Gabriele Veneziano, « Quantum Gravity or Gravity for the Quantum : String Theory’s Lesson »

good morning indeed I was a little hesitant about which precise cut to give to this thought because of the work philosophy we scares me and so well as you will see I prepared something which goes from the very trivial very well known and I apologize in advance for that all the way to something that probably nobody understands so there's a whole spectrum and I hope everybody will find it it's this place of interest in the top so let me give right away an outline of the talk so I will start very very simple and trivial reminding you of non relativistic quantum mechanics how it eliminates Luca Bionic divergences and classical singularities then I will turn to relativistic quantum mechanics which actually has been mostly formulated in the language of quantum field theory the fact that that I would have ayelet divergences again the idea of renormalization and then I will turn to the specific topic of conference which is gravity and quantum gravity so first of all again classical singularities and then the question of no anomalies ability then I will turn to string theory and to its quantum mechanical miracles and then they the basic point philosophical pseudo philosophical point I wish to make is that perhaps string theory suggests some kind of Copernican revolution maybe this is too big a word and I will illustrate this in a worked out example which is a thought experiment a get on can experiment having to do with very very high energy string collisions so we use this as a thought experiment in the good old traditions of quantum mechanics ok and then I will continue a little bit but very shortly on string theory less-desirable quantum effects I said that there are some quantum miracles which I will which are very welcome but there are other quantum effects which are not as welcomed and perhaps what is the weak point Achilles heel of quantum string theory which is the existence abundance of some light scalar fields or even massless scalar particles scalar meaning without spin and I will end up with some comments on as I said something that nobody understands how to do quantum string gravity and the fate of classical singularity ok so and since time is abundant it seems please and since I don't know exactly the which level of complexity I should have followed please interact whenever something is obscure in any case we had one and a half hours including discussion so if some of the discussion happens during the talk I don't mind actually it helps me to renormalize the talk ok so you know that in 1900 Max Planck introduced a new constant of nature which is called age and this was the birth of novel atavistic quantum mechanics an extremely successful and internally system theory at least mathematically consistent theory for instance Dirac gave another in axiomatic formulation of it please spite of some interpretation problems which I'm not an expert on and I will not enter in so plants original motivation as you know was the elimination of a divergence in the blackbody energy spectrum if you integrate out over all frequencies of the emitted radiation from a blackbody the answer is infinity the divergence was an ultraviolet one it had to do with the excessive emission of high frequency radiation from the blackbody and now quantum mechanics cures this problem by introducing an exponential cutoff at high frequency so the spectrum the over the energy emitted in some range of frequency at high frequency goes exponentially down and of course there is exclusive age which appears in the formula if you put H equal to zero you go to the classical theory and there is no exponential cutoff now not only other successes of quantum mechanics are well-known I will only mention the stability of atoms classically a system made of a positive and the negative charge is unstable against the emission of electromagnetic waves and in a short time the hydrogen atoms should collapse classical and in quantum mechanics you can live forever if it sits in its well-defined down state and this is thanks to the Heisenberg uncertainty principle okay the little picture classically the electron would like to as it orbits around the in the nucleus should emit synchrotron radiation loser energy like in the binary systems from which we have seen cavitation waves accept it okay here eventually it will end up crashing into a singularity now quantum mechanically as you know the lectern sits on air from some kind of orbit which is fuzzy but the average distance is well defined is the Bohr radius and it's the best compromise satisfying the Heisenberg uncertainty principle if you try to put the electron too close to the proton you gain some way about you lose somewhere else and this is stabilized now already Dirac was much aware of the problems that originated when you try a relativistic extension of quantum mechanics because relativity allows for the transformation of energy to matter and back so the number of particles quanta is no longer conserved and in furthermore quantum mechanics allows for energy to be borrowed for a very short time lapses for very short time lapses is the so-called et uncertainty principle okay if you want to measure the energy of a system precisely enough you have to have enough observation time or rather for very very short time you can have big jumps in energy if you combine the two the relativistic possibility of transforming matter into energy and back with quantum mechanics you find that an indefinite number of quanta of arbitrarily high energy can be created for a very short time and and this is a source of problems how can we check these more quantitative well that is done by quantum field theory the point is that dealing with creation and destruction of quanta directly turned out to be a difficult task in in the old formalism of Nortel atavistic quantum mechanics when you elevate you know position and momentum to operators and impose the usual formalism so historically people abandoned that formalism and turned to quantum field theory which is also known some of them properly a second quantization now what is the starting point of quantum field theory is a classical figure for instance Maxwell coupled to charge particles or which gives rise to what is called quantum electrodynamics QED and then one applies the rules of quantum mechanics that replace the Poisson brackets of of the classical theory with up to a factor of I commutator and okay similarly you can try to do with general relativity of start from you know two learning books the plastic of your gravity is known as general relativity and you apply the same procedure now the fully modes of the fields become creation and destruction operators for relativistic particles relativistic want so this is how you extend to the relativistic case they the novela ballistic recipes however all of a sudden when you go to this relativistic case UV divergences emerge for the vision I already alluded to the point is that the problem of virtual creation of arbitrarily many energetic quanta pops out again so and it appears true they will prevail the divergences of what I call cognitive Corrections these are precisely some Corrections that quantum mechanics predicts which have to do with the virtual creation of a reabsorption traces of quanta and this can be very energetic want so if you want quantum field theories at least the usual kind of quantum field theories in free space and one time dimensions they do not have this plant like exponential cutoff that saves the blackbody and respect there is actually a classical counterpart to this kind of divergences for instance if you take the electromagnetic energy of a point like charged particle and you compute it as as you go to point particle limit namely your charge particles at zero size that is classically infinite now that is a contribution to the mass of the an infinite contribution to the mass of a of a point light charged particle this divergence is alleviated somewhat but is not eliminated by quantum mechanics say the divergence instead of being linear or quadratic is logarithmic but is still there in spite of these infinities for the non gravitational interactions of the so-called standard model that is at the basis of our present understand of the electromagnetic weak and strong interactions the infinities can be absorbed into a finite number of quantity okay so these infinities but finite number of quantities now this quantities cannot be predicted by calculation even if you were given this quantities the classical level they would change quantum correction will change them by an infinite amount so the best one can do it's a bit of a you know sweeping the dust and the drug is to renormalize the theory which means you give up computing the above man this above mentioned quantities and you take them directly from experiments of course it's not very philosophical not very satisfactory I mean you take a quantity you add an infinite one and you say okay the sum of these two quantities is finite and is taken back I think a much better attitude philosophically is to say that quantum field theories the ones we use as particle theorists are only valid up to a certain distance scale short maybe but finite and then some mechanism which is yet known you know you may have some ideas but we don't know for sure remove these infinities now and then precisely a finite number of quantities will depend on the details of how these new physics regularizes the divergences these are the quantities that have to be measured for instance in quantum electrodynamics the mass and charge of the electron cannot be predicted and as we measured and the same is true for the so-called fine structure constant which is basically the coupling constant of quantum electrodynamics the strength of the electromagnetic force now the rest in principle is predictable for instance again in quantum electrodynamics the anomalous magnetic moment of the electron the MU this can be computed with very very high precision in terms of the quantities that have been measured this is typical of a renormalizable theory okay you give up if you pay a finite price for your ignorance about what happens at the string new short skeins but the price is finite okay it's not an infinite car so you retain predictability not total predictable but now gravity's kind of special well even at the classical level some of pathological we know that singularities pop out even when you start from innocent-looking smooth initial conditions or when we integrated backwards the I stand equation so for instance the first case is the case of gravitational collapse start with some system and matter which under the universal gravitational attraction gets denser and denser and in some cases it leads to black holes and more often than not there is a singularity namely a place where curvature for instance goes to infinity behind the horizon of the black hole in the second category there is a cosmological singularity if you integrate backward the highest an equation starting from say today's universe and and that is usually associated with a big bank I think wrongly so if you want to understand why wrongly you ask me later ok any questions so far my going to - Zoli now then there is a no anomalies ability of Bantam gravity the problem we come to God is that the renovation strategy that I tried to explain a moment ago does not work so well in the case of gravity and the ultimately reason for this failure is that according to the equivalence principle of general relativity gravity couples to energy or energy source of gravity so the ultraviolet divergences are related to high energies high frequencies high energies and therefore they are enhanced by the gravitational interaction so in the presence of gravity this virtual quantum arbitrarily high energy are two copiously produced and make one tuned general relativity no the normalizer at least by standard techniques which means following what i discussed earlier that infinities cannot be lumped into a finite number of quantities okay as you go on in your calculation new infinities come at every loop order if you know what loop order is productivity is therefore lost in principle because you need an infinite number of numbers to make the theory predicted now another problem with contuine cavity perhaps a little more conceptual is that quantization in curved spacetimes at least in my opinion it's somewhat difficult for instance there are quantum effects which appear to depends upon the reference frame if you are in an accelerator or relative to an inertial frame why the equivalence principle would require that you know physics doesn't depend on the reference plane so I think my opinion personal opinion is that it is probably inconsistent to quantize matter fields in the fix curve background but it could be a very good approximation but if you really want to be exact fully consistent mathematically and physically then the background itself should be subject to is part of the configuration and ok it is my vague feeling that perhaps the information paradox if you know what it is how things information pathos could be a consequence such an inconsistent mixture of doing something classical and something now there are of course alternative approaches to quantizing general relativity the most interesting obtains the states are those of look one to gravity which we have represented in the audience and also there is another thing called asymptotic safety both approaches assume that one can make sense of quantum gravity or I should say of quantum general relativity by modifying the way to concise general relativity but without modifying the theory itself now it could work but okay if I take the lesson we learned in particle physics I call it the electroweak lesson which is how people when from famous theory of weak interactions to the present here with interactions which is which is a wine bar Salam Theory well it teaches perhaps that you have really to modify the theory itself it's not just an effect of quantum mechanics or being smart about how to quantize Fermi's theory so for those of you probably make minority of you that don't know in family theory you describe the the beta decay of a neutron into a proton electron and an anti-neutrino so what is called a for firm interactions named with these four particles interact at a single point in space and time in the new in the new theory which seems to work pretty well well there is a padded ready fiber the neutron and the proton are company party they're made out of quartz but this is not so essential from what I'm going to say you could have said well then it's the quarks and electrons and the neutrinos which still interact at one point in space-time but that is not the way the standard model works in the standard model the the quartz coupled to what is called an intermediate vector mess on the W and then this w propagates a little bit and then at some other point in space and time it disintegrates into the left and the the neutrino so there is this displacement between this vertex and this vertex and this is what makes the standard model of the glass of wine wassalam Theory softer okay and the normalizable people tried I remember when I was young before the standard model was invented people were trying hard to quantize directly film this theory which is not normalizable precisely like quantum general relativity you know general relativity has a coupling constant which is the Newton constant feminist theory has a similar constant which is called the Fermi constant and they're both dimension fool and the divergence is a very similar so I don't know perhaps you say it's red herring but seems to me is something to keep in mind now then there is a second lesson from particle physics which will be at the basis of most of the rest of my talk so according to our present understanding of all interactions if you go to a very microscopic level one to level all fundamental interactions which I remind you are electromagnetic weak strong and gravitational as far as we know that's all are transmitted by massless particles of spin one or two two is for gravity and spin one is for the other interactions now the first kind of particles like the photo a massless spin-1 particle gives guys two non gravitational interactions the latter the graviton is responsible for gravity now once you have this particles around okay for some reason then both the gauge invariance and general covariance which are the guiding principles for the standard model and for general relativity they simply follow from the consistency of the interactions of those particles basically you need enough symmetry local symmetries to be able to eliminate some unphysical polarizations because I remind you know that the degrees of freedom of massless spinning particles are different from the number of degrees of freedom of their massive counterparts it's just a spin one and spin two massless patio have two physical polarizations whereas if they were massive they would have three or five physical polarizations respectively so now good general relativity and also the rest the gauge theories of the standard model be a consequence of quantum mechanics instead of saying you know I'm given this classical theory and I'm asked to quantize it so I call it a Copernican revolution and main the main part of the rest of my talk is to show you that perhaps this is what string theory suggests okay now to the extent that since here is right we don't know so so I'll try to summarize very briefly what is yes yeah could be a concept of quantum mechanics of space-time but also about the mechanics of anonymous this time possible to mechanics without spacetime yeah okay I think we will we will see you'll see but I mean that's yeah you'll see that in string theory I'm assuming at least to begin with the space-time is there already okay but not the interactions and talk about the interactions okay so but you you will see the space-time will be non-trivial as a result of quantum mechanics so let me give you a five minute introduction to string theory I think they the best way to answer the question what is string theories to say the string theory it's not my own sentence I have forgotten go ahead this is the theory of strings so - you mean that you you don't start with this grand principle of gauging variance general covariance even the equivalence principle no you just assume that everything in nature is made of relativistic quantum strings they come in two kinds they can be open or closed depending on whether they have ends so you combine these three things special relativity by the way when I say relativity I mean special quantum mechanics state and if you put these three ingredients together and nothing else you get some interesting outcome for instance I want to stress the importance of the quantum yeah okay because if you take a classical strings here there are classical series for instance when you talk about cosmic string in the universe there's no need to do quantum mechanics I could only quantum mechanics to describe the solar system so and classical things have no karate six eyes they have attention which tells you what is the amount of energy per unit length of this for this thing but there is no characteristic size okay a shorter stream is lighter than the longest range and there is a proportionality between the two but when you go to the quantum regime or turn on quantum mechanics then there is a characteristic length then a single characteristic length and it's given by by that expression and you see this the three the three quantities which belong to relativity quantum strings all appear in this formula the Planck constant the speed of light and the string tension okay out of this you can form a length and that length is called the string length by the way sometimes to capital L some other times it will lowercase L don't worries because maybe I picked up some transparencies from other talks so same thing now note the analogy is actually perfect only in four-dimensional space-time so in our case with a Planck length you know the length plan introduced also at the beginning of last century you know H C and G Newton which in you know up to speed of light factors is like the inverse of attention okay now so again there is an analogy with atoms like I show again the figure of one of the first transparencies okay but perhaps even closer is an analogy with the ground state of a harmonic oscillator okay because if you have morning it's later potential classically do you see a ground state and and there is no spread your internal axis is spatial axes but quantum mechanically we know that the uncertainty principle introduces a spread so there is an uncertainty Delta X which again is proportional to the square root of the Planck constant so very similar or put it differently without quantum mechanics strings become lighter and lighter as they shrink so in the in the classical case you take a string and then scale invariance so you can be scale if you if you are given a solution a classical solution the classical string motion you cannot escape everything all the coordinates and make you find other solutions if this thing is simply shrunk and the more you shrink it the lighter it is you can go to the limit in which it becomes a point and it will be massless okay quantum mechanically that's not the case you you have some kind of optimal size which is given by this quantum length and if you go this way or that way the mass increases like the amount of salado you can of course construct this a state in which the the the little ball sits very near the minimal other potential but it will be a very high energies it will not be the ghost now this quantum spreading or quantum size of strings may you know changes very much the way you view interactions you've been interactions in string theory in field theory we have seen already in this fear me or standard model or standard model diagrams that the interactions take place at a point in space and time if you put too many fields at the same point in space-time you get this ultraviolet divergences but if you put the right amount of fields then you get this we normalize Abel in theories but still it's quite different the situation with strings because now the interaction of three closed strings proceeds like this this you have to close things which come together at some point but where I don't know exactly where they become a single string okay so two strings go into a single one perhaps heavier but the interaction is made over a region which is order this l sub s and it is this basic property of quantum strings the cure to the ultraviolet problems of conventional quantum gravity in fact ultraviolet divergences are removed all together it's not that you make in a drink not remember risible theory renormalizable no you make it finite okay that's the beauty and if it is indeed an exponential cut off like plant health in the blackbody spectrum now the second miracle which is even more related to the topic of my Samia is that a light classical strings which cannot have angular momentum without having mass because to have angular momentum do them immediately understand you need some finite extension I don't know anything is the product of the distance Thanks momentum there is no distance there is no angular momentum but by the time too heavy you have a size you also had a mass so in fact in the in classical string theory you can prove a strict inequality between mass and angular momentum through the tension so this is the classical relation is no H bar here but you see it prevents J which is the angular momentum to be to be nonzero its mass is zero no massless spinning strength the classical regime quantum mechanics adds this infinite sum which is formally divergent has to be regularized there's only one consistent way to regularize it and it gives a negative contribution which allows n equals 0 and J equals alpha naught H bar and alpha naught is predicted to take only these possible values the half integers are for the super state so there is so massless spinning strengths are inevitable at the quantum level I mean in fact in the old string theory in which I was working in the late 60s they were a killer because at that time we were not trying to make it here e of quantum gravity were much more modest we attack a theory of strong interactions and histone interactions there are no massless particle we know because the force is short-range and so on so but string theory was very obstinate it was predicting the existence of this mass massless particles and we had to abandon it so and that shows another interesting length of the string theory can be sults falsified by large distance experiments you don't have to go to extremely high energy to falsify the theory by the time you prove that there is a massless particle in the spectrum you have low energy experiments that will tell you whether this is event ok now ok so coming back to our Copernican of evolution now instead having spin one particles of zero mass or mass the spin-2 particle is welcome because you get a photon another gauge bosons which can mediate no gravitational forces and you have a graviton which will mediate the gravitational force an owner mentai patty will correspond to different vibration of the same basic objects which are opened and closed strings so this gives a unified theory of all interactions because they are all geometrical you know they all given by this little little trousers like diagram ok they come out from some geometrical construction and if your is unified and finer it and it is based on quantum mechanics ok I feel if I didn't have quantum mechanics all these things would not be there so in quantum mechanics gives directly some quantum version of gauge and gravitational interactions and then you can take some classical limit and you see you attain the starting point of quantum field theory as the end of your of your construction you start with quantum mechanics and you may end up in some limit with classical field theory but on the way you have also provided some short distance corrections without which the usual one to fill theories would show this violate the variances okay how bad am I doing with time okay okay okay now okay I think up to here hopefully have been simple perhaps too simple I don't know now perhaps we switched here a little bit because I want to go into some more specific details about a worked out example of what I mean by generating a classical field theory in this case it will be a classical gravity theory from some quantum mechanical calculation so and this example has to do with the transplant and energy collision of strings but it will be done in Minkowski space-time so this answers perhaps partially Carlos question I am assuming and the father had been assuming all the way the strings propagate in Minkowski space-time my discussion was there that's where I know how to do my quantization so what is the transplant and energy strings in collision well is the collision of two strings which I can pick up from the spectrum you know from all positive I guess states of the Estonian I can fix the two initials things as well as the energy of the collision and the angular moment the total angular momentum of the system now it's a very simple and pure in the sense of quantum mechanics initial state depending on angular momentum and energy it could lead classically to black confirmation to a possible information paradox we would like I mean this was easily ultimate aim of the of this Gedanken experiment how information is preserved okay or whether there is indeed the loss of information so this was the original motivation but for this talk I will use it not for solving that problem which is still not solved but to you know to explain the the idea of this of this copernica revolution a stress again the calculations are done in flat space-time so but I would like to see the beauty of general relativity in particular the emergence of non-trivial geometry of space-time to emerge from the calculation which we are never putting any curved space-time so this is a picture of the what we have to do these are the two incoming steering Cohen string and I told you the interactions in string theory are related to some surface you know with holes and so on we saw this tousle diagram but when you go through on and on you form things you see I don't know if you see this this surface is supposed to be a a surface with two holes okay these are the two holes now and I depicted in your head the incoming outgoing strings and then green some closed strings that you exchanged between this and this and then the yellow has some produce training system it is and so but never mind that okay this will give you just a feeling of what we do so and there is a certain parameter space you know chickens are this process the parameter space is characterized by different values for the data the data date but parameter of the collision okay how far of how close the two strings collide is related to angular momentum and to energy by this relation there is also a quantity which emerges again it's not poutine which is the so called Schwartzel radius of gravitational radius here I put a generic value port the number of space-time dimensions capital D but okay think about people for just simple so G times square root of s defines the length which grows with s of course proportional to s and this is you know like the Schwarzschild radius of a black hole of mass square root of s but since I'm in string theory there's also these string lengths what I call produces capital LS sorry here instead of the tension I use alpha prime which is one of the tension so this should be to this plain one now this quantity I cannot bury okay it's like a unit of length in the theory but I can compare other lengths that I can tune in my experiments to this fundamental so since I had three relevant length scale I will okay this is a technical detail there is also a plant length but it turns out that if I mean in a particularly simple regime which is with happening I can consider that this length is much shorter than everything else so I will put it to zero this being said this phase diagram depends on ratios of of this length so since I have three three length parameter I can form two ratios or I can put in a plane this gravitational radius on one side and the input parameter on the other side and then you see I will mark the point here which is the string length so so this way look at the blue lines you can divide the phase space roughly in three parts this this and this depending on which of this length is bigger than the other two and on the basis of some collapse criteria the classical expectation is that there is a critical line which separates a region in which you expect the collision not to form any black hole to the region where you expect to have gravitational collapse information of black holes and okay the idea is to study this process in all these regions trying also to go across this critical line and see what happens okay life is a little more complicated than this also the CAC visit the popsicle signal just to gravity yeah I mean the class this is a classical present we'll have to see what we get so this iodine is from classical collapse criteria you can start the process of two particle communion was started by carefully in readings and so on you don the process is rather complicated so you don't know precisely this curve back after it you know for instance when you see when when be is aboard our critical value over the one on the ratio here just yeah I will explain I mean the three regimes I call them weak gravity because I will see life is easy we can do something very simply I will go through the three beaches why so this is strong gravity because they have gravitational collapse this is we cavity because we don't have sufficient a lot the third one is you see a region in which the string length is larger than both the the shorter radius and the impact parameter so it's a case in which the string size cut matters because you know these are like big strings relative to the impact parameter so they really crash into each other whereas if you are here they miss each other almost beats each other we will see that they feel still they further there so we don't wait and then I think it should become clear and okay life is even more complicated if I should go into this there are sub regions let so each region has sub regions and we will see them as we go on I think maybe it's not important to discuss it so okay he in in particle physics we talk about the next matrix this is the certain object whose absolute square gives the probability of a certain process to take place this as matrix can be computed in this transplant and energy position or rather one can argue that it has this sport is exponential away of some object divided by h-bar where this a classical is something like a classical action and it has a leading term which will analyze in a moment plus Corrections the corrections see this explains the word weak gravity because if you go to very large input parameters this at least superficially are old I will negligible and we are left with the one okay now the tricky point here is that one as you know is a real number is no imaginary part now if these two lectures have an imaginary part then you cannot neglect them even if they are small compared to one because you see there is an eye here if this guy has an eye I square is minus 1 and you get an important effect you have a damping a suppression of this amplitude which means of the professional probability as long as this quantity times the prefactor just light becomes immortal one so this is what gives rise to the sub-regions okay so let's start with the weekly habit energy then we tell it the regime we can show that the one the first is introduced simply by summing Feynman diagrams the string size doesn't matter everything is simple this so-called lab the diagrams and you're also cows landed not shown here can be summed up an infinite number of them okay you have to service an exponential series so it's easy to do and then the result is what I had in my videos slide mainly I keep only this term now okay then the question is how do you go back from these asthmatics you need to keep the energy only but parameter fixed to something in which you want to see how if at all the two strings deflect each other so you have to go from impact parameter to what is called momentum transfer okay there is a transfer of momentum between the two guys and you do this past and the metal the fully across for you can do it by saddle point and at the end of the day you discover that this really the two strings will deflect each other and that the deflection angle which is given by this formula with a precise coefficient which gives the collection area of Einstein's famous deflection formula you know for the deflection of light by the Sun one of the tests then one of the first tests of general relativity now that formula chemically analyzed to the case of the collision of very energetic particles you don't need this in the photo also also two photons will deflect each other if they are sufficiently energetic and and that formula works in any number of dimensions the other thing is that you can take the deflection comes from the derivative of this phase shift respect to B if you instead you take three that you expect to the energy you get what is called the Shapiro time delay and that also comes out as lastly right okay third comment this process is unitary there is no loss of coherence but it's kind of trivially unitary it satisfies elastic unitarity means if there is no production of anything no excitation of the strings the initial state goes into itself research ok then you see still keeping in this weak gravity regime we can go a little bit lower I don't tell you how much lower so we are still in this region one but you know somewhat approaching either this boundary of this puzzle now in that case we cannot neglect this correction oh but the reason I told you this is a small number still but it multiplies a big number and if it has a nine you have to keep it and and this will take into account not straight string size effect remember that this L sub s is the typical size of strings so somehow that term tells us that we are not colliding point-like objects and we are colliding extended relatives and the thing is that you can do the calculation the calculation a bit faster remember I had my love diagram where I exchanged I put some gravitas exchange between one line and another line the transverse distance is the simple parameter here it turns out that the result can be expressed as exchanging gravitons between one point in one string and another point in the other string and then you have to average the precise definition of everything over which point here which for them doing that way you get you get the possibility that each each one of the two streams can get excited and the physical interpretation is more than interpretation is really check is that string moving in a non-trivial magnetic field tidal forces we didn't put any non-trivial metric but out of the calculation comes this effect of tidal forces the tidal forces in this case produce excitations on the string classically they would produce deformations you know like the tides all the earth they would stretch or contract the stream but quantum mechanically they you see this as simply making transition between one string state and another so and everything is consistent with the quantum information preserving unitary evolution now it's no longer last that unit I have to take into account that you know you start with two strings but they produce two different ones but the sum of the probabilities of producing any kind of exciting things adds up to one this is what unitarity tend to and we have of course information preserving process so this is the picture and you start with a state with two massless things but the yellow strings that you can produce okay the third topic is gravitational waves from this trans plank and collisions and this we have four so far we have only done it in the point particle limit so there are no actual strings here of course would be nice to extend it it's a highly non-trivial problem the one of computing the gravitational waves which are emitted in a very very relativistic collision it so in fact I gave a talk in June and made me of June here so probably the slides are somewhere in the ihes side you can look for more details so here I will be again very sketchy to say that it's a non-trivial problem it's enough to show perhaps the this paper by new Nobel Prize with the Nobel Prize physicist Kip Thorne who who gave up on his problem although they solved very well a general case they say that they need a condition that the angle the angle of gravitational deflection should be much smaller than this Lorentz factor which of course goes to zero goes to see so they cannot deal with the ultra relativistic cakes so again this still belongs to the weak gravity regime approaching going again in this direction now you can do these things classically so I worked on this with breakthroughs you know at NYU a few years ago three years ago and we did the calculation without any quantum mechanics we obtained the result using the Huygens principle in the front of an approximation which is a bit pretty because in the case of gravity it has to include in an essential way the effects of the gravitational time delay in an external method so certainly this classical theory we heavily used that space time is not flat okay this precisely so you see that the point is this that one string feels the shockwave metric of the other string and there's a pissant when they collide there are several effect there is the deflection which I already discussed but it is also a time delay which I also mentioned by the way so you have to take that into account and then you can construct here I have a graph which is not easy to read and understand so just to give you the feeling this is one particle this is the other particle coming across with an impact parameter B and then you reconstruct the field far away by superimposing according to the Huygens principle many many waves emitted by each point on screen okay a two-dimensional stream now however these waves have their face and their face has to take into account the gravitational time delay once you do that you get a very explicit formula it's not very simple but it's not very complicated either it's very explicit it gives for instance the energy spectrum of gravitational waves as a function of the frequency and there an angle at which the wave goes and it's all controlled by the so-called news functions C and for C you get an explicit form okay and this integral D 2 X is precisely the integral over this two-dimensional screen from which you take whole day on the waves okay there are a few technical details which I don't have to go into but then a couple of years later one year later actually we looked at it we approach the same problem quantum mechanically in quantum mechanically we are back to our final diagrams this is nothing but a rewriting of the ladder diagram which ahead you might be nice a particle particles and these are the orbitals which are emitted now and we had to improve on some previous treatments of our own a very important observation is that the usual the is a is a theorem about how to compute the mission of very very soft habitants in a genetic process the work by Steven Weinberg for instance in the 60s but that work has to be somewhat improved because they exchange gravitons you know like this one it's almost on the math shell I told you that their virtual party which are not really physical this is almost physical okay and therefore if they meet a graviton comes from a coupling here it can be neglected if you will only go to zero frequency but if the frequency of the graviton emit a graviton is not infinitesimal you have a contribution from this so we looked at this this graviton therefore can be emitted and every run in this last there or from this exchange Rabbitohs something up everything we ended up well here there is a little technical detail but we ended up with a formula which looked like the one the classical one but it was not exactly if you look back in there the classical formula this of this function Phi is the same that appears here but the formula is different however then we we found out that we had forgotten something that one should take into account the difference with the face of the three particle final state relative to the two particle state and when this is done we got exactly the classical result of course provided you take the limit in which h-bar Omega is much smaller than the total energy of the process so this shows how we could recover now since time is short I will not go through what we get in detail in many cases not so much of interest for the topic of the conference really produce the so-called zero frequency limit the limit of very soft gravitons is nice to reproduce we can extend it to higher frequencies we still have a problem that the spectrum D D Omega it's not sufficiently damped as very large frequencies so when you integrate aspecting you get still a logarithmic divergence and we think we understand which approximations produce this bad effect but this is ongoing work also have some nice so this is a very explicit result which may need some improvement and the high frequency okay now how about short distance modification because so far we got things which are essentially the same as in generality with even this string size effects could be understood as tidal forces and tidal excitations however if we go to really this regime then we get really something you you expect really deep modifications of God okay it's like when again in analogy with wheat interactions if you go near the W boson energy you know the definitions of the of the electroweak theory completely different from those of a fairness theory okay here we also spent something similar so this case we have to keep these things now we find several interesting things for instance let me mention only the most important one the phase shift which previously was divergent you see for it in four dimensions AB equals zero you get log of zero which is in instead after you include all these Corrections the B goes to zero meaning in this regime is tractable it has a smooth expansion you see actually in B Square over every square no gas and its derivative expect to it gives a well-behaved time delay even all the way to B goes to zero this solves the potential causality problem which was pointed out in the paper by Malthus in a town and for details I refer you to a paper by myself and three collaborators another very interesting thing is that well there is a maximum deflection angle you see if you take Einsteins formula the deflection angle starts to become order one and then seems to blow up of course that's when respect to form black holes in this case the maximum of deflection angle is since we are in the regime are less than and string in this string regime this angle is smaller than one so there is a small maximum deflection angle it is reached when the two strings crazy child okay the barely touched and then what we found also is that at least from this experiment we cannot probe explore distances that are shorter than the string length and this led to the so-called generalized uncertainty principle which I like to call effective uncertainty principle we don't modify the rules of quantum mechanics but effectively when you do the experiment you find that the distances that you can probe and not just the ones you expect from the uncertainty principle there is an additional term which grows with that repeat so that the Delta X is always bigger you know when you have something like X plus 1 over X there is a minimum ok and so that not surprisingly is still the string length finished five minutes ok yeah now the last topics I do very quickly so I told you a very nice quantum effects finite size spinning massless particles so there are less desirable Plantin effects for instance classical things can move in any ambient space time flat curved any number of dimensions as far some strings are much more demanding they need some suitable space-time or more generally background in order to avoid some what I call anomalies which are sickness you know diseases now and if you take the case of weakly coupled superstring theories space-time if it's also nearly flat must have nine space in one time dimension so four-dimensional space-time is not an obvious consequence of string theory quite the opposite so in order to reconcile this with observation one has to assume that the extra dimensions are compact or at least invisible to non gravitational interactions as it is the case in some brane world scenarios so this pushes one quantum mechanics if you want pushes string theory into what many of you must know it's called Colusa Klein Theory extra dimensions that can be used actually to unify also gravity and engage interactions but it does so in a very interesting way of course I don't require a full lecture to talk about t-duality and the emergence of non abelian gauge views and so on and there to this fundamental length plays an important role for instance the ratio of the size of your compact dimension and the string length is a very important dimensionless parameter then I turn to what I consider perhaps the weakest point of string theory which is that it starts very beautiful because you say what are the parameters you know where are the parameters that I use in the ordinary quantum field theory like masses couplings and so on what becomes of these parameters in string theory well they are replaced by fields so are typically a scalar fields spinless fields and if you fix the value of these fields then you fix quote-unquote the constants of nature to instant the overall strength of strain interactions is one such field and its value would determine the fine-structure constant health so add the values of these fields determined by the dynamics well knows of course if you compute alpha you then and also the dream of theories now these constants look to be space-time independen today Tebow has done beautiful work on putting bounds on their time variation now but for instance they could have varied in the early universe who knows and for instance scenario because Marcos name which I have been working uses very strongly variations of the scalar fields now but there is a danger if the particle associated with these fields are too light or even worse massless then they will induce long-range forces and these long-range forces typically violate equivalence principle of the universality of freefall ok this is a still I believe an active field of experimental and theoretical research to detect whether there are some long range where long maybe a millimeter long long range new forces and for the moment as far as I know nothing has been found so but it's again to repeat my previous of the basically you don't need very very high energy physics Planck scale experiments for testing string theory and this is was true as I mentioned already for the old data wrong extreme in fact if you take at face value three level so string theory at the lowest order approximation it has plenty of this massless spins and it would violate the equivalence principle would be completely contradicted by this part so you need to solve the theory beyond three level otherwise it's already ruled out but let me point out that also the standard model this is ruled out if you don't include phenomena like Porto Fineman and so on so in the last slide and I have no conclusions is string gravity and singularities this is something I you know I feel very very important is one of the most difficult but perhaps one of the most fascinating questions is things here is the fate of general relativity singularities the big bang Trek volunteers and so on if you solve the if you look at lowest order in the derivatives which means large distances and in the coupling of strings then the equations that one has to solve in order to ensure a consistent stream quantization look exactly like classical field theory equations so partial differential equations which include with some slight modification instance equation and light Einstein's equations they satisfy the conditions for the singularity theorems of Hawking and Penrose so that means that if you really stick to those equations you'd predict their singularities but of course this is only valid in strings you at lowest order but it's enough the basic idea terms are enough to tell you that the solution is typically driven towards high capital strong capping or both and then the approximations break down so a big question which I don't have any answer to which are the correct equations in those number to deliver genes what hap happens when we're in a situation where they used to be a similarity according to general relativity can we go through this would be single ID and key productivity I think we badly need techniques to study strength you know perturbatively both for this short distance problems and for the large distance problem of the massless particles so with this I think I stopped [Applause] the promise books playing white/black hold on big banks in your life very good I told me to wish them the beginning of the talk you said there oh no no I didn't mean I didn't I didn't mean that that yeah it was not no it was not a question of fundamental difference I said that the big banks in unity you can find it by integrating backward our heist instance equations from today's physics back in the past in the okay so the difference is mainly one is a person right in the past in our past and for the blackphone seniority system right in the future evolution of some initial data I only meant that but no otherwise they are they're quite similar in fact I mean the difficulty is precisely to approach the unitas which are technically called space like singularities so like they happen on the surface of constant time okay they're called space-time singularities and remind people that the singularity in the interior of a black hole is also of that type because the radial coordinates is actually becoming time line inside there so really they the symbolized at the center of the black hole is like a big crime scene right so in that sense they're very see one is a big bank there are there is a deep trench and the question is whether these things here you can avoid however if you can avoid one you can also avoid the other if I'm not mistaken inside I don't know about this how do you resolve this over like is instinctive so if I'm not mistaken this journey steerage singularities don't always come up with blown garbage tensor or something not like things do statistically incomplete business the genetic similarities are Roger Penrose knocking so I don't understand from you talk that how can you resolve those means geodesic incompleteness theorems in string theory yeah well no I see what you say our acted in somewhat different namely we prepared an initial state in Mycoskie space-time which is to find the far past that there are these two strings which come closer and closer and then they start to interact now we okay if you take a straight s matrix approach you are not trying to say what if I measure the gravitational fields here there and so on you only want to look at whether the final state that you get late times is consistent with a unitary evolution which means it preserves the pure nature of the initial state so it preserves information okay you see in quantum mechanics you are supposed to do so so if you start with two states which are orthogonal to each other you should produce final states which are orthogonal to each other now and but we don't ask questions like you know what if I go inside the Arizer we don't even talk about I said that this specifically the singularities of generativity are incompleteness of yes that's right this is the way they are usually formulated yeah so how do you actually resolve things well because you see when if when you do that you you you do take a non-trivial space time and you look at the Soudan see completeness or incompleteness and so on here certainly not in this you can perhaps ask me that question in the context of cosmology pendulum comadre put some back on and so on and there I do have some answer because in our scenario this pretty big bank the initial conditions are very simple and there is no geodesic in completeness in the past however and that's the point you have to pass through a big-time singularities but there is no asymptotic difficulty but okay so there is a trade-off if you are doing inflation for instance there is this problem of initial conditions eternal inflation sort but then ok the rest the end of inflation is relatively simple if you call simple reheating the universe after inflation in our case we have an easy life in the asymptotic past no density completeness well but then the price to pay is to know how you bounce from a collapsing face into an expanding phase by the way collapse and expansion all depends on which battery to use because if you want to have a metric in which the string size is constant the string length is constant then actually our scenario is a is a using expanding universe all time there is no contraction but if you use another method then it would be like the bounce so first of all in my talk on Thursday I'm gonna give several examples of singularities in general relativity which are resolved in string theory so you'll see but one sort of beginning comment is that the definition of a singularity is different in string theory geodesic and completeness is based on the fact that you want a point particle to be able to evolve for arbitrarily long times in string theory you should ask if a string can evolve for arbitrarily long uses it's said that already gives you some differences because conical singularities lead to Gd sick and completeness but because the string is an object it goes right through [Laughter] no yeah okay I didn't have time to go into that of course some in some cases by now we have this tool of ideas safety I didn't want to enter into this because I thought was bit too technical but I'm sure I have seen some of the titles you tacked on that the problem is that they the kind of situations which seems to be mostly irrelevant physically our situation in which the background the geometry is is this time dependent high temperature and so on and so technically speaking he would break supersymmetry spontaneously so even if you start with the super symmetric and the fat you should start with a super strain the the background would break supersymmetry and then most of the techniques which people know how to use seem to seem to fail so I guess that in order to answer the relevant question physically we are still we still need better tools on the other hand I I had always in mind the possibility that at least 80s EFT should help us to resolve some situations like the one I'm talking about because okay for the audience benefit okay this gauge gravity duality connects typically a strongly coupled strength gauge theory to a semi classical or weakly coupled gravity theory and vice-versa so most of the applications so far have been in the direction we use an easy problem in gravity to solve the hard problem in gauge theories but why not to do the opposite and I'm sure there are papers doing that but I don't think some very clean answer has emerged using gauge theory in the weekly topic regime to understand what happens when the ad s radius shrinks to zero which means very high curvature what happens to string theory to gravity in that case so I agree with you I mean at least we should learn some lessons maybe they are not enough to solve the real problems and so on on the other hand I think on this bounce we share with look quantum gravity some optimism right if I understand okay two questions about the strings scattering you describe one is just basically I think a misunderstanding it seems like you were saying the tidal effect was captured by a stream loop effect no not really if I go back no I don't think we can well at some level my diagrams are all three loops okay even before you put in the string size connections these lovely diagrams me right yes see this is why it's an elementary question I'm asking how do I see that that's a classical yeah it's it's a very good it's a very good question now is how classical physics emerges from a loop calculations in fact let me say that the loops are absolutely essential namely if you take the string string scattering amplitude at three level the loops then you know it's modestly my formula of 1968 or its generalization by venusaur now that formula has two big diseases it has it grows with energy too fast so if you take the partial waves okay you go to impact parameter if your pressure waves it violates partial wave unitarity is too big and if you want is too big in the forward direction on the other hand if you go to fixed angle maybe high energy and ten degree angle it's too small it too small where you expect to have day to have events because of the gravitational deflection so so the three-level is completely off both is too large in some cases and who's moving in other case and this reflects the fact that the theory is very soft okay so it does not allow for hard processing in which the two particles deflect each other so this was actually our very very original motivation in 87 to look into this and I think Michael Grimm was the one who who pointed out this the unitarity bound by violation you started to have a look at that and say well how can we recover well let's add loops now it's a little less clear how that would be this way these are loops if you keep the too fast string lines in the final diagram if you replace them by sources of gravitons then there are three died and in fact all the corrections which I think this is worth see ya yes this is the death these Corrections which we took into account for the for the gravitational prime stand for instance these Corrections are also given by three diagrams if you remove these lines and you replace them by some little sources okay now the leading the leading icon all approximations in this one comes when actually is not only three diagram is a completely disconnected diagram because you remove the external lines these such as propagators non-interactive and the classical Corrections they come technically from letting these gravitons interact through it so if you remove the fast lines and you let the gravitons interact three level you get all these Corrections and this is what in 2007 with a matinee Fulani we try to do in some approximation using lipitor effective garden and so on and then by solving this truncated theory we arrived at some estimate of this critical line for Cola maybe we found the singularity now however indeed we cannot see unitarity being restored on the other side of the singularity line but it was done presenting this approximation in which you let this gravitons interact but not forming loops if you form a loop then I think you are adding this kind of courage and whereas the three the string size collections do not have loops they are the same gun the only thing you say well I have to be careful this is an extended object so remember I had this diagram where I have these two circles and the gravitons were exchanged between one form Pringle and put but it was still the same topology of diarrhea the only thing is that if you want this this little blog became somewhat bigger but it's not a loop it's it's a string what you just end it on so you talked a lot about two of the regions in the plot of impact parameter and and once your radius but we didn't talk about the yeah strong gravity part and black hole for me yeah is it like why can't we just dive in there is it just because it's computationally please come today well as I said the most we could do is was because okay the idea is that you don't have at least to go across this this line you don't have to appeal to quantum gravity Corrections which are controlled by the plant planes you can just leave with this tree diagram so this was precisely name of our paper now 20 years ago no there 10 years ago so as I said if you take the three diagrams and you make another drastic approximation somehow you freeze out some degrees of freedom and you keep only some so you reduce this theory from a four dimensional to a two dimensional theory magically okay we get a hint obvious in writing namely some solutions of that you know when you sum three diagrams this will be technical it is like solving the classical field theory now you look at classical solutions which are both real and regular why real because otherwise you lose in eternity right away why regular well because otherwise everything blows up when you put this solution back into the action and now we found that all the way approaching this now we did it only in the case in which we neglected the string so say we are here okay take very far but here neglecting the string length but keeping terms which go like R over B to some power so R over B becomes about the one that means what happens is there a critical point yes there is in the sense that the real regular solutions exist only when this ratio is less than something okay and this two-dimensional theory which is already an approximation to the true one was solved numerically by magazine and on offering and they found the critical value now this critical values are all the time come out consistent with some after a lower bound which come from the classical considerations you know their disk elapsed Kathy Kathy they always come consistent but typically a factor of two or three off of the bound so there is no yeah now whether we don't understand what happens inside but since Nerys they will not take place this afternoon so we maybe we can have a round table and with all the speakers and all the question that we couldn't ask now [Applause]

Channel: ERC PhiloQuantumGravity

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Length: 103min 28sec (6208 seconds)

Published: Sat Dec 02 2017