Timeless Explanation: A New Kind of Causality, Julian Barbour

so let me say what the what the key thing is that I want the which is that there is a huge difference I believe now between if we consider that the universe is open or closed closed means it's spatially closed like the surface of the earth but in three dimensions open that it's infinite and I think that there is this difference is is hidden in general relativity it doesn't look so great in general relativity but I believe that it is is absolutely huge and I want to explain why that is so I'm going to start off by going back to the foundations of dynamics and some very fundamental questions that came up then but first of all I want to say something about space and the role of space in the way we think about the world lightly said in his argument with Newton Newton said that space is real every point of space exists like a like a grain of sand they're all identical to each other Leibniz said this is nonsense and he said that space is the order of coexisting things and by the order when he was pressed by Newton in the Leibniz Clarke control correspondence he said that all there is the distance between objects the separations between them the only real thing are the separations between the objects now I think Leibniz was halfway to the right answer I would change Leibniz his statement to say that space is the order of coexisting facts let's go back to when the Egyptians discovered Pythagoras theorem it came out of surveying of the land surface of Egypt geometry means measurement of Earth and suppose we have n points fixed in three-dimensional space they're not moving relative to each other and we measure the separations between them with measuring rods which nature in her bounty gives lots of them to us and we we debt we measure the distances between those endpoints we get essentially N squared separations it's precisely n into n minus 1/2 but it's of all the N squared those are positive numbers they could be completely arbitrary but a mathematician looking at them long enough would say ha these are actually the separations between endpoints in 3-dimensional Euclidean space and the mathematician can say that because there are very precise mathematical relations that these distances these positive numbers satisfy and out of this a vast amount of modern mathematics comes already you have the possibility of representing those points as vectors in Euclidean space you have Cartesian coordinates you have the similarity group of Euclidean geometry translations rotations and dilatation 'z which take you from one representation of these points to another this is an extraordinary thing and that is the order of coexisting facts that is a fact my hands are of equal length and it's the order of those lengths that underlies everything so I think this is very important so now let me go straight on to what I think is very significant now is you've been looking at this picture for a while I'll explain what what I mean by this here is a triangle in Euclidean space according to Newton it has you need ten numbers to say what's going on in Euclidean diner in Newtonian dynamics you need the position of the center of mass three coordinates the orientation in space three more numbers you need the three sides of the triangle three more and you need the instant of time that's ten numbers now the like Nixon viewpoint really should whittle that down to two if this were the whole universe are not in the environment not in the context of crackles it would be just two dimensionless numbers two angles that determine the shape of the triangle that is intrinsic the size of the triangle by itself if it's the old universe has no meaning whatsoever it's a dimensional number and cannot have any objective meaning its position in space is completely meaningless it's orientation is meaningless so this is what comes and it determines the shape I would say that the key concept that explains everything really that we can understand about the universe ultimately derives from shapes shapes are they're mentioned las' so that's the key thing so that's that's important and this is I think the right way to represent things here that you this is a principle fiber bundle I'm not going to go into all the wonderful mathematics of principle fiber bundles but the base space here is it's going to be the way you should think about a universe of three particles each point in the base space is a shape of a triangle then these fibers up there are all different ways in which you can imagine that triangle represented in Euclidean space position orientation and size and those are all identical as you go up and down the fiber on the left here we have the group the structure group this is the similarity group of Euclidean space which enables you the generators of its lis algebra they take you up and down that fiber which is a seven dimensional space two different possible ways of imagining this thing embedded in space but the reality is just the shape of the triangle there is nothing more but that these are all just ways of conceiving it and then and this is this is what the mathematicians call vertical motions and they are pure gauge there's nothing of physics in that if this is the entire universe it's a totally different matter when I'm talking about this triangle here in Krakov here that pronounced isn't reasonably good the real thing is when you go to a different shape a different triangle this triangle is in congruent to this one they are different and the fundamental question is how do you define the difference between those two shapes what is the measure of that difference that is the key question so let me now go and point out that Newton promised to solve a very fundamental problem and didn't do it in this famous kirlyam at the start of the Principia he recognizes that is there's something very problematic about his notions of absolute space and time because they are not visible and he recognizes as an absolutely key problem how to determine the absolute true motions from the observed relative positions and motions and he says this is not an easy problem but he suggests that it can be done and he says how it shall be done in the treatise that now follows for to that end it was that I composed it and the remarkable thing is he never returns to that problem and virtually no one in the history of science has returned to it seriously people were very worried about it but not even Einstein addressed that question seriously he created general relativity indirectly with great brilliance a combination of opportunism brilliant adaptation generalization of Maxwell's ideas all sorts of things but Einstein did not address those questions directly and this is what I'm going to suggest that when you think about infinite universe or a closed universe things look very very different so that's what I want to come to now what is let me say what is the skolem problem if today you open the book on textbooks of dynamics it will say it will introduce the concept of an inner frame of reference and it will say an inertial frame of reference is one in which Newton's laws hold that of course is is is a truism really it doesn't address the really key question is how do you actually determine the inertial frame of reference from what is observable let me say that the teaching of dynamics at universities is deplorable you open any book on textbooks they will not tell you how to determine inertial frame of reference they talk about climbing clocks that they will not tell you what time is and they will not tell you what a clock is and when you're taught dynamics at university or high school you start with Newtonian kinematics which corrupts your brain because you think absolute space is there then you go on to Newton's laws then you solve the two body problem and then you jump straight to a rigid body theory and then you go to the garage and dynamics all very beautiful but the real dynamics actually begins with the three body problem which gave you headaches so it gave up on it so actually nobody who studies dynamics leaves university knowing really what it's all about and where all the problems are it all sits in the end body problem and it starts with a three body problem and I know a lot I know some of the world's leading experts in the three body problem and they say to me actually after 300 years of studying it we still know essentially very very little if next to nothing the passing so so now we go on to the real issue now is what information given observable information how much do you need to determine an inertial frame of reference and I'm going to pick up here from what pong Harrogate in an analysis in 1902 in his science and hypotheses I'm going to take a little bit further suppose I'm given the shape of my two triangles and nothing more because that is actually all that's really observable and objective these are different is that sufficient for me to determine the inertial frame of reference in even that the Newtonian evolution is taking place that takes me from one triangle to another because Laplace and determinism about which we've already heard quite a bit only works in an inertial frame of reference ponder I said there's been a lot of discussion about absolute or relative motion what precise defect if any arises because Newton describes motion in absolute space and he identifies a very precise defect he says I am a convinced relativist I believe that only relative motions count and it must be therefore the case that if I know the initial I'm going to go a little bit further than ponder and put it in my turn if I know the initial shape of my triangle and the rate at which the shape is changing so there's I'm going from one shape to another if I believe that that is everything that counts I should be able to predict the future uniquely on the basis of that too and that information just those two shapes and nothing else and I put this question to Nobel Prize winners and so forth and say is this true or not and they have that they've never thought of asking that question they do not begin to know how to answer it but it's actually very simple the answer is you cannot predict the future on the basis of that information you miss exactly for vital bits of information the first is that those two triangles in Newtonian terms contain no information about the angular momentum that is in the system I can change the angular momentum at will by holding them in different positions like that I cannot predict therefore and now the angular momenta is absolutely crucial in how system evolves including how the shapes of all so I cannot given those two shapes which are incongruent say how the shapes will go on in the future I'm missing three bits of information and there's one little bit of information which I'm lacking which is that I don't know in Newtonian terms how much there is an overall expansion how much kinetic energy there is an overall expansion that's a fourth thing so there is a four-fold indeterminacy in the future evolution and therefore I that is the precise defect of Newtonian mechanics that for fold discrepancy and it's exactly goes back to those generators of the four generators of the Euclidean the similarity group the center of mass motion doesn't count because it doesn't come into the problem doesn't hook this issue because of Galilean relativity but the three of Genet rotation and the one of dilatation comes in vitally so now what is actually the and and of course the great thing about pong hooray is that he made marks ideas precise muck was very powerful in saying there must be something wrong with Newtonian mechanics both as regards the definition of position and time that he didn't give a precise criteria that is what we get from Paul Murray and I will take poison on the following that there is one correct for a closed dynamically closed universe there is one correct formulation of machs principle which is here it comes in two forms there is the strong must long very principle as I call it a point in a direction in shape space should determine the evolution of the shapes uniquely that's the strongest form that one could require and then there's the weaker form which requires one parameter more to be specified a point and a tangent factor in shape space determine the evolution uniquely so that's what is the requirement so let me say how that's going to be implemented we've got this picture again here I will be able to implement the strong machs principle Mach Bank very principle if I can define a metric on shape space by the way let me just say that shape space is a completely general concept all that is underlying this whole picture here is lit as a lead group all I need to do this is a lead group either finite dimensional or it's generalization to the three dimensional difícil group or the conformal group in three dimensions which I'll come to if time allows so this is a completely Universal way of attacking the problem what I want to be able to do is define a geodesic on shape space on my space of possible shapes if I've got that then a point in a direction in shape space will determine a even even evolution uniquely because I can say the evolution is a geodesic on the shape space and if you have a geodesic principle it's a point in a direction that does it so that's the thing so you need to define a metric on shape space and your away you're done and there's a there's a very simple way to do it which comes which is suggested exactly by the very problem that I started off with telling you about I'm going to somehow rather what I need to do is to define a difference between two nearly identical triangles or shapes of triangles and let's let's stop worrying about the dilatations because it's just a few more words which doesn't really affect the essence of the matter I'm going to try and bring these in congruent triangles in the position where they are most nearly overlap congruence perfect overlap is the basis of your pleadian geometry let's say that's the position where they are most closely best matched closest to being overlapping and there's going to be a measure to define when they are I'll show you precisely in a moment then I've got this distance here between particle one in its in that triangle in that one there this distance here in this distance here now this business of bringing these two triangles together so that they are closest as possible to overlap is background independent it does not it is not affected by where I walk around in this room I will get exactly the same relative position of the two triangles wherever I use it is background dependent independent in space it is also independent of any notion of time time does not exist in this picture it is always derived from things that you can see and get hold of and it doesn't matter when I do this it's exactly the same now as when I first showed you the triangles in that position a minute or so ago and by a minute or so ago I mean that the structure of the world the shape of the universe has changed somewhat and that's what I mean by a few minutes ago a minute or two ago by the way when should I stop so chair please what time the right should I stop this talk I started at 20 past I should stop for questions at 11 at 12 I mean correct in 20 minutes time I'm just about on course I think good great thank you so let me show you if I can the precise quantity to do it with here is here is the basis of everything now the the wonderful thing about geometry and those ways of representing it is that it gives me a high level of geometry I started off with those surveyors in Egypt discovering geometry on the surface of Egypt but now I discovered geometry in shape space at a higher level this is a 3n minus seven dimensional space shape space so for the it's a it's a two dimensional space here but if I got a lot of particles it's a highly dimensional space but up there in the fiber bundle where all those fibers up there there's a there's a metric defined up there which has come because all of this is derived from the from Euclidean geometry in three dimensional space I can lift it up into the fiber bundle and exploit it there and you see this here in the way I've explained it's enabled me to define a distance between triangles we started off with the finding distance between points in Egypt now we're defining distances between two triangles and at the end of all of this will be defining distances between two complete shapes of the universe that are nearly the same but slightly different and all that will be done with geometry which is what holds together the individual configuration it's Euclidean geometry which is defining my triangles so that's what we're going to do and you can see how this comes here this is where the geometry at the higher level comes in is down here I'm going to do this actually something that is scaling there so I first of all I place my two triangles in an arbitrary position relative to each other that gives me a delta X or Delta X and the Delta X so therefore I then consider this quantity here I'm the scalar product of each Delta X with itself weighted with the mass this is length squared in terms of dimension I won't have something which is dimensionless because that's all that comes in reality so I multiply it by something which is a function on shape space which must have length to the minus two dimension so this has no overall length dimension it's dimensionless the masses I can always take out and divide by a suitable part of the total mass to make the whole thing dimensionless so and then there's a square root because I want a geodesic principle and the way to get rid of time once and for all is just to put a square root into your action that's what gets rid of time is getting popping that square root and then I move the time it around here's an arbitrarily the time I move them into the best matched position this means that I'm seeking the minimum of this quantity is positive definite there is a unique minimum which I can find that way so this is where that comes in and this is where I have lifted geometry in three-dimensional space up into the multi-dimensional configuration space and these are those fibers this is all the different ways of representing one triangle and this is all the different ways of representing the other there is that metric on the high dimensional configuration space and what best matching is doing is actually picking up the orthogonal separation between the two so that's what is happening and then we're way we've got it we've got our variational principle we've got a unique evolution and out of this you get a theory where it's just one shape following another and by the way this is completely time symmetric and I think we really should get out of this business of talking about initial conditions there are no initial conditions in this story the shapes go on forever it's completely asymmetrical all that is happening is that the law that is governing the of the shapes encodes information at any one point and processes it and changes it into a different form so you have initial information which is the initial but at any point along that curve you can take a shape and a neighboring one and essentially what has happened is that the law of evolution has just transferred information at one point on the evolution curve to another point so that it's really the information is encoded it's a point in phase space it's the point in the direction in which the system is going in its configuration space so I would like to get away from this thinking about initial conditions it's not initial conditions it's a point in phase space anywhere on the curve that it passes through so that's it there now let's just look at what happens when you do this I'll go straight on to this thing here this is how the inertial frames of reference and time emerge from such a procedure this is an action principle you have here the key things of this action principle are first of all it's got a square root e is a constant which later you can identify the life of Newtonian chemical energy that I would much prefer to be seen as just a constant that you can add to a potential and this is you can take this gravitational potential and then T is a kinetic term that it's not nearly determining kinetic energy but it's not bike because it's divided by lambda where lambda be completely arbitrary parameter on the curve in shape space that I'm thinking of and I'm going to already suppose that I've already found these best matched displacements of the things I'm going to put into the action just these best match differences now I could take that land away completely this is what you say it's repairable causation there it's completely independent of the parameter it's timeless in that same thing so this is the key thing there you you then find the Euler Lagrange equations that correspond to it and you get this pretty unpleasant looking set of equations here with this bizarre-looking square root there but it cries out we simplified lambdas completely arbitrary and this means that T is complete garbage e that is fixed to speak as a universal constant of nature other ways just like a cosmological constant in general relativity and these this quantity which is defined on the configuration space of shape space and you can always choose lambda to make T Harbhajan value so you can always make to you have a family and now let's call that special lambda T and then you get Newton's second law emerges but there are two differences time has emerged it wasn't put in in the initial kinematics and secondly I get the best matched positions of these things there now what this means I'm up exactly what it means is that when I bring the triangles into the best matched position effectively what I'm doing is bringing the centers of mass to coincidence and I'm reducing the net rotation to the smallest value it can have or to zero and that means that what I'm actually picking up for the complete universe is that it's in its center of mass frame that center of mass is at rest that's nothing significant because of Galilean relativity but what is relevant is that the total angular momentum of the universe must be exactly zero and that's a prediction that Newtonian dynamics cannot make but there's there nothing to stop subsystems of the universe having any momentum and any value of the angular momentum and moreover we can pick up the inertial frame of reference the inertial frame of reference just as marks entities is determined by the universe in its totality which must have zero angular momentum and you pick up Newtonian kinematics in its entirety for subsystems it's only required that the universe that each the angular momentum momentum of each subsystem if you add them all that must be zero and that's of course more or less what we see when we look at the universe we see lots of galaxy's spiral galaxies and clusters of galaxies with angular momentum in them but there seems to be no trace at all of an overall rotation of the universe so that seems to be okay from that point of view right let me press on and see if I can get to the end more or less if I now I want to say how time images it's very illuminating just to rewrite this explicitly in this form here this is the increment Singlish time and you see that it's it's a very completely holistic expression you take all of those specials matched displacement you divide it by this quantity here and you get completely explicit expression at this time in terms of everything that's happening in the universe so this is the perfect implementation of what Mark said it is utterly impossible to measure the changes of things by time quadric time is an abstraction at which we write from the changes of things and so PI is a distillation of all the changes in the universe and it's doubly holistic you have to use the best match displacements to get it and you have to take them all into account so this is a completely holistic view of the universe and it's suggesting that you cannot properly understand what is happening here in this room ultimately unless you take into account the home universe and underlying all of this this will work if the universe is a closed dynamical system and Einstein said it is only in this case that you can close the circle of cause and effect I think it's a powerful argument for considering things in that way I better press on this is just a picture of how Newtonian space-time emerges in this picture that you you start with an initial triangle you put the next one in the best match position relative to it and so on all the way up and then you put the vertical separation in terms of this emergent DT that appears so that's exactly how you get Newtonian space-time and there's going to be and I won't possibly have time to go but there's an exactly analogous way but vastly sophisticated how you can build up space-time from this where you have just space like hyper surfaces of us three geometries or even conformal three geometries and I'll get onto what I mean by that where you do an immense a more sophisticated best matching process but you can entirely build up space-time by a similar process in this way and I'll just give you some hint of how that is done so let me just go on let me just remind you of some key dates in the history of geometry in 1854 Riemann introduced the idea of three dimension three geometry which has curvature in it you did it by means of a three metric now it's very interesting if you read reruns paper he says absolutely explicitly to measure a length I have to put my measuring rod next to be interval that is going to be measured but then he goes on to say I'm nevertheless despite this fact I'm going to assume that it is meaningful to say that my hands which are separated have the same length this is very suspicious it's just like whether you can define simultaneity in Andromeda as being the same as it is here what real evidence is there for that and this was not picked up until 1918 in a slightly different form by Hermann Maier the next interesting stage was in 1870 when Clifford conjectured that when my hands are moving around it's just regions of higher curvature relative to each other he had the idea of dynamical geometry but it's three-dimensional geometry which is changing dynamically so then in in 1872 and 1883 ma consists very firmly that all motion is relative and then on parade in 1902 comes up with what I regard was the very precise way to define my principle and now I'm really indulge in a little bit of counterfactual history and suppose it vials inside that there was something not quite right with romanian geometry that came in 1918 had occurred before Einstein discovered general relativity and I said himself a generative addition have been discovered 50 years later and after quantum mechanics had been discovered think about what would how different things would have been then so that could have been what happened so I'm going to conjecture that vials inside became remarkably late considering how clear riemann had been about the assumption he was making had come before and Mark and pong Korea vial had got together to make a theory of dynamics of geometry where only Anders come so what this is saying the assumption I'm making is that the bedrock of science is angles and the distance is a gauge quantity there is there is no real distance out there and in fact when we look out we actually basically see angles when we open our eyes at night we see the celestial sphere we see angles between stars the whole of the discovery of the laws of planetary motion everything was based on measurement of angles nothing else went into it so my conjecture is not only this time not exist but at the fundamental level distance does not exist it's just purely in angles and let me just very hastily give you just an overview of the things so a Romanian 3 metric it's a 3 by 3 matrix which gives you dimension for lengths very fishy this craftsman and so anybody is taught about this is this is at the center of attention when you learn Italian geometry but it's fishy because it's unmentionable but it determines cosines bangles which is potion this is this is dimensions what you get out there so a Romanian three matrix has three bits of coordinate information that's different or physics you can change that by different mortising for your leisure different morphisms there's one scale with an information that's just a suspect and then this food angle data and that's that's reality okay so that's what you have there and super space is the concept that John Wheeler introduced it's essentially so we use the space of all remanded to matrix defined on a free manifold that is closed without boundary and any two three matrix that can be carried into each other by a lithium or person represent the same three geometry that is super space that's the analog lot of shape space with what I call a relative configuration space before I start thinking about dilatation contagions okay and there's a way of generating 3-dimensional different morphisms which I don't have time to go into now much more interesting now is conformal transformations a thought pumpable transformation is obtained by multiplying a clue matrix by a position dependent function purely for mathematical convenience you take four times a positive function of position and I'm not going to go into the details of whether you allow you restrict it very slightly but I want to go straight on to the analog of shape space in this picture here so now from formal super space there are so there are two mental groups that come into this is the three-dimensional diffeomorphisms which is analogous to moving my two triangles relative to each other and then there's the three-dimensional conformal transformations and that's analogous and eat essentially what you have in conformal geometry is the euclidean symmetry group at each spaced point here I can only change the size of a complete triangle relative to the other one but in Romanian geometry essentially I can have a triangle in each base point and so what I'm doing is changing the scale at each phase time and this leads to an immense richness which is what I believe is really underlying general relativity and puts it in a totally different perspective when you look at it from from this way let me so so I call a combination of those two groups the three-dimensional different more for some group group and the three-dimensional conformal transformations the geometrical group it absolutely cries out to be the basis of the dynamics of the world by the way matter can go into this story in a wonderfully simple way and I don't have time to go into that but then a conformal super space which is the shape space of dynamical donnelly is really the space of all remaining three matrix quotient II by this geometrical group which is the combination of the two and so then you so this is how it looks in terms of fiber bundles you have super space where you only motion by the lithium offices this is Jeremy Piven annex which dominated the attempts to create a quantum theory of gravity in the canonical approach from the late 1950s through to today that that's the canonical approach to quantum gravity and then if you quotient ones law you get the conformal super space which is each point here is a shape of the universe a dimensionless shape of the universe and you can add matter fields to it as I say without difficulty and it's all very nice so what comes out of this I'm not going to go through any of the details because I've got just precisely one minute left apologies for going through this I had rather longer and more preparation in Canada last week you get out of this emerges for a closed universe a very special form of Einstein's space-time you get on the right you get space-time as it is in Einstein's theory exactly but in a uniquely distinguished foliation which is called constant mean extrinsic curvature in four-dimensional space-time it's exactly analogous to soap bubbles in three look how beautiful they are soap bubbles have very special mathematical properties and so do surfaces of constantly curvature in four-dimensional space-time then we mentioned that the whole of numerical relativity now which is a major industry relies upon surfaces of constant mean curvature there is no known way to generate initial data for general relativity that does not essentially rely on these services this was the great discovery made by York how to solve the initial-value problem well listener of each machine error which started in 1944 your perfected it in 1971-72 with the help of my decade more collaborator Neela Miroku from Cork in Ireland and so you get and this comes out of the theory with our term necessity you can't escape it in a spatially closed universe treated in this way you get a uniquely defined notion of simultaneity very ironic interestingly when York did his work back 40 years ago we look injected that general relativity might undermine the relativity principle the relativity of simultaneity from within itself because of its inherent mathematical structure and I now if you're very confident I'll not quite take poison on it yet but I'll take a bet on it that Wheeler was right and it's a very very beautiful mathematical structure that is sitting inside general relativity in that way there so I think that's really all I've got time to say I sorry it was very breathless and rush but I'm here to answer questions at least until the end of tomorrow thank you very much indeed thank you very much for your simi interesting lecture you were hard by all so I expect now a debate procedure Bruce is in in your example of two triangles I'm not sure if I understand what you mean by best matching thank you I mean Euclidean geometry as taught by Euclid the basis of it is congruence you say that two figures are identical if by translations and rotations I can bring them to perfect overlap but my triangles are incongruent and this is what happens when used pass from geometry to dynamics Newton was very aware of this that you the figures now change in geometry geometry is about unchanging figures dynamics is about changing figures so what I'm suggesting is that dynamics is based on the least possible change you can make to that underlying principle of geometry that it's based on exact congruence it helped me because the shape of the universe is changing so what I mean by best matching is try to bring my two triangles to the best overlap here they clearly are way way that's much better that's much better than ever below but that's even better that's even better and there is a unique position where they are as close as you can get in that you can minimize a well-defined quantity that quantity is not absolutely uniquely defined but this it's pretty nearly it's very restricted in what you're allowed to use as the measure of how different the two triangles are so that's why I call it best matching you don't claim to you don't claim that any two triangles at that a position of them that you don't claim the uniqueness of the position of best match once I've defined the quantity that I'm going to call to characterize the measure of Inc ngrams what you need is a measure of in congruence which only depends upon the shapes of the triangle that measuring congruence is not uniquely defined it gets incredibly close to being uniquely defined in the dynamics of geometry in fact it may be we're quite close to we're very very close it the most there's a one parameter freedom it's you George how familiar are you with that mysterious parameter in the width super metric the little lambda that occurs in that anyway there's a very interesting in the dynamics of geometry the scale factor is associated with the expansion of the universe has negative kinetic energy it's completely unique to a geometry that no other field no other anywhere has negative kinetic energy associated with it the kinetic energy that is conventionally associated with the expansion of the unit has negative kinetic energy and there's a very precise value that it has now I think that and that map is a one parameter freedom which is now much in discussion with something called Raja Valley Lifshitz gravity it's now actually a topic being investigating but there's a lot of indications that that that one undetermined parameter should have one unique value which is one and so I suspect that we will be able to establish that when you try and best match geometry from homo geometry that incumbrance measure is unique I suspect if you just simplify the situation by looking at segments rather than triangle so pip pairs of points the best matching would mean one so what do you mean by seconds over in the size justice size with respect to loss this is all about treating the universe as a complete entity finally I could just add add one thing there in I would lead it another half an hour under what I'm saying what I would like just like the punchline is that when you are thinking about a spatially closed universe the key thing is actually that you need notion of symbol to narrative best matching its on the line and the general curved areas that you in general relativity these other foliation of space-time which are not constant in curvature is exactly analogous going to non inertial frames of reference in Newtonian mechanics the heart of Newtonian mechanics the essence of Newtonian mechanics is what unfolds in the inertial frame of reference so so it's role in the case of a closed universe to revolve general covariance in four-dimensional space-time of something fundamental it is trivial as going through a non inertial frame of reference in Newtonian mechanics however in the case of an infinite universe it's exactly the same in Newtonian mechanics and in general relativity there is no way of picking up a unique inertial frame of reference it already in Newtonian mechanics was recognized 100 years ago that Logan inertial frames of reference that they could be a freefall so you can pick one up locally particularly in freefall there's no way into the universe that you can pick that up of the same notion general relativity so in an infinite universe the symmetry group that you do have to think of is I believe general care very general different both of them in there it's in four directions and it's utterly different from the one that's appropriate for closed universe and come back I mean compactly you compared closed universes with flat geometry with the flat geometry I understand I mean if you go to could be hyperbolic it could be absolutely this was my question so the same the problem is similar for open universes of negative curvature as well yes that's justice that's a completely different situation in that case there will always be fluctuations and the will be low in that case I do not think it will be any uniquely defined configurations the way sorry foliation in a way that there is in the present I know this to be a very interest I think for cosmology if if we conjecture that the universe is spatially closed because then I would think very strongly that CMC foliation possibly current affiliation is away which one should think about cosmology Julian could we go back to about slide number three something like that where you define your best fitting I think it works which is about slide number three got there hello one walk go no go yeah yeah litora what I can't understand this is the best fitting of shapes right I'll show it to them is nothing in my culture it's a little it's not like wish my crew so if it's a Christian Church wisely as a function called mass in there which that messaging message got nothing to do with shame you're quite right well thank you for bringing it up first of all it's only what only counts is actually mass ratios and you have to put them into I would say this is a defect of a point particle ontology there are no masses when you get to geometry so this is that this is a crutch at this stage George where we have to talk about masses as well but when we get on to geometry that they aren't in there and then watch W W is a it's like a potential it's a function on on shape space and it's there is actually a very very interesting quantity the whole of the n-body problem is not determined by the Newtonian gravitational potential but by something which is called the scale invariant gravitation which are you you you've put Newtonian theory in there because on the right it says W goes as the inverse of the square of the distance or something like that w versus 1 upon length in Newtonian to this is this is gotta go is 1 upon 4 left to the minus 2 it's another power of the length talk about it yes I have the following question are you've mentioned that you're in your approach the the conformal structures are the most basic right as you look through I mean we know altogether that today the the spatial temporal description seems to be in many ways an emergent description and we're looking for more basic structures as you yourself said that probably the conformal structures are the more fundament what is physically real but other like for them I'm kind of trying to look at different programs of for example quantizing gravity when you're when you're invoking also different structures which could replace spatial temporal description at the at the fundamental level so what what really convinces you that the conformal structures are the I'm trying to distinguish them from from different possible proposals of going to more fundamental structure that this is just the conformal structures that are the most basic I know that Roger Penrose also is very much interested in Indies and he pays a lot of attention to the what conformal structures are so why is that actually the shape is so so fundamental because I mean we come across at different proposals for our for fundamental structures and how is it that is just the the conformal structures are what is physically real the well first of all all theoretical work is based on a hypothesis you have to put something in to get something out I am seeking at the moment what I think is the minimum that one needs to put in and I would ask it seems to me it's not possible to do theoretical science without at some stage putting in a notion of quantity so where does what is the minimum quantity that goes in and this leads me to to say that it has I suspect it has to be angles that that you can get rid of everything else if you if you throw out too much more I haven't have to say rather skeptical of approaches which say we start from some discrete set I think this is possibly throwing out too much King Lear said - Cordelia speak again nothing will come of nothing and I would say not much will come of not much which is why I want to keep at least the the angles in the thing now interestingly if you look at today Roger Penrose has spin networks which he introduced about 40 years ago are playing a central role in loop quantum gravity and if you go back to Rogers paper where he introduces it he says with great confidence that the foundation of geometry must be dis combinatorial in discrete there's no other thing that he's very categorical going back to that and a few years ago I asked Roger if he still stood to that view he said well in the intervening years I've become rather impressed by the power of complex analysis and I would say this characterizes my feeling as well I think it's premature to throw these things the cut the continuum seems to me the continuum is one of the great achievements of the human mind so if the human mind can work it out I am the human mind is part of the universe I suspect the universe is using it as well and so I am a little bit doubtful about to the discreet people invoke riemann because riemann twice talks about whether space is discrete but I think really if you look at the whole thrust not only of his 1854 paper but all of Raymond's work it's really deeply rooted in the continuum you

Channel: Copernicus Center for Interdisciplinary Studies

Views: 61,135

Keywords: Methodological, talk, without time, Copernicus Center, lecture, Julian Barbour, Centrum Kopernika Badań Interdyscyplinarnych, no time, Copernicus Center for Interdisciplinary Studies, Explanation, Kraków, time, conference, Interdisciplinary Studies, Timeless, physics, Causality, Centrum Kopernika

Id: 1ogiQ2E6n0U

Length: 54min 12sec (3252 seconds)

Published: Thu Oct 11 2012