Freeman Dyson: Is a Graviton Detectable?

so good morning everybody and thanks to everybody who had a hand in inviting me here and thanks to all of you who took the trouble to come it is just amazing to see all these old friends and new friends so I look forward to sitting and talking and having it having to having a chance to hear what's going on in the world I also just have to say it's just amazing to come to Singapore and see such a vibrant community it reminds me a little way of my favorite city it's edition Switzerland and the the it a Haddon Association is Joshua the that the what was originally just a technical engineering college host which has grown into a world-class University and the same thing happening here it's a similar situation you have a very poor and small country with people who have to work hard to make a living and just have made an enormous success of things and I've just congratulate Singapore and congratulate all of you for doing such a wonderful job I must apologize for talking about a technical subject I wanted to talk about my own field and about real science not just philosophizing I so it will all be equations and I just for those who don't enjoy equations I just I invite you to go and and and enjoy a cup of coffee outside so here are some situations of the literature it all starts with this wonderful paper of Bohr and Rosenfeld in the year 1933 which was a very famous piece of work in which bore it this was the fight or the finest example of Bohr's style it's a very very long and complicated argument written in very long and convoluted German sentences and the unfortunate Rosenfelt had to write it all down 14 times before Bohr was willing to let it go to be published it went through 14 versions and so the title was on the question of the measure ability of the electromagnetic field strength and it is of it's the foundation of this field of quantum electrodynamics it's the paper in which board found the precise physical basis for the quantum treatment of electromagnetism showing that just if you had electromagnetic waves interacting with material objects and then if the apparatus behaved the rules of quantum mechanics then the rules of quantum electrodynamics within a necessary consequence that is what poor and Rosenfelt established so what I'm trying to do today is to discuss the same problem for gravitation that's where this all starts so how about gravitation is it in fact like electrodynamics in electrodynamics of course we have the classical theory of Maxwell and we have the quantum theory which started with Einstein the theory of the photon which is the particle of electromagnetism and the two things the classical and the quantum picture are linked together by this subject which is called quantum electrodynamics does the same thing holds for gravity in that is the big question which we don't yet know to answer and there's been a great deal of talk a great deal of philosophizing and not very much detailed science and I shall try to talk about the detail science today in the case of gravitation you have the classical theory of Einstein the general relativity which describes gravitation beautifully as a classical phenomenon in the classical world wave of gravitation propagating through a universe with equations which have enormous elegance and enormous predictive power and has been verified by observation so it's a firmly based classical theory on top of that you have what's called quantum gravity which is the notion that actually there exists a particle called the graviton which has the same relation to classical gravity as the photon has to the Maxwell theory but there's no observational evidence for that to gravitons actually exist we don't know nobody has ever seen a single graviton so that's the subject which I'm going to discuss roughly speaking there are three possible alternative which might describe the universe we live in those first of all what I would call the the Orthodox view the view of all the experts which is that quantum gravity is a good theory just like quantum electrodynamics that in fact that do exist gravitons and that they obey the equations of quantum gravitation quantum gravity and they have the same base the same kind of behavior as the photon except that it's harder to observe so that's the first possibility second possibility is what I call concealment which is that quantum gravity exists but it can never be detected in the same way that the clock exists that there's a particle called the clock which everybody believes is real but it can never be observed that has turned out to be a very fruitful concept in particle physics what's called quantum chromodynamics which is the theory of the strong interactions which is based on quarks so the clock is this quantum field which has all the properties of a quantum field except observability that in point of fact you can never see a clock by itself all you can see is confined systems in which the clocks are hidden that's why we call it confinement so that's the second possibility so quantum gravity is real but unobservable and the third possibility is that quantum gravity is nonsense that in fact there is no such thing as quantum gravity that gravity is a purely classical phenomenon and the alleged effects of quantization are just all of them for some reason absent so it means that if that were true gravitation is a classical phenomenon it is some kind of statistical property which only belongs to matter in the large not to matter in the small so there's no such thing as a gravitational field of an electron that in fact it's only a collective property of matter in bout so those are the three possibilities and the question is which I'm asking is what is the evidence what can we actually say from what we have observed that's what I'm going to talk about so there are three there are actually four subjects I'm going to discuss which are first of all the ball Rosenfeld argument what happens if you actually try to apply the ball Rosenfeld argument to gravitation so that's the first question so that's essentially just just mathematics it has an interesting answer and then the second subject is a particular kind of gravitational observation which is actually being done in the real world which is called LIGO like o stands for what is it called laser interferometry gravitational observatory I guess it's anyway it's a long vacuum pipe with a mirror at each end and light bouncing up and down up and down up and down and you measure very precisely the phase of the light as it comes back and forth and is reflected at the mirrors so that's a very precise measurement of the distance between the two mirrors when a gravitational wave comes by the gravitational wave is a distortion of the space so it produces a very small change in the separation of the mirrors as it was measured by the light so this is a detector for gravitational waves coming by so the purpose of the apparatus is actually to detect classical gravitational waves coming from astronomical sources if you actually look at the history of this apparatus it's not very glorious the apparatus has been working now for quite a number of years five or ten years and has never seen anything yet there's always a hope and it will and they're going to upgrade it in hopes that they can improve the sensitivity by a factor of a hundred and with luck they will in fact be a detection of the gravity of a classical gravitational wave that will be a big event but the question I'm asking is what about an apparatus of that kind could it actually detect a graviton and the answer is no so that's my first piece of evidence that in principle that kind of an apparatus would be incapable even if it were as sensitive as it's possible to be and even if the universe were totally quiet with no background of incidental noise it would still not be possible to detect a single graviton so that's quite a strong statement that's evidence in favor of an observability of gravitons the third subject is another kind of detection that is a detector consisting of a single atom that's the analog of Einstein's photoelectric effect Einstein invented the photon by considering what happens when an electromagnetic wave knocks an electron out of an atom so you can ask the same question about gravitational wave suppose a gravitational wave hits an atom also can knock out an electron I can knock out and proton or a neutron what that also could be observed so that's another kind of graviton detector and the answer there is maybe you can't prove that that doesn't work but it there's fairly strong evidence that it doesn't work and the fourth subject I will discuss is another way of detecting gravitons which is based on the coherent conversion of photons into gravitons which is an interesting process invented by a Russian called gets and felt Jetson Stein so here's the reference to get and Stein on the board 1962 so it was an old paper wave resonance of light and gravitational waves so what gets from Stein showed is that in classical gravitation electromagnetic theory there is this process of conversion of gravitons into photons or photons into gravitons which you can calculate which gives you a method of detecting gravitons if this actually happens it's rather like the oscillation of neutrinos which was recently discovered that there are three different kinds of neutrinos and they also can convert into each other by the same kind of coherent process so it happens whenever you have a linear field or rather two linear fields which satisfy a bilinear coupling equation so they each they can convert coherently one into the other so that's another way of possibly detecting gravitons so I'll also discuss that so they're all together for different arguments and in the end the question remains open well let me get down then to us through some of the details so I guess the first equation is number 10 this is the ball Rosenfelt argument so what bar and Rosenfelt were talking about is the uncertainty relation for observations of electric and magnetic fields showing that they had to be consistent with quantum electrodynamics so Delta X Delta X is the uncertainty of a measurement of electric field in some space-time region 1 and Delta e x2 is the uncertainty in the measurement in another space-time region 2 and those 2 does this this Heisenberg uncertainty relationship which says the product of the uncertainties of the two measurements is at least as great as this quantity on the right which is a purely classical quantity and a 1 2 is the electric field averaged over region 1 induced by a classical dipole in region 2 and a 2 1 is the other way round it's the classical dipole in region 2 induced by a dipole in region 1 so you take those two classical dipoles subtract them and that gives you the uncertainty in the measurement so that was the result of the Bohr Rosenfelt argument which was this very sort of a verification that quantum electrodynamics had to be true if the classical apparatus who used for the measurement obeys the rules of quantum mechanics well how about it what happens when you apply that to gravitation it all looks the mathematics looks so much the same you have a similar sort of an equation you can write down with the uncertainty of measurement of gravitational fields with classical gravitational dipoles and or quadruples in this case and so it looks as though it should be the same but look at Bohr's argument if you look carefully you find there's one place where it's very tricky the argument in fact requires a particular physical device which is the compensation of the induced currents and charges that Bohr is imagining you have these classical charges and currents which is the measuring apparatus and so they move in response to the electric field that you're measuring but of course when those two classical charges move they in fact induce then further fields which you cannot control those other fields you're trying to measure and that messes up your measurement and in order to make the measurement as precise as possible Bohr imagines that those induced charges and currents are compensated so you have another set of charges and currents exactly opposite to the ones you are using for the measurement which compensate these fields that you're trying to measure which enables the measurement then to be as precise as it should be so that compensation requires that you input you have this other piece of apparatus which carries charges and currents precisely opposite to the ones you're using for the measurement well that you cannot do with gravitation in the case of gravitation you're using masses you have to use masses to to induce the gravitational forces that you're trying to measure but there's no such thing as a negative mass so this kind of a compensation cannot be done so that just for that reason the ball Rosenfeld argument fails that's the that's the end of chapter one that's the so the ball Rosenfeld argument simply doesn't apply to gravitation so it may be true the quantum gravity has the right commutation rule so it may not but you can't prove it as ball did the Maxwell equations well now the second subject is the LIGO and here I can actually prove a theorem that's the only really strong statement I can make it is actually a theorem that a detector of the design of a LIGO that's two mirrors measuring the gravitational wave as it comes by cannot in fact work for a single graviton so here is the argument it's search it's based on equations I'm sorry to say but anyhow so if you look at the energy density of a gravitational field this is the equation one which if you have a gravitational field in which Omega is the frequency and F is the fractional change in the metric that's the fractional change in distance that's measured in consequence of the distortion of space by the gravitational field so F is a pure number it's just the fractional expansion or gravitational expansion or contraction of the space measured then energy density of the wave is given by this formula with the square of velocity of light C and the Newton's constant G and the remarkable thing there is this square of the speed of light which comes in which is an enormous factor so it says that a very very small distortion of the space produces a large energy density so the exchange ratio between the observed distortion and the energy it takes is very large second equation is for a single graviton to take a graviton which is frequency Omega it will have a certain energy density which K you can calculate it carries the the end the energy of a graviton is just H Omega by according to Planck and the volume if it has a wavelength which is C over Omega so the cube of the wavelength is roughly the volume of them the minimum volume that the graviton could occupy so the energy of a graviton is at most this quantity e sub s so then if you put those two things together and you say 1 is equal to 2 then you're talking about the energy density of a single graviton or the distortion of space corresponding to a single graviton it's this quantity F in equation 3 and the quantity which comes in there is the Planck length L sub F is the Planck length which is because there again if this large velocity of light the Planck length is a very very small number 1.4 times 10 to minus 33 centimeters so that is in fact then the standard distortion produced by a single graviton it's the fact that that's so small which makes graviton is hard to observe so you see the the logic is very simple so if you wanted to disturb a single graviton we would have to measure the separation between these two mirrors with an accuracy which is equal to Delta which is just proportional to the lengthen nothing else well now comes in quantum mechanics for the apparatus that if you add the apparatus is just a mirror which has a mass Capital m so you look at equation six that's the consequence of just of quantum mechanics that if you have a mass Capital m and it has an uncertainty in position and it also has an uncertainty in velocity as a concert if you try to hold it still for a length of time T it will wobble around it will have quantum fluctuations which are of order Delta and that's the equation for the quantum fluctuations of the mirror so M Delta squared is at least Planck's constant times the time that's the best you can do for determining the position of a mirror over a time T and the time T is at least the time it takes just for the light to go from one mirror to the other which is equal East the wavelength of the graviton you're trying to observe so if you put those equations together it's a five and seven I guess just just the definition of Delta the the precision you have to reach and the quantum mechanics it the answer comes out that the distance between the mirrors has to be less than GM's over C squared so Planck's constant had disappeared you have in just an equation or inequality for the separation of the mirrors the mirrors has to be close together depending only on their mass to make the measurement possible and if you look at what that tells you this quantity on the right GM over C squared is just the Schwarzschild radius corresponding to the mass of the mirror so it's in fact it's the radius of the black hole of that mass equal to the mass of the mirror so the mirrors are that close to each other it means that each is attracted to the other with an irresistible force and they're both collapse into a black hole so that's what nature does to prevent you making the experiment nature forbids the experiment by this very crude mechanism of fall so you are forced forced to make the mirrors so heavy to make the quantum fluctuation small that they collapse into a black hole so in the end so it turns out that the you can actually so prove mathematically that the apparatus is not going to work this this argument so far assumes the mirrors are just suspended in space as free objects in fact that's the best you can do the alternative would be to have them supported by some kind of elastic framework but then it has to have a finite sound speed in the in the mechanical framework and then if you take a mechanical support you get equations of the same kind with the sound speed replacing the light speed so that actually makes things even worse so if you have a mechanical structure supporting the mirrors in fact you get an even stronger inequality GM over C squared is greater than ratio of light to sound velocity at times to separation so that's even worse so that the conclusion is still true so you can prove that there is no possible gravitational wave detector of that kind which will detect single gravitons well let's go on then to the a more hopeful kind of gravitational wave detector which is the single atom that's just as the gravity electric effect gravity electric effect now we're looking at a single atom gravitational wave comes in any another particle either an electron or a neutron or anything else is kicked out well you can calculate them by quantum mechanics the rate at which this will happen so here is the calculation so you're looking at a quadrupole wave the gravitational wave is a quadrupole so the matrix element for this is equation 11 is the matrix element for transition transition of the electron from state a to state B sub psy a is the wave function of the initial state sy B is the wave function of the final state and x and y are they just two coordinates of the electron at right angles to each other so that's a particular quadrupole with polarization at 45 degrees to the XY axis it doesn't matter you could take the other polarization it would give the same result then the cross section for the kicking out the electron is given by equation 12 which is the standard formula from quantum mechanics for a quadrupole radiation process so you have a lot of numbers in front G is the coupling constant of gravitation which comes out of the new of the Einstein equation again Omega is the wavelength C is velocity of light D is this matrix element and then you have a delta function for energy conservation since the graviton energy H Omega is equal to the difference between the two state energies so that's the cross-section well that's of course a complicated thing to calculate doesn't look very promising but you can make some very I can make a very strong argument by writing down an exact sum rule or some rule in quantum mechanics is a wonderful device for getting simple consequences from complicated equations you just sum over all the frequencies and everything comes out very simple so this soak this quantity s of a is the logarithmic average of the cross-section averaged over energy but with the / o D Omega over Omega so it's averaged over the logarithm of the energy so it's the logarithmic average of the cross-section and that you can calculate very beautifully from this formula if you integrate over Omega and the Delta function disappears and you get just an products of matrix elements which become matrix products and in fact you get a double commutator of this quadrupole with the Hamiltonian and so everything becomes simple and in the result is s of a the logarithmic average cross-section turns out to be just this quantity 14 that's an exact sum rule it's a very very simple but powerful equation and this this capital Q is then a property only of the initial state sum over the final States has disappeared that just gives you a matrix product so you get just the expectation in the initial state of this differential quantity and the amazing thing is that all the constants have disappeared that the the mass has disappeared the potential has disappeared so the charge of the nucleus has disappeared it it no longer depends on anything except just the shape of the wavefunction and nothing else so this Q is a pure number and if you take the simple case where you're talking about a spherical wave function that's just an ordinary bound state of an electron in an atom which you'd expect to be the one which would react most strongly to gravitation that then everything becomes a absurdly simple and you can then prove just by simple algebra that this capital Q this coefficient here is at least three-quarters so it's a number of the order of one which is at least three-quarters and if you take the simple model for the wave function which is a typical of a strongly bound particle like a ground state of an atom or a ground state of a nucleus so Arthur minus n where n is some positive power times an exponential that's a typical wave function for a bound particle then q is 1 minus n over 6 so it's very close to 1 so that this is Q in fact isn't just a number which is improper for ordinary atoms and nuclei close to 1 and the final result of this whole discussion is then that the logarithmic average of the cross-section equation 14 is just equal to the Planck length squared and that's all it is well the Planck length squared is a very very small area of the order of 10 to minus 65 square meters so there's nothing you can do to change that it doesn't matter what kind of an atom you're using or whether you're talking about nuclear forces or electromagnetic electromagnetic forces the best you can is a cross-section 10 to minus 65 square meters so if you consider 4 to be you I can't any longer prove a theorem I can't say this measurement fails for reasons so the fundamental physical reasons I've said it fails just for practical reasons that if you're looking at the so anything that's even conceivably practical to had a gravitational source well let me just talk about gravitational thermal generators that's an interesting by a an interesting subject in itself and I won't spend long on it that was worked out by Stephen Weinberg a long time ago how much gravitational radiation is actually being produced in the Sun this the Sun is a wonderful source of gravitational gravitons with observable energy that the if you take a collision in the now in the in the car of the Sun where the average energy of the particles is of the order of ten kilovolts or so then so you have electrons and protons colliding together all the time very hard they will be generating gravitons and that's about the best source of gravitons that you can imagine it's producing huge numbers of gravitons all the time and they all get out they all escape from the Sun because the Sun is transparent to its own gravitons so in fact that's by far the best source of gravitons you can imagine for the so that turns out to be seventy-nine megawatts for the Sun it's of course it's a large amount of energy by human standards but very small by afternoon comical standards and so it turns out four times 10 to the minus four gravity times per centimeter squared per second if you multiply that by the cross-section it and imagine the whole earth is used as your gravitational wave detector then during the entire lifetime of the Sun you should on the average detect four gravitons so it's just barely possible anyhow that's not very encouraging you can imagine better sources in the Sun you could imagine moving around the universe looking for better sources of gravitas so there are things like hot neutron stars which are much more actively radiating than the Sun they have very much higher average thermal energy so they radiate maybe ten to the ten times more stronger than the Sun but they don't live so long the total amount of energy in the form of gravitons is not all that much greater the amount available is roughly the same whether it's the Sun or a neutron star don't in the case of the neutron star it comes out faster but you don't gain all that much and of course you can imagine a detector which is bigger than the earth maybe closer to the source so in principle maybe you could do somewhat better but not very much and so that the most you get perhaps ten to the ten gravitons could be detected during the lifetime of this off and then there comes the argument about backgrounds that any source of gravitons of that magnitude producing gravitons of the kilovolt range also produces neutrinos and the neutrino background turns out to be enormously large of the the gravitational flux the neutrinos have of course enormously stronger interaction than gravitons by something like twenty powers of ten and so they emitted in much more copiously and also the detection probabilities for neutrinos are also much larger so you get something like thirty powers of ten favouring neutrinos against gravitons so any any conceivable graviton detector looking for thermal gravitons has to deal with this overwhelming background of neutrinos so they're from a practical point of view that seems to make the thing pretty hopeless but it's not the same it's not so satisfactory a conclusion as you had for the LIGO well the final set of detectors which I'll talk about very briefly are the coherent detectors that's non thermal detectors which are then the thing that gets you guessed gets in stein proposed first forty years ago that comes from this process of coherent conversion of gravitons into photons so here are the equations governing that this is the coupling this first equation twenty four is just a coupling of the gravitational field amplitude which is h IJ which is the Einstein tensor multiplied by the electromagnetic energy tensor so capital T IJ is the electromagnetic energy tensor that is then a combination of a classical magnetic field capital B and the quantum magnetic fields little B and so you get a mixing of classical and quantum magnetic fields so the interaction finally gives you a bilinear term Linnea in gravitation and also linear in photon field multiplied by the classical background field so now you imagine your detector consists of a long long long magnet with a strong classical magnetic field and you put in photons at one end and outcome gravitons at the other end or vice-versa and the beauty of that is since the process is coherent the probability of conversion goes as the square of the length so the the final the probability of conversion is actually this equation 29 says probability conversion is B squared the square of the magnetic field times d squared which is the length of your magnet divided by this fourth power of this velocity of light it's always the velocity of light which kills you so the probabilities are amazingly small and again this is a purely classical effect Planck's constant has disappeared it's a classical mixing of gravity with photons and the conversion length capital L is 10 to the 25 centimeters which is as the order of kiloparsec in astronomical units 10 to the 25 centimeters divided by the magnetic field in gauss so it means for any conceivable magnet the probabilities are very small but still again it looks as though in principle it might perhaps be feasible but then there comes a fatal flaw into this argument to that nonlinear electrodynamic it turns out that the Maxwell field after all is not linear and this was in fact of discovery of Euler and Heisenberg already in 1936 is one of the most beautiful things that Heisenberg did when he was still a scientist and they worked and he and his student Euler worked out the theory of the polarization of the vacuum produced by pair creation that is electrons and positrons popping up and down in the vacuum produced this fourth order term in the Maxwell equations so the Maxwell equations are inherently nonlinear when you allow the Maxwell field to interact with electrons and positrons so this is the non-oil heisenberg non-linear electrodynamics which tells you that in fact the speed of light in a classical magnetic field is less than it would be in a vacuum this and so this final equation 35 it's the amount that the speed of light is reduced in a magnetic field so B is the classical of magnetic field HC is the critical field which is 5 times 13 gal 10 to the 13 Gauss which is actually about what you get astronomically in a pulsar pulse is a magnetized neutron star which typically have fields which are just about equal to the critical field so this in a pulsar these numbers can be quite large the maxwell field really becomes strongly nonlinear and that tells you then this coherent conversion doesn't work that if you have graviton and a photon going at different speeds they're not going to be coherent with one another so the coherent conversion simply fails and so that's that happens then to be true in a neutron star and also if you imagine a detector in which your magnetic field is more of a reasonable terrestrial magnetic field of the order of 10 Tesla or something of the kind that was used by the way the people at Sen actually used this as a device for detecting accion's there was a experiment done it's and looking for the coherent did coherent conversion of photons into accion's actually on being a hypothetical particle with mass zero which might exist and be detectable in this way and so they did the experiment also got a null result because they were not looking for gravitons but if you if you took an experiment of that kind with a unreasonably long magnets of the order of say a hundred million kilometres or something of that kind still it turns out that the coherent conversion doesn't work the non-linearity of the Maxwell equation is enough to defeat you so it seems this this this kind of detector also doesn't seem to work anyway I leave the subject there I don't want to get drowned in details but so the the final conclusion is that the promised possibilities remain open that quantum gravity may be in fact correct as everybody all the experts believe or it may be correct but with confinement so that gravitons are always confined not visible or it may be that gravitons don't exist so we can't yet just decide that but I think it's an interesting subject and certainly the possibility of pushing these arguments very much further thank you

Channel: World Scientific

Views: 36,130

Rating: 4.9655914 out of 5

Keywords: graviton, Freeman Dyson (Author), Physics (Idea), General Relativity (Idea), Einstein equation, Gravitational Field (Idea)

Id: l-FSFtoeagc

Length: 48min 13sec (2893 seconds)

Published: Fri Jan 10 2014

Reddit Comments

[u/[deleted]]

I think I'm surprised to rediscover he's still alive every time I look him up for some reason. Nice he was able to hang around long enough to see GW but I don't think any of us will be alive to see the detection of the graviton.

[u/Invariant_apple]

I am absolutely baffled that this guy can give a physics lecture at 90. He looks great for being 90 too, good for him.