 Our special bioliterate of 20th Aston Olympiad OCSC, today we have with us Professor H.S. Mani, for those who already don't know his name, I will give a more detailed introduction later in the second half of the function, but I will just say right now that he has been a physics teacher to many of our senior colleagues, he was in IIT Kanpur for many years and then he went to various other institutes, presently in Chennai Mahal Institute, more about him I will talk in the second half, right now I will give Dias to Professor Mani. Thank you Aniket and good morning to everybody, it's very nice to be here, I feel it probably to be able to attend to such a talented set of people, now what I plan to talk about gravitational waves which I am sure all of you have heard it was very sensational news of this century and so let me start by discussing Einstein, can you people hear me or is this working or had proposed general theory of relativity for theory of gravitation and this was done almost 100 years ago and one of the basic concepts in general theory of gravitation is the principle of equivalence and the principle of equivalence in a simple way is as following statement. Supposing there is a uniform gravitational field, there is no experiment that can distinguish a uniform gravitational field from a uniformly accelerated frame, that is we have gravity here, if I assume the gravity is uniform and if you are in a lift which is freely falling, whatever experiment you do there, if I analyze it, it will be the same as coming from gravity for my frame, so this is the statement, but on the other hand there is no uniform gravity, gravity here is pointing radially down and similarly New York it is pointing radially down, so I have to match all of them properly in terms of various different frames, that is not easy, that requires a certain kind of mathematics which ultimately leads the space to become curved, that treatment has to be like the surface of a sphere. So, let me just go over the slide saying all this, so here it is theory, one of the basic concepts is the principle of equivalence stated simply it says that there is no experiment which can distinguish between uniform gravitational field and an accelerated frame. The concept of equivalence when extended over a large region, over a region where gravity is not uniform, leads to treating space and time as curve like it the surface of a two-dimensional sphere, Einstein wrote the equation for gravity based on curve space and it is different from the Maxwell's equations, all of you are familiar with Maxwell's equation, we study them Gauss's theorem, Biosawart's law with extension of displacement current and Faraday's law and so on, so they are the Maxwell's equations but they are different, but there are also some similarities, charges produce electric and magnetic field when charges move, similarly masses produce gravitational field, this is one similarity, however Maxwell's equations are linear, if I have two charges and if I write down the field I will get the addition of the electric field in a linear way, these follow from the Maxwell's equations whereas the Einstein's equations, Einstein's equation is nonlinear, however there is a way, gravity is not a very strong force, it is a weak force, so one can make a linear approximation, the effects of gravity can be written in orders of the coupling constant, the Newtonian coupling constant and the limit of the linear approximation, there are more similarities between electromagnetism and gravitation, they look very similar in many ways, one such property is gravitation, there are gravitation values like electromagnetic fields, when we have charges moving in for example in an antenna, when in a radio station there are charges moving in the current and they produce magnetic field, electromagnetism, similarly if I have masses which are moving and they will produce a gravitation, so that similarity comes in the linear approximation that one makes, both traveled with the velocity of light, we will denote the velocity of light by c, the standard practice, after an effort lasting over 5 decades gravitational waves were first observed on 14 of September 2015 and it has been labeled as 15 for the year, 09 for the month and 14 for the day and this is the standard method by which gravitational detection has been, soon after one more was discovered on 26 December 2015, four more were observed in 2017, the last one due to a merger of two neutron stars at a distance of about 100 million light years away, the others are all billion light years away 10 times more than these distances, so this is the nearest ones which were observed and they were observed not because of black hole merger, but because of neutron star and electromagnetic signal was also observed with the last one, because it was nearer, the electromagnetic signal was observed simultaneously in 70 observatories in 7 different countries, this opens up a two different methods of observing a celestial object on a gravitational wave, the other the electromagnetic wave, there is also possibility of observing neutrinos, but still that is a long way off, so how are the waves detected, when a gravitational wave passes it changes the distance between two points, the changes in distances are extremely small, they produce changes in an interference pattern in an interferometer, let us see this, see if I have a laser source and a light beam is coming here and there is a beam splitter, beam splitter splits the beam in one in that direction in one direction and the beam comes back and it goes to the detector and this one comes here and comes to the detector, here we have a interference pattern coming because this path link and this path link may not be the same, you firstly adjust them such that these two path links differ by lambda by 2, then in that case you will have a dark fringe, on the other hand if a gravitational wave passes this distance will change as well as this distance will change not in the same way because the wave could pass in this direction in which case some changes may take place here that will depend upon the nature of the wave, so you will see the interference pattern here will no longer be dark, but there will be a change in the pattern as the wave passes, so this is how it is detected, we will use our understanding of electromagnetism to learn about gravitational wave. Now let me refresh your memory on gravity, this thing these are properties of electromagnetic waves, consider the plane electromagnetic wave of wave length lambda travelling along the z axis, the electric field is given by the real part of I write it in terms of the complex numbers more convenient in many ways and here is the electric field E 0 is the magnitude and this is the wave part the part where k is 2 pi by lambda omega is the angular frequency is c times k, we are all familiar with this. Now E 0 is normal to the direction of propagation remember in the previous slide I had it propagated along the z axis, so E 0 will lie in the x y plane, the magnetic field B is normal to both the direction of propagation k and the electric field and it has the same phase as the electric field, when the electric field is maximum the magnetic field is also maximum and when the electric field is 0 the magnetic field is 0, so wave propagation looks something like this, if I have E in this direction and B in that direction E cross B is in that direction, so it moves like this on the other hand this thing comes here, when E is 0 B is 0 and when E becomes negative B becomes negative, so this is how the wave moves, that is the picture of an electromagnetic wave which you people should have. Now the magnitude of B is E by c is here, this is also comes you people must have studied this I am sure, how are electromagnetic waves formed, I have already mentioned about charges moving around an antenna, but I will make it little bit more specific, consider localized source in some around the origin in some small region of space, if it radiates if this radiates energy which travels to infinity, consider a large sphere of radius r around that localized object. The energy density we all know is given by epsilon naught by 2 E square plus 1 by 2 mu naught B square, so the energy flow per unit area is the energy density times c, because if I take a unit area in one unit time all the things at a distance c will pass through that and here the total energy flow across the surface will be 4 pi r square C E. Now if electromagnetic radiation is taking place this must be finite, notice normally that would mean E must the energy density must go as 1 by r square, let me go back to the previous slide, no it is not here we all know E for a coulomb potential goes as 1 by r square, so this would normally go as 1 by r 4, but that will not do, we need E to go as this energy density to go as 1 by r square, so E must go as 1 by r, similarly B must go as 1 by r, this is necessary for the electromagnetic wave to travel. Now consider a spherical distribution of charge rho r t around the r t, this spherical means I have not written a vector there it is only the distance here is a spherical distribution, now if this oscillates then the electric field at any point will be radial, if the electric field is radial we know that there cannot be any propagation of electromagnetic field in that direction, because for an electromagnetic wave E has to be normal to the direction of propagation, so I cannot have a radial propagation given a spherical distribution and just it oscillating back and forth, so I must have some angular asymmetry for it to be able to radiate, which can be taken the way simplest way to do it is take a point charge and let it move up and down along an axis. Now I am making it oscillate along the z axis, now the wave will not travel along the z axis, now the wave will generally travel in some direction, when the now I will draw a picture here to indicate what can happen, here is my charge when it is here at a point here the electric field will be in that direction, which has some normal component, it is no longer completely radial, because the charge has moved from this point, there is also one more effect and that is more subtle and you may not have been studied that and that is the following, I am looking at the electric field here at time t, that electric field is does not come from a charge located at time t, it comes from a time earlier than time t and if it if I call it t prime, it is t minus t prime equal to r by c, the signal which left here must reach here and the velocity of that signal is given by c and that is called the retard at time, if this is at time t and that occurs at time t prime, which is equal to t minus, if I call this vector r prime and if I call this r, that is t minus r prime and then if you use the Maxwell's equation, you will indeed find the electric field has not only a component in this direction, that one goes as 1 by r, that is a reasonably otherwise, if I just think in terms of Coulomb field, it would have been just going as 1 by r square and there would have been no 1 by r term and that comes from the retard at time and calculating it from there, it is a little tricky calculation and it is done usually at the MSC level, but we will just assume that now, so the proper dipole moment of a charge distribution is given by p 0 cos omega t, p 0 is equal to q a, a is the amplitude. Now, I will assume the electric field produced is of the following form, p 0 by r omega to the power alpha, c to the power beta, m cap is a direction perpendicular to the radial direction and cosine k r minus omega t, remember my expression for the dipole oscillates as p 0 cos omega t. Now, m dot r is 0, we can now calculate an alpha and beta purely from dimensional analysis, I will not do the calculation here, it is very straight forward and when you do that, you get alpha equal to minus beta is equal to 2 giving the following expression for the electric field. It has this dependence, I am not worried about the theta, I am only worried about the r, this is some factor which can be calculated exactly in electrodynamics and this is the charge omega squared c squared by r squared, you can check that the dimensions are correct, it is very simple. This is q by r squared, this is q by r squared, this is p 0 a and this has omega by c, essentially I get a lambda omega by c, so I get lambda squared, so this becomes length cube, I have one length hiding in my dipole moment and that length cancels and I get my thing and of course, I have the 4 pi epsilon 0 which always flows around and v is given by e and has the right property for the electromagnetic. So now, I can calculate the power radiate per unit time, I already know the formula for the energy density, it was epsilon 0 e squared by 2 plus 2 mu 0 by b squared and it is straight forward just plug it in and ultimately you get just this result, it is not the algebra absolutely straight forward, I notice why do I get a c cube that also is clear, see I have a c squared when I multiply e squared it becomes c fourth, but I have to multiply by c to get the power which is per unit time and therefore, I get a c and everything else follows. I have also done one more thing, I have averaged over the time that cos squared theta factor has given half and I also have the angular integration done for the exact waves, what are the lessons we have learned from electromagnetic wave, we are almost through with the electromagnetic wave, radial isotropic oscillations do not produce it, the time dependent dipole can produce radiation. So, this is the lesson that we have learned from electromagnetic wave alright, for gravitational waves again we need just like charges moving, we need very massive objects which can give rise to time varying gravitational field, black holes going around each other is a very good candidate, people have analyzed several possibilities this is the best candidate. However, the dipole associated with massive objects like the previous case in a frame in which the centre of mass is 0 is address is 0, I will just show this in the next slide therefore, we have to go to the next one that time dependent quadrupole moment produces gravitational waves. So, this is where the difference of using an antenna and versus the situation in gravitational occurs. Now, let us give the proof which is very good, consider two large masses m 1 located at r 1 and m 2 located r 2 going around each other. So, this is the problem which you people must have solved n number of times from class 9 and here the centre of mass is m 1 r 1 vector plus m 2 r 2 vector by m 1 plus m 2. But this notice is the dipole definition for mass, remember what is the electric dipole definition, if there are two charges q 1 and q 2 at r 1 and r 2 you would write down q 1 r 1 plus q 2 r 2 is the expression that you would have written down. Here you are writing it as m 1 r 1 because q 1 is being replaced by the charge m 1 r 1 and similarly q 2 is being replaced by the charge m 2, but this is nothing but the centre of mass. So, if the centre of mass has to move there must be some other external force which must be there, but when I am thinking in terms of black holes going around each other there is or no other external forces. So, this is at rest or at uniform motion. So, in any inertial frame this is at rest therefore, there will be no dipole moment coming from dipole moment radiation coming from the gradation there is no none like that. So, now I have to go to the centre of mass does not accelerate I have already stated. Now, let me go to quadrupole moment actually you people are familiar with quadrupole moment in terms of moment of inertia. When I write moment of inertia it is m x squared or m y squared and that is now no longer with x dipole moment was with some q times x here it is squared. So, it is a quadrupole moment quadrupole moment is given in terms of 4 numbers if we restrict our motion to 2 dimensions say the x y plane. So, I have here q x x is m 1 x 1 squared plus m 2 x 2 squared and q y y is similarly with y here of this is a misprint and here q x y is x 1 y 1 plus x 2 y 2 which is the same as q y x. So, all these 4 numbers are there and when they are going around each other x 1 will go as a 1 cos omega t and y 1 will go as a sin omega t and x 2 will go as a 2 cos omega t y 2 will go as a 2 sin omega t and they are just going around each other. Remember the quadrupole moment is square of this. So, I will get cos squared omega t that would mean that if the body is going around like that my quadrupole moment will have cos squared which essentially gives me cos 2 omega. So, the frequency with which we will see things will be of 2 omega not omega is the physical rotation of the black hole, but the gravitational wave produced will have a angular frequency of 2 omega. Again we use dimensional analysis remembering that the gravitational field must be inversely proportional to the distance further the charge is replaced by the Newtonian constant. Here it is I write down the instead of the electric field now I am writing here g and now I am writing quadrupole moment and r omega cube by c cube this all these factors come purely from dimensional analysis. Look at it what is g? G is g m by r squared let me just verify it for you. G small g is g m by r squared and on this on the right hand side I have g and m q 0 is m times some length square divided by 1 by t cube for omega cube I have c cube l cube by t cube l cube and I have an r. So, t cube t cube cancels I have r is l 4 and so that cancels and everything like this. So, this is dimensionally correct and notice now it is 2 omega is how the gravitational field is alpha the numerical factor there I have not written can be calculated correctly in the general theory of relativity and that turns out to be 32. Now, two black holes going around each other this is a mathematics you people are very familiar with just take the gravitational attraction of each other and they go around I am using circular orbit. So, life is absolutely simple there is no calculation which you people will not do very fast and here omega square is given by this formula I will write down and the total energy which you all know is the gravitational energy plus the kinetic energy. So, I will keep the two formula here because that is something which I will keep using several times and I do not want to go back to those times. As the two bodies emit gravitational radiation its energy will decrease. So, energy decrease means it will become more negative if it becomes more negative omega has to increase that is the only way in which that can leading to an increase in omega and of course, the relative distance between the two will decrease because omega increases relative distance decrease. They spiral towards each other and merge into one and as they merge the frequency will go up. Now, we can calculate remember now the strategy is very clear I have already calculated the amount of gravitational energy emitted I know what the total energy of the two black hole system is I know what will be I have to calculate only d e d t of this and once I calculate d e I will equate it to the power loss and then everything just follows there is nothing more than mathematics as the two bodies this is done. So, we can evaluate d e d t I just differentiate this expression here omega to the power of two thirds become omega to the power of minus one third and d omega d t is the other term and this factor m 1 m 2 by 2 this remains here and 2 by 3 when I differentiate 2 we go away and I have left it 1 by 2. So, it is very straight forward expression now this is what the astrophysicist do define something called m chirp which is m 1 m 2 divided by m 1 which is because this keeps occurring in the expression several times and they define it to have the dimensions of mass and the observed frequency f. Now, notice this is f is the not the angular frequency the physical frequency 2 pi f is equal to 2 omega or omega is equal to f by pi. Now, I can also calculate the quadrupole moment for two body system I can just write down m 1 r 1 squared plus m 2 r 2 squared and substitute and you will get this this is the quadrupole moment of the two body system m 1 and m 2. So, I can substitute that here m chirp is equal to because I have I have the expression p I will also write that down perhaps I should have written that here it is I will also copy that now oh there is also one more point I have to explain how I got this g which I somehow skip let me just go over that it is a notice here it is for the energy in gravitational field we use the analogy of electromagnetic epsilon 0 e square. Note g occurs in the numerator for the gravitational field whereas epsilon 0 occurs in the denominator. So, instead of writing epsilon 0 here for the gravitational field I will write down my g below that is where this g comes from once I write this g this omega to the 6 and c to the 5 are just fixed from dimensional. So, this is the extra analogy that I use from electromagnetic and ultimately I have written down the answer. Now, all I do is I differentiate this d e d t equate it to that value. So, after equating it I come out with this form. Now, this is very easy to integrate I just take my d t on that side d f by f by f. So, this will just become 8 by 3 and some factors here and that is what I do in the next step. So, I write it down integrating it from 2 times t 1 to t 1 plus tau and that is the expression as tau increases this goes on increasing and so this must denominator must increase that is only way in which this difference can increase this fix t 1 is fixed. So, the denominator must go on increasing and it must go to really large values and this continues till the 2 body merge 2 bodies merge. Now, I am ready to do some numerical evaluation. So, this is the experiment of the very first gravitational wave observed in the 2 observatories one hand for the other links in both in United States. The thing to concentrate there are 2 or 3 points this is how the gravitational wave changes here or there. Notice as it starts coming very close after this this is noise this was noise. So, this is where the gravitational wave exists and the frequency goes on decrease increase it is the time this is the time scale the frequency goes on increasing exactly what was seen and notice the identical things. And here in this last one here the frequency here is small and as it goes on increasing it seems to go towards infinity around a time 0.43 and that is the signal and at say 0.35 is when it starts and it goes on up to point at 0.43 it is going to that is this. So, I will assume notice here at 0.43 the frequency is around 40 or so whereas that is around 200 and more than 250. So, I will just assume the other one is small and I write down f this is very large. So, I just get the form the written down here substitute that. Now, we know f this is 0.42 hertz and it diverges as 0.3. So, tau is 0.8 0.086 this gives a chirp mass of 35 with alpha equal to 32. So, this is how one determines the mass of that and by the way 35 times the solar mass. Now here m total is m chirp divided by psi where I have write psi as the fraction of the total mass for m 1 and 1 minus psi for that. So, given this formula notice this one can be 0 when psi is 0 or 1 or it has takes a maximum value of r. So, that gives a lower bound for the total mass as something like 18 of the solar mass. Now, we evaluate the strain this what is the order of magnitude of the strain. I have the gravitational wave at r 0 which we have already seen and it is given by this formula with a unit vector. So, d due to the quadrupole moment omega cubed is the frequency r 0 is the distance. Now, we already know the q has the following thing I can rewrite q in this form and plug it in to the previous expression for q and that would give g is nothing but d square x by d t square and I substitute that and get this one. This is the acceleration that will be produced on any mass due to cause of the gravitational wave. As we know this g is just the acceleration due to the gravity due to the gravitational wave. In this expression I have an eta which is given there. Now, I can integrate this and when I integrate this notice it is there is a cos 2 omega. So, when I integrate I will get 2 omega in the denominator. So, that is what I have written down. This is the velocity of the mass of the mirror of the gravitational wave. Now, what is going to happen is when light in the interferometer is to going to go and come back it will take a time 2 l by c or l by c and in that time what is the distance this moves is the question. So, one of the mirror with respect to the other way to move because the delta x for the 2 will not be the same they will be different. The gravitational wave wave links are much larger than the length of the interferometer. So, I write down delta l by l is delta x by t times the time that it takes and I substitute all this and get this number. So, this is the relation between strain and various quantities m total we have already more or less made an estimate omega is the frequency which can be seen from there and r 0. Now, the question is how do you locate r 0 and write substituting numbers relative strain and the distance of the source. If the distance of the black holes is 1 billion light here the strain works out to be 10 to the 2. So, how does one estimate an idea of the distances before p. Then the universe was formed at that time still it was all a big fluid there were no black holes or anything and as it expanded it took some time for the matter to settle down and become galaxies and stars and so on. And ultimately became black holes and other kind of content system galaxies and in particular stars. Now, the furthest away are the ones which will have the largest volume 4 pi r squared is a surface area. So, the number of black holes that we will see will depend upon how far are the black holes formed because black hole merger the probability of that will be high if the number of such black holes are there. So, it is a mixture of the two black you should give time for black holes to form and yet it should not be too near us because the number of such black holes that you will see in a given volume our surface will be only 4 pi r squared will be small. So, given that you can estimate and by the time black holes were formed that is the best time for us to hope for the signals to come and that is we know the life of the universe is 10 billion years old and so it must be of the order of billion years for this to be formed and that gives us the factor of n to the minus 2. In fact the experiment of course observes the screen and they know what the value is let me go back to that slide here it is these are all strains at 10 to the minus 21 level and so given the strain they can find out what the distance of the black holes are. Now, I will discuss to a brief discussion of the noise how can one be sure of such a small measurement most measurement most important the observations have been carried in two different places for the detection and free for the subsequent ones. Therefore, if there was a noise in one of the observatories it is not necessary the noise will be at the same time of the same kind. So, if you use appropriate filters you will be able to reduce a noise enormously that is one, but still one must minimize noise and accidental coincidences I will list some of the noise seismic noise they are usually of low frequency and of the order of 100 hertz. The removal of cycle the this noise is an engineering field, but the physics of it is actually what you people are already familiar with and let me say that. Supposing I have a mass is or let me say a platform which by the way this is how seismic things are recorded I hang it I hang a mass with a spring and if the spring is very hard it means it is has a very it is a rigid one if this moves a distance x that will also move a distance x that is not what I want I do not want this to move when this is moving. So, when this this thing is moving if the spring is soft if this will move very much less and you can do the algebra the answer is it is if the frequency of the outside one is omega and the frequency of your spring is capital omega then it will come out to be capital omega y small omega squared. So, what these people have done have put four such suspensions for the mirror. So, if this is going and the at each level the changes of the order of 10 to the minus 4. So, by the time they go down it is 10 to the minus 16 and they prevent this from coming here to one part into the power of minus 5 and so that is how they reach the level of 10 to the minus 21 that is the expression that is there ok. The next thing is that you cannot have the distance of the mirror is 4 kilometers if you send a light beam and come you cannot have that as air because if there is a small fluctuation here refractive index will change. So, there will be change in 5 and you have to handle that and that is handled by keeping it in vacuum and the vacuum you can calculate this and find out and that is the kind of vacuum level. Quantum noise this is actually for many of us the most interesting noise and this gives what is called the standard quantum. Now, we all have studied Heisenberg principle that is if I try to find a position of an object then the momentum appropriate momentum changes given by the Heisenberg delta x delta p of the order of h bar. Now, here when I have two mirrors when I am doing an interference experiment I am really check finding out the positions of these and using light and the light beam when it hits is going to cause a radiation pressure there is momentum in light light is kicking the mirror. So, the mirror will move back and forth and you have to worry about that and secondly the light beam which gives me light the number of photons which reach also fluctuate because it is not as if you get the same number of photons all the time such a noise is called short noise by the experts. So, you have to handle what is called the radiation pressure noise and the short noise and they have different properties and one can do that by using certain other very interesting properties of quantum optics comes what are called squeezed lights and the thing what is done and I will not be able to discuss that in any detail is absolutely a marvel and this is the actual state of the apparatus that I have. Here is the laser beam going and here is the 4 kilometer the reason it is kept as the light beam is made to go several times here and here for reasons again to reduce the detecting signals. What you do is you also send in here through the other port what is called a squeezed state and that successfully removes many of the quantum effects associated with it and the mathematics of it involves quantum field theory of quantum electrodynamics which is a very fascinating. Ultimately this is the way it has been tackled all one knows when one reads about it unfortunately I have never had a chance to be at the places where these work goes on one just is completely astounded by the physics and the engineering field that these people have done over the last 50 60 years. Remember 10 years earlier if anybody had been working many of us would have advised them saying you are wasting your time and now the thing is in the central state. Thank you. Thank you Professor Mani we can take few questions. Actually I had one interesting story I do not know how true it is first when the first decision was done that time it was said that they looked at all possible noises including possible lightning strikes in different places. Is that also important? No it turned out that it worked out well because of the fact queens were different places where they actually calculated the chance of this and I forget the number it is something like their sigma level was something like 27 or something of confidence I do not remember the numbers but it was answered. Other questions? What material do you use for detecting this? Material. There is a these mirrors are made of a certain kind of glass which requires 90 I forget again almost 100% reflectivity and it should have no it should be very strong it should not bend because of the weight and so on but are you asking for the quality of the mirror the nature of the mirror? I mean you said you are I did not fully understand that you are trying to detect some waves and but there has to be some material whose movement you are trying to detect. No there are massive the mirrors you remember I showed the Michelson interferometer. The mirrors because the gravity wave comes the mirror distance changes to use the detector. When that happens the light beam travels a different distance. So your mirror is serving as a detector in a way. Yes the entire thing of course is serving as a detector when I meant by detector I just meant the detecting the photon this whole thing is the detector. Next question. Sir I did not understand like you said like if we want to detect the. It is a wave which is at the it is a wave of what is called the metric and the metric is what decides the distance between two of them just like you have an electric field which is passing there is the disturbance of the metric and that is what causes the change. The gravitational wave consists of a metric which travels through and that metric essentially changes the distance between. No electromagnetic waves will change the electric fields. Yes. No please say that again. Yes no that depends upon the kind of power they need and the kind of distances that is the purely take it will not if I use shorter wavelength it does not mean that things will be better. I think that the events which cause actually cause gravitational waves that we can detect are very rare. So if the gravitational wave like the curvature is coming at an angle to these two. Pardon. Like if it is coming at say 45 degrees so it will cause the same contraction expansion. So it does not become very difficult to detect them if they come at an angle. That is why right now they have done it in only two different places. If you see it in a third place you will be able to locate exactly where that is coming from. No. All the three places are separately aligned. Of course they are aligned in their own ways. No. But then. He is worried that if it comes at 45 degree angle. Right. Then it will change the distance between the mirrors in the same way in the two arms. Yes. But it is correct. But then the one in Livingston supposing this happens is actually on the curved right. It is on the surface of the earth. It will see a different angle. So those things have not yet been really come. Right now only signals of a certain nature have been analyzed. So the kind of disturbance is the next thing which people would like to study in detail. That just like in electromagnetic wave there is a polarization of the electric field. Whether you have electric field along this direction or that direction there are again you have to write down the polarization of the disturbance. Okay. And that has been done. It has been classified completely. And it is more complicated than the case of the electromagnetic. Gravitational waves can also be polarized. Yes. They are polarized in different ways. In what? Actually because gravitation I did not want to discuss that because they are described by a tensor. So there are different notion. Like vector is all I need is one direction to talk about. Here a tensor needs two directions. So how one would be just elongating like that. Another one will be elongating in one direction different from elongating in another direction and so on. So these properties can be analyzed once more gravitational waves are detected. Yeah. Good. The LIGO had been built in order to detect gravitational waves. Right. So now that gravitational waves have been detected already. So what is the next step that is being climbed? The next step is just what he had asked about what are the properties of these gravitational waves. In particular one of the very interesting questions which people are asking is that where gravitational disturbances must have taken place at the birth of the universe when huge bang happened what kind of signals will that need to. And we still have no such answers are known and such signals are observed we may have much better understanding of what happened before what is called the era of inflation. That is something which is a very topic. Yeah. Is the change in length detected independent of the masses of the mirrors? Yes. Yes. They are independent. Okay. So probably that means that I mean the detection of the wave I mean if you move out in space say a few light years away or several light years away you would detect the same wave. No. It will be one over our effect will be there right. The black holes were not at 1 billion but 3 billion my answer will be the strain will be one third because my gravitational field will be one third. As long as the distance is the same it is the direction. Right. It will be the same. Yes. On passing of the gravitational waves one of the arms is supposed to change in length while the other has to change less. Yes. Right. So won't the wavelength of the light that is going also change proportionally so that like it won't matter. No. It does not. No. Wavelength change is not there. That's the point. In gravitational waves one can show that. Yes. I had just written out that we talk about decoupling of light from matter. Pardon. We talk about decoupling of light from matter. Right. So can gravitational waves from before that time can also be observed theoretically? No. I didn't understand. What is asking is for our optical instrumenting like that, CMDR acts as a opaque barrier. Yes. So can we see gravitational waves from time before CMDR? Yes. Of course. Because gravitational waves don't have gone face that barrier. If you have a lot of ionized matter, electromagnetic wave cannot travel through that because it will excite atoms and so on and it is the mean free path is less but not for gravitational wave. It's a very weak one. Okay. So, if you have no more questions, it's time speaker. Okay. This is one point. Stop the speaker. Sir, to find the interference, to find that interference pattern, we first need to know the wavelength, right? Yeah. The wavelength of that light is 1064. You know the wavelength of the gravitational wave, we'll have some different. Pardon? But the gravitational wave which is coming, how do we know its properties like it is coming from a very large distance? Correct. So, how do we know how to set up the distance? We don't know how to set it up because we don't know where the black holes are going to merge in the universe. So, we set it up in some general directions and keep doing it. There is no set pattern. Yes. Sir, do these waves face some sort of effect of expansion of universe because we're considering waves coming from? No. No. This is really due to some very massive two particles coming to the very near each other. The expansion of the universe is a different story. I meant the red shift of gravitational waves. No. No. This is, that's a separate story. That's not the gravitational wave talking about. Here, you're talking about the red shift of the Hubble constant which is there. No. This is two things which are just merging with each other. In a very short time, the time as you saw was almost 0.1 second. No. The question is, would the gravitational wave be affected during the propagation? No. The whole thing is lasting 0.1 second. No. But that is when it is created. But it's since it has come from such a large distance, would that affect the? No. By the way, Z for this is known for these black holes. It's something like 0.1. Okay. But that's where it is and that's where the merger took place and because of the merger there was a ripple this time and that ripple is what you have seen here. We do need to consider the Z factor. No. We need don't have Z factor is only another information. By the way, you cannot measure Z directly. To measure Z you need optical signal. So there is no optical signal here. No. So I calculate the Z factor by noting my R0. R0 is a billion light years. So I know what that Z factor is. No. It's that for light I mean even though let's say in the same merger let's say some light signal is emitted. That light will suffer some cosmological redshift. Correct. When it comes here there's a gravitational wave emitted also suffer some kind of cosmological redshift. That's the question. Okay. Even if it does in the propagation. But that doesn't bother me as far as signals go. It's originally there was one and there was some change in the gravitational G mu nu that as a function of time and that's what I measure and that function of time is for 0.1 second. Whatever I'm measuring is something now a 0.1 second. See that. Which might have had a different wave that doesn't bother me. Yes. How do you like from the gravitational waves how do you distinguish from between the events that happened or even if it came before C and how do you differentiate between them? That is still an active part of research where the strength of these things for black neutron star is much smaller than for black hole black hole. So the one which was observed was workout to be is thought to be a neutron star neutron star and the experts in that agree. I do not know the details. So in EM waves we have two fields E and B so in gravitational is one field is gravitational what is the other? No that is the point. They have just not been named there is supposing there is a gravitational wave going in this direction. There is a tensor which has 10 components. If I look at electromagnetic field it has 6 components 3 for so they have been named only as G 0 0 G 0 1 and things like that. Nobody has named them as different kinds that is all. Pratish We could have named them E 1 E 2 E 3 E 6 or something like that. In fact we do that when we do we call them F 0 1 F 0 2 and so on. Is there a condition on the speed of the gravitational waves? Because the speed limit of light it exists only for particles which move but gravitational wave it is so No. When you write the equation it works out because it has to become consistent with Newton's gravity and also special theory related. You have to satisfy both. So it works out that it travels to the velocity of light. There is just one speed. So let us all thank the speaker and then now we have a T break at 1130 for the second half of the function but before you go for T let us all just go outside outside the building in the lawn for a group photograph and then we will have a T break. Thank you.