Why Wolfram Physics May Be the Key to Everything with Stephen Wolfram and Jonathan Gorard

you have fallen into event horizon with John Michael Gautier [Music] [Music] in today's episode John is joined by stephen wolfram and jonathan gerard stephen wolfram is the creator of Mathematica Wolfram Alpha and the Wolfram language the originator of the Wolfram physics project the author of a new kind of science and other books and the founder and CEO of well from research jonathan garage is a research mathematician at the University of Cambridge and algorithms R&D consultant at Wolfram research and one of the principal researchers and the Wolfram physics project his work lies at the intersection of mathematics physics and computation with interest ranging from mathematical logical and computational complexity to general relativity in the foundations of quantum mechanics stephen wolfram and jonathan gerard welcome to the program hi Hey great to be here Stephen you you initially started as a physicist right indeed long time ago I don't know where the PhDs expire but if they if they could mine would have done now but you never stopped thinking about it that's true now you have come up with a somewhat controversial mu Lawrence seems to be becoming controversial view of cosmology an alternative cosmology this has happened before I remember astronomers like Halton ARP also you know sort of tried to think or rethink cosmology what is a basic layout of your view of cosmology so we can unpack it well so what I've been tested and is kind of what's underneath space and time you know what is our universe made of so to speak and back when I did physics in the 1970s and so on there was a sort of orthodoxy of how things worked that mostly had to do with general relativity Einstein's theory of gravity and quantum field theory the theory of how small things like electrons and so on work and back in those days I was mostly taking those theories as given and trying to figure out what consequences they had and that's hard enough then I kind of got interested in things that are in a sense more general than physics because physics is the way our particular universe works and I got kind of interested in question of well how could any possible universe work and that got me into thinking about sort of computation and programs as kind of a a an underlying material to make kind of representations of things out of and so I spent a long time kind of studying the computational universe of all possible programs and discovering that that was a really good way to do science and building lots of kinds of things about that but the main thing that came out of that conceptually for me was that there was sort of a there was the potential for a different underlying stuff to make theories out of four things that included physics and in a sense one of the big discoveries in the computational universe is when you have a program you have a very very simple program let's say you have a program that's like one line long tiny program just has a few little rules in it about how it should work you might think programs simple enough all it can do is very something very simple but you would be wrong and that's what I kind of discovered in the early 1980s by doing actual computer experiments is actually even when the program is really simple what it can do can be really complicated and so that kind of got me started they've got me started on understanding a lot of things about sort of complexity in nature and so on but it also kind of sowed the seed of well okay if you can make all this very complicated stuff in the computational universe from these very simple programs what about our physical universe is it conceivable that our physical universe could be the result of just running some extremely simple rule a gazillion times and so that idea that's sort of a long technical story about about what kinds of programs might be relevant to the universe and so on but in the in the kind of early 90s I kind of got started thinking about sort of what can be underneath the space in time because you know the idea of space you know what is space well space is just something where space as in the three dimensions of space you know left right you know up down you know forward backward type thing you know people don't really think of that as being a thing that has sort of content to it they just think of it as being the thing we live in so to speak and what I kind of realized is that one of the first things one has to think about is what really is space and you know people thought about that back in in ancient Greek times people had theories about what space is um but in kind of modern mathematical physics particularly starting with Einstein's original special theory of relativity it kind of got to be well there's space and time and we kind of know what they are and there's a mathematical representation of them and all we have to talk about is the kind of mathematical representation there's no there's no there's no they're there so to speak there's nothing there's you can't take apart space so to speak I kind of realized that that was there was sort of what what's it what's underneath space and go ahead now that's one of the strange aspects because as I recall it was Newton that did an experiment that started the question of is space is something and yes it is a something it's not just a nothing well I actually which experiment mutants you're thinking of because I think if you're thinking of the Apple falling no this was actually it may not have even been Newton I'm digging way back into knowledge but it was the bucket of water where you can you know return the bucket of water and the water stays stationary so it suggests that there is some sort of frame of reference with space which I also it's an Einstein he got amok with the Hunstanton office it was a very big proponent of the bucket thing and it's not clear what it but yes there's a but but again that's thinking about you know for example one of the questions is if you take I don't know something like water okay you might think Oh what is just this continuous thing but in fact we know if you use a powerful enough microscope so to speak you can discover actually water as made of molecules it's not just a thing that you could have an infinitesimal amount of you know if you start subdividing your water you say I subdivide it I subdivide a subdivide it you might think oh I can get an arbitrarily small amount of water but you can't at some point you you get stuck you say well I've got one molecule and then you know that's that's the smallest indivisible piece and for space people have always assumed that you can subdivide it as much as you want doesn't you know you can go down in fact Euclid sort of the the person who sort of systematized geometry back in in antiquity you know his very first common notion the thing that is sort of obviously true he thinks is a point a geometrical point is something that has zero size so in other words you can keep subdividing space as far as you want you'll never it won't be like water where eventually you get stuck in this sort of an atom of space now you know that's that's been kind of an assumption in well in mathematical treatments of geometry and things it's been kind of an assumption for the last couple of thousand years when people were first starting to discover atoms and then quantum mechanics and so on they were starting to discover there were photons particles of light things like that there was a brief period of time actually in the 1930s when people thought oh space must be quantized as well must be in and kind of made of atom like things as well but it never worked out and they kind of gave up on that idea actually rather quickly gave up on that idea and so it's been something that's been sort of you know the what is space question has been kind of when people have built sort of the whole structure of mathematical physics and things like general relativity quantum field theory they just take as an assumption the same thing that Euclid took as an assumption a couple of thousand years ago space is something that is infinitely subdivide a ball and you don't really have to discuss what space is it's just a thing that things exist in so there is no lowest level of space right that has been the traditional view so I started thinking about well particularly when you think about things in terms of computation computers as we understand them operate in terms of bits and they have sort of discrete digital things that they deal with and that's if we think we might be able to make a that our universe might work a bit like a computer then at least in our current view of computers we kind of have to think well maybe it has it's made of things like bits and so then the question well is that right or is that not right and you know we might have thought people for for many many centuries argued about whether atoms existed turns out atoms exist now the question is well what about things like space are there is that again an example of something which is truly digital truly has you know discrete points in it and so on or is it something that isn't that is that is really continuous and not digital and so there had been no real way to make a theory that was sort of a consistent theory that reproduced the kinds of things that one has discovered in particularly twentieth century physics using an idea of space that wasn't it's just this continuous thing that can be described mathematically but I kind of started thinking back in the early 90s about sort of a different view of space and I mean it gets there several pieces to this that it gets it gets kind of interesting the the so the you know the first question is well what if space is just a bunch of points and all those points do is to be connected to other points they don't say this is the point at this position there's a point of that position they don't have any idea of position it's like it's like a friend network of points you just have these points and each point has certain neighbors set certain friends certain other points that it's friends with it's just a network and that's kind of and as such doesn't seem like that's going to be anything like in space as we experience it but what turns out to be true is that if that network is big enough has enough points in it it can be the case that it the points are kind of arranged they're sort of friend relationships are just like the kind of who's next - who relationships that you get in the three-dimensional space that we know about for example so in other words space could be an emergent thing even though at the lowest level it's just bunch points that sounds eerily familiar it almost sounds like a quantum superposition applied to space or am I out of my feel a little a little far okay so so the idea that there might be sort of quantized things that make up space would be something that you might think would be the case from mechanics maybe but the idea it so I mean what will what will come - I can talk about this and you know how quantum mechanics works in in our model is something you know first we have to understand how space works then quantum mechanics is kind of another level and it's a thing we call Branch Hill space and I think that's one of these words which has to be pronounced differently in British English and American English but Branch Hill or something it's a space of branches and that when we think about ordinary space physical space the three dimensions and so on that we live in that's a certain that that's that's sort of an ordinary notion of space then there's this idea of Branch Hill space which is essentially a space of quantum states and that is a thing that also exists in our model and it has a very interesting relationship to ordinary space and actually the two things kind of come together when you deal with exotic things like black holes those the Branch Hill space and physical space sort of intersect in in things related to black holes but I think the you know the thing to sort of understand where this is coming from the first step really is you know what is space that there's really I think there's a couple of steps the sort of what is space what is all the stuff that exists in space matter particles photons whatever then there's what is time once one's got those things it's kind of then one couldn't start thinking about well once one has those things one can start figuring out things about relativity and gravity and so on then kind of the next step is understanding what turns out to be really inevitable in our model that quantum mechanics has to be a thing and that's but you know one of the features of this is it's when you think about what what is it what might it take to make a fundamental theory of physics you know what kind of a thing might it be like and is it going to be a kind of thing well it's good to have pieces that are immediately familiar where we say oh that's just like something that we are commonly we commonly experience the answer is probably not because it's operating it's the very very low level machine code of our universe operating way below kind of the level of our experience and so on and it's it's sort of inevitable that it's going to seem pretty abstract to us at the beginning and you know the challenge is to build up from those very abstract that very abstract extremely low level machine code for the universe and build up to things that we can recognize but the kind of Waypoint for that so there's things that we kind of in our everyday life recognize and then there's things that sort of the achievements of physics have shown us and you know the great achievements of physics in particular 20th century have been too deeply abstract a bunch of ideas that came from sort of everyday experiments and experience and so on and you know what our best chance to kind of sort of really understand what kind of theory we have is to try and connect with that sort of abstraction that exists in 20th century physics but I mean I I think the kind of the idea you know this this idea about space well okay so so one question is okay so you have this notion of space some network where there's a bunch of points you know each point is just connected to other points don't say where the points are that emerges then the question you might ask is okay well what about what about us what about everything that's in space because in usual physics you say well there there's the spaces of this background thing and then there's all the matter and particles and everything would exist in space in in this theory it's very minimalist there really isn't anything except space and everything that exists in the universe is just sort of a feature of space and that's kind of a weird idea actually it's an idea Einstein had this idea as well actually Einstein people keep on sending me these these sort of quotes from Einstein which he said he said in the end it will turn out space is discrete in the end it will turn out there's nothing but space but we don't have the tools he was writing in the 1940s 1950s we don't have the tools yet to be able to see how to work this out others in within this model how does the expansion of space play in so interesting I mean it's it's in this model tribe I've sort of described kind of what space is in terms of these points and connections and so on the the essence of the model is rules that say if you have this little piece of network that looks like this then it will turn into a piece of network that looks like this and as soon as the network that it turns into has more points in it than the network that it came from you have kind of a that that immediately starts talking about the the underlying expansion of space however it's a little more complicated than that I mean it's kind of a amusing piece of history that that in this model it is pretty natural that space expands it's also pretty natural that space could subdivide progressively subdivide that is that when we think we have you know a meter of length the number of points of space that correspond to that meter might actually be getting larger even though we keep on saying oh that's a meter that's what we think of as a meter long it could be that you know it starts off being you know 10 to the 93 points and then before we know it it's kind of the 95 points and so on that that all along that meter we're not sure how that works yet but it's kind of a you know a historical footnote back when Einstein was developing his general theory of relativity in 1915 one of the things that was true about that theory was that it implied the expansion of space and Einstein kind of said no no no can't possibly be right we know the universe isn't expanding so he added this thing called the cosmological term that was to correct for that and to sort of prevent the expansion of space now of course it turned out 10 years later it was discovered actually spaces it the universe is expanding now actually what has to be a little bit careful because the the expansion of the universe is different from the notion of the expansion of space because if you know if for example everything was just getting bigger you know let's say every second everything the universe was getting twice as many points in it it's not clear we would know that we wouldn't directly know that because for us you know the thing you know the the the piece of chocolate looking at is a certain size I'm a certain size we both double in size we can't tell what that happened and it's it's the same you know it's always quite subtle I mean for example in the expansion of the universe in current cosmology people say well the universe expands well okay are we expanding no we're not expanding is that galaxies expanding no our galaxy isn't expanding ok so what's actually expanding well the answer is there's a little sort of tug of expansion that's applied to like clusters of galaxies and things and as soon as you get to things which aren't sort of themselves held together by gravity or something like that then there's this sort of there's this flow of expansion in the universe and that's in our models one sees the same general types of things one of the questions actually for our model is those cosmological constant that I mentioned okay so so Einstein introduced this and there's been a lot of flailing around about the cosmological constant and that's relates to the whole idea of dark energy which has become popular based on some observations to the acceleration of the expansion of the universe and so on but I think it's it's some the thing that um okay so one of the one of the problems I mean there there are a whole bunch of problems in physics that physics is kind of a little bit embarrassed about so far that you know our model actually is very own it's very unembarrassed thing in our model so here's an example of one so quantum mechanics implies that in what you think of as the vacuum there actually are these virtual particle pairs that exist in essentially infinite numbers so all the time you know in a vacuum there's you think there's nothing there but actually there's electrons and anti electrons positrons that are being formed and they're coming out of nothing they're existing for a very short time then they're annihilating again that's that's a consequence of quantum field theory and it's a it's the the idea of zero-point energy zero point fluctuations it's it's a necessary feature of quantum field theory it's and okay so that's a little weird the problem is that all of that activity produces the equivalent of a huge amount of energy in the universe or a huge amount of mass in the universe and if you try to take count of all of that activity the universe should be curled up in a tiny ball it should be like there's so much mass in the universe that it it's like produces huge amount of gravity and it should curl the universe up into a tiny ball which we kind of know it has it hasn't happened so there's been you know there's that there's a lot of a weird sort of a fancy footwork that's had to be done into the the current approaches to physics traditional approaches to physics to avoid that problem so for example in in our model that problem never happens because well roughly the reason is that all of these particles that quantum field theory says should exist in the vacuum they exist as features of this network that would produce same and they are in fact the things that create space all of those little sort of quantum processes and things are the things that in effect create space and so it's not like in the traditional view where we have space and then we have things in space and the things in space are just sort of like going crazy and they would lead to space curling itself up instead those very things that are sort of there all that activity is what actually makes the space and so you don't have the same problem of trying to explain oh my gosh why you know how can there be so much you know how does the universe not curl itself up into a tiny ball now does this does this negate certain questions about other dimensions being curled up how does this relate to that yeah clines pastor doesn't just say this is not reality in so what happened in you know you're referring to string theory which is a very interesting mathematical theory which was actually developed for as a theory of something completely different but eventually became sort of a theory of gravity meets quantum mechanics and so on in the 1980s the string theory has an embarrassment because to make very consistent the world has to be let's say 10 dimensional which we kind of know it isn't and so generally when you're trying to sort of assess science theories it's a pretty good a good heuristic that that term well my my old friend Richard Feynman used to be very very insistent on this heuristic which is do you have a theory way you put you know where you where what you get out is significantly more than what you put in or do you have a theory where what you get what you get out is only you know is pretty much what you put in and do you have a situation where as the theory as you start trying to apply the theory you keep on saying whoops whoops there's an issue here let's add this little patch to the theory to to deal with that issue and so on so what happened in string theory is that it's a very elegant mathematical theory very interesting probably quite relevant in its mathematical structure to some things that we're doing but it ran into a snag and its snag was to make the theory consistent it had to be in ten dimensions and so then there was this kind of well let's add a hack basically and let's say all these other dimensions the the seven that we don't see all the six we don't see depend on how you're counting it must be curled up in little balls in our period it's just nothing like that I mean it just doesn't and in fact for me the appearance of a quotes hack like that would be a you know a red flag and the development of our theory and I'm it's to me something quite amazing has happened that I really didn't expect that is very different from that which is you know every stone that's turned over it seems like we're seeing more stuff that's like oh oh that's you know that's what we already know from physics it works that way rather than oh whoops we just saw this nasty colony of ants or something that we now have to somehow do something about I mean it's it's a but yeah that that that particular idea you know it's it's funny because one of the things that's a surprise about this this theory of ours is that I had thought that so the foundations of the theory are really different from the foundations of other theories in physics these ideas about computation and networks and all this kind of thing just doesn't look like theories that exist in physics even even the methods of using both ideas from mathematical logic things like this they don't they don't seem like they're they're what people have been used to in physics and so I thought and I had thought when I started working on this back in the 90s you know I had thought there's going to be a different prong it's gonna be something that is really alien and unfamiliar to existing mathematical physics the big surprise which happened really last late last fall is as we develop the theory more we realized actually it's a lot of its structure is you know really meets existing mathematical physics so in other words there are things where the underlying machine code is totally different I mean the underlying sort of how things work underneath it's nothing like what existing physics the way existing physics describes things but once you build it up and you say well what consequences does that have they end up being very much like they end up really really connecting with the kind of mathematical structures that people have investigated in the last probably 50 years or so in particular in the last 50 years in mathematical physics one of those things we think string theory is probably one of those now as I say string theory already had one reset because it was originally invented in the 1960s as a theory of interactions inside nuclei and it didn't really work out for that and it kind of got re sort of retooled to to work on this different thing I suspect it might get retooled again but the mathematical structure which is the vast majority of what people who study string theory are really concerned with that mathematical structure is just you know a structure in and of itself and I think it's going to turn out to be quite relevant to what - what we're doing I mean the the okay so there's one thing it's just the weirdest thing just one of these things that at least amuses people like me one of the sort of as a the main way that our models work involve studying these networks or actually hypergraphs that of you know points that represent things in space and so on that is a kind of toy model you can just think about strings of characters like a B a B a a and things like this and say how does that transform to you know a a a B ba etc etc it's kind of a just a toy version of the of the real model of what what's going on but I suspect that that toy version which is dealing with stray of characters that the the limit of that if you have strings of infinite length will turn out to be mathematically equivalent to what is called string theory and that's the craziest thing because the name string comes from a completely different origin in those two cases and so it is a pure pun but I think it's a pun that's going to turn out to be actually a piece of science mathematics sort of mathematical reality so to speak that's an it's a for me that's that's one of those things that sort of shouldn't shouldn't work that way but I think it's going to now we'll come back to that but your work in the 90s you sort of sat down for a while and Jonathan please chime in here what brought you back to this well so the couple of things so I started working on this in the 90s it turned into a piece of a big book that I wrote called a new kind of science the thrust of that book was kind of exploring the computational universe and trying to apply these kinds of computational ideas to understanding sort of everything and I mean kind of kind of the premise of that book was for about 300 years since folks like Newton and so on we've kind of used mathematical equations to describe things in science but actually there's a broader range of things that can be used that come from ideas from computation of programs and so on what does science look like can we make a new kind of science that is based on the idea of doing that and you know the the it's pretty cool cuz it worked I mean in the sense that if you look at what's happened to sort of modeling of things people always used to say oh you know they're they're modeling it you know in well for example in epidemiology of current interest I mean the sort of the traditional models were based on mathematical equations the modern models are all based on essentially programs and that's been sort of a transition that's happened that I think I was a something of a contributor to to from this idea that had really been there for 300 years of you know used mathematical equations to model the world a model how things and science technologies social things work to something where we're using programs and copy to model these things and so that was that was the main thrust of the book but the book as one of the kind of use cases of this idea I talked about fundamental physics and I talked about what I had figured out so far about fundamental physics and it was a big book it's like a twelve hundred page book and about a hundred of those pages were as it turns out devoted to fundamental physics and I have to say I just viewed it as a as a use case I didn't view it as as the main story when the book came out lots of people in lots of different areas were interested in it and so on but the it was kind of funny because the the people in physics particularly fundamental physics were like oh my gosh we've got you know bring out the pitchforks so to speak you know this can't possibly be right this can't you know you can't change physics like this etc etcetera etcetera etcetera and it was a little disappointing to me because you know I was a I have been kind of a leading member of that field and also basically people in that field pretty much universally use the software tools that we build to do their work so a little bit like you know guys you you really would be smart if you actually try to understand what I've done because I think it's useful to your field but um but I kind of my own personal response to that was mostly look you know there's a lot of things I'm interested in doing that particularly have to do with sort of creating computational languages creating things like well now for which now powers bunch of your friendly intelligent assistants like Siri and Alexa and so on a lot of a lot of things that are very interesting to do and so I didn't pursue physics so much partly because I felt like I'm kind of spoiled because I've spent most of my life building tools that fundamentally people find useful and they say thank you for building these tools which is great and it's like I'm happy they're happy it's all good but in the area of fundamental physics kind of the the basic sentiment from you know friends of mine and people in the physics community which it's not a very big community actually and I know most of the people that are kind of like please don't do this project you know if you do this project if you're right it's gonna kind of invalidate what we've been doing in physics for last 50 years it's like well you know at some level you get what you get because the world you know the universe works the way the universe works and none of us really control that so to speak so eventually you know the gig is going to be up so to speak but I thought from a personal point of view it's like why work on something where the target market profoundly doesn't want it and so I kind of set it aside until and although you know every so often it came back to it the other thing that that bugged me was that some technical details of the way that was doing this kind of networks and rewriting rules about networks and things I thought was kind of unnecessarily fragile I thought it wasn't I didn't it didn't quite ring true to me there wasn't quite didn't quite aesthetically make sense to me and then about what was it he a little bit more than half ago or something I I kind of as a result of thinking about kind of the construction of computer language computational languages and things and and trying to understand sort of types of abstraction and so on I realized that was sort of actually a pretty obvious should have been obvious to me there was unfortunately there are these things where it's like should have been obvious to me but it took me 30 years to realize it um but anyway it's something that in a sense was staring me right in the face but it should have realized a lot earlier but I kind of realized this way of making a slightly better kind of abstraction as the underlying sort of raw material for these models so that was some so then every year we do a summer school we've been doing it for like 17 years we're about science and technology where people do interesting projects and so on and somebody and and I meet lots of interesting people there and it's it's a great collection of folks anyway somebody who'd come to the summer school several years back was was Jonathan here and Jonathan came back to the summer school as an instructor and I was like talking about oh you know I made a little bit of progress I kind of thought about this thing and that thing and there was another person who'd come to the summer school actually several years earlier come back again name max pass Knopf and Max was like I want to work on this physics stuff you need to work on this physics stuff why aren't you working on this physics stuff and I was kind of giving these excuses about how well nobody really seems to want one to do it and etc etc etc and you know the fundamental bottom line between I would say particularly Jonathon and Max was look this is really interesting this deserves to be worked on and hey we'll help you do it so that's that's at least my version I mean there was some there's some other pieces to this I mean Jonathan had a bunch of ideas that sort of helped me at least unlock my hang-ups about particularly things to do with quantum mechanics and that's that's kind of how I'm how last fall we got started on this and I have to say I didn't think it was going to go that quickly I thought we were going to basically take what I had done in the 90s kind of package it up put it out there as a kind of a project where we were saying okay world you know we think we've picked the right mountain to climb now go help us climb it I did not think that we would make as rapid progress as we did and it's kind of outrageous I you know I kept on saying it's it doesn't you know it's not supposed to work this way we're not supposed to be able to figure stuff out as quickly you know physics look should have been harder than this but but it seems not to be anyway that's my version Jonathan might have a a more colorful version of this Jonathan would give you those ideas sure okay that's an interesting question so obviously my perspective is a little bit different because I was actually not alive for the first section of the time when Stephen was working on @ks so I was a little bit late to the party so I actually read the new kind of science I think when I was fourteen fifteen when I was in high school and it merely opposite profoundly changed the way I view the world but the two sections of the book that I personally found kind of most intuition shattering were those this chapter 12 which is about the principle of computational equivalence which is this rather deep idea that Stephen has ever about so some fun the you know the fact that the you know the reason why systems look complex is because ultimately they are all performing sort of computations that are of exactly equivalent sophistication and that there's somehow there's like a computational battle going on between observers and the systems that they're observing and if the observer and the system they're observing and performing computations of the equivalent sophistication then the system will look complex because the observer can't readily decode it and things like that so that was that was the first kind of really kind of deep intellectual idea that stuck with me but the other thing that I found really really quite quite remarkable was this was chapter nine this chapter on fundamental physics that Stephan already mentioned this you know this idea that and I think by the way it's worth stressing that um there's there in addition to the fact that this was a you know potentially a model for physics that was based on computation rather than based on mathematics which even already mentioned there was also to me there was a there was a really nice philosophical feature which was that it was a complete as with the rest of nks it was a complete sort of inversion of the conventional scientific paradigm right in normal for the last you know three hundred fifty years since people like Newton Descartes Galileo Kepler that there's been kind of one key methodological idea in physics which is actually in the exact Sciences in general but but physics in particular which is that you you find some phenomenon in nature that you want to try to explain like celestial motion or electromagnetism or whatever and then you you drill down and you try to find the primitives find the fundamentals from which you can then build up a quantitative mathematical model that describes what's going on and that worked out really well for people like Newton and Maxwell and you know it gave us general relativity and quantum field theory and things but what Stephen was proposing back in 2002 it was a radical reconstruction of a scientific method which is safe it was a kind of perverse inversion of this of this general technique where instead of starting from the phenomenon drilling down finding the fundamentals it's like you were starting from the primitives and explicitly computing to build up to the phenomenon so you know rather than you know building models based on things you observed you if you were basically starting from the models and trying to build up and compute their their consequences and then sort of do the analysis to work out whether those things overlapped with with things that we actually see in nature and the idea that this was that this was a valid paradigm and that this could potentially yield kind of success in fundamental physics for me at that I was a really really exciting idea so then you know I went on to college and the end of my second year at college is even mentioned I am I went to this to this well from summer school where I knew that I wanted to because I had these two you know because chapter 9 in Chapter 12 for the two major things that I was interested in and for and within chapter 12 I was particularly interested in the the section on the foundations of mathematics about sort of this new intuition for things like undecidability in in mathematics in terms of a limit a limiting process of computational irreducibility which is where I've never really thought about it before so I knew that I wanted to do a project that was either related to fundamental physics or related to the foundations of mathematics in the end I thought that I did this project related to the foundations of math that was kind of trying to develop a means of producing and representing automated proofs of mathematical theorems which I think went reasonably well and it ended up I was sort of recruited and then that ended up becoming a function in the Wolfram language in its own right and it was actually also around this time that I fell in love with with general relativity as a sort of subject and in mathematics and I got really interested in the foundations of general relativity and things to do with differential geometry and functional analysis and stuff and then as Steven mentioned I came back as an instructor to the summer school in 2018-2019 still working at Wolfram and okay at this point I have to confess that there was always a section of chapter 9 that I found relatively unconvincing but you know all of the stuff about the network models the representation of space representation of space time special relativity general acidity all of that stuff made sense but Stephen had some notes about quantum mechanics that I personally didn't find particularly convincing and the United I by the way right and so I hope this is a reasonable summary but basically I think Stephens idea was was that you know in one of the the foundational features of quantum mechanics is this notion of entanglement and as there's this thing called Bell's Theorem that kind of places constraints on what kinds of models can be pretty useful for the phenomenon of quantum entanglement and Stevens point was that in the in these network models because you can have edges that are kind of not part of the normal structure of space you could have distant you could have at regions of space that appeared to be very far apart but were actually connected by kind of long-range edges in the network and that this would be sufficient can reproduce the behavior of quantum entanglement now that itself seemed ok but it felt like there was something missing and so partly as a result of working on these things related to mathematical logic and automate it there improving I had a sort of a slightly different 2d wishing for how something like quantum mechanics could emerge in these models which was that these when you're when you're evolving the model and you're applying these replacement rules that these replacement operations that Steven mentioned it turns out that there are cases where the order matters and there are some cases where the order doesn't matter and the cases where the order doesn't matter turn out to be relevant to its relativity but I was interested in it in the cases where the order does matter and in effect where you get a whole different Ryo possible histories for the universe that seemed very kind of many-worlds ii and very quantum mechanical and i kind of came up with this rough scheme by which you could have an observer you you think about the observer not just as existing on a single branch of history but actually existing across all branches of history and then the observer is trying to make sort of sense of the things they see on all these different branches of history and in doing that they can try they can produce a representation of the world where it appears like there's only one branch of history and it turns out if you do the math it turns out that's exactly what sort of automated they're improving algorithms and things do it was it was a just a direct application of the intuition that I'd built up from working at Wolfram research and so I I mentioned this idea to Stephen and I mean we went on this long walk and I eventually succeeded and I think convincing him that this is a possibility that was worthy of investigation and so there was this there was this really you know from my perspective it was like there was this really nice confluence of factors because you know Stephen had just had this idea about how to generalize the formalism to do to deal with the typographic cases that were removed some of the concerns he previously had about the old model max Fiske INAF had had been had just finished writing a whole bunch of low-level code for evolving these models really quickly and really efficiently and and I'd come up with this kind of this rough scheme for how I thought quantum mechanics could work within its formalism but I personally found more convincing that than the one that was given in nks and so it seemed like given that these three things that happened all around the same time it seemed like it was exactly in the right moment to kind of to make us various assault on this project and that's Steven mentioned that's basically what we did at the end of the summer of 2019 now gentlemen one of the hallmarks of relativity is the connection between space and time how does this model affect time you know what what does it tell us about time let's see I can try taking that we can either of us can take this but but basically you know I think it's it will be viewed and mmin of the wrong turns in the history of physics to think that space and time are the same kind of thing that had been a thing that wasn't before relativity they once thought oh really is the same kind of thing what you know it's like you move around in space but time is this inexorable progression of things happening in the world that's kind of the the common view of time and when you think about things computationally that's also the view that you tend to have time is sort of the progressive doing of computation the progressive kind of changing of the world by virtue of the application of rules and so on but in the mathematics of special relativity it turns out it's really convenient to package space and time together and so by you know special relativity was invented in 1905 by 1909 or so particularly trapcode minkovski was really presenting this as you know this is a very elegant mathematical idea of space and time the same kind of thing and it's like we can convince you all space and time the same kind of thing imagine these strange you know thought experiments about you know trains moving at this close to the speed of light and so on and if you do this and this and this it really looks like space and time is the same kind of thing in there and changeable and that is indeed what the mathematics says but in in our model that's not how it works space is the sort of the extent of space is determined by these connections in this hypergraph time is the progressive rewriting of pieces of this hyper graph by the application of these rules and there's no there's nothing that sort of says there's no clock that says rewrite now rewrite now and so on it's just the model just says whatever can be rewritten will be rewritten doesn't say how long it's going to take because there's no outward outside way to measure that the only the only way you know how long things take is because you're experiencing it too because you're you're part of the system so the now the question then is in this view where time is something very different from space you know we we have very pretty accurate experimental verification that the ideas of relativity and the mathematics of relativity actually do work in the physical world you know how does that how does that come to be well turns out it's you know it's a piece of math to show that I mean I had I had done that back in the 90s that there's a property called causal invariance that is a feature of the way the rewrite rules operate that basically guarantees that what will emerge when you look at a large enough system is something for which space and time sort of appear to be the same kind of thing in the same way they are in relativity and that's so in other words even though going into the model space and time are completely different what emerges in the end is that to to a very precise it's as you as you look at you know 10 to the 100 you know elements or something for two incredibly high accuracy they will satisfy what special relativity says they should how they should work so it's it's a it's an interesting thing I mean what we found is these kinds of it worked out really nice for the math so we package these things together I think there are a couple of those mistakes that got made in physics we've just realized in the last few weeks another one of them which has to do with quantum mechanics so you know I think mistake number one 19:09 space and time the same kind of thing I mean mistake zero probably in the time of Euclid is spaces indivisible um but the other one is something to do with quantum mechanics one of the features of quantum mechanics is that quantum amplitudes one of they're sort of branding features so to speak is that they're complex numbers numbers that involve square root of -1 and things like this and that's been that's been kind of like how do you explain the complex numbers in quantum mechanics has been kind of a something that's been sort of a big mystery well I think that turns out that the maybe a little bit technical but but the the saying it's a complex number turns out to be the wrong way to look at it it has a certain magnitude and a certain direction and that's equivalent to complex numbers mathematically it's equivalent to complex numbers but it's a different way of thinking about it and the it turns out that the it seems that the the magnitudes of these amplitudes sort of come from a different place than the directions of the amplitudes and that's something that once you have the idea as I had had because you know I learnt quantum mechanics when I was pretty young and you know so for me it's been kind of that's though you know that's just the way the world works since I was probably a oh I don't know probably 12 13 years old or something so unfortunately very long time ago now and so you know I kind of quantum amplitude so complex numbers and that's just the way it is I realize that that that idea turns out to be something that has confused a lot of issues about how to think about quantum mechanics and we've just in the last few weeks I think we've been untangling that point and it's it's really interesting to me to see kind of you know it's it's I'm person who's interested in kind of ideas and how things get figured out and one of the things that one always has to be aware of is how do you how do you get it wrong so to speak and this this thing where you have made a formalism that has a particular structure and then you operate within that formalism and you never think is that formalism really pointing me in the right direction that's a that's a characteristic form of sort of how to get things wrong and it's something that well people like me who like to think about you know how ideas develop it's it's an important thing to be mindful of and and one that certainly I I think is something what has to apply to one's own thinking so to speak and that's part of what was going on between the 1990s and and recent times in terms of my my thinking about these the sort of the the technical formalism of these models so was Einstein wrong and if so how no Einstein actually was very much right he was it's interesting because I I have much more i've some amount of time studying sort of scientific biography and written a lot about it I haven't really studied Einstein as much detail as I've studied some other people but in his time Einstein did physics in a methodological rather different way from his contemporaries I mean it was a much more much more almost a throwback to sort of ancient Greek let's just figure it out by pure thought let's see what logical consequences of things there are I think that the thinking that he did in relativity particularly was that's it's it's right it's very appealing it's very useful turns out the idea he had that led to general relativity turns out that in in our theory the same idea applied not in physical space but in brawn she'll space essentially gives you the core results of quantum mechanics so that's something 9 Stein never you know he that was far from what he had figured out but you know his that the sort of methodological ideas that came out of his kind of almost logical way of thinking about about physics very much on track I think that you know it's a it's an interesting human story at some level Einstein did well I would say that Einstein kind of got it right the people who came to package what Einstein had done in terms of you know the mathematical packaging they got people confused and I think that the I also have a great you know one of the things that Einstein would always say when he when he made up general authority he was using some very fancy mathematics of the time to do with differential geometry it had been invented a few decades earlier but but it was very kind of leading-edge fancy mathematics and you know people would say to him that it was what impressive mathematics and he would say look I don't really understand this math I'm just using it to make physics so to speak and what we're seeing in our theory is we need absolutely leading-edge math unfortunately we need math Einstein was lucky because the math he needed had already been invented a few decades earlier the math we need is a few decades ahead I know this this sounds familiar because there's also Newton and yes well so so Newton you know his invention of calculus you know he he he developed calculus as a way to be able to do celestial mechanics to be able to figure out orbits of comets and planets and things like this and I think it is sort of interesting that one of the things we have to do is generalize calculus so calculus is sort of built on this tower that comes from Euclid and so on that thinks of space as being this so in in in in Newton's time he was thinking about space he's thinking about time he's thinking about motion he's thinking about things moving velocity acceleration these kinds of things um and he's got his his idea of calculus had to do with rates of change of things in something like time later on Newton didn't really get into this you know in multivariate calculus the next course you take after ordinary calculus so like I'm not even sure it's the next course maybe you take something else I know I don't know how they teach all these things these days but but I think you know it's like there's a calculus course and then there's a fancier multivariate calculus course the multivariate calculus course is about not just rates of change of things like in time or in in one direction but it's rates of change of things in many directions and it's it's sort of the underpinnings you need to do a lot of kind of traditional mathematical physics sorts of things well turns out we need kind of generalized multivariate calculus which is something that just hasn't been invented and we need something where instead of operating on spaces like three-dimensional space we need something that will work in 2.7 dimensional space we need things where you can kind of describe things like curvature what when you when you describe how something is you know as a sphere you would say well it's a it's a sphere with a certain curvature describe how that works when the sphere is a 2.7 dimensional sphere or when it's a a 5.6 dimensional hyper sphere or something that's a that's one of the pieces of math that we need that there are little you know that the the very leading edge of a bunch of modern geometry and things is kind of poking into that but hasn't really done it and it's kind of an interesting situation because because a lot of what we're doing is based on sort of computer experiments and the methodology you know for me this methodology I've been doing this methodology so long I don't even mention it I'm grateful to Jonathan for mentioning the the the kind of the idea of you know you start from the computer experiments than you build up from there what we're seeing in something like this kind of generalization of calculus and so on is we can sort of see how it has to work as we're doing experiments and we can computer experiments and we can see this is how this limiting process works and so on and so on and so on and computer experiments very much keep you honest because you know you run a computer experiment it does what it does and the way we're setting up this project all of the tools that we're that we're using to do those experiments are immediately and completely available to anybody anywhere and in fact even the the notebooks that we create like the ones I made last night when I'm doing some things about black holes those already up on the web and anybody can play with them and I think the somebody can figure out what's going on in them I will be very grateful because I I it's one of these things where where there's a certain sort of mathematical idea actually Jonathan I was just talking about this just before just before the just before this although only for about two minutes so we didn't have a chance to to get as far as we would like but you know there's something that I found in this computer experiment last night and it's like what the heck is this and it has probably Jonathan has a first hypothesis about a mathematical interpretation which I'm not completely convinced about yet but it's a it's a it's an interesting methodology because you're kind of being you know reality you know in a lot of what's done in science it's like this loop that involves doing physical experiments and seeing what how things work here we've got a different loop going that's involved with doing computer experiments and understanding they're sort of theoretical consequences but yes we've there's a lot of I mean the whole thing is really nice is that the the math that has to be invented is just really elegant I mean it's it's really the that happen a very they're not just very general very I don't know they have a they sort of fit together in a very beautiful way except that it's very hard work and um the you know there's a there's a lot of concepts that are not yet familiar to us that are clearly going to be needed I mean this is one of the challenges and in building up something like mathematics you're building this big tower abstractions so you know first you have to have the idea of things like numbers then you have to have the idea you know eventually you get the idea of things like integrals and derivatives and so on these are all sort of a tower of abstract ideas once you have integrals and derivatives then you can start thinking about oh no differential equations or you can start thinking about oh I don't know Jonathan help me out I don't know tensors um the no but it's it's a it's a it's an interesting human process that in the case of mathematics has been going on for a few thousand years of kind of building these progressive layers of abstraction and we happen to need a few more we'll get to that in just a minute Jonathan tell us about your hypothesis oh hang on sir and just before I do can I add one thing to the to the Einstein question course yes absolutely mentioned I mean that there's a lot of a lot of these kind of apparent wrong turns happen because of just weird historical serendipity so as it turns out you know Einstein actually wasn't a huge fan of the notion of space-time at least initially so his 1905 paper on special relativity did not meant did not make any mention of it it was his version of special relativity was formulated entirely kinematically it was only later in 1908 that an in Cacak Hermann makovski introduced this notion of space-time that Stephen mentioned and my personal hypothesis why that happens is that it's a it's a it's kind of a historical accident that has to do with minkovski zone background minkovski was a was a number theorist who was interested in these things called what there are these things that are studied in in number theory called quadratic forms and he was interested in quadratic forms over n variables and it turns out that a very natural way of thinking about quadratic forms and n variables is to think about them in terms of the geometries of n-dimensional spaces and the geometries of n-dimensional space city so when koski developed this whole theory of geometries of n dimensional spaces that was based on earlier work by people like Lorenz and Frank RA that turned out to be exactly what you know ended up being the basis of the formalism for general relativity so in 1908 he recast Einstein's original theory in in the as this Jimenez this geometrical non kinematic thing using a you know using this four dimensional structure known as space-time and then mathematicians started adopting that because they understood minkovski as intuition better than they understood Einstein's intuition and so in the end Einstein had to kind of had had to defer to the mathematicians and so his 1915 paper was written using this language but I think if Minkoff C hadn't done that or if a different mathematician had liked latched on to it with a different set of intuitions the the story of what what happened there would have been quite different and in fact I think that one of the reasons why this whole computational paradigm hasn't been applied to fundamental physics earlier also has to do with another of these historical accidents so it's conventional you know up until relatively recently you know a bit based and I think one of the things that's kind of shifted this is is the advent of the recent advent of excitement about quantum computing but up until that topics in kind of theoretical computer science were generally viewed as being a branch of mathematics rather than a branch of physics but I don't think that's necessarily true or I don't think that's the only way of viewing it I think what basically happened was the the abstract concept of computation was invented was developed in the 1920s and 1930s by people who happened to be pure mathematicians by people like Alan Turing Kurt gödel Alonzo Church and others and they were using it to study the nature of mathematical proofs so you know in mathematics you have this notion of proof where it's like you have some some axioms that go in and then you do this proof according to some rules of inference and then a theorem comes out and then they came up with an ultimately desiccated version of that idea where it's like you're an input that goes in you undergo some computation according to some algorithm and then an output comes out and it's a it's a very abstract way of representing that process but it turns out that you know since the neuter is since the days of mutant that a very similar thing has happened with physics that you know that the general Newtonian conception of physics is it like you have you start from some initial core some initial condition goes in you have the system undergoes motion according to some laws of motion and then a final state comes out and so all of these that you know all both of these things are perfectly well captured by the computational paradigm it's just the mathematical intuition one instead of the physical intuition and I suspect that that that historical accident the fact that it was the fact that you know the pioneers of theoretical computer scientists happen to be pure mathematicians who are interested in mathematical logic probably set back fundamental physics by about a hundred years but anyway so actually I want to add something to that because it's it's a um I mean because I kind of lived through it so to speak which was that people had this idea computers work using discrete bits and so on and that was an idea that had been introduced theoretically by by people like Alan Turing in the 1930s it became a very practical thing one thing went digital electronic computers started to be real in the 1950s and 1960s but the physicists were off thinking it's mathematical equations mathematical equations that involve continuous variables and so on that are the way that physics works and it really was quite separate I mean people said well those Turing machines and they represent computation and there's mathematical equations and they represent physics even Alan Turing himself late in his life in the in the 1950s he thought about some things in physics and biology and even he having invented the Turing machine in the 1930s he went back to mathematical equations to study things in biology and physics so so even he hadn't really sort of gotten convinced that computation that his kind of discrete computation would be a thing that we're relevant to physics and up until the 1980s basically it was people really thought they're these two branches there's either mathematic equations or there's computational stuff and they just don't connect and there were in fact physicists involved in and not in the theoretical side of early computation but in certainly in the practical side I mean you know people well john von neumann was arguably much more of a mathematician people like Vincent as an ass off was the person credited with having made the first stored-program computer he was a physicist you know that people like Hartree was a physicist although the the bunch of people who were involved but they were not doing the theoretical side of it that was all mathematicians um but you know in the 1980s so so I started introducing kind of notions of computation into using them as ways to think about physics not ways to think about fundamental physics and the way that we're thinking about it today but ways to think about physics that you would just use to compute to properties of snowflakes or physics that you would use to work out motion of planets and things like that and I started introducing kind of the idea of of thinking about those things in computational terms and boy did it get a lot of resistance from from physicists because it's like no no no you know we know it has to work according to these equations and so on I think by possibly through my own efforts actually probably by the end of the 80s people were less up in arms about how there was a sort of dichotomy between physics and and computational ideas and then I think Jonathan is right that the interest in quantum computing which is really weird historically because like people were thinking about that in the nineteen sixties I even worked on that in the in the beginning of the 80s it was sort of a thing that was hanging around for a long time and it finally sort of about what 10 15 years ago when was Shor's algorithm must have been what was it midnight yeah it's about your 15 years ago um it it as a result of some sort of cool results oh and David gorgeous stuff as well it kind of suddenly quantum computing became exciting and people have been you know and I think it is certainly true that once you're doing quantum computing you are merging physics and computing in a certain way I mean it's a in fact the history of you know the future of quantum computing we shall see how it works our Theory has very definite things to say about it and Jonathan actually has some very interesting ideas and results about how that all works the end of which will probably be that the quantum brand of computing will be just fine but it's not clear that it will actually be officially doing quantum mechanics Jonathan Wilk quantum computers should they be possible what is the benefit that's an interesting question so as Steven mentioned you you have to be you have to be careful about what exactly you mean by a quantum computer so one possible interpretation that I think you know is the interpretation that Stephen and myself are kind of more more optimistic about is you could interpret a quantum computer as just being something that uses users quantum mechanics in its own in its physical operation at a level that goes beyond standard you know metal oxide semi conductors and that you know that's kind of that's definitely something that I think it's great I think it's pretty heat likely that's something that that's going to come and it's going to be really useful and it's going to lead to all kinds of practical speedups and things over over current computer hardware but there's this there's also this theoretical notion of what a quantum computer is which is in which is represented in terms of this thing called a quantum Turing machine as opposed to the to a to a classical Turing machine which is the thing that Alan Turing and people were initially studying and the interesting thing about quantum Turing machines is that on paper they there are classes you know although they're in terms of the raw computational power they are exactly the same as classical Turing machines they compute exactly the same sets of things there are certain classes of tasks for which theoretically a quantum Turing machine offers potentially exponential speed-up over a classical Turing machine and that's kind of what's led to a bunch of a bunch of hype around moderns of the you know the modern quantum information movements for what I'm a better word but the abstraction or the idealization of a quantum Turing machine makes one that there's one very crucial approximation that it makes which is it kind of it which is you have this you have this quantum computer it applies a bunch of gates it's part of a quantum circuits or self to some piece of information you get a result and you obtain that result sort of faster than a classical computer could have could have computed it but then you actually have to read out the results you have to apply a measurement operation and you have to get you to so at the end but you know you have to go from this quantum representation to an actual classical state that you can read out and make sense off and in standard quantum information theory that measurement process is idealized as this thing called an instantaneous projection and which which amongst other things means that it basically that that in itself is not a that's a totally trivial computational procedure and that's a reasonable approximation to make but at least in the standard formalism of quantum mechanics but within our new formalism it--with in our new formulation of what what a quantum mechanical system is u1 actually has a very different intuition that the measurement process is also politically because all aspects of our model are computational in addition to the actual computation of the quantum computer the measurement process you do at the ends to read out the result is also a computation and one of the really interesting things is as the computation you do on the quantum computer gets more sophisticated the measurement operation you have to do in order to read out the answer and get a sensible result also gets more complicated and that's not something that people conventionally consider an unusual quantum information theory and it implies that actually that some of the predictions that get made about how much more efficient quantum computers will be sort of maybe more on the optimistic side we don't yet know exactly how that's gonna play out but but what you know one thing that's becoming increasingly clear is that if our if our interpretation if our model of quantum mechanics is is really correct then it's gonna lead to a bunch of really interesting new results about the limits of both classical and quantum computers and sort of a deeper insights into the nature of quantum measurement and things like this why do we have to move and why such a large moving Laurie the internet here in the volcano lair in Borneo is terrible Internet is still terrible better internet then yes indeed broadband I can finally get rid of this 2400 baud dial-up modem [Music] wait I'm still in the bag also I'm supposed to be the one driving it's in the rental contract what are we on so many books what [Music] [Music] [Applause] you

Channel: Event Horizon

Views: 178,353

Keywords: Stephen Wolfram, Wolfram Physics, Wolfram physics project, theory, physics (field of study), science, solution, documentary, universe, galaxy, life in the universe, john michael godier event horizon, event horizon, A Path to a fundamental theory of physics, theory of everything, is there a theory of everything?, jonathan gorard, the theory of everything, einstein, general relativity (theory), Quantum physics (field of study), Quantum Computers

Id: LpK1d8mTEhI

Length: 70min 15sec (4215 seconds)

Published: Fri May 29 2020