Approaches to quantum gravity

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Approaches to quantum gravity
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At this time, we do not have a theory of quantum gravity. In this talk I will first reiterate the reasons why such a theory is absolutely needed, and then review some of the proposals towards it, with special emphasis on `non-string' approaches. The presentation will be kept mostly at a general and introductory level.
Euler angles Standard Model Multiplication sign Direction (geometry) Mathematical singularity Mereology Mechanism design Many-sorted logic Different (Kate Ryan album) Atomic number Physical law Diagram Series (mathematics) Commutative property Moment (mathematics) Physicalism Perturbation theory String theory Complete metric space Measurement Connected space Arithmetic mean Order (biology) Mathematical singularity Quantum Right angle Summierbarkeit Metric system Fundamental theorem of algebra Resultant Spacetime Point (geometry) Finitismus Continuum hypothesis Feldtheorie Quantum field theory Distance Theory 2 (number) Hypothesis Number Frequency Degrees of freedom (physics and chemistry) Modern physics Divergence Manifold Nichtlineares Gleichungssystem Quantum Initial value problem Scaling (geometry) Autocovariance Consistency Model theory Algebraic structure Variance Line (geometry) Vector potential Formal power series General relativity Universe (mathematics) Gravitation Table (information) Körper <Algebra> Quantum gravity
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Group action Dynamical system Metric system Graph (mathematics) Kopplungskonstante Dimensional analysis Variable (mathematics) Mechanism design Different (Kate Ryan album) Monster group Potenz <Mathematik> Geometry Constraint (mathematics) Interior (topology) Food energy Asymptote Repeating decimal 10 (number) Arithmetic mean Phase transition Arithmetic progression Spacetime Point (geometry) Slide rule 12 (number) Momentum Constraint (mathematics) Connectivity (graph theory) 3 (number) Maxima and minima Perturbation theory Canonical ensemble Quantum field theory Event horizon Number Wave Morphismus Degrees of freedom (physics and chemistry) Term (mathematics) Finite set Divergence Modulform Nichtlineares Gleichungssystem Quantum Maß <Mathematik> Initial value problem Dean number Standard deviation Scaling (geometry) Autocovariance Theory Group action Binary file Dirac delta function Perspective (visual) Loop (music) Asymptotic analysis Quantum gravity State of matter Multiplication sign Direction (geometry) Set (mathematics) Parameter (computer programming) Proper map Independence (probability theory) Heegaard splitting Positional notation Gravitation Series (mathematics) Area Continuum hypothesis Point (geometry) Moment (mathematics) Physicalism Inverse element Two-dimensional space Price index Dirac equation Variable (mathematics) Measurement Connected space Curvature Renormalization group Quantum mechanics Normal (geometry) Quantum Hill differential equation Convex hull Flux Classical physics Geometry Computer programming Functional (mathematics) Decision tree learning Line (geometry) Modulform Autocovariance Limit (category theory) Distance Theory Hypothesis Local Group Field extension Canonical ensemble Operator (mathematics) Differential operator Canonical commutation relation Spacetime Loop (music) Euklidischer Raum Dynamical system Addition Hamiltonian (quantum mechanics) Diffeomorphism Multiplication Quantum field theory Evolute Conjugacy class Physicist Gravitation Holonomiegruppe
Group action Presentation of a group Randomization Model theory Water vapor Likelihood-ratio test Special unitary group Dimensional analysis 19 (number) Expected value Prediction Invariant (mathematics) Insertion loss Different (Kate Ryan album) Kinematics Negative number Physical law Lipschitz-Stetigkeit Uniform boundedness principle Monster group Flux Invertierbare Matrix Link (knot theory) Constraint (mathematics) Proper map Interior (topology) Asymptote Symmetric matrix Symmetry (physics) Order (biology) IRIS-T Mathematical singularity Arithmetic progression Spacetime Point (geometry) Vacuum Free group Variety (linguistics) Constraint (mathematics) Feldtheorie 3 (number) Maxima and minima String theory Similarity (geometry) Quantum field theory Canonical ensemble Infinity Product (business) Number Frequency Divergence Manifold Modulform Nichtlineares Gleichungssystem Quantum Maß <Mathematik> Supergravity Standard deviation Distribution (mathematics) Dot product Uniqueness quantification Model theory Physical law Theory Independence (probability theory) Limit (category theory) Supersymmetry Mathematics Formal power series Field extension Loop (music) Universe (mathematics) Strategy game Musical ensemble Hydraulic jump Weltlinie Family Quantum gravity Force Standard deviation State of matter Standard Model Multiplication sign Direction (geometry) Parameter (computer programming) Mereology Diffeomorphism Proper map Food energy Grothendieck topology Order of magnitude Derivation (linguistics) Duality (mathematics) Order (biology) Mathematics Plane (geometry) Strategy game Many-sorted logic Thermal fluctuations Gravitation Matrix (mathematics) Series (mathematics) Position operator Stability theory Family Generating set of a group Point (geometry) Physicalism String theory Perturbation theory Measurement Distance Connected space Gravitational wave Quantum mechanics Normal (geometry) Special linear group Convex hull Hill differential equation Classical physics Computer programming Existence Functional (mathematics) Image resolution Real number Modulform Limit (category theory) Distance Theory M-theory Supergravity Well-formed formula Natural number Operator (mathematics) Differential operator Ideal (ethics) Uniqueness quantification Spacetime Cosmological constant Summierbarkeit Loop (music) Condition number Rule of inference Supremum Addition Hamiltonian (quantum mechanics) Multiplication Axiom of choice Variety (linguistics) Consistency Graph (mathematics) Quantum field theory Entropy Number Logic Lie group Partial derivative Gravitation Object (grammar)
Logical constant Complex (psychology) Group action Presentation of a group Mass flow rate Model theory Thermal expansion Special unitary group Dimensional analysis Group representation Connected space Descriptive statistics Physical system Link (knot theory) Interior (topology) Coordinate system Infinity Maxima and minima Symmetry (physics) Duality (mathematics) Chain Helmholtz decomposition Mathematical singularity Nichtlineares Gleichungssystem Summierbarkeit Mathematician Spacetime Point (geometry) Connectivity (graph theory) Maxima and minima Division (mathematics) 3 (number) Similarity (geometry) Mathematical analysis Student's t-test Subgroup Number Hyperbolischer Raum Manifold Energy level Modulform Configuration space Nichtlineares Gleichungssystem Quantum Maß <Mathematik> Newton's law of universal gravitation Supergravity Standard deviation Wave function Physical law Model theory Theory Algebraic structure Ultraviolet photoelectron spectroscopy Quadratic form Mean value theorem Universe (mathematics) Family Matrix (mathematics) Superposition principle Standard deviation Structural load State of matter Direction (geometry) Multiplication sign Mathematical singularity Peg solitaire Parameter (computer programming) Food energy Variance Duality (mathematics) Tensor Many-sorted logic Gravitation Diagram Körper <Algebra> Series (mathematics) Geometric quantization Position operator Presentation of a group Process (computing) Generating set of a group Repetition Term (mathematics) Connected space Time evolution Energy level Reduction of order Geometry Finitismus Link (knot theory) Real number Modulform Graph coloring Theory Supergravity Local Group Degree (graph theory) Formal power series Canonical ensemble Symmetry (physics) Reduction of order Spacetime Analytic continuation Evolute Approximation Film editing Lie group Physicist Gravitation Diagram
Standard deviation 12 (number) Model theory Gradient Modulform Feldtheorie Thermal expansion First-order logic 3 (number) Complete metric space Distance Order (biology) Duality (mathematics) Degrees of freedom (physics and chemistry) Equations of motion Helmholtz decomposition Set (mathematics) Energy level Aerodynamics Nichtlineares Gleichungssystem Körper <Algebra> Maß <Mathematik> Surjective function Condition number Family Rule of inference Supergravity Potenz <Mathematik> Weight Point (geometry) Model theory Interior (topology) Exponential function String theory Geodesic Time evolution Lie group Order (biology) Gravitation Nichtlineares Gleichungssystem Manifold Energy level Family Körper <Algebra> Spectrum (functional analysis) Spacetime
State of matter Direction (geometry) Multiplication sign Mathematical singularity Thermal expansion Parameter (computer programming) Open set Likelihood-ratio test Mereology Perspective (visual) Proper map Dimensional analysis Mathematics Many-sorted logic Different (Kate Ryan album) Kinematics Gravitation Arc (geometry) Area Continuum hypothesis Moment (mathematics) Infinity Mereology String theory Einstein-Feldgleichungen Oscillation Distance Category of being Symmetry (physics) Order (biology) Mathematical singularity Quantum RWE Dea Hill differential equation Convex hull Right angle Energy level Identical particles Fundamental theorem of algebra Resultant Spacetime Classical physics Point (geometry) Computer programming Einstein-Feldgleichungen Module (mathematics) Momentum Link (knot theory) Divisor Variety (linguistics) Real number Image resolution Continuum hypothesis Modulform Feldtheorie 3 (number) Maxima and minima Quantum field theory Average Polarization (waves) Graph coloring Theory Hypothesis Frequency Symmetry (physics) Manifold Spacetime Newton's law of universal gravitation Standard deviation Classical physics Model theory Quantum field theory Field extension Geometric quantization Voting Combinatory logic Gravitation Object (grammar) Family Quantum gravity Maß <Mathematik>
she all the time and if you can to Hey to well thank you very much and thank him for an inviting me here it's 1 I've ever feel greatly honored to you the soul of closing lecture this conference the resources saves as always in all immense pleasure to be here and there I really regret that I couldn't about to take part in previous part of this conference because you from what filtered through from the questions and allusions to previous talks it's only have many intriguing after some ,comma consultation with the table of decided to give a more general talk so I apologize in advance to those of you have reduced specialists said listing series will not learn very much from the store as as it's going to be a brief surveyed will be Rolla .period idealistic I would say in the sense that it's just touch on a few things and make a few remarks and there also not cover everything but it will certainly take the liberty to spend the last part of my talk on things that are very close to my heart but when it comes to what potential suitors from gravity could be coming so I would like to start up by recalling the reasons why we should be interested this year from gravity because at this time there's actually no pressing need from any experiment observation To really proceed in this direction because the series that we have at this time seemed to be working extremely well this is applies both to gentlemen activity but also to the Standard Model of particle physics with gets which get better and better With so that every measurement so the reason to be but nevertheless to be interested in this year of quantum gravity comes from basic to the fact that the 2 series that we have not incomplete and possibly even inconsistencies in the ultimate on the general relativity side it's the the issue of singularities which which seem to be generic this falls from the singularity theorems that were approved by walking and penned roles long time ago according to its generic initial conditions like the exists in universe will inevitably lead to a singularity formations and of course there's the cosmological singularity the big-bang singularity at the beginning of our universe and this is the greatest possible in some sense this is what we really would like to understand I 1 amazing stories of modern physics that with the understand when we have we can get very close like 10 to the minus 30 seconds or so to to the next to the singularity but it's just this time between that that cost all all our headaches and of course there's the strode the question of structural space time and the smallest distance on the other side in quantum field theory there as well we are faced with working with some in all locking inconsistencies possibly the 1st so as you all well know and perturbation theory encounter ultraviolet divergences and finding diagrams for the Standard Model symmetries these can be removed but removed by inflated realizations all about order this is rather sophisticated the procedure has been developed over decades actually and and as the at the 2 amazing agreement was his experiment if you think about things like Jim miners to toward while precision experiments that not doing for the last 2 weeks a series but nevertheless I think All-Stars shoulders so quoted Iraq on this whenever accepted Infinity's he said the rights series should give finite answer period and so so we're not really sure what all this somehow I feel that this cannot be the end of the story and it in some sense you can make anything more precise because you can ask yourself if you want to go beyond perturbation theory thus the standard model which worked so well in perturbation theory doesn't make sense beyond perturbations and I think there is also reason to believe that it is will probably not exist in the rigorous sense of constructive or axiomatic a quantum field theory and this is the reason why people are talking about this possible ultraviolet completion of the theory that the sum all those years contains the standard model is limiting case so the difficulties In both cases in some sense they have a common origin because in bowls of general relativity and quantum field theory treat space-time as a continuum more defensible manifold meaning that we can in principle should be able to go a small to a small distance as dissidents as we like and secondly there is an equal and field theory has so far we treat elementary particle as mathematical point exactly .period like excitation this is of course the origin of the of ultraviolet divergences but there's also the difficulty when you try to introduce pledges the described .period article mechanics to end in general relativity so the conclusion of all this there is at least a majority of the community believes in this and this is independent the of the string theory of quantum gravity you expect something dramatic to happen at the scale at which which would be well we believe quantum gravity might be relevant to adjust the blank scale so the question is really what happens how these series modified what happens to continue space-time is it's all of dissolved in the kind of discrete too this to continue replaced by discrete along or what is it that or maybe it's non-commutative video of stamp on but something is expected to happen and this at this scale so this is the relevant scale that we're talking about set in the past was well we have to do well the months it well and now with regard to 1 6 at this point of view that he can adopt to different kinds of attitudes and this sort of this also marks the dividing line between the different approaches to quantum gravity I 1 hypothesis is that quantum gravity is centuries just a moment per tablet of conversational Einstein gravity In whatever formalism metric connection discreet and once to solve this entreated suitably you just have to complement this theory by the standard model of particle physics and that this together incorrectly describes the physical degrees of freedom also the very smallest assistance the opposite hypothesis is that actually general relativity is just an effective for low-energy series arising at large distances from more fundamental Pong scale theory and that we do not at this time no what the basic degrees of freedom of this series are except that we suspect that very different from other generality of quantum field theory as we know that In this case general relativity and with it space-time ,comma variance such motions based on general covariance are assumed to be emergent much like microscopic physics emerges from the quantum world of atoms and molecules From this point of view this fast approach would seem as sensible as trying to find out about the microscopic world by say applying conversation techniques to the Navier-Stokes equation I mean everyone would agree that this very unlikely that you would find out about atoms and molecules in this way no basic fact about look quantum gravity the ships for the quantized gravity that sets it apart from the matter interactions that characterize this summer model is the fact that the "quotation mark of gravity I sent series but tablet of number in all of this means that each border in order to get sensible results we have
to introduce a new kind of counter town to render the theory predictable and finite so he the famous to counter time was whose coefficient he was calculated some 30 years ago so it's but I should like to emphasize not just the fact that you have divergent this because you might think well it's subtract them and make the Serie finite it's the fact factored in need to adjust an infinite number of parameters and this is believed to render this theory of long predicted because then it would include number of coupling constant no chance to pin down what the serious it gained their 2 possible conclusions in line with what I said before the 1st conclusions that somehow you have to have consistent condensation of gravity requires that we need to introduce a radical modification of the theory at very short distances In particular include matter supersymmetric matter family owns and maybe even something more radical like going from point to particles to extended objects like a string of Member interior and thereby to get rid of this evidence the opposite kind of you also expressed most of the colorfully I would say by what Japan roles but is that acts as the ultimate divisions as simply an artifact of but over the treatment of the serious because we do but I believe quantum gravity we do some violence this year destroyed some houses geometrical structure general covariance all of this is no longer there and a nice and manifest form and therefore the hypothesis is you that these would disappear upon proper non-productive condensation of the theory however and this is something I would I mean whatever you are attitude toward this is I think no approach to quantum gravity can claim can claim complete success that does not explain in full gory detail what happens with this evidence that this is more heat is easier for approaches that start from particle physics because their long somehow tries to get rid of the division's right directly but this comment applies more to the Mumford habit of approaches because sometimes they say they don't even see the evidence I just want to say she's claim you don't see that evidence and I think that you need to investigate your report little more closely because whatever you humankind approach is it should be semi classical limit and then once you do this and this thing will reappear so there's no way around anyone who claims to have year ,comma gravity does not explain to me what happened with this evidence will not have it I will not accept this as a as a as announced additional litigation what was on the basis of the hundreds of them to the evaluation hearing our sorry human double make their use storage but now there's also the thing about gravity matter this is what Einstein himself said about his equation is to the left side is built from marble beautiful and unique right-hand side he said is made from timber is the integer momentum tensile walked past whatever start model of producing the new so he they would part of his later part of his life trying to move on and see what they could understand this and a geometrical when as of wish would be to somehow right to left or right side bring it to the left side and somehow understand as some kind of uh we knew that it's just a way of action this is just the Canaries eating well and this is the marble you mean the opposite of what I instances you will the the I think and on this I would side with Einstein anyway this this had led has led to an enormous effort over the past decades really for example concludes outlined series in a tent in this direction when take Syrian higher dimensions and explain the matter energy momentum tense as coming from I had a mental geometries part sort of going to war in this direction and the although uh uh thing is that you can to introduce supersymmetry which is like introducing firmly on court it's that also the lodging of space-time and then also involving this right hand side with the kind of John symmetric interpretations but there's also the question of gravity versus not quantum field theory or Kwan gravity would just stand of quantum mechanics because we have this kind of schizophrenic uh slot would probably situation where this is treated completely Castiglia this should really be thought of as a quantum object on expectation value this has also led to a long debate In particular the question is whether we need to change the basic rules of quantum mechanics as was suggested original hawking but for example is it should be really allow for the possibility that pure states can evolve into mixed states and the other thing I would like to mention here is that because after all the is my favorite approach space and time I somehow thought to be merger and as we should also followed with serious all have space and time and then I would just like to meant to emphasize that many of the paradox is that we think spectacle :colon quantum mechanics appear in a completely new guys because most of these paradoxes have to do is known localities and there you really need some emotional space will be time in order to make sense of it the whole question I just want to raise it answering is if if you really in a solitary dimension what's what's this about what is this is a different question all heart should we address I finally the final point is the so-called higher-rate problem which is the fact that gravity is so much weaker than the other forces In my popular lectures are illustrated by taking a plane a little magnitude and the previous drawn toward slacker than necessary in all this little marketed the gravitational pull of the whole planet and this is a rather direct evidence of this hired the problem namely that the scales of so much different so in particle physics we talk about the masses who actually cover right wide range they already have something like a middle acute problem but all of this is tiny Missouri the Planck scale of 10 to Minden GTE which stood approval under 33 the new union so key challenge and perhaps the the crucial issue in this whole game it is but for any proposed years ,comma gravity is that you should offer quantifiable criteria to confirm or falsify the theory and in particular you should they should be such that you they allowed to discriminate you on south from somebody else's answer you know it's there's not much as gained if it all I had know some theory that explains structure formation whatever will be Miniseries or things like the pope hypothetical things like violations of Lawrence and variants this was really seeing that would probably remain the and in fact conventional explanations of such facts so I think that challenges him much much much more pronounced and of course you can always say in all my objects are quantized in units of the plant but this is something that will never be able to measure here some degree of sophistication is required and so here is a list of the approach is not complete all I would say that roughly speaking to the community is divided into majority apart the of a string series of our gravity and so on just the In the past integral or something in between I as canonical conversational gravity of which we develop traveled on discrete approaches likes being formed school feels and but apart from this also have known community of geometry of something called us and public safety and they can go even more abstract To the end sense that you couldn't look for Serie where everything is just information are and I should say there is no agreement it's it's really that we have different communities In fact with very little communication
and as you know Europe showed there is a different picture but this is the same historical event and as in all this event for this effort failed because at some point people could no longer communicate with each other and this is something else to see happening a little bit in the different communities working on Towards quantum gravity and I think if you sold us zeroing in on the right theory which should see things falling into place and this should emerge from so I want to know goes through some of them but just very briefly but the
1st thing I would like to mention month late slide is this idea asymptotic safety I said that most workers believe that something has to happen the blank scale but not everyone because there's the question of whether standard quantum field theory concepts are actually enough to quantized Einstein's theory our so this approach in some sense is very close to the spirit to conventional ,comma fueled fears apology floors on the Cubans on an effect does not require anything special to happen to the continue space time so I assume that he can go as much as you like to build a plant so you on hypothesizes that there is a small strip of non Gaussian fixed point and this really means is true that the moment the analyzable clung put their refund gravity really the normalizable in disguise because the song it is in imprint dimensional space of couplings there's a hyper 2 which things can flow and the so in fact you would just have to fix a finite number of parameters while an infinite number of them so they understand 1 constructs a scale dependent effective action 1 can discuss in some detail what this means because in generally covariance theory you know the measure of flying said satirizes something that that's not fixed a priority so this requires some rather sophisticated 7 assumptions but this approach is essentially a candlestick about the microscopic series essentially just a normalization Cove equation and what you put in as initial conditions the hope that maybe these things falling universality classes what would be observable here well we don't see him running Newton's coupling constant look outside the window so all of this is going to take place after the blank scale which is you thought to be analogous to lump accusing so far observable effects would be very hard to come by the only thing I can imagine is somehow that you know this way you can predict that there should be a small cosmological constant at large distances but this is remains of hope so let me know if a few words about but canonical quantum gravity because this is the 1st serious was the 1st serious attempt to tackle the problem and that that that I was actually the 1st moment but I believe that penned an attendant which was also back cannon but which it is a direct attack on Einstein's ice Sunseri in terms of textbook methods of quantized what you need to do here is of course you have to give up man of Espy's to space-time covariant spies Split of space-time into space and time so that space-time geometry can be viewed as an evolution of spatial geometry in time according to Einstein's equations To metronomic stand is defined as follows the dynamical degrees of freedom of the spatial components of the metric the components with long with the time of the index on Lagrange multipliers deleted constraints and the associated canonical momentum and the dynamics is defined by the constraints then the Hambletonian constrained that goes with time repair registration areas and the spatial the diffeomorphisms associated with special 2 from authors and constraints of the telecom variants of this hearing classical context in this a quantity in this constraint algebra which is more complicated but suppressed all industries but the difference between this and the gage standard gage theories that the dynamics is somehow encapsulated in this Hambletonian constrained so what you would do in this approach is to are replaced despite the functional differential operator expressed everything terms of operators and then when he expressed Tony unconstrained you get the famous Wheeler which aggression this equation has been around for well almost 60 years ,comma nobody to this state has been able to make any statement full sense although it because it's ill-defined even by the slope of the slope is kind of physicists and and in particular would you would have to satisfy you'd have to say what becomes of his elves as you replace classical variables .period quantum operators and as we know from many examples they would expect the anomalies just like in the case of two-dimensional different morphisms where the algebra or becomes the virus or algebra and for the medicines you would expect you more trusting modifications and I'm just saying this because the classical space-time covariance in this series would be picky be replaced by Quantum space-time covariance just like 1 here has a very concrete example how this could happen but it's something that you have to prove and this has proved to be impossible or at least not there's no solution people agree on left proposals of course so this whole and we let the week program can to a halt there is no longer the homes and was really able to making progress on this and the golden rule impetus with the harsh to go variables which is a command switched to another set of canonical variables of which are essentially the following it's like in quantum mechanics when you replace Cuen plea by creation of additional operators Q plus RIP so here you have the spatial spin connection and this is the extrinsic covered services essentially the canonical momentum and with the promotor which was later called Bobby remitted parameter and reaching this was plus-minus side and then there he was able to show us to Cozumel to show that have canonical pair and what he was also able to Seoul Carmichael's plus-minus then this case constraints all legal constraints status simple and while Nice form and in particular it turns out that everything that depends on this variable does so this curvature tens which we know very distressed young wheels field strength associated with you too so so it's almost like that Of face space of young males the institutional security steps that you have to war the constraints that these are diffeomorphisms and promote Tony constrain his hostility the CEO meaning of weekly 0 can put it weekly 0 in the Dirac This is the Durocher notation I have now I think it usually was classified as I later people put this to a real constant and I should say in my opinion this is where this whole subject to go wrong turn because once you make this real than nice form is destroyed to get some or all currently the is very hard to handle anyway the modern version of this is Yukon and gravity we don't work with the connection with the parcel that exponential Hollymead along some pages and the costs conjugate variables use the flux defined like this in terms of the variable and then new way functional depend on these allotments a new feature is dead the king ematical Hilbert space can be defined but it's small inseparable which is kind of weird but he should keep in mind that all the physical new physics that is claimed to be associated with the loop quantum cosmology which hasn't suppressed version of off Yukon gravity analogous to the old a space of Wheeler that with all the new phase it's really comes from this monster proper ability this is 1 of the reasons they don't see divergences this because it all normally would people cheered delta function for this things ,comma mechanics so when you square the standing of the usual difficulties but he this difficulty doesn't appear the fall so this is 1 of the reasons they so far cannot see also was evidences and small anomalies in the other peculiar feature is that all
working with connections then no negative norm state this has to do with this monster problem monster problem and to carry out the head of a high school coach at the end of this year no hazard this this program has not led to any kind of valuable new insights for example that this year we know so while wanted well there's a dead guy will not say anything on that site is just resent the fact that this is going OK now and know the crucial mean much of this is just kinematics defining states pays its scalar products it's just kinematics the core question canonical gravity is the Hambletonian reversible lock and define it and then can you anything to anything with it and it will not describe this in detail because just as a mother LeBaron elaborate formalism was mainly developed by Thomas the money and that this is claimed to be made success namely that if the Hambletonian can be defined the rigorously is all operator on the scanner medical Hilbert space but by the way this is the ugly that nobody talks about it which would vanish if you could come up with Barcelona I This is a little bit like the McDonnell the formulation Gates series which is the longest off to work with field strength and note the proper different definitions of volunteers and the 1 thing I would maybe raise here because this is a valid question but the question is whether Hilbert space is really the right concept because would you find here it's more you need to go to some kind of distribution space and is also the question when talking about the way function of the universe doesn't make sense when you calculates killer product does this make any sense or is it such that you need to give up even such things that we take to be the to be granted an ordinary quantum mechanics you anyway there's also some argument that this Hambletonian is is is not a very physical because what got was that these pictures of the spin networks which was I'm sure you've seen the networks or graphs with letters and ledgers and things like this so what the action of this Hambletonian dozens of ads will be called spider webs fluently so it doesn't really no question we know is that it doesn't make sense for us so we know that some of our growing in the ground and consumers which brings together with his former lover's won 1 of the difficulties here is that the metric is not represented because it's like switching from Q to uh like creation motivational operators for metric is represented by Cingular functional differential operator like this x x flew collided 2 points and so in order to define the classical state you have to find the size of the well that's all I did a I guess that this is something like this would be like a classical expectation value energy I'm doing X and of course all kinds of difficulties in making this well-defined so is this is this is 1 of reasons the people who live in the future we will have problems but indicated that people should know what the people of this state please don't no no they say eventually they will be able to define summer classical limit and that was all I'm saying is this is why it's too difficult for them to find classical limit because the Midi operator is represented by a singular functional difference it so I can be used to fund the plane in united the peace but there is there is additional raised you asking you know the near-riots gravitational waves conversation would require solving this problem 1st said Wednesday it will not the they call it the fluctuations because it's it's only problem is that the original iridescent there's no time to because this is just a part in the survey as solid some arise in the debates honoring critique of his last over there is not any way that that the non-potable approaches this is Alic Yuji but something that developed out of his being forms of no time to talk about and who feel theory but I put the main emphasis not on the things that we like in quantum field theory about the things that we delightful marginal relativity which is background independence although very often what it really is only spatial background independence because space time back on independence would imply that he sold the real underwent equation ,comma Tony constraints on that small vessel is it this is a bit kinematics however these approaches so far but they're not able to recover the severed classical um but they also do not incorporate essential insights and successes of son 1 of your series which I think is a big shortcoming like anomalies there is that you see this is 1 thing that's been usually not emphasize master tonsils conversation ambiguities so the matter couplings the restrictions that will go to hold from model like anomaly cancelations for the quirks and wept on slips of very interesting and very subtle consistent the condition is small seen in these approaches but as I said these issues will be hard to settle without a detailed understanding of how Standard quantum field theory and silly classical Ltd would emerge from this framework so that we don't move on cost us get married a beautiful review of of string theory so it the oldest you said the poor man's full-bodied so this is a poor mothers a poor man's version of cost presentation so a super world basic strategy is not quite different coming from quantum field theory that 1 tackles this but I really the evidence is directly by trying to modify gravity at short distances but this is by introducing supersymmetric matter because formulas have a tendency to cancel balsamic divergences so this is real life since I was a magic series it's also nice because in some sense and gives a vessel that for the existence of matter in the world and also there such things as maximally fine if you really want to push the notion of symmetry to the end actually symmetric .period field theories and super Rabeni to which our comeback dimensions of remedy and then also 1 can go to supersymmetry extended objects where the hope is that the the point like singularities due to the point like interactions of solved by blowing up .period like objects to extended objects so this has led to the super strain but I would also like to remind that there's a theory called Super membranes theory which you can think of as a mom but I believe with a version of string theory and from it follows the use famous Matrix model of this there is much harder to to deal with them strings strings is basically free field theory on the world sheet but here on the world volume this remains interacting theory and the best and not been so much progress and understanding it does cost us explained beautiful lady well just with good on the list are of course this is a huge subject has very much modeled on concepts from particle physics so there's no problem with limit however there is a problem with 1st say the formulation beyond perturbation theory but we now understand that is not simply a series one-dimensional extended objects that the brain stem and brings the and was outlined expectations of what have you this is 1 of the big successes explaining give me a microscopic supranational tackle entropy including
including Ohio order corrections to use of can formula there's all these ideas about filmography some people think that filmography is the key to quantum gravity and on quite sure that the Book of the year physical consequences that might be union it is a measure of this formula for years all well you know this formula has been proven for no very ideal extremo black holes and the 1st of all you would have to find extremo black hole in the universe and it's suppose the Federal said this is the lack hole of the music and not much really because visible black holes or while the other thing is that the derivation is found in a completely different domain is it's using the brains the way of course and history the I didn't have a start of another guy I think there's a days of the slight problem here because the derivation is done in the domain which is far far away from classical and then you extrapolated over it and I 20 orders of magnitude and for this you have to invoke supersymmetry and BPS stability if it deeply DPS Sunil B. P S is invoked a lot these days have for doing all kinds of arguments and strings here but you should keep in mind BPS is light years away from the real world it's not at all so so you know the Commission is of course it's the real to remains a challenge to sort of drive this formula standard for real life .period when the way there's a lot of new ideas that are currently being tested low-energy supersymmetry logic so mentions and so on and of course I will not say anything about the implications for mathematics because this is something everybody knows and appreciates only year so what are the open questions well I mean it's stings years been a massive intellectual collective effort that's been going on for almost 40 years of but was still struggling to reproduce the standard model as he is not so I don't fancy extensions with stones of extra soup multiples and so on but just is assume In almost super particles of founded LHC then what are we going to do here this is a real challenge similarly struggle to incorporate there's no nice way to get a positive cosmological constant super Reveille super string theory lot negative because water reconnaissance but you look outside the window and turns out to be positive but I will say little about facts will extend over rabbit also in connection with fine is because the question is what is the place of this series here in this hall sky so that's been impressive progress but I would say there's still no convincing scenario for resolution of space-time singularities certainly knelt cosmological of space flight and the question those posed initially namely what happens the space-time continuum and bundling is as open as there will be but in the real question is really what string theory in the sense that nobody thinks that at the end of the day it will be let the way it's done nowadays you simply assume a classical manifold and then you have these blank size extended objects in the new quantized among the classical background we all think that this is not going to be the final answer so 1 thing I would like to emphasize this is littered with a problem with all is the lack of that too many ambiguities that little bit polemical here because he has still this well-known number of consistent vacuum which is far from March 4 what we need but this is as I said this is a bit harsh stop but if you look at trades traced the ambiguities conversation ambiguities and on you will also find that they're similar None uniqueness In a new common gravity indiscreet quantum gravity by the way also an asymptotic safety because you know I keep hearing these talks had enough for quite a while and I always sit there and think you know what this is working too well because no matter what they try they find a fixed point for example if you do gravity and 67 mentions laws fixed .period and I find it hard to believe that this should also work in 67 anyway so you know there's all this ambiguity which is precisely the opposite of what I said you should try to force his theory to make some kind of statement that can be checked all verified of falsified so the question is really does nature pick the right whatever is on sale and random from a huge variety of possibilities are the criteria to narrow down the number of possibilities so I think that in order to discriminate between growing number of ideas that have started inviting consistency what else and this is something Gary Gibbons said to me about certain approaches in quantum gravity said this is going to remain fantasies if you can come up with a solution to this problem so the last part I would like to call the loom on the direction that unlike and they need the question What is the role of enables superintendent not Eagles 8 soup super gravity was in fashion 25 years ago and then it became Honor fashion with the advent of string theory and the whole obvious problems but has recently turned out to be it's much more finite than was originally expected and fact up to 4 groups and used behave exactly like generals marks William L. if it were to continue like this then it would be a just as finite as illegals were animals theory of 1 of the largest in the world and Ramon Reyes this savings while young yellows Jong-il's is that yes it's diverted the ball for damage there's a formula the Tallassee which dimensions the the the leverage a start and hit a claim is that when he late Super rugby up to form groups when you serve a different dimensions it's exactly the same formalizing as in general skiers so it could be sold ruled out so excluded that it might be financial orders and that you know this is 1 of the things and I'll start worrying about other grow old older will ever know whether it's fine I don't know I'm not sure anyway that there's no effort toward 5 loops but as we heard yesterday that this effort seems to be thoroughly stock sell-off of spoke was going to happen interestingly In the difficulties he had 5 loops are somewhat it may be related to a similar phenomenon appearing string theory is that as well as 5 moves the Piazza Puca peculiar differed difficulty to do with the fact that supermodel space is no longer splits which means you're not alone allowed to 1st integrated over the family only moderately and then of the balls this is at least a 1 sentence I stood understood from witness presentation 2 years ago I didn't understand much more about so uh this is not excluded here but even if it is fine of course you can raise the question What about non-potable if common gravity what does it tell us about the dissolution resolution of singularities and secondly is there any relation to real physics and most people would ask this question the negative but I would like to advertise some recent work which goes back to some population of 30 years ago which could become irrelevant if they really continue not to find new 1 after Greece of freedom college and the following his release very strange coincidence which is the following if you count acquire number of walks and that columns 3 generations and the other 48 and this number is the same but Pistons super gravity when you take the 56 family owns than one-half remove 8 Goldstein also recall supersymmetry is
the same number and furthermore her following strange coincidence if you break the Salazar of the Super gravity U.S. 3 three-course you want these are the representations get for this history 3 and this is an idea of moms really strange and I've never had such an idea but he said he described it as a last-ditch effort to salvage annually over gravity so he assigned to the standard color assignments for the quirks electrons and then furthermore soon sign the 3 evidence of this course electrons 2 representations of a family issue 3 so this is a new symmetry that acts the horizontally among generation in this peculiar way here and when you work it out it's exactly the representations that appear upon this making this the composition of the enables laid family owns and is also a little bit curious yeah I think it just indicates some should start looking in unusual directions because the 1 thing you see you that this is his 3 family would not commute with be issued to weak because it puts the opt-out and law components of it would be electorally doublets industry 3 Barton's 3 Of this family symmetry anyway this this this is strange agreement and furthermore if you calculate the electric charges of these particles so that a given year and then you calculate what you get from sober gravity that they're all that dazzle sort of systematically shifted away by 1 of 6 asserts 106 and the home for the 3 of family and its finest almost exclusively so this this this this was this being old for long time because of you think this is a mirage of residents something real and in fact we follow a long ago was Nick Warner that the scheme is actually realize that this is recursive on stationary point of was it's over revenue engaged in because it's a parameter not very recently we've figured out a way to fix up this summer this discharges by deforming the you want but you have to be folded in a certain way that goes outside of an eagle at Super gravity so there's no extra motivation to look at I need you more cemeteries and I think this is really the core of the subject namely the duality cemeteries that were originally covered by current GDR because we now believe that the symmetries are more important ultimately than space-time cemeteries it would was well realize already long ago always said these exceptional cemeteries become bigger Siegel pounded that message would dimensional reduction at the missile eduction means you drop the dependence on internal coordinates assess Lincoln's outlined theory but what also happens here is that it by doing this you transform you want space-time fall was space-time synergies into duality symmetries and if you carry this process to the extreme all space-time symmetry has disappeared and everything is well in the cemetery and by doing this you follow this chain shows seen this before so this is 37 appears in four-dimensional sober gravity 8 and three-dimensional maximal sober gravity and the Lord becomes infinite dimensional so this is this is not really been working on for the last 2 months to bowl for the last 12 years of all so this is the signature was already conjecture to be in the dimensional reduction to 1 dimension no longer goal I thought well know who is interested in one-dimensional reductions because the year becomes essentially generally you can drop the dependence on all the special coordinator but then came the other a mysterious hand with connection of link with work that was initiated done by billions he held Lutnick often if long ago speaking the characterization of the singularities his based singular big banks face time um and what they hypothesis size is that as you approach the singularity spatial points the couple Of course this is just the horizon-problem problem of inflationary cosmology and what what you get is a continuous superposition of one-dimensional systems and 1st approximation so this effectively means something like an effective reduction too 1 that mentions 1 time dimensions as you go closer to the singularity or in other words the truce similar Serie becomes only apparent pass you go towards the singularity so this is somewhat analogous to the High Energy Ltd of gage theories as you go to a higher and higher energy system or more distant the media should not this this and this and all you know just to explain the philosophy as I said before the cosmological evolution can be the view as a one-dimensional motion in an infinite dimensional model the space of 3 geometries This is what we look also persuaded I which is rather complicated moduli space and that such that you know the cosmological evolution is really that like the motion of a point particle is in three-dimensional manifold this is what leads to the will of the week equation the wave function of the universe and we with this is the space lives on but of course that we believe that unification space matter great Haitians should tell us that there's something more and not simply something you just due to the space but this would be more unified structure the question is will they can understand that full space and simplified sums inspired and betting it into groups here at a golf course this is the proposal that we have been following with bold mainly to some map this evolution of 11 original Super gravity 1 to oppose space which is of this type with this is that this still hyperbole cuts would group of algebra you which is the maximal extended hyperbolic because we algebra so this is worse than during the last 12 years with the ball back and actually find Schmidt in particular so the 10 of no time to tell you what the tennis but nobody knows what is so that's 1 of the many challenges so he is a sort of the way the mathematicians would define it so it's a stinking diagram generators of relations alleged said and but in all the states of course work for finite dimensional the elder Rosin stumbled that no big deal but it's just you know using just adding a note to the Dinning diagram doesn't mean very much but what really happens is an explosion of symmetry In particular for these Eldora Switzer calf ,comma tricks is indefinite you have what's called exponential growth just no way known so far harder to have sort of global description of al-Jarallah not to speak of the group that you more complicated so we've approached the subject in somewhat pedestrian manner but I think this is something no mathematician would do because this is just too To simple-minded in way this is the level position and and the nice thing is when you do this with the 10 year just that .period topped the this is the both on the fields of 11 dimensional super gravity Garrett on 3 forms and also that Wells but the explosion you see this is 1st 3 levels of you go to 28 you already have more than 4 billion the young tableaus of resulted just just to illustrate the monstrosity the monstrous complexity of it and the algebra because he tried to calculate that structure constants get stuck at level 4 or 5 my student fish followed try his genius with the computer try to go to level 6 but he also failed and what's worse is that no matter how far you go His so that if you continue gets even more complicated anyway we as physicists would not have to worry about this would just go ahead and so we've been really with this idea of your mapping the evolution
of the Cosmo together emotional onto such a course that
space and this is exactly what we did just restricted to the lower level things that we can identify with 11 mental sober remedy and on this call said space and this is something like the VAX supper and then we found agreement under certain conditions but non-trivial between the sober gravity equations of motion and the signal model equations and the emergence of space time years conjecture to emerge as follows In this sense that the information that was previously in the space dependence of the fields of field theory now in some sense gets spread all over the weekend the elder brothers no more space time to stop with the distance the algebra and indeed all the degrees of freedom that you would like to see the corner of the field theory but of course there's a lot more that it's not just because the spectrum here at this level decomposition when expanded has about the same kind of exponential growth as the string spectrum so this is the thing I wanted to mention just because there's a fine this really surprising because I told
you that you have a list of myself we found a way to embed this wonderful the you want to take care of that to get the correct electric charge assignments for the cost of electrons and I said in order for this you have to go outside Super gravity but will believe included papal the net
just yesterday when we show that these this the formation is contained In this Compaq must subgroup which is that you can think of as an infant dimensional extension of the or symmetries that appeared sober revenues traders 16 and and I mean 1st of all I find this rather amazing that in order you know it would really be striking moment it in order to link it relates a program in the real world courts electrons you would have to go to such a fancy infinite dimensional extension of the standard of all symmetries assignment to throughout develop inventories the other thing I would like to and as it With these Puno somehow completely change the picture on how you Woodgate stand model family owns all punk skill theory and particularly this summit is also Cairo I think there's more than enough room in the 2 also accommodated elect two-week Cairo Cajun interactions so this is something I'm quite excited about but you should keep in mind the moment they discover a new spin one-half Millard LHC so at least this proposal satisfies the requirement it's clearly falsified OK so I'm almost finished so he is once again the philosophy that was sort of been following with the bull market and Axa so he is again the space-time .period our cosmological space-time and of course the detail of course was just classical all the way down to the singularity but of course everyone knows that all expect something happens of the blank time so that point you should really furor the classical part of manifold replaced by something else which was slower but the ball was reminds me that this is the famous objections Elbow Beach to be Keller said it's all very nice but after a few oscillations you already in the blind regime and knock and forget about classical theory so the idea here is really to sort of take this as a guiding principle bye looking for the theory that comes here below the plants handed replaces space time by something else nearly hypothesis is that it's the 10 hour signal model possibly well certainly quantized with is something we haven't really done and also of course taking into account the family on which I didn't really know much about the new concluded come back to my initial comment the Inc the strongest argument for quantise and gravity it's the incompleteness of the Standard model and I general the army the main question now is how do we these resolve the short-distance singularities uh and how can it and of course should be stunned in such a way that this resolution can be reconciled with classical Einstein equations and continuum quantum field theory and so on and this may happen either by dissolving .period like interactions like string theory membranes and so on it could happen and we are the cancelation of ultraviolet Infiniti's envisaged variety is a candidate could just be that this theory go down there is no evidence that all council or is there some fundamental discrete it's something that the speculates about all these and modern discrete models like spoonful models and so on the old models of discrete quantum gravity and they all have difficulties and is recovering the continuum space time and that's the major challenge there or is it just the most conservative thing that quantum field theory basically remains valid but in with a version with us and public safety so I would say Just do you know where do I place my bats I think signature-based approach offers promising perspective when he was a sober gravity attendants absolutely fascinating to me I've been fascinated by use of through all my professional life but what about those 2 little we go through were or things here we have to ability to single in their very units will disappear he said warns to of changes year well there are various merchandise does the kind of obvious emotionally string theory because you build close strange states of the left right moving open string states and you put to spin want to give me expand to select has been obvious for 50 years or so now in field theory of what these people many Eagles late it's rebounding company of doing just famous collar kinematics duality where they actually for the fine into grants that actually replace the the animals into ground by a gravity into ground and the procedures that for the kinematics part try to find combinations that also satisfy you called me like identities and then you simply replaced the color factor by the kinematics factor depends on momentum and polarisations but this is act whether not having difficulties it thank you so it's not clear whether this really works too although orders so what we had yesterday sounded more like a city you have to give up on that idea or if it works you have to modify it in some want substantial manner "quotation mark in which the issuer of the media the movement for years to life so harsh unless you watch for option he said he had Wal-Mart's that's so that's where of course the time reversed pictures but of the eyes ideas that in all shops using of areas also space-like like you fall into it it's a priest well-to-do looked the makes you will be stretched and squashed and I always like to emphasize to all this His quashed to .period ultimately but this will happen in extremely interesting way because before you get there classic immediately you would be USX stretched and kph squashed in many different directions and of course there and ultimately you know once get to the blind dredging of course the classical 0 breaks down and then you have to you know in Volk whatever the quantum proper condom in they're not with us what used to Of course what happens in the quantum theory I don't know because this this is just normal so that he can do with the fact that most of the information and last year this is the result of the of and I think we all the year you go to the lot and this is not In the latest varieties from the finite this is mm what hearing on the bridges that doesn't want to hear the play was the year in Watson's amended them more than 1 theory as property with with his chance items during the 3 dimensions with you have to work hard and they seized however the authority the hearing the association and in the and then had the votes to fight him because she will you make your contributions fury 2 this is something that is well there certainly ambiguities here are in the sense that the Eagles 8 can appear with with gaged notion that different versions of the gage timber revenues although there so it is almost unique use what except for some reason the fall modifications I but what I would like to emphasize here and this was my last remark instead you know if there is any link to the real world it's not just an a over gravity even with this courtship seeing this seems to indicate you know you have to go beyond that and a certain controlled way that's I hold controlled by this this fancy included election rallies images you go with Thank you
thank her In


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