Wolfram Physics Project Working Session: Quantum Black Holes and Other Things

Anyway, so, okay, we're talking about entropy and there's several different entropies here. There's the, you know, there's the counting of the number of microscopic states consistent with some macroscopic constraint on space time. Then there's something about the counting of the number of states that a coarse grained observer. Coarse grained at the level of looking at the structure of space time, but not coarse, I mean at the small scale structure of space time, but not coarse grained at the level. What are we trying to say? We got several different levels, right? We've got the box that the space time is in, which would include kind of the donut shaped box that includes the black hole and so on, if that makes sense. So we've got a certain number of microstates that are compatible with that box now, but many of those microstates are probably incredibly wild to a, you know, to a somewhat local observer. Like they correspond to space times that have no notion of flatness things. So I mean, I, I kind of think then, right, so that's an additional constraint if you want the, if you want, you want the kind of observers of our scale to not just live in a totally turbulent space time. That's an additional constraint, isn't it? I mean, and then, then what? So I mean, and isn't that the, the kind of entropy for that second case when it's been, when the space time is tamed? That's the kind of entropy that's talked about in standard black hole thermodynamics, not the entropy that includes the full microstates.

Well, there isn't a way of counting full microstates in the semi classical case, right? There is in supergravity and there is in string theory, but not in just semi classical gravity.

And in string theory it's a vacuum. It's the string field theory in the vac, the vacuum state of the string field theory. That is the thing that you're counting mode.

Yeah, exactly, exactly.

But now why does that. Okay, so, but what we're saying is we're counting. So what does that say? What does the string case say?

So the string case agrees with the semi classical calculation for sub extremal and extremal black holes. And that's this famous BPS bound. Because I mean, so in the semi classical calculation, extremal black holes don't radiate, right? The Hawking temperature goes to zero as one approaches, as one evaporates to extremality and this BPS bound in superstring theory and supergravity Also says that the Hawking temperature of a supersymmetric extreme or black hole is zero. And that's kind of heralded as this big result that it nicely agrees with semi classical gravity.

Okay, so wait a minute. So what's happening is M is decreasing, but J is staying the same. In a Kerr type solution, that means that it would blow out its extremalism.

Yeah. So if it was allowed to radiate away to nothing, you'd eventually yield a naked singularity if you had any non zero charge or any non zero spin. And so in the semi classical theory, the Hawking temperature converges to zero, so you never get a naked singularity. The same is true in string theory. What's interesting about this calculation is that although it agrees with both, with both the semi classical case and the string theory case, in the sub extremal for sub extremal black holes, it diverges for extremal and super extremal black holes. There's nothing in. Because in the branchial space picture, nothing special happens at the. Because no mass is actually being lost. All that's happening is you've got a reduction in amplitude. Nothing special happens.

Well, okay, but this is your interpretation that the reduction in amplitude is sufficient to talk about mass. And I would think that the issue is, you know, what is the mass? Some kind of flux of causalities? Go ahead.

Right. I'm not sure that it is. It's more about, you know, okay, what, what does a macroscopic observer see? And I guess the. So the hypothesis that I'm making pro tem is that if you see an amplitude, if the amplitude associated with the existence of the black hole goes down, that's equivalent to, you know, up to some point an observer will interpret that as the mass going down.

Okay, but, but I think the reason has to be, is that the.

Yeah. Is that the flux of causal edges goes down for, you know, through the.

Average flux of causal edges goes down.

Right.

Although the interpretation of mass is this kind of weird delay in the sort of causal delay, how long things sit. Right. As I recall. I mean, I haven't thought about this actually for a couple of years.

Right.

Do you have a good interpretation of mass versus energy, rest mass versus energy? We had a nice way of thinking about that in terms of, of what part of the causal edge flux. I think the mass is. It's kind of like E squared minus P squared and it's somehow the, the. You remember this business.

I don't know specifically what you're referring to.

Well, I mean, we had an interpretation of mass. Look, if energy is the total flux of causal edges through space like hypersurfaces, what is mass?

Right. And so, but I mean, you can do exactly the same thing as you would do in standard relativity and just do a, you know, you decompose the, the diagonal into two sort of perpendiculars.

Yeah.

One of which is, is, you know, is relativistic energy, one of which is rest energy. But are you talking about something different or.

Well, yes, because I'm talking about there's momentum. Right. Which is associated with the flux of causal edges through the timelike hyper surfaces and so on. Right. And mass, I mean, I just don't remember how mass is the, you know, is E squared minus P squared. Right. Is M squared in.

In sr, not in gr.

I understand there, there, there is, there.

Is no local definition of mass in gr.

I'm aware. But. Okay, but locally, how do we understand the. Well, okay, so what the hell is the mass of a black hole? It's just a parameter, right. That determines the gravitational.

Yeah, yeah. In that sense, black holes have no mass by any standard relativistic definition. They don't have any mass. Just like they don't have any. Just like. They don't have any angular. Just like a curved black hole has no angular momentum.

Yeah, I know, I know. It just has the effect of mass, sort of the effect of angular momentum, although rather unconvincingly, I think.

Yeah. So in the kind of stress energy definitions that. Yeah, obviously because it's a vacuum solution, it doesn't have mass. It does have admm. Mass. So there's a thing you can do which is a highly non local definition which is defined in terms of an integral over the boundary of your spacetime.

It's basically Gauss theorem applied to the thing. And then you.

Yeah, exactly. So it's effectively a topological version because you're integrating over something that contains what amounts to a delta function.

Right, But so let's see. I mean, so then. And the argument would be if you look across all the. The across branch hill space. So here's the thing. We haven't. Maybe we've defined, I mean, so the quantum, okay, flux of causal edges through a. You know, what the heck is it? It's not a space like hypersurface, it's a hypersurface. There's both the space like hypersurface and a branch like hypersurface.

Right.

And the intersection of those. Those. It's a thing.

I guess the argument would have to be that on any branch like hypersurface there are many space like hypersurfaces. And what the observer sees is an average over the space, over the flux through all space like hypersurfaces on that branch, like hypersurface.

That's what I think. Yes. And that therefore the effective. I mean, you know, mass is squiggly at the best of times here, but that the effective mass is somehow. I mean, but okay, zooming out for a second. I mean, the key assumption in all of this stuff is that the observer is extended in branchial space.

Yes.

Which is, I think, you know, in a sense that's, that's a version of your original contention. But I think that is a, a.

If, if they're, if they're localized to one branch, then they can't ever see evaporation in this.

Well, yes, but more to the point, I mean, you know, the interpretation of quantum mechanics that we have involves, you know, the traditional view of quantum mechanics is everything always degenerates to one branch after a measurement. Degenerates things to one branch. But I think our interpretation is rather that the observer is. I mean, it would be like saying, okay, what's the pressure of a gas? Well, you see, whether there's an individual molecule that hits every so often, as opposed to saying, as an observer, we're aggregating over large numbers of molecules. So similarly, I think we're saying you're aggregating over large numbers of large region of branchial space. That is again, like, like in thermodynamics, it is small compared to the universe, but big compared to the individual molecules.

Right.

And so that means that, that in, you know, and the reason that things are uncertain, you know, the reason we don't know what's going to happen in branch hill space or in, in quantum mechanics is because we are, through our history, we are at a particular position in branch hill space. And in a sense, it's a bit multiversey because we could be at a different position in branch hill space and then we would observe a different history of the universe. But I mean, what's sort of interesting about this is that we are, you know, if you say, why do we observe the sunrise that we observe? Well, it's because we're at this place in physical space. And the reason we're at this place in physical space has to do with this, you know, the coincidence of us being observers here. But, you know, the whole history of the universe, we don't get to just like say, oh, we don't like this place in physical space. Let's Go somewhere else. At least not without an interstellar spacecraft.

Right.

And so the question is, in Branch Hill space, I think the same thing has happened that we are at a particular place in Branch Hill space with a certain history. And one question is, we've discussed this before is. Is how we change. And you've made the statement that we change our place in branchial space merely by choosing different experiments. But I think there has to be more to it. In other words, you could say, well, we change our place in physical space merely by positioning ourselves at a different place in physical space. But that's incredibly non trivial to do.

Sure.

So the question is, in branchial space, what is the impediment to repositioning oneself if it's merely the choice of experiments? It sounds like you could be anywhere in Branch Hill space, but I don't think that's true. I think you have to go and actively. I don't really know what, what does it take to move in Branch Hill space? What do you have to do? Just like in physical space you are. I mean, what's the analog? I mean, okay, why is it hard to move in physical space? Possibly because it costs energy to move in physical space. And I bet the same is true in Branch Hill space.

Still.

But can you explain that? I mean, in other words, what are you expending energy? If I want to be in a different quantum reality, so to speak, how do I get there and how do I end up expending energy to do so?

I'm not certain that I completely understand the question. Let me understand the premise. You think my statement was incorrect. That if we say saw a different region of the. If we had the direct ability to observe a different region of the electromagnetic spectrum or something, that that would not be equivalent to. And therefore we'd be imposing a different equivalence relation on multi way states that would not be equivalent to moving in branchial space. There's something else.

I don't know about that one, but I mean I think if it's like what is.

What is the. What is the something else in that case?

Well, I mean, just you're rotating a polarizer or something.

Yeah. Okay, so you, you wouldn't consider that to be motion in front shell space? You wouldn't.

I don't know. I think it is probably. I. I don't know. I don't know. I think it's, it's. Look, it is changing our point of view in bronchial space whether I. Let me give you the example in physical space. Okay, I can look Left, I can look right. So that takes me very little effort. I want to go to Alpha Centauri. That takes me a lot of effort.

Sure.

What's the analog and branch hill space?

Well, it's. I don't, this is what I don't understand about the question. It's the same phenomenon, right, that moving further away requires almost trivially a greater flux of causal edges in that direction, so you require greater energy expenditure. So if you want to sample a set of microstates that are more distant to the ones you're currently sampling, it requires more energy.

Okay. Okay, but let's make we have an intuitive sense of why that's true in physical space. I don't think I have an intuitive sense of why that's true in branch field space.

Okay.

Do you. I mean, that is to change one's, you know, for sure, one is changing which branchial edges one is sampling, just like in physical space, one's changing which, you know, atoms of space or whatever. One sampling.

Okay.

And to get there requires kind of running against the rain, so to speak. As in there's all these causal edges that are just raining down and in order to actually move, you have to.

You know, okay, maybe, maybe the. Maybe the problem here is that you and I don't have the same intuitions for why these things are difficult. So, you know, my position is which I. Which may be your position too, but I don't know, it's hard to tell, is that in both cases it's a computational irreducibility story.

Right.

So the reason why one has inertia in physical space is because, let's imagine by default you've got some localized topological obstruction. It's moving kind of vertically downwards in the causal graph, so to speak.

Right.

And the reason that's happening is because we know, because of ergodicity, the net flux of causal edges in any given direction is going to converge through any time. Like hypersurface is going to converge to zero. So kind of the default state is it's going to be moving vertically downwards to change that requires. So you could try and go in some direction, but how do you know that you're persisting in that direction? Well, that requires computation.

That's a nice argument. I agree. That's a nice argument.

And so you have to kind of counteract computational irreducibility to continue going in that direction and not get buffeted by causal edges going in other directions.

That's a nice argument. I mean, basically you're saying in a very mark like way, okay, you're saying the existence of inertia is a consequence of vacuum fluctuations in some sense.

Yes. Right. And therefore it requires real computational work to, you know, do the necessary predictions to know that if I go in this direction, I'll keep moving in that direction and not get pushed somewhere else.

But hold on. This is actually, I mean, that claim that inertia is a consequence. The existence of inertia is a consequence. So basically, the claim is motion. It is non trivial. To have coherent motion.

Right.

To have coherent motion requires computational effort.

Right. Because you have to guarantee two things. You have to guarantee that you yourself remain coherent, that there's enough of your structure remaining that it's still meaningful to say that you're the same entity. And you have to ensure that the direction remains consistent so that you're not just microscopically bouncing around in some ergodic way. And both of those require computational effort.

What was Mach's idea in Marx principle? This idea that the inertia was a consequence of the gravitational forces of everything in the universe.

Yeah, exactly. There are a few different formulations of it, but the one I prefer is the idea that. So the reason why you have this, because, I mean, okay, I'm probably going to explain things that you know perfectly well. Right, but so original thought experiment was you go onto a hill, you spin around and you feel your arms pulled out to your sides as a consequence of some centrifugal force. But now if you do a relativistic transformation of that, you remain static and the sky around you spins around. Why should the motion of the sky around you cause your arms to be pulled out to your sides? And so the Mach argument is. Okay, well, if you think about the geometry of the setup and you think about the fixed masses, the fixed stars in the sky, the stars that are sort of closer to your plane of rotation are going to spin faster than the stars that are at the antipode at the poles. And so their relativistic mass will increase more than the relativistic mass of the ones at the poles. And so there's a greater gravitational interaction in the plane of rotation, which is what pulls your arms out to your sides. That's still not a. I should say that's not a universally accepted. You know.

Yeah, but Marx didn't yet know about relativity, so how did he. That wasn't quite his argument, I think, but it's an interesting version.

Yeah, and so that, that's the. That's the most complete version I know, which I think is due to Dennis Sharma. I, I don't, I'm not sure that I know Mark's original or I only know that he posed the problem. I'm not sure what his formulation was. I think he had, he had some ether related thing. Right?

Yeah, yeah, yeah. Because he didn't know about relativity yet. Yeah, okay. I mean that, okay, so hold on. So that, but your view, I mean, that's pretty interesting. If the presence, if the existence of inertia. So, so that means that how does inertia scale with the kind of size of the object? And that it's kind of weird because when it gets too small, there isn't a space to even discuss motion then.

Right, Right. Well, yeah, when it gets too small, there isn't a meaningful distinction between you and space.

Yeah, but wait a second. I'm still trying to internalize this. This, this is saying that the reason motion isn't free is because it takes computational effort, which. Yes, we know this. Right. But it gets computational effort to recreate yourself at that different place coherently and to not get buffeted to pieces. That's also the reason for time dilation and so on.

Yeah, exactly, exactly.

All right, so let's take the analogous thing in quantum mechanics and by the.

Way, I mean, that's why I think it's useful to make that decomposition into. There's computational work associated with maintaining coherence of yourself and there's computational work associated with maintaining coherence of your direction. Because one of those is mass related, one of those is momentum related. And that gives you kind of the two components of the, of the Lorenz transformation.

Okay, but, okay, but let's look at that from a branch point of view. Right. So we've got the same type of thing happening. You've, you know, most of the time you're, you're chugging along and you know, I don't really understand the analog of massive particles branch space. I mean, in physical space we're not just radiating out to infinity on a light cone. Right, Right. Unless we're Mazoroids.

Right. No, I mean, I, I don't, I don't claim to fully understand that either, except in as much as that, you know, the, the, the analog of a, of a, you know, a topologically stable region is some, you know, is some quantum system that maintains coherence. Right. So if you like, quantum computers are all about kind of setting up top, you know, persistent topological structures in brancheal space.

Yes. That don't essentially in your sense, evaporate.

Right. I mean, in other words, diffuse out to infinity.

Right. So I mean, your black hole Hawking radiation is the enemy of quantum computing in this picture.

Yeah, It's a decoherence effect, which has been suggested before, I mean, in different contexts.

Yeah, but yeah.

Anyway, just to complete the thought. So all I was saying is, given that interpretation, my way of thinking about why it's hard fundamentally to change your position in branchial space is you essentially have to make some sort of translation. Okay, so think about it like this, right? You're currently perceiving the world with a particular set of sense apparatus. Apparatuses or whatever, what the plural is when you make a branchial space transfer, to make a branch of space transformation, you have to be using some different set of sense data, but you have to be able to make some translation so that it still makes sense within your model of the world. The further out you go, the more alien you become, the more complicated that translation becomes. And so you hit the same, I would say, same computational irreducibility problem, that to have coherence of your own internal representation and to have coherence of your own direction of motion requires increasing amounts of computational work.

I agree. So let's walk through that.

Just as without that computational work, you would be shredded by the random buffeting of causal edges in physical space, you would have your internal representation of the world shredded by, you know, random buffeting of weird sense data in bridal space.

Well, let me think about that for a second. By the way, you know, an intermediate between these things is gauge degrees of freedom.

Yes.

And so let's talk about those for a second. So I mean, and we, you know.

We should really, I feel like we don't yet have the right data structure for representing this. Right. That there's so, you know, generational multi way systems were a way of trying to get all the gauge stuff out of multi way structure. Right. That if you like, you know, the only branches in the generational multi way system are true multi way branches and not kind of gauge specific ones. But I feel like there should be some kind of. I don't really know how you represent it, but there should be some kind of representation that makes a very clear delineation between what are gauge branches and what are kind of true multi way branches. But I don't think we have that yet.

Well, hold on. But I mean, first statement is the traditional view of gauge things is fiber bundles, where there's a base space and fibers.

Yes.

And we can, even in our hypergraphs we have this question of what's the base space and what's fibers, right. Even before we're in any kind of multi way story.

Right. And I mean, so this is something where, this is where we intersect potentially with the infrageometry story. So, you know, my view about this is. Okay, a very simple way that you can set this up is you just say, okay, I start with some hypergraph. I look at a given vertex in the hypergraph and I look at, you know, I look at its immediate out component, I look at all vertices adjacent to it, and I associate each one of those vertices with a sort of a point in some. So, you know, each one of those vertices is a point on some discrete fiber. Right?

Yep.

And then, you know, then by gluing all those different fibers together and I have some choice of how I glue them together and that gives me a choice of connection, I obtain the discrete analog of a fiber bundle. So if I had just.

When you move, look, you've got these different directions from a given vertex. You effectively have edges, you know, hyper edges that go out in different, you know, directions. And the sort of naive point of view would be some of those directions aggregate into physical space and some of those, in other words, base space, and some of those directions aggregate into fiber space.

Right. And so I, I was interpreting the hypergraph itself as the base space. I was talking about how you would, how you would construct a fiber, you know, a discrete fiber bundle on top of that.

No, but I think, look, isn't it the case that. Okay, so here's a kind of a. I mean, I think we had, you had examples of this, I mean, where you go around the, the hypergraph and there are some directions where you can just keep going, you know, you just keep going like a coordinate system. And there are other directions where you follow those edges in the hypergraph and they're like S1s, you know, they're cyclic.

Right. But I would argue that happens in the fiber bundle, not in physical space.

Sure, sure. That whole thing is the fiber bundle and only the things which are coordinate directions map onto physical space, AKA the base space. Right. You're decomposing the hypergraph. The hypergraph is.

I understand. I'm just saying that's not the construction that. I mean, what you're proposing is quite a different construction from what we've been working with, which is also interesting.

But what have you been working with? That's what I thought was the.

No, I mean the construction, Graham, for instance, based on the Manson paper and that I've been implicitly using in the stuff that I've been doing is that the hypergraph is physical space and has the dimensions of physical space.

Yes, I'm not sure that's right. I mean, but then how do you get the gauge degree of freedom? You have to go multi way.

Yeah, exactly. So the basic interpretation is. So if you imagine, okay, imagine having a very simple rule where. Okay, this is the way I've always thought about this. So I have a rule and I apply it to some patch of vertices. But amongst other things I have freedom in how I orient that rule. So in particular there's at least one possible orientation for each outgoing hyper edge from that vertex. And so each one of those corresponds to a point, to a local choice of coordinate basis and therefore to a point on some fiber bundle on some fiber.

I think this is what we had originally talked about.

Yes, yeah, exactly. So my intuition had always been that at that vertex, that vertex is a fiber in the fiber bundle and each point on that fiber is given by a single outgoing hyper edge from that vertex.

Yeah, I understand. And the agreement between different places on the hypergraph about where the updates, in what orientation the updates happen. That's the connection, effectively.

Right, exactly. And so then the thing that's nice, or one of the things that's nice about that interpretation is that it gives you a really nice intuition for gauge waves because it means that as soon as you enforce an orientation for one rule application, it places constraints on the orientations of all other space like separated rule applications in that hypergraph. And so you get a nice propagation of those constraints as a gauge wave.

I think it is worth us looking at this decomposition of hypergraphs into. So there's quite different.

No, I agree. So, so, but no, I'm not, I'm not saying we shouldn't investigate that. I'm just trying to point out that that's quite different to what we've done so far. Yeah, I mean, so the idea there is would be. I guess. So your idea would be the hypergraph rewriting happens not at the level of physical space, but in some higher dimensional hypergraph which then gets decomposed into physical.

Space, which is a bit, you know, compactified dimensions. Like it's very Kalutza Klein.

Yes, but it's an interesting model and perhaps like Kaluza Klein, like the fact that in KK compactification theories you can have classical Einstein equations satisfied by both the higher dimensional and lower dimensional theories. It's possible that there's an algorithm that lets you kind of from either the lower dimensional rewriting rules Construct higher dimensional ones or from higher dimensional ones construct lower dimensional effective ones. Which would be kind of interesting.

Yeah, yeah. Right. I mean both of these things could be true. Both of these phenomena could be happening that is that our projection into physical space. So imagine that the hypergraph has all these extra degrees of freedom running around.

Yes.

And we are picking out only certain degrees of freedom to view as physical space.

Right.

And these other degrees of freedom might be compactified, they might not. Who knows?

Yeah.

And I mean most extremely, it could be that something to do with us as observers picks out three dimensional physical space, for example, And that the only reason we believe the universe is three dimensional is, You know, is that, is that we somehow our mechanism of observational perception is, is. Yeah. Well, anyway, okay, so the thing that's.

Slightly, the thing that I'm. That I find a little bit mind bending about that is that, you know, from the, from the fully top down, you know, ruliad point of view, that's already true.

Yes.

By making the hypergraph a higher dimensional object, you're making, you're, you're making dimensionality of space, space, time, observer dependent at two levels rather than just one. That it's not just the observer is picking out. The observer is already picking out a certain class of hypergraphs which it's kind of, you know.

Yeah. Based on the rule that is used for hypergraph evolution.

Right. And then, and then further is, is then decomposing. It has an additional kind of effective rule for, for, you know, for decomposing those data structures into things that it's going to interpret as physical space.

Well, you know, but those might both. Look, it could be the case that actually that you can trade off one for the other.

Right.

Pick a different rule and have a different interpretation. And it could be even that there's some kind of duality between those two that basically says, I mean, if all that we can understand is three dimensional space, then we might get there by saying, well, we're just picking out a fundamental rule. I mean, it's kind of like what we discussed before.

So, okay, here's what. Maybe this is the wrong way to think about it. Here's what I think is really going on in this idea. It's another way. So in the ruliad picture, you've tended to think of there as being. It's like you're applying all possible rules and each state is its own separate kind of data structure. But one of the lessons we learned from universal computation and from ideas like universal Turing machines is, is that you can encode the rule as part of the state. Right.

Yes.

So what you could do is you could have a single hypergraph, some infinitely large hypergraph to which you apply a computationally universal hypergraphy writing rule. But that hypergraph, the initial hypergraph, is set up that it has this very diverse collection of sectors, one of which simulates each possible rule. And then it's like, okay, so there's only one rule in that setting, but it's still somehow computationally equivalent to the whole rule you had. And then you could just say the observer just picks out which. Which parts of the hypergraph it's going to interpret in what way?

Exactly. But, I mean, that's very much like saying the observer lives at some particular place in royal space, except now it's.

Making it a particular pace in. In physical space in some sense.

Right. That. That's called, you know, off the edge of the universe is another universe that's different from ours.

Right.

Kind of the tessellation of universes.

Right.

That, you know, is not obviously wrong. I mean, I don't know if our universe is, you know, it's. Our universe is encapsulated. There could be another one just right next door type thing. And we never know it, but.

Right.

I think that's, You know, that is indeed, as you say, dual to an idea that we don't see it because it's right here, but we are not operating on that plane of existence, so to speak.

Right, right.

As opposed to saying, so, I mean, that's a duality between. We can say it's physical space. We have to move in physical space. Okay, so this is.

I mean, it's also quite an interesting interpretation of what universality is. That it's the ability to trade off physical branchial and rulial degrees of freedom.

Yes.

What you're doing when you build a universal Turing machine is you're taking what would otherwise have been a whole collection of degrees of freedom in rulial space, and you're saying I can just localize myself to one rule, to one point in rule of space, and I can instead spread those degrees of freedom out in physical space.

Right. By having a compiler that puffs out your initial condition, your program, into whatever machine code it's puffing it out into.

Right.

Or something. Right. Let me think about that for a second. So, Yes, I mean, it is. Right. It's a. You're saying that universal computation is the statement that in a sense, roughly, motion, but not quite motion. Let's see, that. That. Yeah. What it really is Then is that if you imagine the dent of the observer somehow. Okay, crazy weird claim, but it isn't quite right. Is it saying something about how the observer sort of has a spherical extent with respect to all these different physical branchial rule. Let's think about that for a second. It's saying that you have a certain volume and that you can rotate yourself around if you want to, to make yourself extended in physical space or rulial space or whatever, but that the. In a sense the volume of the observer or the.

Yeah, you could argue that, you know, computational complexity theory, both space and time. Well, specifically in this case, I guess. No, no, Both space and time complexity place lower bounds on the volume of the observer in that geometrical picture. In the sense that what space complexity for instance is. Or sorry, no, not really space complexity. I guess algorithmic information or algorithmic complexity is saying that I can take a rulial distance of this much and I can rotate it into a physical state of this extent, but that physical state has. The extent of that physical state has some minimum value.

Yes, I understand, but I mean that's saying the rulial. Okay, rulial distance. Okay. Basically we're saying there's a speed of light in all these directions or something like the speed of light.

Right?

Because we're saying, you know, as we trade off time for each of these directions, there's a way in which that gets traded off. And, and somehow. We could somehow say that. I mean, there are cones, light entanglement. What the hell do we call little cones? My God, maybe we don't have a name for that. We have at the maximal rural speed. I even had a symbol for it. I think I called it row. But anyway, so, so I mean, we're saying the observer has a certain. Let's see, they have a certain time ex. You know, they have a certain experience in time. Well, anyway, but there's some way of trading off rulial for branchial. You know, rulial is algorithmic complexity theory. Branchial is non determinism and you know, spatial is, you know, like P space and so on.

Right, exactly.

And there's a trade off between these different. Things. And one of the claims is that branchial space, the claim of P equals NP or P not equal to NP is the branch real space matters. If P equals np, then branch real space is irrelevant. I think, I think it, it, it. It's kind of like it, it somehow. Well, anyway, okay, but, but, but, but coming back to this question about, about what it takes to move in Space and branchial inertia. Your statement is, okay, if you move in physical space, you're recreating yourself in a different place in physical space. And that takes working against the forces of irreducibility. And the claim would be it's the same thing for Branch Hill space, that you're working against the sort of forces of irreducibility.

Right. Except instead of your physical self, it's now your representation of the world.

Okay, but I mean, we're very familiar with inertia. You know, I can push something and it. It definitely has inertia. What is the analog? I mean, is the analog. Okay, it's one thing to say you're converting from one data structure or something or one sensor type to another, but that feels very computational, whereas inertia feels very in your face, so to speak. So the question is, is there something like physicalized like that in the case of quantum inertia, or is it merely computational?

Yeah, I understand. I mean, I'm not too perturbed by the idea that it's not as physicalized as in the case of physical motion.

Yeah, I think it's right. Because we haven't been as familiar with quantum effects.

Right, right. And we do, you know, so what? You know, okay, it's another one of these sort of pun science type phenomena. But one thing that I think is quite reassuring in that sense is that people do use intuitions like inertia when talking about difficulty of understanding. You know, like, okay, if I were to suddenly show you a bunch of data points that have been extracted through some new experimental method and you say, oh, I don't completely understand this yet. I need to do some work to kind of build up intuition for what I'm really seeing here. You might use a kind of analog to other. There's inertia involved in me kind of figuring this out.

Yeah. I mean, in other words, you have to. You have to form a framework which is otherwise known as. You have to kind of move your coordinate system or some such other thing.

Right, right.

But let's get that a little bit more physicalized. I mean, there's a. Okay, so, okay, you're readjusting all your polarizers. You're doing all this stuff.

I mean, in the purely physicalized case, you could just say I'm taking certain observational data that lie outside of what I can readily observe and interpret, and I have to expend energy to convert it into things that I can readily observe and interpret.

Example.

It requires, I have to expend electricity to convert data from a particle calorimeter into pixels on a screen that I can actually see and understand.

Interesting claim. So your claim is. That data conversion, a subject about which there has been nothing general said.

Right.

Except in universal computation.

Right. But I mean, you know what, what measurement apparatus does in some generalized sense is it takes things that otherwise would be impossible or difficult to observe directly and amplifies, translates whatever them to bands of sense data that are easier to observe and interpret.

Yeah. I mean, in the end, it stuffs it into a mind.

Right, Right.

But the question is, As it moves it from one. I mean, okay, one issue is that we're not used to. Whereas in physical space, we're used to this idea that we can go here, then there, then there, then there, all the way along down the line. Okay. So the question is, in measurements, is there a way of just progressively moving from one thing to another? You know, we don't tend to do that. We just say, but I mean, you know, we could do that. Look, in physical space, by the time the duck, all the, the rubber duck or something falls into the particular bin in your fair, you know, thingy, it's all over. In other words, even though. And so you could say the same thing. So in other words, there's no continued motion there.

Right.

The duck ends up in a particular bin and then sits there.

Right.

Whereas we're used to motion being never ending. I mean, that's obscure metamathematical space as well. And never ending motion in metamathematical space is. Yeah. Oh, by the way, totally irrelevant point I need to mention to you. I got some invitation to some gravitational wave event at Yale, which I don't know whether you also got one, but I was going to send it to you because I'm not going to be around at that time.

I don't think I did receive it. No.

Okay. All right, we'll. We'll deal with that in a few minutes.

Sure.

The. Anyway, but, but okay, the question is sort of continued, you know, how do you get continued motion in this measurement in. In data structure space. Right. I mean, one naive way to do that is you just saying, you know, rotate your coordinate system or something. Progressively rotate your coordinate system. It's not very exciting, but you could certainly do that.

Oh, sure. There are plenty of ways in which. In which branch of motion can be continuously parameterized. Right. You know, continuous polarization angles, continuous frequency bands of electromagnetic spectra, things like that.

Right. And the claim is, I mean, the only thing that's different in the case of physical Spaces, you're going into a fresh region of physical space.

Right, right.

I mean, you could go in a circle as well. So that, that's.

Yes. The, the fact that you're more limited in your motion in branch, your space, I consider to be relatively unsurprising given how comparatively high dimensional it is. Right. You can't go very. You could, you can't go that far without hitting the edge when you've got something that's, you know. Yeah, that high dimensional.

Right, right. Well, okay, but, but, okay, so fine. So we've got this idea that I think still needs to be fleshed out, a branchial motion. And what you're proposing for black holes is essentially branchial diffusion, not branchial motion.

Right, right, exactly. Uncoordinated branchial motion.

Yeah. Now, I mean, I do have to ask, do black holes scatter?

Depends what you mean by scatter. So you can certainly have two black holes in spiral and then get kicked out. And then one of them gets kicked out or both of them get kicked out. And in fact, that was one of them. So that was sort of one of the big kind of killer apps of early numerical relativity in around 2006, 2007, was the demonstration that when you have those inspirals and sort of near mergers of black holes, that the resulting remnant objects can be kicked out with much, much higher velocities than anyone had predicted that you can have. The remnant black hole can be kicked out with sort of 99.997% of the speed of light or something, which is a little bit terrifying because it means that there's probably a decent number of black holes going incredibly fast, just zipping through the universe destroying stuff.

Oh, well, good stuff. It happens to us. Time will end.

Right. But that was one of the early discoveries from these inspiral simulations, was that that can happen. That along with the fact that such a high proportion of black hole mass gets lost as gravitational waves were kind of the two most surprising things about those initial simulation results.

Right. Well, if black holes are particles, what does that mean?

Well, I guess you could argue that's a scattering event.

Yeah, but what does it mean that, I mean, do they have momentum conservation?

Yes. I mean, so, okay, really clear. Yes. If you, if you cheat, so to speak. Right. That they. The momentum is conserved if you also include the, the momentum from the gravitational radiation. But that's kind of cheating given that gravity. You know, one way you can kind of define gravitational, the moment of gravitational radiation is that it's what you need to make the you know, the non gravitational part of the field equations. Momentum conservative.

Here's a question. If particles are black holes.

What where's the gravitational waves?

Well, should we see violations of momentum conservation? So what's happening is the particle interactions are doing what they do, but they're setting up sort of wiggles in space time that aren't really particle like.

Right, right. I mean, I can't, Yes, I, I can't see a reason why that wouldn't happen right.

Now. I mean it's probably a very small effect, but it's still. And, and quite possibly, I mean, you know, in proton, proton collisions there's got to be gravitational waves generated. Got to be. I mean, they're accelerating masses. Right.

Yes. Let me, I'm trying, I'm trying to think of why that might. So the, the only reason I can imagine why that wouldn't happen, which I don't think is true. So you're probably aware that four dimensions of spacetime is, that's the smallest number of dimensions in which you have a non vanishing Weyl tensor. So effectively you don't get gravitational waves in two plus one dimensional gravity. So the only plausible, potentially plausible case in which I can imagine you wouldn't get gravitational waves from particle interactions if they were black hole interactions would be if the particles somehow interact in a lower dimensional. Effective.

Yeah, yeah, I understand, but they don't because it's a three dimensional, you know, the space time diagram is still non trivial.

Okay, okay.

By the way, question for our models. Can we see that you can't get gravitational waves in, in, you know, if the hypergraph is two dimensional, you can't get gravitational waves.

Yes, yes you can.

How? Construction of the Weyl tensor doesn't work effectively.

Yes, okay. It's basically because to construct the Weyl tensor you have to use a notion of inner product. You have to introduce a notion of inner product because you have to essentially measure angle deviation. And there is. So the only case in which you get an inner product construction that has enough degrees of freedom that you can actually have deviations that are measurable, that actually are non zero in the Weyl tensor is if you can have at least three perpendicular Gad 6, which you can't do.

Right, I get it. You have to have a construction with these various pieces of webbing and you can't have enough.

Exactly. So if you try and do that construction in a limiting two dimensional hypergraph, you essentially get geodesics crashing into each other and you end up with a vanishing file tensor. One thing which I have wanted to look at, which I haven't done yet, is what happens in intermediate 2 plus epsilon or 3 minus epsilon dimensions.

So just remind me in the interpretation, like in a bundle of GD6 in, you know, if they have vanishing in the Ritchie curvature determines the overall area of that bundle.

Yeah, exactly.

And the vile curvature determines the shape of the bundle.

Right, right. So. So on a numerical level, it's sort of effectively saying, you know, if the GD6 gets stretched out or squashed down, then it's a, you know, that's a, that's a Ricci curvature term. If the subtending angle between them gets distorted, that's a Weyl curvature contribution.

Right. And the point is that you can't have that bundle to construct that bundle and discuss its shape. You have to have a certain number of dimensions.

Exactly. And so there is a. So the Weyl tensor is the, you know, is conformally invariant in four dimensions. There is a conformally invariant tensor that works in three dimensions, which is the cotton tensorflow, but that doesn't give rise to gravitational waves. You can construct a cotton, therefore you can have a two plus one dimensional hypergraphy writing system with a non vanishing cotton tensor.

Okay. But I mean, now that I think about it, I'm pretty sure that I might have worked this out like 40 years ago. The gravitational radiation from a proton. Proton collision.

Right.

Yeah, we can certainly work this out. Lots of music, there's some. Yeah, there seems to be some discussion of these things. A gravitational bremstrah. You know what? I worked out something about gravitational bent. Well, this paper by Veneziano about this very topic. Compared to this recent 2016. Wow. Anyway, here it is. Classical gravitational bram. Starlung gravitational scattering. Two massless particles. I'm talking about other kinds of scattering. Deflection angle. Okay. So the basic point is there is some sort of wiggling around of space time as a result of. We can expect, you know, I mean, one feature of our models is that it's possible to have gravitational waves without having gravitons, so to speak.

Right, right.

And we kind of see that in the videos because, you know, you could decompose, you know, at some level. Like all the things that are happening with all those little micro black holes forming and disappearing. Right. That, that is, you know, in that video, it's basically we're seeing sort of the one classical path of black hole fluctuations. Right. Space time.

Huh.

And. Yeah, I mean, it is kind of an irony that in our models, you know, in our infinitely discrete model. Okay. That we're basically saying there is a continuous form of gravitational radiation distinct from particles.

Right? Well, I mean, I guess my, my, my interpretation of that is, is that we're just saying that, you know, the relevant scale of discretization is, is a lot lower than the scale of particles. So there's particles.

Yeah, yeah. So there can be other stuff going on that isn't particles. Right. Just like fluids can move around and not have vortex, you know, vortices, not have eddies, even though eddies are a good decomposition of quite a lot of what happens in fluids. But eddies are not such a useful decomposition. You just got a random turbulent field of velocities. Eddies. You could in principle decompose it in some kind of vorticity thing. But it's not extremely useful to do that. It's only useful to do that if you have little vortices running around.

Right. Particles like vortices are only discretization, are only a kind of effective field theory discretization.

They're not a. Yeah, yeah, okay. But in any case, so that means.

That, so one thing, that one thing that is, I mean, that I'm thinking about now is, you know, what happens to the Hawking. Well, you know, what happens to the Hawking temperature of an elementary particle?

Well, I mean, your claim would be that there's branch shield diffusion if, if particles are black holes.

Yes.

Even if, you know, whatever, they're, they're little localized regions of space time.

And I mean, that, that's, that's an important thing to note about this, which is that this calculation. Yes. It can be applied to black holes and it gives you the Bekenstein Hawking entropy. But actually it's a feature that you would see in any ordered region of the hypergraph.

Yeah, I understand there. Diffusion.

Right.

But you see, but here's my point. I mean, if, if all else fails, you're being buffeted by computational irreducibility and all you're going to get is diffusion.

Right.

But it could also be that the nature of the topological obstruction forces some kind of more structured, kind of, you know, just like. Look, look, I mean, here's the, here's the thing. There's a topological obstruction that gives you a localized thing in physical space. Why do you think it doesn't give you a localized thing in branchial space?

I mean, I, I don't. The, the argument doesn't necessarily rely on. I mean. So. All right, I understand what you're saying. And, and I think which more or less translates to, you know. Yes, Sort of at a. At a global scale. You know, this particle is diffusing in branchial space, but the observer only samples kind of the observer is slicing that apart in a way that makes it seem like the amplitude associated to the existence of that particle never decreases.

Yes, right. But the particle is getting smaller, which is different from saying.

But. Yeah. So why would that not hold in the case of black hole? There has to be something weird about particles. That means that observers kind of lock onto them, but wouldn't lock onto black holes, so to speak, to microscopic black holes.

Well, okay, one point is this notion of pure irreducibility leading to diffusion. Why do we think that these things are not. I mean, we could perfectly well have the same kind of localized event horizon type thing in branchial space, couldn't we?

Yes.

We don't yet know what a branch hill black hole is. We think it might be related to the, you know, Penrose objective reduction type stuff.

Right, right. And I mean, the whole reason for doing this construction is so that we. One doesn't have to deal with those issues. I mean, that the beauty of this construction is that you don't require any geometrization of branchial space.

Which construction. The one where they're just diffusing.

Yeah. Again, diffusion. I don't like using the term diffusion in this case. I understand why you're using it. But the point is that the black hole radiates even at a global scale, even if you sample the entirety of the branchial graph. Because if you assume your amplitudes are normalized, the total number of branches in which the black hole exists goes. You know, the number as a fraction goes down. And so.

Yes, go ahead.

So you could say, well, okay, then an observer that's localized to some region will also see that thing reduce. But then you have to make some assumptions about geometrization, the nature of observers and whatever. And I'm trying not to do that at the moment.

I understand. Because there's a physical space aspect to this. There's a branchial space aspect. You're saying with a reasonable region in branchial space, your aggregated flux of causal edges, AKA your effective mass. Let me make another point. In some sense you've got a superposition of black holes.

Oh, well, yes. It's not. In some sense you do have a superposition of black holes.

Right. And you're making the statement that unlike traditional. See, okay, this is the point, I think in traditional quantum measurement, right, you've diffused across many quantum eigenstates. And you say, when you do the measurement. The nature of that quantum measurement is such that you, you know, you. You go into a single eigenstate. Whereas what you're saying is for the black hole case, you're saying, no, that's not how it works. Instead, the physical quantity that I measure, namely mass, is a thing that is averaged over those quantum states.

Right. I mean, there would be a pure quantum measurement version of this, which. Which would be to say that as the black hole evaporates it. If you consider the black hole as a quantum mechanical system and it's in a superposition of existing and not existing, that the probability of observing it. If you were to collapse the wave function, the probability of observing it existing is proportional to its. That probability goes down as it radiates.

Oh, I understand. But look, there's two different interpretations here.

One is, no, I'm aware. Right. I'm just saying that would be the pure quantum measurement interpretation.

Exactly.

Rather than the reduced mass interpretation.

Right. The point is, you're talking ensemble averages, and you're talking just sort of. I don't know whether it's spatial, but you're talking sort of. You're talking, you know, you're saying you've got all these quantum branches. And the observer spread across these quantum branches is just averaging the mass across all those quantum branches. Right. As opposed to a traditional quantum observer who says, well, I've got all these possible branches, and I'm going to pick one. Now, by the way, that may be incorrect. That view of quantum measurement may just be incorrect. I mean, I don't know how. Well, that's, you know, that's what people assume. They just say, we're going to pick one. I don't know. They know that's true. In other words, maybe the. The. The question is, does the observer. You've got, you know, spin up, spin down? They occur with probabilities 1/4 and 3/4. For example, one possibility is in the ensemble, you're measuring up as one quarter, down as 3/4, for example. But the nature of standard quantum measurement is you always get plus one or minus one or plus half, minus a half. In that case, you do not get in the ensemble average. You might get 0.27 or something. But in the individual act of measurement, you get either up or down. So you're claiming that in the case of measuring quantum, you know, measuring black holes, that you don't just get, oh, the full black hole is there, or, nope, there's no black hole here. You instead get this kind of averaging process. I'm not saying that's wrong, I think that might very well be right. But it's a difference in the behavior of the observer in those different scenarios.

I would view that as just being the difference between quantum mechanics and quantum gravity.

Well, okay, but explain the nature of the observers and their difference there.

My view on that hasn't changed. Right. So quantum mechanical observers are imposing completions. So in the spin up, spin down case that, you know, they're introducing rules that say, you know, I guess for those particular numbers there are three effective rules that map the up state to the downstate, and one effective rule that maps the downstate to the upstate. And they just evolve that multi way system that's now causally invariant, even if it wasn't before. And a relativistic observer is coarse graining over a large number of microstates to infer geometrical quantities. So when you combine the two, which is the quantum gravity case, you take ensemble averages, both of spatial degrees of freedom, which you need to do to get gravity, but also of branchial degrees of freedom, which then give you things like Hawking entropies or Hawking temperatures.

Your notion of completions though, in a completion you are forcing these two things to be equivalent modulo the rules. Yeah, yeah. As opposed to in the more traditional sort of aggregate thing where you're just averaging over many possibilities.

Right.

In one case you're forcing things to pick one, in other, in that case you're averaging over many.

Right. And as I say that from my perspective, that's just the difference between pure quantum mechanics and quantum gravity.

Well, I understand that, but the question is that's the theoretical difference. But the question is an actual observer, what do they do as the observer stuffs the thing into their mind.

Right.

In one case it's like up, it's spin up, the other case it's spin average 0.27.

Again, my view has been that the observer wants to see a definite outcome. There are two ways an observer can see a definite outcome. As far as I can tell, in a multi way system, they can either impose some effective equivalence relation that coarse grains everything, so that coarse grains all branches so that they effectively evolve as a single branch. That's modulo that equivalence relation which is the completion approach, or the only information that they care about doesn't depend on microstate details, but depends on coarse grained macro state details, which is what general relativity is all about. And so when you apply that in the multi way case, that's what gives you quantum gravity, because you're Essentially saying your underlying multi way system cares about all these microstate details of the, of the hypergraph. But if all you're caring about is the. If all you're observing is the Ricci tensor, that Ricci tensor is coarse grained involves a large number of these coarse grained microstates. So the effective multi way system perceived by that observer may only have a single branch.

I get it.

Those are two different. I would say those are two different, or at least morally different things.

No, I agree. They're two different assumptions about how measurement works, how observers work.

Right. Yeah, exactly. So purely quantum observers imposed completions, purely classical observers coarse grain over hypergraph states. When you combine the two, you get this kind of interesting quantum gravity case, which is where I would argue things like Hawking radiation lie.

Well, except in your description there's no completions part.

No, but it's, it's combining the two in the sense that you are doing it. You are a classical observer who is. Whose coarse graining also induces a multi way system collapse in some sense.

Indeed. But the branch shield collapse, there's two forms of branch or collapse. Basically. One is you complete onto a single, onto a single branch and the other is you average over a bunch of branches.

Right.

Let'S take the complete onto a single branch. So I mean most measuring devices, in my little effort to survey measuring devices, most measuring devices do averaging. There are however, counterexamples. For example, a balance.

Right.

Is more your left or your right. That's sort of an interesting case actually, because that's, that's more like the, you know, That's more like a completion case.

Yeah.

What is another example of that? Maybe a particle counter. Yeah.

Yeah. I guess anything that does binning rather than averaging would be that Nature.

Right. That's interesting.

And so. Yeah, so what that means is if you were a purely quantum observer who had no notion of geometry, you would see Hawking radiation as just a. Yeah. Literally a decoherence of the black hole. So the probability of its observation just goes down.

Say that again, Sorry.

If you were a purely quantum observer who didn't care about, who knew nothing of geometry, so you only cared about multi way structure, then you would see Hawking radiation as just a quantum decoherence story. You would just see it as the amplitude, you know, as the, as the probability of observing the black hole going down.

Right.

It's only in the quantum. It's only if you're a mixture of a quantum observer and a classical observer that you see the mass apparently decrease.

Yeah. That's an interesting claim. Right. The purely quantum observer, it's either black hole or no black hole. Well, I mean, in our models, the nature. You know, if you just, if you just run with that update rule, do you preserve the effective mass if you look at infinity, at the ADM mass or whatever the heck it is you mean.

Do you mean classically?

No, I mean in the model, you know, you run the, the update rule for the hypergraph.

No, no, I understand, but do you mean classic. Do you mean.

Yeah, I mean classically, I mean, with a particular part.

So classically on for that rule with appropriate gauge, then yeah, mass is or approximately conserved. I mean, I use that as a sort of diagnostic test for gravitas, whether the ADM mass of a static or boosted black hole is conserved.

Right, So. Right. So you're claiming. That's actually pretty interesting. I mean, the, the, the. You're either in this brown shield thing. Can we see that in this picture that the black hole is just disappearing in certain branches or what, what happens there? It can't disappear immediately. It has to involve maximum entanglement speeds.

But wait, no, no, but it doesn't just disappear. So in this particular case, there's no evaporation. Right. In this picture. Because this is me starting from a black. This is like a primordial black hole in the sense that it's a black hole whose existence is in the initial conditions. And one slightly interesting feature of this is that again, unlike semi classical gravity or string theory, primordial black holes in this model don't radiate because there's no counterfactual history. There's no branch of history on which the black hole doesn't exist.

Yeah, I understand. I don't know how primordial primordial is though.

Right, right. I mean. Yes. That's why I use primordial and inverted commas in the email. Right, Yeah.

I mean primordial in the sense it's in the initial conditions. But we don't know what the heck that means because we don't really have initial conditions conditions.

But for any black hole that forms at finite time, it means that there's a branch of history in which it doesn't form. And so the argument is simply that those branches of history, you know, sort of like some viral takeover. Right. Those branches eventually become entropically dominant.

Yep.

But. Yeah, so if you, if you started from initial conditions that don't contain a black hole, but where there's a probability of forming one, then yes, you would see that you would See, progressive swamping of the, of the, you know, the black hole branches with non black hole ones.

Yes.

I can send you some pictures of that, but they become quite hard to. They become quite hard to interpret after a few steps.

Well, let me think. Okay, so, so, but. Let's see what our original. One of our original questions was. In the case of particles, We imagine much more the on off completion type measurement.

Right.

And why is that.

So? My feeling is because with a particle you're not. The information that you're inferring from it is not typically geometrical in nature and therefore geometrical information you only obtain from a hypergraph by coarse graining over a large sub hypergraph. But if it's just information about where was it, what was its energy, did it hit this thing, et cetera, you can do that without any such course graining procedure. And that's much more like the binning case of measurement, I would argue. That's not to say that. I mean, I think it probably is possible for you to do kind of more geometrized measurement of particles. I'm just not sure if that's what we typically do as well.

It's mostly we do scattering experiments. We measure S matrices, which are at infinity.

Right.

Which are very non geometrical.

Right.

Insofar as you're measuring the S matrix for black holes. I mean look, with three body problems you can measure the S matrix too. But there's more there there inside the three body problem.

Right.

Which in particle physics you don't usually consider. So you could argue that sort of were you to get inside that. Yeah, I mean it's more like chemistry. It's more like chemical reactions and I don't even know, people have a really hard time describing those things. But in chemical reactions, actually it's sort of interesting because in chemistry, right. One talks about polarization of electron clouds and things like this, which is definitely not very quantum mechanical.

Right.

Because one can see the innards of what's going on as opposed to just looking at the scattering experiment.

Right.

Where you just have the discrete result.

Right. Incidentally, it's worth saying that, you know, I don't yet know what the. I thought about it a bit, but I don't yet have a good story for what the particle interpretation. So when we tried to think about Hawking radiation before in the context of these models, we always tried to go for the particle interpretation first rather than thinking of it as essentially a bulk quantum field theory or quantum gravity effect. I haven't yet worked out what the particle interpretation of this is we don't.

Know what particle thought. So doesn't really help, I mean, because. Because in a sense by. You're saying that there's pieces of space time that have a different form than they would if there was a black hole there.

Right.

And pieces of space time we can decompose into particles in certain cases.

Yes.

So you're just saying there's a difference in space time in the case where, you know. So I don't, I don't think that's inconsistent. I just think it's rather hard to do the particle decomposition of it.

Right.

But it would be interesting to see black holes scattering. I mean, I, I think if you think about black hole scattering and what happens in branchial space when two black holes scatter, because there's probably, you know, not only is there a spray, so to speak, in physical space, but there's also probably one in branchial space.

Yeah.

Which is effectively to say. Okay, so here's a question. Is there a notion of branchial momentum transfer?

Interesting. Probably, yeah.

I mean, you know, there's an analog look, the particle is just tooling along at rest, so to speak, in branch hill space, or not, as the case may be, or it actually has a momentum in branch hill space. So, you know, one point of view about what does it mean to have momentum in branch hill space. And in your interpretation, it's like the polarizer is changing even as we, you know, the particle is staying in one place in physical space, but the polarizer is changing.

Right.

I don't think one's ever thought about that momentum of the measurement device, you know, branch your momentum of the measurement device.

Right.

Because the dynamics, the measuring device as a dynamical system has not really been thought about. So I mean, in other words, if we imagine.

In part, I suspect, because I think inertia is a lot stronger, you know, inertia has a much stronger influence in branchial space than it does in physical space.

To what effect?

It's just, I think, a lot harder to move in branchial space than in physical space.

Why?

Because there's. Precisely because it's higher dimensional, because there's higher connectivity, any given persistent structure is going to be hit by many orders of magnitude more causal edges than it would in a purely classical evolution.

Interesting claim.

You have to do a lot more computation. It's a lot more computationally expensive to ensure preservation of direction in branchial space than in physical space. I think.

Yeah, that makes some sense. But then.

Yeah, so my suspicion is part of the reason why one doesn't really think about it is because I don't think there are that many systems kind of naturally occurring where they have measurement devices which have non trivial or non negligible branchial momentum. Momentum transfer in black hole collision seems like one place where you might end up with that. And that's kind of interesting, right? That you have two black holes that sort of interact and one of them gets kicked off not just at a very high fraction of the speed of light physically, but actually with a high branchial momentum. I don't really know how one interprets that. It's kind of interesting to think about.

I think high branch momentum means that in a certain time the observer with a certain branchial extent just doesn't see it anymore.

Right, right. But, but that's, I mean, that's kind of bizarre, right? Like you see, that would predict that you could in principle have a black hole inspiral which results in one black hole being kicked out and then it just like.

Yeah, I don't know, pops out of the universe. Pops out of your observation of the.

Universe, but in a continuous way or in an apparently continuous, you know, it just like progressively shifts, I don't know, lower and lower in the electromagnetic spectrum until you can't see it anymore or something.

Well, no, wait a minute. What's going to happen is it's going to, I think less and less of the black hole is going to intersect with your peephole in branchial space.

Right? Exactly.

And therefore the black hole, I suspect. Here's what I think. I think it's stimulated emission. Basically. Basically, in this situation, the black hole is going to radiate super quickly and what it will look like is this black hole as a result of the momentum transfer it got, except it's actually a bronchial momentum transfer, just vanish, you know, just radiated away.

I see what you mean, but that's pretty exciting.

That would be pretty interesting.

No, and that's a nice interpretation for at least some classes of branchial momenta, right. That it's related to Hawking temperature in some very direct way. You get a black hole in spiral and it just results in one of them getting heated up somehow.

So branchial momentum is essentially means that as you pass out of the zone, so to speak, you radiate away.

Right.

What happens if you pass into the zone?

Well, I mean, so white holes have, you know, have an inverse Hawking, you know, have a Hawking absorption effect. Right. My guess would be you just see a time reversed Hawking radiation, which is a white hole Undergoing Hawking absorption.

Yeah, probably, but. Okay, so then the claim would be. So let's compute in this collision in physical space. No. So your claim is it's harder to move in Branch Hill space, therefore, most likely the momentum in branch Hill space is lower. But nevertheless, there can be some momentum. And the measurement of momentum is. Is relative to the maximum entanglement speed.

Right. Or maybe the momentum is. The momentum might be the same, but velocity is lower or something. It's. It's harder to move in Branch Hill space is my. My basic guess.

Yeah. Right. But if you did, you would see stimulated Hawking radiation, basically.

Right. Which is a super cool idea.

I. Yeah, yeah. How similar is it, in fact to stimulated emission? How. Probably not quite the same phenomenon. I mean, I have no idea in our models how stimulus intermission works.

I wonder if there's stimulated Hawking radiation seen in, you know, condensed matter analog systems.

Yeah, that'd be a reasonable guess. I mean. But I don't understand stimulated emission because I think it requires bosons, which aren't, I mean, you know, black holes. I have no idea what black holes are. They're not. They're neither bosons nor fermions. They're way too big. There's some kind of average.

Right, right.

In the same kind of a way that molecules are not eigenstates. So they are. Momentum operator. A water molecule has a shape. It isn't, you know, in its ground state. The water molecule is not spherically symmetric, even though.

Right.

The quantum ground state you might think would be, but it's because it's in superposition of states that has this form.

Right.

Well, interesting. All right. I think I'm probably saturated on this particular issue at this moment, But this is great. I mean.

But yeah, on a very mundane level, if you have suggestions for names of this framework. So, I mean, this. What I'm trying to do here is make a, you know, a general quantum gravity extension to gravitas.

Something which call it quantum gravitas.

Quantum gravitas.

Okay. Seems obvious since it's. It's gravity. Unless you want to change the quantum to be some other. Since you're talking about gravitas, you know, quantile gravitas or something. But I don't think you want to do that. They just call it quantum gravitas. I mean.

Okay, Yeah. I mean, I. I thought, Yeah, Q gravitas or quantum gravitas would maybe. Obvious.

I think quantum gravitas is the obvious thing. I mean, sounds cool as well. Quantum always sounds cool.

That's true. But yeah, so the, you know, the, the idea is that there'll be quantum analogues of all the standard gravitas, at least all the kind of the evolution related gravitas functions with a parameter that just says how far in branchial space do you want to go? And so if that parameter is one, it reduces to ordinary classical gravitas, but otherwise you get progressively better approximations to solutions to the Wheeler DeWitt equation.

Right, well this is all quite lovely. Second here.

Are you still there?

Yeah, just about.

Oh yeah, no worries.