Dimensionality of Time (contd.) / Spacetime & Noncommutative Geometry

0:00 And is, where's the feed into the, into the report? That's these two, okay. Okay. Record events here, so, hopefully we'll have a record, not only in the presentations, but also questions and answers. I think I've actually gotten a request from historians of science to make them record. It was memorable again. I wanted to say a few words about the conference itself. and this event grew out of a meeting that I had with Ms. Lange Perrette and Alexis de Saint-Bruyre at a conference on history of general relativity a couple of years ago. And that actually was my first prolonged interaction with philosophers, and it's something from which I've benefited in this. So it occurred to us that since they were going to be in this area, that we could make a party to get lots of folks together to debate some of these issues concerning the nature of time. The organization is somewhat unusual, I think, as you will yourself observe as you look at this program. Since we are doing this at a small civil arts institution, undergraduate institution, we felt it was appropriate that we should devote a fair amount of time in this conference to presentations for a non-expert undergraduate and public audience. So you'll notice that we've scheduled over four hours of presentations for the general public. On the other hand, we also wanted this to be an occasion for experts to interact, and hopefully we've built in enough time on the schedule so that we'll be able to encourage that sort of interaction. And hopefully people who are involved in some related fields of science and culture will also benefit from these discussions. Because we're going to be addressing here some of those fundamental issues that have perplexed the human beings since at least the beginning of the recorded history, probably early, having to do with the age of time.

2:30 There are many, many unresolved issues. Some of them that, some of which arise in the context of our attempt at producing a quantitative graph, that is an attempt to unify Einstein's genesis of quantum mechanics. In fact, I think, particularly in this domain, philosophers have something very useful for us to say. We're actually going to have our full public opening of this meeting at 11 o'clock, at which time, in fact, this archery will be packed. I'll tell you a little secret here. So when the sign-up sheet is passed around, please don't sign it. It's for those people who are devastated in the day of the year. So I think we'll begin immediately with our presentations for this morning. And as I say, we'll undergo a more formal introduction to the meeting for the general audience of Robert Todd. Our first speaker this morning is going to, and of course these are technical sessions that we're undertaking here. There's a bit of a challenge about this, and we say technical. On the other hand, most of us who are trained in physics, as I am, will encounter some notions that are unfamiliar in philosophy, And I'm sure the same thing will happen to the philosophers. So we're trying to formulate everything in the manner that will be accessible to everyone. So Juan Carré is going to begin with a talk on time at the juncture of relativity and quantum physics. And I hope we have all this equipment working properly. I'll be standing by just to make sure. Yes, probably would be fantastic to use this time.

5:00 Well, thank you, Donna, for putting together this conference. and also thank you to Austin College for hosting it and the Foundation for supporting it as well. And I'm going to get quickly ready to the topic later and I'm going to try to express some further remarks at the conference. And philosophers looking at the foundations of physics tend to be interested on conceptual foundational issues, of course, and sometimes that takes us technical questions and we've got to navigate those waters as best we can with some training. Here, we're going to go through some basic preliminary notions and the straddle of water between physics and philosophy. And I'm probably going to do it fairly quickly and then I'm going to focus on what quantum physics may tell us about the status of time, status of And this is from a relational point of view, okay. That's the abstract of the talk, you have that. Taming classical physics is an interesting phenomenon, and when I mention taming classical physics, I think, of course, of Newton. And before Newton, there were different accounts of time, a very predominant one from Aristotle, according to a relational view of time. And Newton took, because of the idea of his physics, took a different approach to the question, the concept of time, and view time and space as independent as absolute and absolute. And what that means is that you need a background, a framework from which to be able to measure locations in space, velocities, and anything that transfers in time. So in this view, time is unique. And it has an absolute metric, meaning that when you measure a particular interval of time for, let's say, an individual, the three seconds that I just said the statement, then that will be the same for all possible terms, for all the points of the universe. Also, once we go through a particular tangent tool, once we go through T1, we can never repeat that if it's gone.

7:30 Even though the idea of classical physics, we can also say that it's potentially reversible, but I'm not going to get into that. Time and special relativity then changes the story. Einstein changed the story for us. And the suggestion was that the notion of time is replaced by the notion of space-time. Time is no longer an independent variable, independent of space, but is now interconnected with the notions of the configuration in space of different entities. So when we speak of an entity in existence, we don't think of it as possibly being in time or possibly being in space, but it isn't necessarily in space-time. And a suggestion there that we cannot think of maybe, the beginning suggests that we cannot think of entities or processes as instantaneous. Partly also because the sharing of coordinates also tells us that different operators are moving forward, different stories, different metrics, different events, time events. So the third metric is not unique, and then it's dependent on the reference frame. It's not now absolute or dependent on a background, absolute background, that Newton thought it existed. In general, relativity even gets more complicated, and what spacetime becomes, because in special relativity, spacetimes can be conceived as a sort of a, as a still as a background. background, the background that we have in the zone of space and time is replaced by the background of space-time. In general, it really tells us that when we take the gravitational field seriously, that the relations between events are not in reference to, let's say, space-time or their relations to each other, that could be really, you know, a bit provocative. So, in this view, time is not unique, and then the metric is also very hard to find because we're having a hard time defining, well, in short, of what a clock is, and of course we can, maybe for short times or for small scales, but maybe in larger scales, that seems to be good evidence that we have not hard time constructing such a clock to work for us. And in that view, then, it's probably mistaken, though many have used space-time as a background.

10:00 They shouldn't think of it as a background, but instead as a place of background independence, a place from which relations between events can occur. And the idea behind that is that we cannot conceive of space-time as a separate entity, or even as an entity at all, but instead is sort of a term, an idea that provides us to the framework on which to have relations between events, or in this case, let's say, a particular event affected by a very digital field, or fields on fields. The fields are not in space-time. We have the fields interacting with or creating with space-time. So this is very quick. And I want to focus, like I said, on what happens in time in quantum mechanics. And this can be also a bit of provocation for a theory. I'm not sure. We'll see. It's my book. And just take a quick look at the very famous Heisenberg inequality, often referred to as the Heisenberg's uncertainty principle. And immediately we say uncertainty principle we realize it contains a little bit of a prejudice, of a systemic prejudice. And what I want to suggest is something that has been done the way we interpret the Heisenberg inequality is metaphysically or not, just as a model. So let me explain how it works. In Heisenberg inequality, what we have is, this is not the only one, we also have others for positional momentum. We have conjugate variables that turn out to be, what I like to think of them as sort of entangled, correlated, that properties of a system that, of describing the inequality, they tell us that we have a limit in our system, that if you want to know the precise energy of the system, then that we give up exact knowledge, or knowledge of the time that occurs, and vice versa. The way I presented that is sort of the traditional view, when finding many quantum mechanics texts, it also describes the uncertainty view, principle, and that's an epistemic interpretation, really. Because what we're saying is that this particular inequality is that it has something about our knowledge of the world,

12:30 meaning that Heisenberg's principle limits as to how much we can know about a system. Of course, a system can be perfectly fine, but we just don't know about it. And that was one of the problems Einstein had with this inequality because Einstein wanted to understand the physical equation metaphysically and he didn't want to accept it as it was and propose many, many, many thought experiments against it, the most famous ones related to EZU-PR, I'm going to get into it right now. Also, not enough, about five minutes left. Then what we have is the possibility of interpreting this very basic idea from quantum, very foundational idea from quantum physics, or more deeply, metaphysically. And the suggestion here is if we think metaphysically, what we're saying is outrageous. And in many places it says, oh, please don't interpret it like this. So I'm going to do it. So what we have is metaphysically, if this equation is something about what the system is, is that if we have a system with a given energy, then that energy, the uncertainty of that energy is given by the delta E, is correlated with the uncertainty that we have in the time that always that system exists or gets interacted with. And so imagine the situation in which the uncertainty for E becomes very small. In other words, we try to very accurately know the state of the system. Then there's a little bit of a problem, we would say, with the uncertainty on time, that the L and T becomes very large, and vice versa. If we try to figure out a system or try to take a system into an instant, delta t becomes very small, close to zero. Then what we have is the energy sort of explodes. And the idea or the challenge that I want to propose is that if we take it this way, then what we say is something about the systems themselves. the ability, given Heisenberg's inequality, to encompass a system fully. Because they encompass a system fully to completely have an oscillatable system with precise energy, a closed energy system. Then what we're saying is that we're

15:00 going to have it at an instant. We'll have to have it at a very long period of time. And Heisenberg, so we want something in an instant. Then we may lose the ability to speak coherently I want to say in your five minutes that maybe somebody can say it better than I can, all right? Maybe Cecile can, because she knew our husband very well. This is an insurgency that happens between the curvature of a simultaneity and the temporal curvature. That's as best as I can say it. It makes it better later on in this conference. found of uncertainty in the geometry itself, not just that thing up there. And I want to make a point now. Yeah, I wouldn't say nothing. Sure, sure. And I think some, yeah. And I'm sure we'll come back to that question. But for now, let's skip to this. And I call it the problem of the instance. And some resolutions have tried to go beyond this. And one way of looking beyond is, of course, to ignore it. And one way to look beyond is to take it very seriously. because I think it's very serious when I get into that. But one way to think about systems that maybe gets around or helps us think through, not only tax-improvement equality, but the well-known problem of measurement and other, is Robbelli's relational account, which came out in 1996, and proposes a very simple claim. I think I have some slides. I have a lot of slides. That suggests that the relational view, what we have is what we cannot do is take the notion of a system as defined absolutely. What really tells us is that what we need is the idea that systems have to be defined by another system. And this is constant of what we find really in classical physics. We find the energy in a classical system, we find the energy of the system is not basically absolute. It's depending on the choices of the boundaries of the system. And we also have that very, of course, in relativity. It can mean different things in different contexts. But here, the way I want to take it

17:30 The notion of relation is we need to rethink a little bit on how we understand systems and systems of interaction. We tend to think in physics, and even in philosophy, it's very common, that we can do that without that. I isolate the system, then I do my experiment, and then I'm fine. Well, relativity needs to show us that we need to think about events in connection and interaction. And we see that one of the physicists who It needs to suggest, as a matter of fact, one of the very promising, very popular now way to resolve the problem of measurement is decoherence, which tells this idea that in decoherence, you cannot just take the system and be fully accelerable. What you have is the system also be open to some, all the systems, cosmic rays or whatnot, like the cat coming from them, that will upset the coherence. the state function of the system will then begin to wane away, begin to decohere, and not collapse instantly, it might take some time, eventually it will be so small, that a human effect will be so small that we get, certainly it's going to be an impact on micro-systems. So it's a similar idea, it's a very simple thought that I'm presenting, but one that if taken fundamentally seriously, can sort of help us rethink maybe how we understand time. So let me say a little bit more on, how am I doing in time? I'd say 15 minutes of discussion. Okay, so five minutes. So, very quickly what really does gluquantum gravity is, is, of course, Luquantogravi is the camp to think relatively in quantum physics and bring them together, take both very seriously. Other approaches to Luquantogravi have been to really disregard some of the conceptual ideas of relativity, some of that sometimes to be really known what quantum physics offers, but really think both seriously. And Luquantogravi suggests that time maybe is a notion that should be left out of our conceptual consideration, that we can take time out of our equations and just simply speak about the analytical variables. And some people have suggested that by doing this, well, we have a view, a view in which we have a frozen universe.

20:00 And using the equations, then, since time is not there, And my claim here is with this idea of the original view in mind, thinking about time is that I think that's completely the opposite, I think, and I don't want to prove it in place, but rather than being left out, I think what so fundamental that it's sort of built-in into your system. That's why we speak of dynamic variables. You can not have a variable or a property of a system at a given instant. You're ready to have it immediately in this sort of dynamical, at least with sometimes times, dynamically engaged with other systems. So rather be like that time is just built-in. So physical variables, and Rebelli says precisely, there's evolved with respect to other physical variables and not with respect to a need of time, an absolutely or independent time, where you have fields on fields, those fields are identical. The dynamism and interaction together, we can then eventually, at certain levels, be able to draw out from that this notion of what we call time. It could be classical time or psychological time. But time may vanish, but of course, the idea doesn't. What I'm saying is more fundamental. would be a mistake, as we know, that we sometimes conceive the notion that we can stop time, that we can sort of put a stop into the system, and consider the system of time to be zero. Well, these ideas suggest that we can do that, that we inherently, we inherently hold the notion that there's a delta t, so to speak, an minimum delta t that we have to consider. So there's not going to be frozen, ever frozen. Maybe at the end of the universe, there's not going to be a frozen moment, or there's not going to be an instant. So this is the suggestion, no instance. So what are the problems, especially in philosophy? Well, why end of this in one year is that maybe we made a mistake, the policy of misplaced concreteness, in which we took time as we experienced it. We gave it, it was a concept, it was a very hopeful concept. We agreed to do some things with it, and then we said, okay, well, it must exist in a particular way.

22:30 Well, as we've gone farther in our physics, we realized that that way we have to spend time, it appears less than us. Well, time is independent, continuously flowing, but then, especially where the degree in, and the degree we found is interconnected with the space coordinates. And the way I would like to think of time is not as a complete entity, independent of brother, is, of course, as a round of potential for interconnection of systems. As another result of saying, oh, we have no time. What we've got a bit of is the misconception of time. We really didn't get rid of time. It would be absurd. We don't want a frozen universe. We cannot do anything in a frozen universe except freeze. So what we can expect is fundamental theories to build on this dynamical evolution. And this dynamical evolution entails a relational view. to forgot the notion of time as an instant, or really even as an entity. So for the sake of discussion, yeah. If I have another hour, then I'm going to go more quickly into that, but good enough. Oh no, you have five minutes and then five minutes of discussion. Oh yeah? Then it's very quickly. I'm going to go through some of this, but I'm going to go through the end of the hypothesis related to... You won't have to find that at such a moment, right? After looking at Morelli's relation to telepronics and physics, of course, keeping in mind what we learned from relativity, philosophy of thought about time, well, some philosophy of thought about time, because some have thought that maybe there's a way to understand time, as an entity, time made up of instances, and there's an infinite amount of instances. And my suggestion is that that's the wrong way. It goes against the flow of what our class-specific theories are doing. So now thinking more about quantum mechanics and time, my hypothesis is that we can think about quantum mechanics as relational. But to fully make sense, my thought is that we need to think of what happens to the systems. But what the systems is, if you keep in mind, as per as equality, the suggestion is that we are approximating when we say we have an energy of a system, and we have a system at a particular time.

25:00 That approximation doesn't work very well about quantum physics or foundational issues. And instead, what we need to realize we have with our systems, and of course when we come in and measure, that's a pretty strong type of interaction that's going to affect the system in some significant ways, as we would expect it. We have a little electron and a microscopic type of experiment comes in. Yes, we're going to find the electron smashed in, looking like a particle on the screen, but in fact a strong interaction has affected the state of the system. So the way to think is with the idea of the coherence, but also the notion of complexity, and there's I'm particularly thinking of here's notion of quantum event. And by quantum event, he's thinking about taking metaphysically serious the notion of latency, the notion of probability of the way of functioning. And that's telling us something about the world. It's not something about that knowledge of the world, but it's something real about that and that coherence, which most of us . And then the notion of complexity of scales, that, for instance, if you're thinking about a very small scale, then you get especially the kinds of interactions to produce, maybe what we call measurement, but not some others. Other scales, let's say, human scales, different kinds of measurements will provoke different type of interactions, and maybe what we call measurement would differ. So the idea behind not just using time conceptually differently in the difficult physical theories is that artificial scales and interactions might affect as in how the notion of time comes into play a particular role, or just the notion of time, then also what we call a measurement, or even what we call the energy in the system. At the classical level, we would probably, it would suffice to say that we have the energy in the system, But at the fundamental level, we take seriously that into consideration, maybe not as a practical result, but from foundational issues, the idea that those systems are inherently open. Open interactions aren't actually considered the system unless it's already described by another system. That's the point of Robelli's relational view. So maybe I'll just finish with this, and there's been a lot of gaps in the data, and we can explore some of those.

27:30 But in short, the notion of time has to be really thought, thanks to these ideas. And the most promising way to do so is by, I believe, thinking of interacting between systems, So I think we have five minutes for questions. If you could identify yourself, perhaps just the name of the question, that would be useful for our residents. I remember the story about the meeting of Laplace and Napoleon. So Napoleon asked Laplace about what in his construction. Laplace said that I don't need that hypothesis. So in the sense that the equations tell everything at that time, at least about the evolution. What about your hypothesis? What do you think about it? Well, with this hypothesis, it really is more like an idea to be pursued in the line of development. I'm not suggesting it. Okay, this is a form of experiment, but it's going to be a linear line of direction. And I think that the line that I'm suggesting is to take a relational account for a series, metaphysics of relations, and you can say many things about this. There's been quite a few authors that work on relational metaphysical accounts from Whitehead to Sinatra and others. But maybe that hasn't been in tradition, though. Tradition doesn't mean to avoid relational views, because the question is always the end. Relation between what? Where are the entities? We always wanted something solid as well. And you had the ideas of it, okay, so maybe if you're looking for it, you cannot have it. But then also, when we do that, we look at relations, but we don't take away the version of systems as already made. We need to realize that systems are given by other systems. And then, in fact, the coherent suggests that we need to be very that we need to keep the systems open to interaction. And at some levels, at some scales, that interaction could be pretty decisive. At some other levels, it might not be. So it's sort of a suggestion for a line of further inquiry

30:00 and rather, behind this, God, and God. Chris Biegler, what in this approach would separate a good clock like my watch from a bad clock like my shoe? Yeah, that's a good question. It depends on how well the shoe takes. Well, I think I presume there's more in terms of relativity rather than quantum physics for that. But what I would say, well, it depends what you want to do. I mean, of course, in terms of maybe this clock or maybe a pulsar, I mean, what constitutes a better clock? Well, it depends what scale, it depends what you want to do. And at some cosmological scale, maybe your watch is not going to do very well. I think Pulsar would be able to do as a nice way of hearing. I put another dispersion class on that question, but that is my initial thought. So this seems again to—so you're describing characteristics like lifetime and so forth, which of course is a temporal notion. When you identify the scales, there seems to be a bootstrapping problem. You want everything to be absolutely relational. Yeah, there's a time scale associated with my shoe decay, and that does. Then I'm already assuming a particular clock ticking behind. Is that what you're suggesting? Yeah, that's what I'm suggesting. Well, the answer to that is no, I'm not assuming a clock ticking. What I'm saying is that the possibility of a notion of a clock is given by interaction between systems. I don't think you're going to have a clock even to have the kind of interaction. In other words, a clock is already an interaction between, let's say you have a quantum-mechanical experiment, what you do is you measure how long a decay occurs. Well, that needs to be thought quantum mechanically, already, that interaction. Not that, oh, we have a clock, and then this is quantum-mechanical, and then this. Of course, semi-classical approaches don't work very well, but what I'm saying is that the interactions between quantum mechanically and if you do, then, of course, as we understand from uncertainty, energy, uncertainty, regulation also applies to that clock, and that idea, as I'm taking it, then suggests that there is not going to be an absolute clock that we can run with, but in that, we're going to get the objectivity because we have a particular way.

32:30 and function well enough what we need to do. But for a cosmological scale, I know it will work for us very well. Thank you for the conversation. I'm here as our next speaker. We'll get a chance to ask more questions and plenty of opportunities. So our next speaker is Steve Weinstein, who is going to talk about the dimensionality of time. And I think we'll have to make a few modifications here for him to be able to speak. Yeah, there's an off button on there. Can you find it? I'll find it. And you're going to use the platform, right? Yeah, I'll get it. That's what I was trying to do. Well, I'm not going to write very much.

35:00 How's this? Is this good volume? Not that I know how to adjust the volume. Okay, I can mumble if necessary. Okay, good. I'm only going to use that a little bit. I wanted to talk today about some thinking. I was thinking I've been doing about the dimensionality of time, and it's part of a, well, it's part of an old kind of philosophical issue. It's a new aspect of an old philosophical issue, which has to do with asking how much of our picture of the physical world is a projection of our minds, a projection in some sense. And as a couple of precursors to the work I'm doing, I mean, I would cite fairly obviously Kant. So Kant thought about space and time, and he thought that they were both, in a sense, projections of the mind, that space and time were constructions imposed by the mind, not so much on experience, but that experience was built out of the mind's action on this, the world of things in themselves. The mind sort of shaped, presented the faculty of understanding with experience in the form of spatial and temporal events. So Kant thought that space and time came from the mind, and he thought, as a result, that this was, for him, an interesting way of explaining why space and time had the properties that they had. He thought that, among other things, that space was three-dimensional and it was Euclidean. Conk was paid a big price for claiming it was Euclidean, because we all know it's not Euclidean now. So he thought that space was three-dimensional and Euclidean, and that it was necessarily so, that experience wouldn't even be possible if it were not. So, now, that was a fairly strong and bold claim on his part. Later on, kind of in the Kantian tradition, Poincaré, who was also one of the famous mathematicians, as most of you know, who also was one of the developers of the theory of

37:30 relativity, investigated the conventionality of geometry, spatial geometry, and he held, like Kant, that not that space was necessarily Euclidean and presumably three-dimensional, that Poincaré was a kind of conventionalist, and Poincaré thought that it was a convention that we adopted, that it was Euclidean, but that it was a convention that we were unlikely to ever discard. So that lasted another 20 years until the general theory of relativity came along, and Theory of Gravity, which regards space and time as well, space and time as united into a unified framework, which is known Euclidean. Okay, so there's a bit of a history of sort of thinking about these things as, thinking about the features of space and time and wondering about the extent to which they're, in some sense, and to what extent they've given to us, imposed on us by experience. And what I wanted to do for this talk, pretty briefly because I don't have too much time, is talk about the dimensionality of time. And so not really, this is not a question of geometry, it's a question more of a topological nature, I suppose you'd say. This is motivated by these kind of older investigations of Kant and Poincaré, but more recently by thinking, in part by thinking about string theory, okay, and string theories, as you know, have been developed over the last 20 or so years. Actually, I suppose 30 years is the real beginning of the whole exercise, and string theorists have been pretty free about multiplying the number of spatial dimensions. This is actually an idea that goes back at least to Kaluza and Klein in, I guess, the Is that right? Kaluza-Klein theory. But it's really sort of taken off in the last 20 years, and so modern string theories tend

40:00 to be formulated in nine space and one time dimension. So you look at that and think, well, people seem to be pretty happy to multiply spatial dimensions, but why not time? Can you do that with time? And I think that there has been a little bit of work done in string theory and very little elsewhere on this, but not so much, in part because it's philosophically and conceptually difficult. But I think it's a really worthwhile exercise for a number of reasons. One is that you might get some new physics out of it. It could be that a more convenient and informative description of the world is one that has more than one time dimension in it. But furthermore, even if that doesn't turn out to be the case, get a much better grip on, by studying multiple, the possibility of multiple time dimensions on the role that time actually plays in physics and the difference between time and space. Because I think one of the things that you've noticed is that despite the unification of space and time into space-time that we've got in the theory of relativity, they still, space and time play quite different roles in the way that we think about the physical world and the way that we think about experience. And I think this helps to, thinking about this helps to clarify, helps to bring out some of the roles that time traditionally plays in our thinking. So what I want to do is just sort of investigate to sort of set up this problem. I just want to give a simple example. of how this might work, and then suggest a couple of the directions that it might go as far as the sorts of physical problems that it might explain. So now I leap to the board. And what I want to do is I want to consider, well, first of all, I just consider a particle moving in one spatial dimension, one time dimension. So we'll just get something like this.

42:30 And we're going to describe our particle by some world line. We'll assume that the world line continues on. Okay, so this is a standard toy example. A point particle traces out a line in this one-dimensional space-time. So, and similarly, usually when we're doing physics in one dimension or three spatial dimensions in one time dimension, we're not only going to, well, we model observers in the same way. So, there's the question of how you model in various dimensions operas and how you model observers. to assume that observers are, that all observers are objects, but not that all objects are observers. And this is not a huge, deep point. This is just really saying that I'm going to be a physicalist, and that I think that observers are some sort of species of physical objects. So typically, in a one-dimensional space-time, you might idealize an observer as at least a very slender observer as a world line. I'm approximately a world line. But some people are sort of world twos. And the things you observe might be, I mean, I should say, not all objects. Particles re-idealized as lines, fields, of course, filled, in some sense, all of space. But moving back to the side, how we might generalize particles of observers to two-time dimensions. So this is absolutely the limit of my drawing skills. We have T1 and T2. Now sometimes what people do when they're studying this is they just continue to assume that, well, world lines here, going to world lines here, that just to talk about two-time dimensions still represent objects and observers, when they discuss observers, as lines.

45:00 However, this, well, there are reasons to do this and reasons not to do this. One reason, not the difficulty of doing this, is that it's not obvious what you, how you describe interaction, because you can have two lines which are parallel, even though they're occupying the same path in X and T1. So in other words, you could have things that are projected to this point, and you just look at what's happening in the X and T1 plane, you could have two objects which are moving side by side, which are crossed, which are set aside in the T2 direction, and d2 directions and directions coming out of the board, so that they don't interact, at least they don't interact by contact. So what you might do is you might think, well, you know, the natural generalization of a one-dimensional, one-spatial-dimensional object, a point object, in one time dimension is something that is also extended in one spatial dimension, but is extended in both time directions. And you might draw that as a kind of a membrane, a sheet. So this is supposed to be kind of a, this is terrible. So these are some fuzzy boundaries, I'm assuming. I'm drawing this because I'm imagining this sheet is an infinite sheet. Okay, it doesn't have to be a finite sheet, just in the same way that this line is really, it doesn't matter if it isn't that fine. We might have a sheet, this is supposed to be a sheet coming out of the board, so projected onto this plane, it looks like a wrong line, but it's actually extended in both time directions. So that's one way to think about what an object might be or what the generalization, I should say, of a particle might be in a theory of two time conventions, and this gives you a a different way of thinking about interactions. You might think about interacting with your membranes. You might still, if you were doing this,

47:30 insist on, you might say, well, that's all good for objects. But I know from experience, from either my own experience or my philosophical investigation into the nature of experience, kind of a funky thing, that experience is something that only happens through one-dimensional objects. So what you might say is that observers, you can imagine that observers have to be things which are effectively one-dimensional, okay? So being an observer is trapped on some sort of one-dimensional, of what the surface is one-dimensional is, extended at one time dimension. This is a kind of analogy to the way that some people who have done, what some people have done in string theory with extraterrestrial spatial dimensions is this so-called green world scenario of the Calcobar or the Sun, in which the conjecture is that our universe membrane in a nine-plus-one-dimensional space-time. Somehow there is some physical mechanism that confines us to this membrane, but that physics actually is, in general, is going on all through the nine-space-at-one-dimensional. So there's a, if you, I'll say one more thing about this really formative diagram is that it gives you some idea that observers can be represented in this kind of way. And you might not want to talk about observers. You might say, well, I don't want to get all, you know, get too subjective. I don't want to talk about measuring devices. I want to talk about my conception of observation as merely to do with, say, forming records, okay? Okay. But you might ask whether or not, well, if you thought about this as an observer, is this something that would be multiply conscious? Okay. Is there a single consciousness, a single string of experiences that you would associate with such an object, just like here? This is a representation of an individual who perhaps has a memory of events and interactions that occurred along here, but doesn't know about, at this point, doesn't have a record of stuff up here, this would be the future.

50:00 you can wonder about whether or not there's a possibility of physical objects which represent multiple consciousness and there's two sort of ways to think about this you can ask well is it possible that I'm one of them or you can think well it's pretty obvious I know pretty well what my experience and my consciousness looks like and it's pretty definitely one dimensional but I'm interested in thinking about a broader spectrum of possible worlds and I'm wondering just by the nature of consciousness is it possible to conceive of something that has kind of multiple consciousnesses, multiple streams of experiences associated with it in virtue of the fact that it's extended into time dimensions. Okay. So if you're to be a very useful, they're giving the pragmatics to be a very useful exercise. Okay, so what do I have? I have 10 minutes, right? Is that right? Okay, well, I'm going to just view a couple of interesting possible consequences and then open this up to questions. So what could you do with this? Why would you even look into this? A couple of thoughts have occurred to me. well, what they are is you can ask, can a world of multiple time dimensions be deterministic so formally, is there an initial value problem in such a world well, in general, this is going to depend on what the equations are governing for physics in such a world but this has been studied a little bit and it's interesting in that so for the wave And I guess I'll actually just write that down. The wave equation in two time dimensions, three space and two times, would be t squared pi. And it squared is a constant, of course.

52:30 So it just looks like a regular equation, except it has an extra regular rate, but it has an extra T. This does have an initial value formulation. In other words, you can give data on a 3 plus 1 hypersurface, an initial sort of surface in this large spacetime, which is extended in free space in one time dimension, and evolve it uniquely. and have a deterministic evolution. What you can't have, interestingly, or what you don't have is a well-posed initial value formulation, which just means that you can't freely specify initial data on such a surface, okay? Whereas an ordinary wave equation, you can give any smooth initial data, any smooth scalar field phi on a three-dimensional hypersurface and evolve it forward and backward in time. Here you can't. Now, this looks, well, obviously from a practical point of view, it makes life somewhat difficult. It does strike me, though, that it's a potentially interesting way of explaining initial conditions in the universe. Because this is something that cosmologists worry about a lot. where we have these equations, but our universe is a solution to, is a single solution to these equations, and it looks like a highly special solution. It looks like the universe started out in a fairly homogeneous, a highly homogeneous initial state. Why is that? Well, this is one way of potentially understanding it. I mean, it may be, the idea being that if you regard what we describe as our universe as a kind of a slice, a projection onto one time dimension of a universe which is governed by partial differential equations, and two time dimensions, you might find some serious, or you will find real constraints on the possible initial data there. Now, there's a general difficulty in any non-trivial case about trying I mean, it's not straightforward to write them down analytically. But it's an interesting thought. As far as quantum theory goes, I think that there is also some interesting ideas here to play with. One very kind of simplistic, I think, idea, which when X brings on path,

55:00 then it will probably shoot down immediately for some probably highly technical reason. is that you might think, in quantum mechanics, what you find if you're doing path integrals is you sum over, you can take the possible trajectories of a particle, whereas in classical mechanics, particles follow paths of extremal action. That's a technical term, but this is the technical session, so I can use that line. Paths of extremal action, in quantum mechanics, you sum over paths of all different actions. If you have more than one time dimension, what you might do is you might conjecture that what's happening is that particles are following paths of extremal action, and only extremal action always, but in some sense utilizing the extra time dimension. And what you see when you're doing quantum mechanics is what you're doing, again, is you're projecting this physics in two-time dimension into one-time dimension. So it looks, when you do this projection, as if the particles are following paths of non-extremal action. So it's a way, this, as a suggestion anyways, is a way of thinking about what quantum mechanics represents physically, which has long been a problem. People know well how to use it, know that it's a very effective, predictive tool, but it's not clear what it says about the universe. So these are both actually, I think, relatively conservative ideas in that they both operate by quickly taking whatever physics is hypothesized to be operating on the multiple time dimensions and projecting it back onto a single time dimension. So it's sort of insisting that our experience is an experience of a world, or we experience the world in one time dimension. It's kind of almost like a holographic screen, but the world actually is extended in more. You might go further and actually try to reconceptualize experience. But, you know, given that I have six minutes including discussion, I'm not going to reconceptualize experience right now.

57:30 but I would say just in closing that the other advantage to thinking about this seemingly far out subject is that I think well as I said at the beginning it gives us a better sense when you think about the difficulties of actually pursuing a program like this it gives you a better sense of what the role that time is playing in physics in terms of things like determinism things like conservation laws conservation of probability and information quantum mechanics and unitarity. And in general, I would say we'd better know what it means to say that our universe has one time dimension if we had some idea of what a universe with two time dimensions might look like. Okay. A couple of questions. From what I understand, you're talking about a diacronous experience. There's a diacronous experience, that we have a diacronous experience of reality. There's been a lot of work in, well, I'm sure certain aspects of physics and philosophy. Philosophy we talk about that physically detenses the time. In respect to that, there's a, I've heard of this, I read an article by that was very interesting as far as our approach, and I think Whitehead actually has a lot to say about it as well. I'm not sure that the model that you're presenting here is implying that there's a tense notion in time. I think that that's something that we have to really consider, is that there, is there a tense aspect in time, or is it an aspect of, I guess. You mean of existence? Yeah, existence. In what we're dealing with right now, the one-dimensional model that you're presenting is a model of, I guess, what you could see metaphysically as being an ever-present reality. That you're traveling through an ever-present reality. And the question then is how long is the moment of T1 being our, what is being revealed to us at the present, how long does that last?

1:00:00 Nevertheless, the frame of reference that we're dealing with, one, is arbitrary in regards to where we align with ourselves. The only thing that we have is where we are now. So you have it. The question, I think, has to be, I need to ask is, are you conceiving of this physically? I guess, within the physics, are you conceiving of it as being tensed, or are you treating the frame of reference of this diachrony as meeting in the present? Right. Well, the way I approached it was not phenomenologically, which is kind of how you were coming at it. You immediately started talking about experience, and experience being diachronic. So, you know, you can do whatever you want, but what I did is I took some... I started with some abstract models. I mean, these are barely even worthy of being called models, right? Because there's really, I haven't said anything about interactions and dynamics or anything. There's not that much physics in here. And then kind of backing off and then trying to figure out what you might say about the contents of experience in life. If the world was described by such a model, what would the implication be for experience? and I imagine you would still have some ambiguity so even in this single this world with one time dimension you have many of these questions that you raise coming up which is the context in which most of them are raised does time flow what is the difference between the future and the past and so on I don't know that any of these frameworks is going to come down on one side or another although it could be that you're forced to what looks like an optional view here becomes mandated when you add a time to mention. That's an incomplete answer, but it's a huge, huge topic. So sorry.