A Network Scientist Takes On Quantum Gravity

[00:00:00]If I recall correctly, in 2021, you were speaking to the Network Science Institute and you said, I think you were working on this and at that time you said it wasn't physics yet. Let me know if I'm mistaken. And anyhow, the point my my question was Well, I was wondering when in your mind did it then cross over into physics? When did it become physics?

[00:00:21]>> Yes, so it become physics practically immediately when I decided to go in the continuum.

[00:00:26]>> Ah.

[00:00:27]>> Because it's really strange but in in in complex system, most of the problem are in the discrete.

[00:00:34]>> [gasps] >> So, if you want to go to the continuum, you know, gravity is is is is the most likely way to go. And and this came, you know, after a trip that I made in in in the state and, you know, and also this seminar at the ICTP.

[00:00:52]I felt the need, right, to establish the relation between this theory that I was trying to formulate in complexity and something perceived as more fundamental.

[00:01:05]And this this is the outcome and I'm very happy because, you know, for me, I'm kind of new in in in gravity and, you know, traditional theoretical physics and it it it it is a a fantastic playground. It's fantastic progress that been made, you know, in gravity.

[00:01:24]Somehow, there are so many different direction that you need to be guided by your physical understanding of of of the problem. But for me is a nice new direction at this point of my career and I embracing it and enjoying it.

[00:01:44]>> So, what's the reception been like?

[00:01:46]>> Yeah, the the reception has been open. Yeah, so there people, I think mostly in in cosmology, are quite interesting and they feel the need to work on modified gravity approach. You know, there is this Hubble tension. There are different problem.

[00:02:07]There are of course dark energy somehow dark matter. So, cosmologies are now becoming very welcoming for for this theory. And yes, I had a very nice conversation. Of course, you know, I'm not in the stream of thoughts that start with holographic screen. So, there is also some some clash there of our understanding.

[00:02:36]Of course, I think that, you know, the area law is fundamental, but I think it is a macroscopic field. So, what I want to say is that actually gravity from entropy to some extent reproduce the area law from the microscopic degree of freedom. So, this is So, practically the the Lagrangian is is is defined over volume. So, if you integrate over a black hole, you know, until the Schwarzschild radius, you find a dimensionality reduction. And this is essential because practically holography uh has been, you know, kind of explanation of the area law coming after Bekenstein. Bekenstein didn't use the holography.

[00:03:21]And is a very simple conceptual idea is that just if you have the entropy, which is the logarithm of the number of degree of freedom, typically the entropy is scales like the volume. So, in order to have it in in such a way that it scales with the area, the degree of freedom must be only on the surface on on the horizon.

[00:03:43]But actually this assumption builds on the idea that, you know, the degree of freedom are the same in every point, you know, inside the black hole.

[00:03:55]And in gravity from entropy, because gravity from entropy doesn't depend only on the Ricci tensor or Ricci scalar, but depends also on the Riemann tensor and so on on on the Weyl curvature.

[00:04:08]>> Mhm.

[00:04:09]>> So, what happens is that the degree of freedom in a black hole, right? The degree of freedom inside are not always the same. Depends on the distance from the origin. And and and so when you integrate something that is not homogeneous, you can get a a dimensionality reduction. So, that that's the beauty of gravity from entropy. And so, for the moment, I I don't feel the need to use a holographic screen. And I think that, you know, there are many important insight coming from the area law, but if we are looking for a fundamental theory, we need to to go beyond the area law.

[00:04:52]>> So, is this an emergent theory of gravity then?

[00:04:55]>> So, gravity from entropy assume that the geometry exists.

[00:05:01]And so, it builds on Einstein insight that gravity is a theory of geometry.

[00:05:09]But it provides new understanding of the interplay between matter field and geometry.

[00:05:16]But it doesn't want to explain where geometry comes from.

[00:05:20]This is not the goal of gravity from entropy. So, as long as Einstein theory might not be considered emergent gravity, but in some sense it is because, you know, Newtonian forces come from geometry.

[00:05:35]Also, gravity from entropy is is is at the same level, right? So, it assume that the metric [clears throat] exist and capture the information content of this metric and of course, you know, Newtonian gravity comes from from the geometry.

[00:05:54]Exactly as in Einstein gravity. Of course, a problem could be, you know, where geometry comes from from the beginning, but this is not tackled in gravity from entropy. What is emergent is instead this dark energy term that is dynamical and is is is new because it emerged from the theory and is is is driven by this G field.

[00:06:23]>> Kurt here. Note that if you'd rather listen to TOE, we're on Spotify, iTunes, everywhere with a podcast catcher. You can just search my name or Theories of Everything. And also, remember to hit subscribe.

[00:06:34]Right, and it's positive.

[00:06:36]>> And it's positive.

[00:06:37]>> And that's a positive thing.

[00:06:38]>> Yes.

[00:06:39]>> So, what are some of the open problems that you're working on right now or or some of your colleagues are working on or maybe your students? What's bothering you right now about this theory and you're tackling it?

[00:06:51]>> Yeah, so of course, there are the cosmological implication and the relation with prediction and you know, possible experimental validation of the theory.

[00:07:04]Then there are aspects related to the second quantization and then there are aspects related to entanglement.

[00:07:13]So, how this gravity from entropy uh action is related to entanglement and entropy. And then of course, maybe if if one wants to go also going in the discrete. But what, you know, keeps me awake at night is the second quantization of this theory.

[00:07:32]>> What is the second quantization? And why is it so difficult or tricky in this case?

[00:07:39]>> Yeah, so I mean, this is a real problem in gravity, right? So, to combine gravity with our field theory second quantization approach of the other fundamental force. It is notoriously difficult. There are, you know, this is a word the community as explored different direction.

[00:08:03]And of course, there might be the need for define the graviton, right? Or which mediate the gravitational interaction, but the quest is open, right? There are many different approach.

[00:08:19]>> The graviton would be emergent in your view?

[00:08:22]>> Uh probably not.

[00:08:24]>> It would be fundamental?

[00:08:26]>> Yeah, you know, it's also to be questioned if if the graviton really exists, right?

[00:08:33]But maybe there is something else, right? As this, you know, because the metric is is described by vierbein, is described by, you know, spin connections. So, there are different option. It's not that you need to start from the metric itself. You >> I just spoke with Philip Mannheim who doesn't believe the graviton exists, actually. Did I hear you correctly that you use Weyl curvature as well?

[00:08:59]>> Yeah, I I use the entire Riemann tensor.

[00:09:03]So, this includes the all the component, also the one that vanish that that do not contribute to the Ricci scalar, yes.

[00:09:11]So, this is an important aspect and this is what makes, you know, the entropy of the black hole non-trivial because practically in empty state in in the empty space the gravity from entropy action is non-zero. And so, also if the Ricci scalar is zero, right?

[00:09:29]The gravity from entropy action depends on all the component of the Riemann tensor. So, it's it's non-zero. And so, you can integrate over over the volume.

[00:09:40]It is not homogeneous all over, and this is an important aspect. And another important aspect is actually that this theory provides also some correction at the Planck scale, also in in flat geometry.

[00:09:56]>> Interesting.

[00:09:57]>> So, the theory treating geometry together with matter field finds some correction at the Planck scale already in flat in flat geometry.

[00:10:09]>> And what about what's going on at the singularity?

[00:10:12]Now, I know that's a question that's notoriously difficult, and I'm asking you at the beginning of developing a theory, but I'm curious.

[00:10:21]>> Yes, so, the idea is that, you know, possibly the singularity would be avoided by the gravity from entropy theory, because you have this G field that enters into the action, and this G field is dynamical. So, for instance, for the Schwarzschild solution, the Schwarzschild solution is is a good approximate solution to the black hole, because, you know, is solution of the Einstein equation that are approximate equation of of the gravity from entropy theory.

[00:10:52]But actually, you know, close to the singularity, this G field becomes dynamical. So, maybe there is no single static solution of the black hole in gravity from entropy, and maybe, you know, this singularity is avoided.

[00:11:08]>> Professor, what advice do you give your PhD students?

[00:11:11]Consistently.

[00:11:13]>> Um one advice, which is I think easy to follow, is to read articles and to study.

[00:11:24]Uh another advice is to try to follow your what you like, you know, your try to express your vision of of reality in what you do and enjoy enjoy what you do, you know, try to have fun. It's not always the case, but you know, I think that that's part of why we do science we do because we want to enjoy it.

[00:11:50]You know, >> What's a piece of advice that you keep coming back to that someone gave to you?

[00:11:56]>> Um So for instance, one advice is why don't you go in there continue, right? This is an advice coming from a random person that was at my seminar. We didn't spoke, we didn't discuss, but it was very important for me. And another thing that I learned that possibly was not an advice, but you know, try to explore and to go in other community and and see what what they do.

[00:12:27]So if you are in a big conference, you know, but interdisciplinary, I do pop up sometime in a session from another community and you will find answer to your question possibly if you think about your problem quite abstractly. So this is has been very important for me to formulate gravity from entropy. I had this idea and I was at the DPG meeting, you know, speaking about my topology in networks and then I went to to listen at session about uh gravity and information and it was inspiring and useful.

[00:13:08]>> Mhm.

[00:13:08]>> So try to to look at nature with surprise and maybe it thinks will turn nice.