous? Do black holes even form if you take into account the full quantum physics? What is the nature of spacetime inside a black hole? Is it even a meaningful thing?
As to your other questions: – Everything we do in science is models and tools. Nature is nature. What we do to understand it is make models and some models are better than others. Confusing models with nature seems very common in the way science is taught, but really we shouldn’t. Newton’s laws of motions aren’t nature. They are equations that we use to model (very successfully) nature. Same as general relativity, same as quantum field theory. And so on. So when a physicist is working out new models and calculations tools, the only issue is whether/when/how they’ll be tested, not when they’ll stop making models. That’s all we do. Models and experiments. The other stuff is philosophy, which is interesting, but has a different goal.
As for SYK and all that. Google is your friend here. Google SYK model. Google it in combination with words like black hole, etc. You’ll find papers, talks, all sorts of things of use.
Cheers,
-cvj
Oh, forgot to ask. What are quantum black holes? Quantum black holes in regular 4D general relativity?
How do we know what models of such black holes might look like?
“relate to aspects of the physics of coupled fermions that are realizable in laboratory settings”
Relate in what way? As in a calculational tool? Philosophically speaking, how does one distinguish between a “calculational tool” that actually corresponds to the way the world works, vs a bona fide calculational tool that can only be interpreted as such?
“There are actual experiments being planned to learn more about those classes of system. ”
I’m interested in learning more about those experiments. What are they called?
Thanks again.
Hey, excellent response. Thanks for the info about what these models might provide us.
Well, it relates to models of the low energy physics of quantum black holes. So ultimately this may teach us about their physics. Experimental signatures of the quantum nature of black holes might be far off yet, but maybe we’ll get some hints from astrophysical data coming from collisions/mergers of black holes… perhaps? That would be great, if maybe a long shot. On the other hand, these same models relate to aspects of the physics of coupled fermions that are realizable in laboratory settings (the SYK model and cousins thereof). There are actual experiments being planned to learn more about those classes of system. So non-perturbative knowledge of the spectrum and other aspects of models like this could well be important for understanding the output of those experiments. Thanks for asking!
Does this graph show agreement between string theory and anything that can be measured in our universe?