Wolfram Physics Project: A Discussion with Jim Gates

you want to get this off to a good start I think we're live so let's say hello to the people I can I can still introduce you this is your show so for the people joining us we've been having breakout sessions talking about our

physics

project

for a time. While today we start a new and different type of work session which involves talking to outside people and trying to learn from them about the things they have been doing and whether or not they might be relevant to our

physics

project

, maybe other people discover things about our physics project also today for the first of these, we're pleased to have Jim Gates, who actually I guess we met like 40 years ago, that's right, so Jonathan at Caltech, yeah, right, so it's a few and then and you were you. we were already doing supersymmetry, that's right at that time, that's where we wrote our book on superspace that has become a kind of standard and we felt, oh, that's what a thousand and one is with lectures, lessons on supersymmetry, That's exactly right, okay, then.

So now you've been training, okay, that's good, maybe you want to say a few things to introduce yourself or maybe we'll call it safe, so as Steven mentioned, I've known him since 1980. I was a postdoc at Caltech and there, along with a colleague of mine named Warren Siegel, we were working on something called supergravity and this is like 1980, maybe 2, when that was a very unpopular topic, that's true, most people, that's true, most people I thought we were something like that. Crazy, in fact, I muttered my first thesis on supersymmetry and when I did it at MIT I was the only person in the entire institution who knew anything about supersymmetry, so it's a peculiar situation.

One of the interesting things I met John Schwarz. and I came to Caltech in 1979 and we started working on a problem and I was there for like a month, we didn't solve any problems, this problem was once solved in the field of supersymmetry, no, what I'm doing now, Steven. In fact, I'm trying to finish my homework from 40 years ago and figure out why we couldn't solve this problem and no one in the world solved it. It's quite remarkable so you and I are working on the task from 40 years ago but tell me what that problem is so let me eat the chemicals air screen now so we can potential let's go ahead stop the video share the screen and here we go, let me come over here.

I prepared some notes of this as you can see there is a familiar name on the side, everyone sees my desktop, yes, many, many, many points from those files, yes, so this is an introduction to supersymmetry, so let me talk Of that first if you look at all the particles in the standard model this is what we see in nature and we have a set of particles that we call force carriers, they are all bosons, which means that they do not obey the Pauli exclusion principle, like You know Steam well because you started as a particle physicist. right when you were in school at Caltech, but all matter particles are fermions that obey the Pauli exclusion principle, so you look at this table and if you see that most of the elementary particles are nice and symmetrical, you'll notice that this doesn't It's like that. and the reason is because I have classified them according to whether they are force carriers, which is the top row, or if they are objects on which forces are exerted and then I classify them if they do not obey colleagues, who is the best when they don't?

No, you can see it's a crazy table that would do it like this. It's so crazy that you might think something is missing and then you might think the world might look like this. This is a supersymmetry, so what are the currents? I do not follow. These things in great detail, but the efforts to find these associated supersymmetric particles that people expected the LHC to succeed in, etc., how far away do they have to be to be consistent with current experiments? So I think so. the LHC, which has now completed its second scientific run, has put a lower limit for masses like this, which is something like between, say, 14 and 20, its TTP.

You know these things don't have masses smaller than those numbers, so let me ask you a question. about that, I'm sorry to get into a conversation about particles at UM, so you know, back in the day, when I was at Caltech, I did this thing with David Pulitzer where we were looking at how the Higgs particle gives mass to particles and well. I know that one of the things that happened there when you try to have a very high mass particle, like a fermion, for example, with a mass given by the Higgs, the second order corrections in the effective potential cause one to have this instability. and the Higgs as a result of the Higgs mechanism, how is that avoided in supersymmetric particles?

So it turns out that in supersymmetric systems you are absolutely right, a great question, but in supersymmetric systems the voids tend to be more stable than in non-symmetric ones. systems, so that's part of there's kind of a built-in buffering process, so we can increase that number much more than it would if they just built meaningless medical systems, so a little bit of it is the Higgs coupling the fact that there is a Higgs high. coupling that leads to a large negative term in the effective potential when you have a Fermi loop, somehow there is the fact that that exists because you are canceling it out of the boson terms, that is exactly the mechanism that basically observes the fluctuations of the vacuum or so they moisten it is so you can get away with a lot more if you want to think about it that way, but you still have to pair it, I mean, if you have a 20 TV Fermi on, it has to be paired with a order 20 T V so that it's exactly right when you get to energies, let's say near the Planck scale, where essentially all masses will be neglected or negligible, but you don't even have to go high, but you're right, the pairing and the mass they're high energy abilities, you expect the spectrum to be the same, here's what yeah, go ahead, I'm curious, okay, let me ask you some basic questions here because, or you know, we're trying to understand in our models. for example, we are trying to understand how particles emerge in general in our models, we understand something about how localized structures can exist in these hypergraphs, etc., but we still haven't got a good understanding of fermions versus bosons.

I mean, I asked. next question so you know that a defining characteristic of a fermion is that you know that it is a spinor representation that it has, you know that when you rotate 360 ​​degrees you get a minus sign, etc. in your setup, I'm referring to the fact that we only have fermions and bosons and we don't have, you know, we have any z2 graded algebras and things that we don't have. The fact that we don't have things with weird Para stats, right, is obvious why it should always be that way. That's nothing. Although it's not that obvious, let's say wait if you assume that only z2 grids are possible, but what you will find is that this is supported by a lot of extraordinary mathematics that you would think is not related to this at all, so for example, example along the way and we'll get to that later in this talk.

I'll talk about yes and right, deal with that, look at the ratings, but if you follow the arc of our research, say, over the last 10 years, you'll find things like because this is the e2 rating, Oakley we can reach variety juggernauts even though that we are not talking about string theory, aha, the people on the surfaces make their appearance as a result of a series of simply impressive mathematical results. of this z2 classification, so we think there is something very special about it, but could it also have? I mean, if I had, you know, fermion bosons are plus 1 or minus 1, you know?

Could I have any other? Know? fifth root of or in In fact, those are called, as you mentioned earlier, pair statistics, as you probably remember, Steve. I spent 33 years in Russia, Maryland. I'm currently at Brown University, but at the University of Maryland I'm one of the world's experts on peer statistics, or in some ways the father. a physicist named Worley Greenberg. I remember yes, yes, but what color was before QCD and the color became before it was clear that you know when you had three, you know three up quarks in a what is that? a delta plus plus or something, it wasn't clear how that could work with the exclusion principle and I guess that wasn't exactly correct, so Warley is one of the people who said maybe there's another kind of statistic at work here and so he's an expert on that and so he actually came in while I, in the early 2000s, was actually proposing experiments that I think some were done at NIST, they didn't need colliders to do these experiments to look for this type of parity violation and there was nothing. found, but the mathematics that he had explored and developed to an extraordinary degree, but just to understand if we're looking for particles in our, you know, in our system and you know, remember we don't have and we're going to talk about this at length, we don't have , you know, a fixed dimensional space, we're dealing with this network that can have an affective dimension that can even be fractional, etc., so my question is the fact that in our more one-dimensional three-dimensional space.

The time of traditional quantum field theory is the fact that we have fermions and bosons, it's not something from Paris statistics, something that's somehow related to that dimensionality or it's something where, oh, you might know that you know Paris statistics with a permutation group. of I don't know how many elements or something good, as I said mathematically from Wall-e's work, we know that mathematically there is nothing that prohibits that from happening, the fact that we haven't seen it, it may have something could well be mine. The intuition is that I think it may have something to do with Laura's representations, but you mentioned it before and also since you mentioned the networks in the scheme that we are going to talk about, what is the set of objects that they call input networks, they are actually our starting point, although they are not the kind of networks that you are clearly working on, but they are networks, yes, okay, so I wanted those to be the ones that are related to irreducible representations, it's that right, okay, so I wanted we should.

If you clearly have a few more slides here, I think I'm doing well with one, so it looks like Boris was also in our chat and maybe we should introduce ourselves. We have at least two other people. Here we have Jonathan Gorod and someone with you, Jim Boris, who was actually my former student. I taught him quantum field theory. Okay, let me finish this and then we can start to improve, so I'll talk about JA's problem, Josh Schwartz. He invited me to Caltech to solve this problem. If you look, you can see that there are some operators that I call them D alpha D beta and then there is a factor 2 and this thing called Sigma is basically a gamma matrix, so the question is what in arbitrary. space times what are the irreducible solutions of this equation and believe it or not, if you don't impose dynamics, no one has been able to answer this question and this was the question that in 1979, in the context of something called n equal 4 theory of super yang- mills this is the question I tried to answer with Josh Schwartz and we couldn't find an answer after a month and no one has found the answers so let me understand what this equation is about.

So what are these D's in the left covariant derivatives of some kind, whether they are, in fact they are what are often called supercharges, they are the generators and we will talk about this in great detail later, but these are the generators of supersymmetry transformations. are the things that change the bosons in the firm bounce and vice versa, ok, so there is a contravention, since the nature of those types equalize and what is that partial derivative on the right, it is a survey derivative, that index that you can think it was D. mu and more conventional notation, so you have a spatial sugar bar which is a zero disease component and then you have the one which is the derivative general if you were an arbitrary dimensional space like, for example, in theory, if there were 11 dimensions, then that D, that D, the partial derivative must go through all directions, okay, but let me understand about the supercharges on the left, yeah, these are superchargers, enter a Lagrangian, for example, as you know it's like a charge multiplied by the field operator, it's true if you want to talk about some property or formula, but the basic idea is let's talk about SU 3, which is something that we all know.

A su 3 we normally represent the generators. correct matrices and we represent the states by small column vectors and you allow them to use comma column vectors and then they move the entries of the column vectors, so in that configuration of their 3 the mass called gamma and the matrices play the role of the DS here are the things that cause the movements of the representations of whichexactly right, so there's not as much work for experimentalists to go and try, but there's plenty of work for theorists here. I mean the problem that I was talking to you about that I started trying to solve with John's Schwartz is really the same problem that I'm Trying to work on Young II now with Young II and Hazel in the context of, in theory, it's essentially that the problem It appears in many different forms, so I mean, there's a lot of work to be done here mathematically, it's ridiculous, right? contact with the kinds of things that we're thinking about that I don't fully understand, but you know, we have this very simple underlying setup and we're trying to take essentially, we're trying to understand how in the continuum of limiting certain kinds of things arise, for example, and I guess the question well, not really, so let me make a proposal, Stephen, yes, since I think the common feature in both investigations is at least from my point of view as graph theory.

Yeah, so what could really be useful is to try to use our results. I mean, we have a lot of assumptions built into our result because we're only interested in supersymmetry, but to somehow try to use our graph theory results to see if they're like you said in a certain limiting case, you can see that maybe it graphs in some way. way coming out of your work, yes, aspects of your graphs, that's what I think is most interesting here, very good, very good, but I think the type of touchpoint would probably need to know this about fractional dimension.

I mean this about generalizing ordinary lis groups because you know that you are using these graphs to somehow illuminate how the representations of these groups are represented. works correctly and what I think is going to happen is that your graphs are good perfect cases where things close because they are whole dimensional spaces, which I assume is that there is a, you know if you are not so perfect that in some limit you will get something in specific cases where you know a nice interdimensional space you will get what you have and then you will get these rare intermediate cases where things don't close properly, but you can still say as an approximation that you are getting something analogous to something, let's say, fractional dimension Lee group, yeah, and then you know it, so the question is: can we get it because what we will naturally do?

What you have are things that are these sort of messy things that open up that you know might have boundaries that correspond to - you know the entire dimensional space or maybe you don't, but I think in some ways that's the point of contact. We're representing things, you know, the question is, can we go from our graphs to something where we understand how to extract something that's like representations of some symmetries from our graphs and then go back and forth from what you're doing to where you are? moving from groups of understood lis, so to speak, to a graphical way of representing representations, yeah, I mean, that's going to be what potential correspondents agree to, um, yeah, that's interesting.

I think you know we had. I know you have to go, but I realized. okay, I mean, we were, we were, we still have questions about fractional derivatives or did we, um well, I just hope someone actually does the calculation indicated by my suggestion and gives me the answers. I am so curious. to what the answer looks like, okay, I think it looks like we have Oleg, who is even Harewood from a video, actually Oleg and I have been talking and chatting in a sidebar, okay, okay, okay , okay, yes, he is the expert. in these things um and um yeah and I look like we're not going to get a chance to see the end of Hazel and we're mad we're doing well we don't know yet because actually this is our first one so let's move on , I mean, we, and the question is how long can I stay away from my day job and my job primarily, yeah, yeah, right, right, right, no.

The answer is that we are going to make a lot of these. and it would be great to continue this at some point. I mean, we've been doing live streams of some kind almost every day, but a lot of them are our internal efforts to understand different types. of things, but I think maybe some of the people here can interact separately and see if we can get to the next stage of understanding. I mean, again, I'm sure there's some correspondence between you. I just have a feeling there is some way to use representations to get closer.

I mean, you know, to sort of form this way of thinking about some rough generalization. By the way, does anyone on this stream really get it? the lien category merging category business is that someone here like a like really knows how it all works. Kevin Woodchuck will be able to do that for us. Yeah, I guess Chuck would be the person I would start asking, but I don't know for sure, okay, that's fair, I mean, I think because that's the closest case I've seen of someone trying to define these fractional dimensional Lee groups and I mean, maybe you see, see, the thing is I mean, and then in terms of the supersymmetry aspect, well, we didn't really have a chance to talk about this, but everything that is a Fermi and what a boson is really true, how do we try to understand that?

Yes, and I mean. For you, you know you've been living fermions and bosons and putting them into super super algebra and so on forever, but you know we have a pretty definite idea of ​​what they might correspond to in our systems, what, what, um. but yes, we could explain that it is important in the way that it is worth mentioning that the history of the fusion category is deeply related to the history of supersymmetry, since I am sure many people here know that the tensor categories of representations of supergroups are exactly the Deline. categories and so at some level you can think of these generalized tensor product spaces as being encompassed by super multiplets, so where does the fractional dimension thing come from, as I was saying before, from the fact. that when you do that, when you apply this generalized integral functor, you can end up with the Adaline category of tensor where your tensor product basically has a non-integer arity, well, in good, that comes out of super multiplets.

I don't understand supersymmetry well enough to know the answer, I just know that there's a duality that Tanaka cries between that sense of product categories and and, like I say, these spaces encompassed by super multiplets, so the question would be for these guys if they are you know that very long number that Jim was reciting the question is if there is an intermediate case where it is not that very long number but that would only work if you didn't have you know if in the end your space the correspondence is something that was not one of those nice things of integer dimensions, okay, there are a lot of questions that we are not going to have the opportunity to address further here, but it is a great thing, you have also done a very important job.

The important thing is that you have shown that these types of

discussion

s can really work. Can I just make a quick comment and know that I apologize for holding everyone up? It would be something very similar to you. You would have a classic twist. which is not quantized and so you know it's not an integer, but then you want to somehow get an integer representation of that in our I've seen something like this, if you know, you imagine angular momentum which is classical. angular momentum and can take any correct value, but in quantum mechanics spin only requires certainty, so we have a guess.

I guess at least Jonathan still disagrees with my assumption, but my guess is that in our systems. We think we know what angular momentum is and we think it has to do with the fact that if you take pairs of jd6 from a point that essentially defines a plane, you can then, on a graph of any hypergraph, you can effectively define a generalized plane with pairs of gd6 that emanate from a single point, then essentially you can think of angular momentum as something like what you get in terms of edges that extend across this plane in some sense and then e, so you can think If you look at these edges, you can visualize them as something like an edge vortex to some approximation.

I suppose there is a relationship between a kind of homotopy associated with the way those edges have to work and the way one can and the existence of essentially quantized spins oh yes, in physics, they are applications that work and consider how you know that It's how to get the semi-classical borderline semi-classical twist back, look, you know what, which one, what part of that. I mean the semi-classical limit that you're looking at spins very high, so you and then if you want to reduce it to a quant, then I don't do it, so I would have to charge.

Myself and I get a little bit more, but it's kind of I've seen things like you go to where the tiny terms are and then you get back the turn 1/2 or turn. I think the normal thing is to think in semiclassical limits. We're really looking at high spins, I mean, that's because, while what I'm thinking is that essentially it's like you know you have a vortex in some vector field or something and you ask there's a discrete, you know there's a you know, something topological, it's a topological discretion that arises because in that particular case, you might have a PI, one of your spaces, and I know this is very vague because I don't really know. how does it work yet, I still understand quantization there is something that is like a quantization condition.

You could look directly at the rope on the rack. There is something you can, yes, it's true. I like it like a Dirac string, but it would be nice, go ahead, Jonathan. I was about to say that what I'm still not convinced about is why if you're defiant, if you're defining spin quantization in terms of effective topological obstructions in the causal network, why don't I get classical angular momentum quantization because I don't? you are using any feature that is peculiar to the multidirectional causal network as opposed to the space-time causal network. Well, then that's a more complicated topic.

I'm sorry. thank you, thank you for joining us and we should probably end this now and continue another time. Okay, all I can say, Steve, is that this is the first time I've tried to get you interested in your house. Was it ten years ago, five? I don't remember us traveling a long distance if this

discussion

continues yes, yes, sure, sure, no, no, you seem like it, but this is what I want to say. I've been away from physics for quite some time and in case you haven't noticed. and now I'm back to physics, so also now this was very helpful in terms of understanding what you guys had been doing and I think you know I'm convinced that there's a, you know we're operating from two extremes. of a bridge that crosses a beautiful, you know, this fast moving river, so to speak, and I think so, yeah, I mean, it's not, no, it's not trivial to fill in the, you know, the middle of the bridge, but I think it's a really interesting, okay, but we should end here and thank you, thank you to everyone who joined this zoom session and thank you to the people on a live stream and it will continue and thank you Jim, okay, very good , Steven, okay, I have the conversation. and bye everyone thanks for joining us let's do this again sometime it was fun great bye