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The Structure of Time and Space | Stephen Wolfram — Transcript

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0:00The notion of time is the progression of
0:03computation. So something we say this
0:06event happens and this other event can
0:09only happen after that first event later
0:12in time than that first event because
0:14that second event is using the output
0:16from the first event. It's consuming the
0:19kind of atoms of space that were created
0:21in that first event.
0:25[Music]
0:30Welcome to Closer to Truth. I'm speaking
0:33with Steven Wolfrram, the distinguished
0:35physicist, computer scientist, and
0:37software entrepreneur. We're discussing
0:39in depth the Wolfrram physics project.
0:42Steven's grand indeed radical vision of
0:44a new kind of science in which
0:46computation via simple rules is the
0:49foundation of physical reality. The Wolf
0:51from Physics Project is a closer to
0:53truth multi-part series. This is part
0:55three on a path to a fundamental theory
1:00of physics. Stephen, let's start by
1:02giving a quick overview of the physic
1:05the wolf from physics project itself and
1:08then we'll get into how you get to this
1:11path to a fundamental theory of physics.
1:14>> So the the question is what's the
1:17universe made of?
1:18>> And our physics project basically says
1:21the answer is it's computation all the
1:23way down.
1:25And so let's see what that means.
1:28Essentially the one sort of historical
1:31path we can take is back in antiquity
1:34people were sort of wondering what's the
1:36universe made of? Is it made of atomic
1:38discrete things? Is it made of kind of
1:40continuous flowing things or what? By
1:44the end of the 19th century partly that
1:46was answered. Matter is discrete. It's
1:48made of discrete molecules. Little bit
1:50later, you can think of light as being
1:52made of discrete photons. At the
1:54beginning of the 20th century, a lot of
1:56physicists assumed that space would be
1:58discreet as well, but they couldn't
2:00figure out how to make that work. In
2:02fact, they published very little about
2:03it. It's only very recently that I
2:05learned that all the greats basically at
2:07that time thought that space was
2:09discreet. And even like Einstein made
2:11comments like in the end, it will turn
2:12out that space is discreet, but we don't
2:14have the the appropriate tools to see
2:16how that works yet. Well, 100 years
2:19later, I think we do. And uh the sort of
2:22beginning of a project is to think about
2:26what's what's the universe made of and
2:29what is space made of. We don't usually
2:31think of space as being made of
2:33something. We just usually think of
2:34space as being this background where we
2:37can put things here or there or or
2:39anywhere. Um but like a fluid like water
2:43we now know is made of molecules. So we
2:46think of space as being made of discrete
2:49atoms of space, not atoms in the in the
2:52sense of of material atoms, but these
2:55indivisible points that uh we can think
2:58of as sort of the raw material of space.
3:01And kind of the the starting point for
3:03thinking about what the universe is made
3:05of is to think it's it's this giant
3:08collection of atoms of space where the
3:10only thing we know about atoms of space
3:12is how they're related to each other.
3:14sort of what the friends of one atom of
3:16space are. And so we can represent that
3:19at a sort of mathematical level as a
3:21graph or actually more in the way that
3:24we set it up as a hyperraph. Uh a
3:26hyperraph is just something where you're
3:28saying we have these these points these
3:31nodes and have these hyper edges in
3:34which we associate we relate some number
3:37of nodes together. So an ordinary graph
3:39we'd always be relating pairs of nodes.
3:41In a hyperraph we can relate any number
3:43of nodes with a hyper edge so to speak.
3:46So
3:47>> and so this is a key point using
3:49hyperraph which is uh a a a
3:53representation of a computation to
3:55represent space. This is the is this
3:58kind of the first step in the path to
4:00the fundamental theory of physics.
4:01>> It's not representing a computation. The
4:03hypograph is just it's kind of like if
4:06you're a computer person it's it's a
4:08data structure. It's the data structure
4:10of the universe so to speak. Um so it is
4:13it is just that is the structure of
4:15space and everything in it. So another
4:17feature of of of our model is that
4:22there's there's nothing in the universe
4:23other than space. Everything that we
4:25know the electrons the photons us and so
4:28on. It's all just features of space. So
4:31it's like we if we were dealing with a
4:33fluid like water we would say well
4:35there's this eddy that goes through the
4:37water. That eddy is ultimately made of
4:40molecules just like any other feature of
4:42the fluid. But the eddi has some some
4:44independent identity to it. And that's
4:46kind of the way we imagine something
4:48like an electron works in in in space
4:51where the space is built up from this
4:53hypograph. What at the bottom everything
4:56is just represented as this hypograph.
4:58And that's that that everything about
5:01the universe is represented in the
5:04structure of that hypograph. When you
5:06say represented, do you mean represented
5:08in a modeling sense or in some ways as
5:11as of the reality itself?
5:15>> Well, you know, usually we're used in
5:17science to saying we make models of
5:19things, which means we're making an
5:21approximation to how something works,
5:22right?
5:23>> Where we say we capture some features
5:25and ignore other features. This is the
5:27unique case where we're trying to nail
5:29it. This is you know this is the
5:32ultimate model because this is this
5:34there is no approximation we're talking
5:36about this the idea is that this is what
5:40a representation of the way the universe
5:43works now I say representation because
5:46it's it is what is what is the nature of
5:49a model a model is or is is something
5:53which is trying to translate between
5:55what the universe is actually doing and
5:58what we can understand with our minds.
6:01So when I say it's represented as a
6:04hypograph, that's the way that we can
6:06conceptualize what's going on. If we say
6:09in some sense what is actually there,
6:13it's that that's that's that's sort of
6:16that's a different kind of thing. That's
6:18not it. It's like saying we have uh
6:21Newtonian you know the the equations of
6:24mechanics uh from you know the calculus
6:27equations that that Newton produced and
6:29we say you know the earth is moving
6:31according to this law of gravity and so
6:34on. We don't imagine that the earth has
6:38a computer inside it that is you know
6:40solving those equations. We imagine that
6:42those equations are representing what
6:44the earth does. And and this is the same
6:46kind of thing with the with the
6:48difference that instead of saying this
6:50is an approximation to what's going on,
6:52we're saying this is the whole story of
6:55what's going on. And so you know the the
6:59the the first step is to think about
7:02sort of the structure of space and
7:03everything in space. The next question
7:06is so what happens with this? How does
7:08time work? This is the static structure
7:11of space. How does this progress through
7:13time? And the idea is that this network,
7:18this hyperraph at every moment pieces of
7:21that hyperraph are being rewritten into
7:23other pieces of hypograph. So the basic
7:26thing is that there are rules that say
7:27if you see a piece of hypograph that
7:29looks like this, it will be rewritten as
7:31a piece of hypograph that looks like
7:33that. And that's happening all the time.
7:35That is the progress of time is the the
7:39progressive rewriting of this hypograph.
7:42And that's that's kind of the story of
7:44of what the universe is and what it does
7:48is the hypograph and the rewriting of
7:50this hypograph.
7:51>> Okay. So that's this is a very uh
7:54powerful idea. It it's actually quite
7:57easy to understand the way you just
7:58described it. um as the the the space is
8:03the hypograph and the rewriting of the
8:06hypograph into new structures is the
8:08progressive of time and what we see as
8:10uh as events whether they're molec micro
8:14or or macro. just to get a sense of
8:16orders of magnitude if if this is at all
8:19uh possible of uh how you would describe
8:23I mean we know the size of the
8:25observable universe at least I don't
8:27know 10^ the 26 m or whatever uh we know
8:31plank a plankton plank lengths um and
8:36plank times 10us 43rd or 10us 27th
8:39various elements that we think are the
8:42simple so putting this together. What
8:45kind of orders of magnitude can you
8:46describe in terms of uh the actual
8:50hyperraph of the universe if to
8:53represent it using
8:55>> in your sense and uh the number of rules
9:00order of magnitude that you would need
9:02in order to make all the transformations
9:04necessary.
9:06So okay in terms of you know what is the
9:09elementary length if we were to convert
9:12kind of the the kind of one edge of a
9:16hyperraph into meters how many meters
9:18would it be right
9:19>> we don't know there's there's in our
9:22model there's one parameter you can it's
9:24the elementary length the elementary
9:26time the elementary energy it's also
9:28related to a thing we call the maximum
9:29entanglement speed which we'll get on to
9:31when we talk about quantum mechanics but
9:33the we don't know the value of
9:35I have a a very vague estimate that it
9:38might be around 10us 100 m. That the
9:41elementary length might be around 10 -
9:43100 m. It's much smaller than the plank
9:45scale.
9:46>> Much smaller than the plank line.
9:47>> Right. And it kind of resolves a a a bit
9:50of a mystery which is the plank energy
9:52is actually quite macroscopic in the
9:54usual setup. Our elementary energy is
9:56also microscopic which is kind of the
9:59way you would expect it to be. So, you
10:02know, there's a question of will we be
10:04lucky enough that there's an experiment
10:06that we can do or that even has been
10:08done that will detect the elementary
10:11length.
10:11>> Yeah, that that sounds very improbable.
10:14>> Well, let me explain why it's not quite
10:16so improbable. Okay. So, I think people
10:19were really lucky in at at the beginning
10:22of the 20th century that molecules were
10:24as big as they are relative to the kinds
10:27of equipment that existed to make
10:29measurements at the time. Yeah.
10:30>> But even despite that actually they
10:33could have known molecules existed
10:34earlier because Brownian motion which
10:36was the thing that kind of clinched the
10:37whole story that was discovered in 1827.
10:41So all the time that people like
10:42Boltzman were worrying about do
10:44molecules exist or not actually there
10:46was already evidence that they existed.
10:48It's just it wasn't interpreted right. I
10:50will be I I think it is very likely that
10:53there was already data in astrophysics
10:56in various areas of of of quantum
10:58mechanics that already is a clue that
11:02there's discreetness to space but it
11:05hasn't been interpreted yet. And that's
11:06a that's an interesting project to try
11:08and sort of mine the literature before
11:11you spend tens of billions of dollars
11:13building experiments to to look for the
11:15next thing. But what happens is that
11:18there are some effects that are
11:21predicted by a kind of model that are
11:24very different from what's been seen
11:25before. So here's an example of one. So
11:28when you have this big hypograph uh it
11:32it does not define what the
11:33dimensionality of space is. We normally
11:36think space is this thing that we can
11:38describe with three coordinates and it's
11:40three dimensions and so on. But this
11:43hyperraph it doesn't have any fixed set
11:45of coordinates. It's what emerges when
11:49you have a big enough hypograph is
11:51something which can approximate space.
11:52But at the beginning it's not defined
11:55whether that space is is two-dimensional
11:57or threedimensional or 3.1dimensional
12:00or infinite dimensional or whatever
12:01else. And so it's one of the things that
12:05we expect are dimension fluctuations
12:08where the dimensionality of space is not
12:10exactly three. That's a bizarre
12:12phenomenon. It's mathematical analysis
12:14is difficult. I mean people study, you
12:16know, they study calculus of one
12:18variable. They study calculus of two or
12:19three variables. They don't study
12:21calculus of 2.7 variables because nobody
12:24knows how that works. And we have to
12:26build kind of we're kind of trying to
12:27rebuild the sort of the whole tower of
12:30geometry and calculus and so on when for
12:34for what you build on top of on top of
12:35these hypographs rather than on top of
12:38kind of Uklid's version of space.
12:40>> Okay, let's go then get back to what you
12:42said. Give you your 10 to the minus
12:44100th is the is the ultimate
12:48point structure of space. Nice round
12:50number we can we can easily remember. uh
12:53what are the implications of that given
12:55the size of the known universe in terms
12:58of a hypographic representation?
13:01>> Well, I mean it it's
13:04the first question is when you have this
13:05hypograph and it's sort of doing its
13:07thing at this discrete level, what what
13:11does it do on the scale of of human
13:14experience, so to speak, or on the scale
13:15of of astronomy? It's a similar question
13:18to asking if you have a fluid that's
13:20made of a bunch of molecules, you've got
13:22all these molecules bouncing around.
13:24What is the large scale aggregate
13:26behavior of the fluid? What we know in
13:28that case is that the large scale
13:29aggregate behavior follows the equations
13:31of fluid mechanics. And so one question
13:34is well what is the large scale
13:36aggregate behavior that we see from this
13:38hyperraph doing all its rewriting at
13:40this very small scale? The answer is
13:43Einstein's equations for the structure
13:44of spaceime. So what is in the case of
13:47fluid mechanics from molecular dynamics
13:49we can derive the Navia Stokes equations
13:51of fluid flow from this hyperraph
13:53rewriting we can derive and when I say
13:56derive mathematicians will say there are
13:58many many footnotes there's a century
14:00worth of footnotes that still has to be
14:02filled in to see how that derivation
14:03works by the way the same is even true
14:06for fluid mechanics the derivation of
14:08fluid mechanics from molecular dynamics
14:10has never been done in a mathematically
14:11rigorous way but we can you know one of
14:14the great advantages that I've had
14:16methodologically in the things that I've
14:18done is that there is both the
14:20mathematics side of analyzing things but
14:22also there's computer experiments and
14:24you can see a lot of what's true from
14:26computer experiments even though you
14:28can't necessarily say here's how I can
14:31give the full sort of mathematical
14:32narrative for how this works but so the
14:35first thing to say is that the the kind
14:37of largecale behavior of spaceime is
14:42that you get from this underlying
14:44hypography writing
14:45follows the Einstein equations but it
14:47has some deviations like these dimension
14:50fluctuations and so on.
14:51>> The other thing that happens is that a
14:53lot of features of physics that one has
14:56just had to say oh well you follow the
14:59equations you solve the equations then
15:01you work out how things will work. A lot
15:03of features of physics now become things
15:05that you can kind of almost mechanically
15:07explain. Let me give an example. So in
15:10relativity one of the sort of classic
15:12phenomena is time dilation. when things
15:15move more quickly, time seems to run
15:17slower for them. Well, in our physics
15:21project, we can really see quite
15:22mechanically why that happens. So, if
15:24you have a thing like an electron, let's
15:26say, and it's represented by some
15:28structure in the hypograph and it is
15:31progressively uh kind of uh it is it is
15:34it continues to exist because as the
15:37hypograph gets rewritten that electron
15:40structure is preserved by the successive
15:42rewritings. it's it's recreated at every
15:45moment in time um by by this hypograph
15:48rewriting process. Now we say let's have
15:51the electron move from here to there.
15:53What happens is some of its sort of
15:55computation budget if it's moving has to
15:58be used in kind of recreating the
16:00electron at different places in space.
16:02So if it's using some of its computation
16:04budget to recreate itself at different
16:06places in space, it has less computation
16:09budget to just sort of be continuing
16:12through time. So in effect of in effect
16:15it is it's used up its computation
16:17budget on motion. So its time has to run
16:20slower for it. It has less computation
16:22budget to sort of run itself forward in
16:25time.
16:25>> And that that assumes there's a there's
16:27a finite computation budget.
16:30>> Yes. But that but the the whole point is
16:32that the the whole notion of time is
16:35that time is associated with the
16:37progressive doing of computation. our
16:41what what happens in the universe in a
16:44sense we experience time because
16:47computations are going on in us and we
16:50are but if if you were to just look from
16:52outside the universe you could say well
16:56you know I'm just not going to do the
16:57next step of computation then the
16:59universe is frozen but so are we we we
17:01our perception of the passage of time
17:04>> is a is a consequence of of the fact
17:06that these computations are going on in
17:08us as in the rest of the universe
17:10The fact that there is a sort of
17:11uniformity to that computation both
17:14inside us and in the universe at large
17:17is why there is a sort of invariant
17:18notion of time. It could be the case
17:21that time is was was very different for
17:24different kinds of entities. But the
17:26fact is that in a sense it's it's it
17:29comes back to the principle of
17:30computational equivalence actually that
17:32there is a a sort of uniform notion of
17:34time that applies both to our experience
17:37of time and to what happens in time in
17:39in in the universe at large. Let's take
17:41a a simpler example from classical
17:45physics energy and momentum um which are
17:49have been thought to be understandable
17:52in Newtonian physics um how would those
17:55represent to get to to see how the the
17:58hyperraph system works for physics in in
18:01a simple way
18:02>> right so well I didn't think energy was
18:05going to be simple actually I thought we
18:06were going to have to understand
18:07particles in order to understand energy
18:09I was wrong turns out that we can think
18:12about energy as a bulk phenomenon and
18:15roughly energy is the density of
18:17activity in the hypograph. So roughly
18:20the um and momentum so so put a little
18:23bit more precisely the way that one
18:26thinks about things is every rewriting
18:29event is this is this is an it's an
18:32event and you think about all these
18:34different rewriting events and they all
18:37they have a certain network of causal
18:40relationships. So one rewriting event uh
18:43has to have happened before another one
18:45can happen because the next one is going
18:48to use the output from the first one and
18:50that builds one up this kind of causal
18:53graph of causal connections between
18:55these rewriting events.
18:57>> And so put a little bit more formally
18:59energy is essentially the flux of causal
19:02edges through what we can call
19:04space-like hypersurfaces. So in in um
19:07it's kind of like the the way that um
19:11This is this is one of the tricky things
19:13which which was not known when people
19:16were thinking about sort of discrete
19:18space in the early part of the 20th
19:20century. What was not known uh people
19:23were imagining that space would have to
19:25be some sort of discrete lattice or
19:27something. What emerges in the physics
19:29project is that the key thing to look at
19:32is this causal graph of the causal
19:35relationships between different events.
19:37And it's it's invariances of that causal
19:40graph that lead to relativity.
19:42>> Um that lead to the fact that you uh
19:45well the notion of time is the
19:48progression of computation. So something
19:52we say this event happens and this other
19:54event can only happen after that first
19:57event later in time than that first
19:59event because that second event is using
20:02the output from the first event. It's
20:04consuming the kind of atoms of space
20:06that were created in that first event.
20:09Now what can happen is there are all
20:10these events taking place and you can
20:13say well which events can we think of as
20:16simultaneous and this is very similar to
20:17the kind of way one thinks about
20:19relativity. One says what what events
20:21can one think of as a space-like surface
20:24as events that can be thought of as just
20:26laid out in space all at the same time.
20:29And there are many different possible
20:31choices of space-like surfaces, many
20:33different choices of simultaneity
20:35surfaces. That's the same kind of thing
20:37that happens in relativity, but it
20:38happens very directly in our models. And
20:40it's it's um uh and it's it's that um
20:44and and the sort of the the key thing
20:45that one's looking at is this is this
20:47causal graph. Energy turns out to be the
20:49flux of causal edges through space-like
20:51hypersurfaces. Momentum is a flux
20:54through timelike hypersurfaces. Those
20:56are sort of the formal statements. I
20:58would say that one of the things that
20:59was a mystery for a long time is why in
21:01relativity theory the transformation
21:04rules for space and time have the same
21:06mathematical form as the transformation
21:08rules for energy and momentum
21:10>> in our model that's it's obvious why
21:12that's the case from what I just said
21:15it's not so obvious
21:16>> that's an interesting point because that
21:17that is the case I mean in your model
21:19they're both related to the same kind of
21:21structure so it's it's it's it's not
21:25it's almost trivial because they're both
21:27caused by the same transformations of
21:30hypograph as as opposed to two radically
21:32different kinds of things.
21:35>> Let me go back to an ear earlier
21:36question. So we we we we got an order of
21:39magnitude of the nature of the hypograph
21:42by 10 the minus 100th and we know the
21:44size of the universe
21:46at least observable universe. Let's go
21:48to the the the order of magnitude of the
21:51number or kinds of transformations or
21:54rule the rules that cause these
21:57transformations in the hyperraph which
22:00generates the the physics that we know.
22:02How many different kinds of rules do you
22:05need?
22:06>> Okay, we're we're now about to descend
22:09into the deeper parts of the rabbit hole
22:11because the that's ultimately the story
22:14of the rouad.
22:16>> All right. Well, we're going to do the
22:17rouad in another completely.
22:19>> I think I think we should not let me
22:21just say that for our there are many
22:25different rules that we can use to
22:30describe how a universe works and they
22:32are all ultimately equivalent in terms
22:36of the things that we observe about the
22:38universe. And let me give a a a way to
22:41sort of see why that might work that
22:44way. It relates again to fluid
22:46mechanics. If we look at the equations
22:48of fluid mechanics, it's the same
22:50equations for water and for air. Even
22:53though the molecules that make up water
22:54and air are quite different, right?
22:56>> And it's it's um but it is a bit more
22:59complicated in the in the full case of
23:00the universe because we are observers
23:03embedded within the thing that is the
23:06universe. And so if we're the that when
23:09we say we are thinking about the
23:11universe in this way in terms of these
23:13rules but we are also made into made of
23:16those rules and it turns out that it we
23:19can we can attribute sort of the
23:21behavior of the universe to different
23:23rules and end up coming to the same
23:25conclusions about the aspects of the
23:27universe that are observable. So the the
23:30you know the the I think the the way to
23:32answer that is to say there actually can
23:34be just one rule that uh or you know a
23:38very small number of rules that we can
23:41we can run those rules and get what is
23:45at our observable to us as what happens
23:48in the universe. So let me give an
23:50example of that. I mean so so we have
23:52simulations now of things like black
23:54hole mergers in our models and the you
23:58can use a whole range of different
24:00possible rules and you'll always get the
24:03same kind of behavior at the scale you
24:06know if you look at the absolutely
24:07microscopic scale you'll see different
24:09things going on but if you look at a at
24:12a sort of zoomed out scale you'll see
24:14these black holes merging and some
24:15gravitational waves produced and so on
24:18and uh it's uh So that's it's it's a
24:22slightly it's a slightly weird thing
24:23because it's a little different from the
24:25way that one's thought about physical
24:26theories before and that that will tell
24:28us that will take us into into the story
24:30of the rouad.
24:32>> Okay. Well rullad's coming coming soon.
24:34Uh so this is this is great. Uh viewers
24:37can watch all the videos in closer to
24:38truth the wolf from physics project on
24:40the closer truth website and YouTube
24:43channel and including the rouad which is
24:45coming which is going to be I think my
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This page contains the full transcript of The Structure of Time and Space | Stephen Wolfram by Closer To Truth, generated from the public captions YouTube serves with the video. The transcript has 4,367 words across 627 segments, with the original timestamps preserved so you can click any line to jump to that moment in the embedded player.

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