 Good afternoon. As Professor Patak introduced, my name is Shiv Prasad and we will be going through some of the lectures on relativity and quantum mechanics through me. When I start teaching I have lot of issues and which makes my life difficult. How to, first of all, you know, I do not know how to teach my own colleagues, you know, who are supposed to be all, we are all supposed to be in the same boat. So, I thought, you know, my talks will be probably more of my own personal experiences, what I have used as a teacher myself. And probably just to tell you this is the way I do things, okay, maybe you will feel that, you know, there is something, some value with my own experience and my gray hair that, you know, can probably, you know, sort of work together about that thing. So, second issue was, you know, something, you know, we are given a course content which is normally in IIT we will cover for one year, two semester course and was told to us that you should finish it in five days, okay, even though we have sort of four lectures per day, I think this is a very, very difficult task to cover almost everything, the way I would like to cover for my own undergraduate students. So, you know, we had to make some choice which is not probably the best choice. And the way I decided to do these lectures, I mean, I will tell you the philosophy with which I started was to give a little bit more idea of the concepts rather than going to the mathematics, because the concepts are something which is, you know, which comes more with experience. Well, mathematics, etc., are all given in the book, you know, so you can always look into the book and find out the mathematics. Though in my transparencies, I have covered the mathematics which probably I run through very fast. And so, these transparencies will be made available to you. So, if you really want to go through those mathematics, then you can probably work them out. And of course, I am always available for any discussion or any questions. So, you can always ask questions. Of course, needless to say that, you know, you are always, you must always ask questions. I think, personally, I would feel that nothing motivates me more than the questions, because that's what, you know, at least makes you feel that people are not sleeping, people are, you know, sort of, you know, aware of things. So, that I'm, this is something which is actually very, very important. So, as I was telling that, you know, I will probably run through the mathematics which I will not go too much in detail. In a normal course, I would have liked to put a large number of examples in these things, you know, whatever I'm covering to explain my things. And I think examples are always very, very important to make the point that I want to make through theory. But unfortunately, I do not have time to do examples. In the December course, when we have little more time, at that time I will try to do more examples. I would just like to say that almost all the content which I am going to cover in these things are available. And if you are interested, okay, for example, the lectures on relativity, as Professor Ghosh had told in the morning, I have a 24 lecture course on special theory of relativity, which is done by NPTEL, which is also available on YouTube. So, if you want details, they are given in much more detail, they are given in a much more slower pace, because this was meant for a student who has just passed out 12th standard and would like to learn about special theory of relativity. It goes extremely slow pace. So, if some of you are interested in learning more about that, if on YouTube you just search my name, Shiv Prasad in relativity, you will get a series of 24 lectures. And then, you know, you can sort of go through that. About quantum mechanics there and also crystallography, solid state physics, my lectures which I have been giving to IT students have been recorded by CDP. I am pretty sure that so long you are in IT, you can always access to them. Outside, if you want to take them, okay, probably you have to buy them, which is not very expensive. I think they charge only the cost of CDP. It is not for making money, it is only institute, you know. So, those things can always be bought by your organization if you are interested. So, they will just charge the cost of the CD and the packing of the thing and they can send the videos to you. So, in case you are interested. So, I think the details can be obtained from some of the organizers here. So, almost everything which is, which I am telling in a much more slower form or which I am actually conducting for students are available. So, for any details you can always ask them. Of course, I am always available here. And of course, this is my email ID. So, in case you have a question, you can always email to me whenever you want. And normally I try to reply to every mail, but it does happen that sometimes I slip, especially if I am traveling. Then if you don't see my reply, don't mind asking again. So, that's what I would like to say. Now, what I have learned through my lectures here is that when you want to start a, let's say, undergraduate class, like first year BTEC and normally these things are covered in the first course in the physics which when the students just join IITs. I have always found out that people come with varied background and it's always better to launch your course at a time, at a place where people are very comfortable with. I always say that teaching is something like, you know, almost fitting like a jigsaw puzzle. So, you have seen all those puzzles and you have their various type of things, you know, various shaped small pieces and you have to fix them to make the complete image. So, it's a sort of a jigsaw puzzle that students have certain information and then you want to fit your information into those jigsaw puzzles. If you start at a, launch your course at a level which is somewhat higher than what the students are fairly familiar with, then it generally does not stay with them. Whatever actually fits into their existing knowledge, that's something which stays with them, that has been my experience. So, normally I always like to start at a level at which the students are fairly comfortable. Especially teaching, special theory of relativity, which is generally believed to be fairly tough subject, this is what I have always felt that I always start with one of the most basic things. Now, this is my plan of the whatever I'm going to cover in special theory of relativity. We have only two lectures. First of all, I would like to identify issues with the classical physics. I think this is the most important aspect. If I just start with Lawrence transformation, I don't think it gels well with the first year students, okay? First I must tell what is wrong. So, that people should get convinced that, you know, and I mean I always find it very, very interesting that special theory of relativity 2005, 1905 was discovered. We are more than 110 years and especially, I mean in first year when I teach, the first thing is always the shock. The students feel that it's not possible. Is not there any other way of tackling the problem? How it could? So, that's the impact of the special theory of relativity. You know, even it surprises people today. When people know that special theory of relativity has been established, still people get a shock when we tell about the implications of those special theory of relativity. So, first of all, I want to like to tell what are the issues with the classical physics, then how SDR, we generally call special theory of relativity is generally acronymed as SDR. How SDR helped in solving those problems. Then give a flavor of the new definitions. I will not be able to go into the details of four vectors, etcetera, where we'll tell how we don't derive it, but how do we come across these definitions, okay? So, I will not be able to go through, but I'll just give you the new definition. And as I said, I'll focus on the concept and not on mass. That's what's my idea. And again, I repeat, questions are always most welcome. Now, let's switch ourselves back to late 19th century, when physics was getting developed. And at that time, there are some famous statements made by some very well-known scientist who said that almost everything of physics has been understood. And there's hardly anything which is to be discovered. And at that time, the physics consists of these things, I will give many things, but three things which are especially matters to us as far as this course is concerned. One is what's called electromagnet theory. Electromagnet theory was well-established, okay? Maxwell's equations were pretty well known, okay? Concept that light consists of electromagnetic waves was well-established. So, all those concepts, when I'm coming to the end of the 19th century, these were sort of established concepts. Then what was established concept was Newtonian mechanics. Newton, as you know, was fairly old. So, Newton's laws of motion were known. And other things which are based on Newton's laws of motion, like conservation of mechanical energy, et cetera, all those things were fairly well known. And the third thing which is fairly well known is classical statistics. In fact, that was the time when almost everything people used to work out on the basis of kinetic theory of gases, which used Maxwell's Boltzmann distribution, or Maxwellian distribution of velocities, Maxwellian Boltzmann distribution of energy, which is basically, if you are giving a certain energy to a system of particles, how this particular energy is going to be used by the people, what is the probability of a particular particle having a given type of energy. So, these were essentially the concepts which were existing at that particular time. Now, let us look at what are the problems with those concepts, where everything, all right? So, this is what I called clouds. They were two clouds, two major clouds. Though everyone seemed, I mean, many people felt that everything in physics has been understood, but there were two clouds which were still unclear, which eventually led to what we now call as modern physics. And if you call me that what is the birth year of modern physics, I will probably say 1900, which was the Planck's hypothesis, about which we will discuss from third lecture onwards. But let me just first define the two clouds. The first cloud is the motion of earth in ether, about which I will be describing quite a bit of detail today, the motion of earth in ether. This is the first cloud. Now, let us come to the second cloud, which we will describe from my third lecture onwards, which was the failure of Maxwell Boltzmann Doctrine regarding Equipartition Law of Energy. These are very strong statements. Doctrine is something like a religious preaching. You give a doctrine, everything, you do this particular thing, everything, all problems will be solved. So, essentially Equipartition Law of Energy, which was based on Maxwell Boltzmann distribution, was being used as a doctrine. You have any problem in physics, apply Equipartition of Law, Law of Energy and you will get the answer. That is the way things were being worked out at that particular time. I will give you some examples little later in the course. So, it was found that this law does not seem to be working everywhere, especially the most important place where it did not work was the concept of black body radiation, about which I am pretty sure all of you would have known that, you know, that is what led to Planck's hypothesis and that is what I would always call was the birth of modern physics. So, let us now look at these two clouds, especially the first cloud. So, let me go to the first cloud. Before I go to the first cloud, let us define certain things. As I said that I always like to launch thing from which people are very familiar with. So, please excuse me, many of these concepts you must be very familiar. The first concept which I would like to always start with is concept of a frame of reference and especially inertial frame of reference. Now, generally whenever you describe any mechanics, you have to be very clear where is your observer law. So, one of the most common problem which the students have is they confuse with the frame of reference. They will take one observation from one frame of reference and try to couple with another observation which has been taken from a different frame of reference. So, first thing that we always teach in mechanics to the students, be sure what is your frame of reference. It means where your observer is sitting. Now, as far as that particular observer is concerned, things have to be consistent only in that particular observer's frame. If you go to a different frame of reference, things have to be consistent in that observer's frame of reference. And especially if you are doing special theory of relativity, this confusion of frame of reference can really cause havoc. In fact, one statement which I also make often to the students that once you do special theory of relativity, you realize how poorly you understood classical mechanics. Because in classical mechanics, in spite of that, people tend to confuse ideas, ok. But special theory of relativity, this will not work. You have to be very, very clear which frame of reference where your observer is sitting. Never to get the ideas mixed up. Now, as we generally know that there are two type of frame of reference, one which you call as inertial frame of reference, another which you call as non-inertial frame of reference. And if you take any book, people always say that inertial frame of references are those in which Newton's laws of motions are obeyed. And non-inertial frame of reference also they can be made to obey, but then you have to give rise to some pseudo forces which do not arise from the physical phenomenon and things like blah, blah, blah. I like to go with a slightly different definition which I generally find generally more useful, more conceptually, I'm not saying correct, but it's probably a little more conceptual. See, generally in classical mechanics, that's what Newton's had law of motion, that when any force which arises on a body, it must arise as an interaction of any other body. So, if there is a force which is being, if it is a real force, if this particular body is experiencing a force, okay, it must have been caused by some other body, whatever might be the body. A model might be the type of force, it could be just gravitational force, it could be forces between two charges, whatever it is. So, if there is a force on this body which is a real force, there must be some other body which must be causing that force and on that body which is causing that force, there has to be equal and opposite force, that's what is Newton's third law of motion, all right. What is another thing which is important is that in classical mechanics, if you remove the distance between these two bodies which are interacting and causing force on each other, this force will always decay, it will come down. See, you know, typically inverse square law forces, gravitational forces goes down as 1 upon r square, leptostatic force goes down as 1 upon r square. So, if you remove the distance between the two charges, the force will come down, which essentially means that if I can imagine that there is a body which is really isolated, which is far off from any other real body, okay. I can assume that the force on that particular body must be 0, because it is so far away from any other body that there is no body which can apply a real force on this particular body, okay. And then in a frame of reference in which this particular body is found to move with a constant velocity, I will define as an inertial frame of reference. So, this is the definition which I always like to give, that isolated object move with constant velocity, I think. You understood the idea of isolated objects, because we are so far off from any other real body that chance that any body will experience a force on this particular thing is essentially 0. So, therefore, this body must move with a constant velocity. If it happens in a frame of reference, then that frame of reference I will call as an inertial frame of reference. Now, when I am calling special theory of relativity, the word special means that in this we are dealing only with inertial frame of reference. So, though I may be using words many times frame of reference, but unless specifically mentioned, it always means that I am talking only of inertial frames of references. So, there is general theory of relativity where Einstein tried to take into account also the sort of accelerating frame of reference in a different manner, but that is a totally somewhat different concepts. But in special theory of relativity, all the frame of references that I am dealing with are all inertial. And also it goes by definition, if there is one particular frame of reference which is inertial and there is another frame of reference which is inertial, the relative velocity between these two has to be constant. It cannot vary with time, because this is also inertial, another is also inertial. So, they may be moving relative to each other, but then that velocity must be constant as a function of time. Now, I make certain statements, which I will prove it, which is not very difficult to prove it. Probably you already know again these statements. The velocity is a frame dependent quantity. If I go from one inertial frame to another inertial frame of reference, the object velocity can be different. Okay. So, if I am sitting on earth, okay, observing moon, okay, this velocity might be different. But if I am sitting on sun, the same velocity of the same object may be different. So, velocity is supposed to be frame dependent. If I move from one inertial frame to another inertial frame, the velocity could be different. However, acceleration would be same. All right. So, this is very simple to prove. Let me just give this particular diagram. I will go rather hurriedly, okay. So, let us suppose there is a point, there is an object which is a point object here. And there are two frames of reference. One I am calling a red frame of references, which is given by x, y, z. Another I am calling as a blue set of frame of references, which are given by x prime, y prime, z prime, okay. Now, the origin of this is here is o prime. The origin of this is o here. So, the position vector of this is RT, because this I am calling as un-prime frame of reference. This I am calling as a prime frame of reference. So, from the origin, if I draw this particular vector, this is r prime t. Now, by simple vector addition, RT must be equal to RT plus r prime t. So, this is what I have written as the equation. You differentiate it once. Once you differentiate, you will get Vt is equal to V0 plus V prime t. The particle could be accelerating. What I am talking is instantaneous velocities. So, instantaneous velocities will add. So, it means the velocity that is being seen an un-prime frame of reference will be different from the velocity seen in the prime frame of reference, which we know, okay. Because to this, there will be vector addition of the relative velocity between the frames. We differentiate it once more. We realize that V0 has to be constant, because both are inertial frame of reference. So, that derivative will become 0. So, I will get a is equal to a prime, which tells you that the acceleration of the two frames, acceleration of the particle in the two frames is going to be same, okay. Now, I know that Newton's law of motion talks of acceleration, not of velocity. It talks of force and big point. Here we are using t is equal to c prime, that is the same. I am talking of classical mechanics. I have not come to the relative t. I have not come to the relative t yet, okay. So, you are going a little ahead, which is expected. But you know, the thing is that in this particular thing, I am doing only classical mechanics. I am only talking about the problems about the classical mechanics, okay. In classical mechanics, t is always same as t prime, okay. There is no relativity as far as the time is concerned, until we come to special theory of relativity. So, this particular concept, in fact, all those things will fall down once we come to special theory of relativity, okay. So, at this moment, I am talking of purely classical thing, which was before the special theory of relativity came, all right. Now, in classical mechanics, you expect that forces may be frame independent. If frame forces are frame independent and accelerations are same, then it means Newton's law of motion will be valid in all inertial frames of reference. That is what we always believed in the classical mechanics, that Newton's law shall be valid in all inertial frames provided the force is same in all frames. In fact, under the special theory of relativity, this statement will not be correct. So, I am saying that let us not go to the theory of relativity at this moment. Imagine that we are just doing straight way classical mechanics. We are just come out of our high schools and that is what we have been taught, all right. Now, what is the problem? This looks perfectly fine that, you know, Newton's law of motion is valid in all the frames of reference. But what are the issues? So, let us look at the issues. Are we familiar with some forces which depend on the velocity? Remember velocity is a frame dependent quantity, all right. Acceleration is not. Are we aware of some forces? Yes. Okay, let me just read this thing from Newton's law of velocity. From Newton's law, velocity can be evaluated any frame provided we know the initial conditions. So, thing is that you have a famous Lorentz force which depends on the velocity of the particle. Just now we have said that velocity is a frame dependent quantity. If velocity is a frame dependent quantity, then force would be also, if there is a Lorentz force on a particular charge, the force will depend on the frames. And if force depends on the frames, do we mean to say that acceleration f is equal to ma is not valid on all the frames? This is one of the problem. Second problem which probably I am not sure that you are aware of this particular expression. It is a very well known expression, electromagnetic theory gives. Problem Professor Hose also will cover it that once Maxwellian idea of basically to say that light actually consists of electromagnetic wave and the speed that he calculated turned out to be exactly equal to the experimental speed of light. People started believing which people still believe that light is an electromagnetic wave. Okay, if light is an electromagnetic wave, the speed of this particular thing is given in terms of what we call fundamental constants epsilon not and mu not. See epsilon not is a constant which determines the force between two charge carriers. Mu not is a fundamental constant which determines forces between two current carrying currents or magnetic forces or whatever you want to call it. Okay, the speed of light is given by fundamental constant. Okay, epsilon not and mu not are supposed to be fundamental constants determining the basic forces. Okay, let us look at, let us illustrate the problem, a very well known example. Let us suppose there is a person standing here on the ground. Let us assume that ground is inertial. For all of our discussions it is simpler to imagine things if we assume that ground is inertial. Though we know that strictly speaking not in an inertial frame of reference, but let us assume it. Okay, and according to this person there are two trains, train A and train B. One is going towards right with a velocity v and another train B which is moving towards the left with a velocity u. All right? Both these velocities are measured according to observer sitting or standing on the ground. Now you would all agree that if there is a observer sitting on A, this particular person would actually measure a velocity which is v plus u. Of course, they are both in the same direction so it is just numerical addition. There need not be any vector sign. Similarly, in this particular case if the observer was sitting here, this particular person will notice a speed which is the difference between, if it is here then it will be u minus v. Okay? So very clearly depends on where your observer is standing. If observer is here, he measures two different speeds of these particular three particles. If the observer comes here, in this case he would find that this particular velocity would be different. If the observer is sitting here, it will find the velocity to be different. A very, very common phenomenon which we see if he is sitting on a railway track, on a train, a train passes by A's. Okay? If it passes in opposite direction, we feel it has passed very fast. If it is just trying to overtake us, we feel that is extremely slow. It is a very well known rate of velocity. Almost everyone has experience in the life. Okay? Now let us try to do the same experiment with light. So let us suppose you have same thing other than this compartment v has been replaced by a source of light which is emitting light. Now I carry off forward the same argument. According to observer here, this velocity is u and this velocity c. Whatever it is c. Okay? Now if an observer was sitting here, using the same expression, he would measure the velocity u plus c. Exactly like the example which you have given before. Okay? Something is coming towards me. I am going towards it. So it will appear to be coming very fast to me. So he will find the speed here to be c plus u. Here he will find c minus u if my observer was sitting here. Agreed? Exactly the same example which I have given here. Okay? It is being translated here. You find the velocities to be different. It means the speed of light that this person has measured which was c will be different in comparison to an observer which was standing here which will measure c plus u. In comparison to this, there will be different speed of light which will be c minus u. So all three observers will note three different velocities of light. If that is so, then what happens to this expression c is equal to one upon under root epsilon naught mu naught. We just now agreed that epsilon naught mu naught are fundamental constants. If c is different in different frames of reference, remember all frames are inertial. Okay? As far as Newton's law of motion is concerned, it was equally valid in both these frames, all these frames. All right? But now there is a different velocity of light which is measured in different frames of reference because we have just now said velocity is a frame dependent quantity. Now what are the possibilities? Just one minute. What are the possibilities that may be this expression is correct not in every frame of reference or epsilon naught mu naught themselves have become frame dependent. It means they are no longer fundamental constants but they are frame dependent quantities. Yes. Sir, if we see the speed of sound that you also can be expressed in some constants. Elasticity constant. So these constants also are constant given temperature is constant and other things are constant. So but we cannot conclude the same thing for the speed of sound. See the speed of sound always requires a medium to travel. Yes. Okay. So whenever you are talking of all those things, you are talking, you know, that expression assumes that this particular light, this particular, see when you are talking of sound, okay, you are pressing something, a medium is pressing. So you are talking of elastic constants in respect to that medium. Okay? In that particular thing is clear. Now, whether the same concept can be applied here or not, that's what I'm trying to sort of. No, I'm just trying to make the point that when this expression was derived by Maxwell, he assumed that even light also requires a medium. That's what I'm coming to that. See, that's what is the basic thing which is being objected to it. Okay. That's precisely what I'm trying to say because there you assume that there's some medium. I'm coming to that particular thing. If you wait for two minutes, I'm basically coming to that particular issue, what you are trying to say. Okay. So is this point clear? My, my fallacy, my difficulty that just now I said that everything of classical mechanics was correct. C will be frame dependent. Fc happens to be frame dependent quantity, then epsilon naught and mu naught should be frame dependent. If this expression is correct. If they become frame dependent, let's suppose your epsilon naught becomes frame dependent, it means the charges between the two, I mean, force between the two charges also become frame dependent. Then what happens to my f is equal to ma? I'm coming to a contradiction. I started with assuming that f is equal to ma is valid in all the frame of reference. Now certainly I have landed into a contradiction. Say that no, see if this is happening, then epsilon naught and mu naught also becomes frame dependent quantity and therefore forces also become frame dependent. So this is what I've written. Is the speed of light frame dependent? If yes, is the following expression also valid in all the inertial frames. Which means fundamental constants epsilon naught and mu naught are also frame dependent. It means basic electron magnetic force also become frame dependent. This is what is the philosophy and this is what the difficulty. The other possibility we say that okay, mechanics says that all inertial frames are equivalent. But in general this may not be correct. This expression that I have just now written may be valid only in one of these special inertial frames. It may not be valid in all inertial frames, but there may be one special inertial frame of reference. Only in that particular frame of reference this expression might be correct. In other inertial frame of reference, this may not be correct. It means you are coming into a slightly different argument in comparison to mechanics. In Newton's mechanics, all frames are equivalent. Here we say no. As far as electromagnetic theory is concerned, no. There is a special frame of reference. Only in that particular frame of reference, this particular expression is correct. In other frame of reference, this expression need not be correct. This is what I have written. Or is it that the following expression is valid only in some specific frames? Are there two types of inertial frames? One in which our expression is valid. Another in which this expression is not valid. It means we are not saying all inertial frames are same. There are some special frames. This implies all inertial frames though equivalent from mechanical point of view are not equivalent from electromagnetic point of view. That is what it will imply. A special inertial frame may then exist, which I can call it absolute rest. That is what we will be thinking is absolute rest. Now, these are basically your two choices. One choice is that you allow fundamental constants to become frame dependent. Or choice number two, you allow a special inertial frame. Now, if you have to pick one of these two choices, what will be normal tendency for picking up? Ideally speaking, we will not be happy with any of them. That is what eventually Einstein argued. Ideally, I would not be happy with any of those situations. But if I am forced to choose one, I will likely to choose one which is a lesser evil, which is not which is probably better of the two, which is the second one. Assume that probably there is some inertial frame of reference which is spatial. And because of that special frame of reference, it is only in that frame of reference that you will be able to write the expression C is equal to 1 upon under root epsilon naught mu naught. In other frames of reference, this expression will not be valid. This, if you want, you can call your absolute rest. So, people thought that that particular medium is what is called ether. So, that is what people thought. All classical physicists at that time thought took the second choice. There is one special frame of reference. Also, it is rather simpler to assume this particular concept, one because of what he said because soundways always requires a medium to travel. Light does not seem to be requiring. It is coming from all other where there does not seem to be any medium. But probably there is a medium. We do not see it. We have not observed it. That might be our limitation. But there is a medium. And therefore, C probably has to be with respect to only that medium. After all, like he said, when sound we talk, we always talk of a medium. Sound travels in a medium. So, better there ought to be had to be a medium in which light should travel. We may not have observed it. So, that is what I said. Earlier ideas favored the concept of a special frame. Light also does not seem to require a medium to travel unlike other waves like sound waves. It was imagined that universe is filled with ocean of ether. Everywhere, you know, it is all like ocean. Everywhere, there is ether. And when we are talking of velocities, we can always talk with reference to ether. And light needs this medium to travel, actually light. And when we are talking of the velocities of light, we must talk relative to this particular medium. So, that was the concept which was originally existing at that particular time. It is implications. All planets, star, galaxies float in ether. There is ether filling everywhere. And whenever a galaxy moves or whatever it is, it is all with respect to ether. It is nothing. You can never get out of this ether. Ether is everywhere. The speed of light C is given by the following expression only in ether medium. In no other medium, this particular expression would be valid. In principle, you could measure different speeds of light in different inertial frames. And you can assign its actual velocity to a given frame. It means I can ask a question, what is the speed of earth without specifying the frame of reference? I can ask you what is the speed of sun at a given time, okay, without describing the medium, assuming that every speeds have to be measured with reference to ether. See, it is unlike the mechanics, where mechanics we said velocity depends on the frame of reference. Okay, if I go to different frame of reference, velocity has to be different. Velocity has no sanctity as a sort of a somewhat a fundamental quantity. It is a frame dependent quantity. There is nothing, if I am saying that velocity of this particular thing is 60 kilometers or karyat 60 kilometers, this is with respect to earth. Okay, if we are sitting in moon, the velocity will be different, all right. Now here we are seeing something different, which is slightly different from that particular thing, that this particular expression is valid only in one particular frame of reference. This is a sort of universal rest, universal frame of reference. I can ask you a question, what is the speed of earth without specifying the medium, assuming that it has to be with respect to ether. In other frames, the speed of light would be different from C. One can determine the speed of the frame by measuring the light velocity. If I measure the light velocity and you find this, let us say, whatever you get from this equation, plus V naught, then you know that this particular frame of reference is actually moving V naught relative to ether, all right. So, that is how the concept of ether was well established. And that is what was my cloud number one to understand the motion of earth in this ether medium. This particular ether medium, which was evolved using that particular concept that light requires a medium, should require a medium. And in that particular medium, the velocity must be given relative to fundamental constants. Ether can be thought of signifying absolute rest. Hence, we can ask the question, what is the absolute speed of sun or earth without specifying any frame? What is broader implication? This is what basically Einstein objected maximum. Though all inertial frames are supposed to be equivalent from mechanical point of view, they need not be from the electromagnetic point of view. I mean, two different branches of physics give you different contradictory results. One says all inertial frames are equivalent. Another says, no, that is not correct. But then there is always a question, is there any process which is purely mechanical when we are observing this? We do not have a purely mechanical process. If the two bodies are colliding, the light has to come there, light has to get reflected and then we have to watch it. I mean, there is everywhere there is a mixture of phenomenon which is electromagnetic theory. And that is what Einstein always objected. It does not look nice to say, it is not really good to say that different branches of physics do not talk to each other. They give you different conclusions. Is it a chance that nature has made mechanical processes equivalent in inertial frames but not in the electromagnetic processes? This is what is the basic question. Are we happy with the situation? Are we really happy? If you are a really fundamental thinker like Einstein, of course, none of us can boost to be similar to Einstein. But now probably you can think, when we have learned from this legacy, doesn't seem to be a very happy situation that if you have no other option, as I said, we take whatever is the back part of it, the lesser evil, but we are not really happy with the situation. I would have liked that situation should be better. The two branches of physics should shake hand with each other. They should agree with each other. It cannot be just by chance that in mechanics, all inertial frames are equivalent and electromagnetic theory, they do not turn out to be equivalent. So, can we look at experiments? Okay, probably all of you know that experiment, the well-known experiments, the failure of which led to totally different physics which is called Michelson-Morley experiment. So, let me just give you the brief of the Michelson-Morley experiment. I will not go into the total details of the calculations as I said, it is just the idea of giving you some feeling of overall. So, basically what is the scope of our experiment? If I have to perform an experiment, if I am an experimentalist, what I am supposed to do? If I can measure different speeds of lights in different frames, I would have agreed with the old concept of ether. If I could really perform an experiment and take two different frames of reference and I really measure, find that speeds turn out to be different, I have solved the problem. Okay, there is also another way of thought which also people do the experiment, that okay let us look after all if the earth is moving in ether medium. Okay, so if I am putting a particular charge at rest in earth medium, probably there should be some magnetic force because V cross B, then V should be relative to ether. That is what people thought. Okay, and if this V is related to the earth, to the ether, and if I am sitting on earth, okay, even if I am stationary on earth, okay, earth is moving relative to ether. So there should be some magnetic force. People even try to do that. There are many series of experiments, but the most famous experiment is this Michelson-Modell experiment. And if you can confirm somehow that there is a really ether frame of reference in which this particular speed is given by this thing, then I have essentially solved the problem. As all of you know that this experiment was a failure. So let us look at the way I just want to give the concepts of the experiment. Let us assume one object O which is moving with the velocity V. All the velocities that I am talking now are with respect to ether medium. Let us assume that ether exists. Everything floats in the earth, ether medium. This particular object is moving with a speed V relative to ether. And this particular light here moves with the velocity C and this C, the magnitude of this must be given by under root 1 upon epsilon naught may not, because I am assuming that this particular light is moving in ether's medium. So all these speeds have been given in ether medium. Now if I am sitting on this particular object, what I would be measuring as the speed of light will be the vector difference between C and V. So let us call Vm as that particular velocity which is being measured by an object by a person sitting in that particular object and that will be given by Vm. So if this is C and this is V which I have taken from the previous transparency, this was my C and this was my V which I have just translated to the next transparency. So if this was my C and this is my V, then actual velocity which will be measured by a person sitting in the object frame will be Vm. So I put subscript m to say that this will be the measured speed of light. Now the only thing which I want to tell that had this particular C direction would be different, had this direction of C mean different, magnitude is same because this is ether medium, then Vm would be different, both magnitude wise as well as direction wise. So this is what I am trying to say, I have just drawn two figures here. So V is same, this length of C also have kept same, but I have just changed the direction C here, C is here. So you can see this is Vm now and it is this Vm here. So Vm here is much larger than this particular Vm magnitude, even the directions are different. So all I am trying to say that if I am sitting in this particular object frame of reference and if I measure speed in different directions, I will measure different speeds, that is all I am trying to say. If whatever my expression says, if whatever I am trying to say about ether is correct, then if I am sitting on a frame of reference which is moving relative to ether, then in that particular frame of reference, if I see a light coming from this particular direction and a light coming from this particular direction, if I measure these two speeds, these two speeds in general will be different because though in ether frame of reference, this is same C, this is same C, this same V, this same V, but this Vm would be different if C direction becomes different, that is all I am trying to say. The magnitude and direction of the measured velocity would depend on the direction of velocity of light. Hence if we measure velocity of light in object frame in different directions, they will in general be different. And that is what was the Michael experiment designed for, created two different situations, two special situations, one in which light was supposed to move in the direction of V, was supposed to be measured in the direction, okay, supposed to be measured in the same direction as V and in the second case was supposed to be measured in a direction perpendicular to V. So, this is what says. Let us assume that two different situations, one in which measured velocity Vm is in the object frame is along V and another in which it is perpendicular to it. So, this is what is the situation. See remember, in this case if I am going to measure perpendicular, this is V, if I am going to measure perpendicular to this particular direction, this C actually has to move in this particular direction, then only I will be able to have a measured velocity in this particular direction, okay. Of course, here C has to be in the same direction because both are actually this is not really now vector sign is needed because all the velocities are in the same direction, okay. So, in this case, C has to be in the same direction as V, in this case, C has to make a slight angle such that Vm measured by a person sitting in object is perpendicular to the direction of V. Now, a simple, you can calculate what will be the value of velocity, which is very simple calculation, you just take Vm is equal to C minus V, just take the dot product, this is what you will get as the velocity magnitude, which will be measured if everything whatever I am saying is correct, this will be Vm perpendicular magnitude will be C square minus V. I am not going through the mathematics, if you want you can go through this, this transparency will be available to you. In a parallel situation, it will be C minus V, that is much more simpler to visualize. Yes. How much should be the magnitude of V? How much should be the magnitude of V? For what? When you are taking the difference, if the magnitude is small, then C minus V or C plus V, there will be hardly any change. That is right, you know, if you can really imagine a situation in which object velocity is much larger than C, okay, these expressions, I mean, still will be valid. So, science will become different. We have to take the sources where the object should move with comparable velocity. In this case, no, it is not necessary. See, provided you can measure the differences. See, the velocities that we are talking, of course, people know, new even at that time, the C is very large. For example, velocity of light is 3 into 10 ratio of 8. And if we are taking that object is moving 2 meter per second, 2 plus 3 into 10 ratio of 8. See, it is a different question, whether you can measure that small difference or not, that is a different question. Okay. But the expression is going to be same. See, all I am talking about, I am not talking about the expression, I am talking about the values. I am talking about the miserability. That is a different question. Okay. That is the reason, you know, Maxson Wolde, he was basically an optics person. He decides something by which you can take a very, very small amount of, I mean, I will give you the numbers. I will give you the numbers with the numbers which he used. These numbers are extremely small. Because practically, we cannot able to achieve such a high velocities. If we have to make the measurement like C plus V or C minus V, we have to take the objects which should move with very, very high velocity. That is not necessary. And only then we can able to make the comparison. That is what I am saying. That is not going to be necessary because I will give you example. Because using optics, you can measure in a very, very small shift. Yes. That is the reason he used optics. And as I said, I am going to give you the numbers. Okay. It is not going to be that large. Okay. Even if the V, I mean, is much, much, many orders are smaller than that. See, what we are thinking, you are thinking in terms of a normal mechanics experiment. See, what he uses is an optic experiment. You know, depending upon the wavelength that you are using, all you are looking is a small shift of the, you know, a small shift. And I will give you the numbers and you will realize that it is actually measurable. In fact, that is what Michael St. Bouldin did. Okay. In fact, he was very, very sure about his errors in this experiment, how accurately that person can determine the print shift. And that is what he did. I will give you the numbers. You will see. Yes. Okay. That is not. See, V is the velocity of that, I think. You see, here V is the velocity of Earth in supposed to be Ether's medium. I mean, here, in this case, because here we are going to perform this experiment in Earth's frame of reference. In order of central path, both. What about it? But it is still smaller than the velocity of light. You know, it is still many orders of magnitude smaller than velocity of light. So, what he is objecting is correct. I mean, it will not be 2 meters per second. It will be much larger than 2 meters per second in an actual situation. But nevertheless, these velocities are going to be significantly smaller than this bit of light. Whatever you say. So, his objection is very valid objection. There is nothing wrong with that objection. Only thing, we have to have a device, whether you can make, we have to have an arrangement, why we can measure that small difference. That is all. Yeah. Sir, I was just adding to your point, this micro question interferometer is very sensitive to you. Yeah, that is precisely the idea. Actually, basically, Microsoft, you know, Microsoft for Microsoft interferometer. He was basically an optics person. He knew how to measure small shifts. Okay, small. See, the two beams of light makes a small difference in their path difference. That is what is measured by print shift. That is what was the beauty of this particular experiment. Okay, so, using our idea, Michael's and model are designed and performed an experiment to test this hypothesis. And let us assume at this particular moment that the only velocity that Earth has is the orbital velocity. And we take this stentenous velocity of orbital velocity. Just assume it to be constant because we are assuming inertial frame of reference and work out the thing. Okay. So, this was basically the experiment. So, you have a source of light, monochromatic source of light. You have a half silver mirror, which allows half, approximately half the light to go pass through. And approximately half the light to be reflected. This particular branch, there is another mirror here, which is fully silvered mirror. The light gets reflected. Similarly, the light which goes here gets reflected from this particular mirror, comes here. Okay. Then through this particular mirror there again, there is a part of the light which comes from this side and part of the light which comes directly. They are coming here. And telescope, you try to see fringes. In fact, in order to see fringes, you slightly make a small angle here and small angle here. So, path difference becomes slightly dependent from where they get reflected. Therefore, you will start seeing fringes. Now, what he did, he actually assumed that let us suppose this particular direction is pointing along the direction of V and let this be along perpendicular direction to V. Just now, we have seen that the speeds in these two directions would be different. Okay. Therefore, you can calculate how much time it will take for the light to go this way and come back here. And how much time light will take to go this way and come back here. Remember, when light travels in this particular direction, it travels with a different speed than when it comes back. Because in one direction it will be C plus V, another it will be C minus V. While when it goes, it will be the same velocity, under root C square minus V square, while going as well as while coming back. Okay. If we assume that these lengths are approximately equal, L, you can calculate what will be the time difference. So, which I have done in a few more transparencies. So, this is what I have said. See, it goes with this velocity, comes back with this particular velocity. Here it goes with the velocity C minus V, comes back with the velocity C plus V. Because this is along the direction of the X motion. Now, you calculate the phase difference. You calculate the time L divided by C by plus L divided by C minus V. This is simple calculation. I will not go into the details. So, this is what is the final expression. Then you do in the parallel case. In this case, you just take, yeah, this is parallel. So, there is a C minus V and C plus V. So, in the parallel case, you make this particular thing. You get this particular answer. Then you do approximate. You will get this answer. Then you do T perpendicular. You take 2L divided by root C square minus V square, assuming we much less than C. See, this is what you will get the answer. As you see, this difference is very small. You can take the time difference. We should turn out to be L upon C, V square by C square. As he says, this is very going to be very, very small. But important thing is that to see how much is the, this will cause an additional phase difference between the two. So, what to say? See, this phase difference, see, there is already going to be some phase difference because these two mirrors are slightly inclined, okay. But there will be additional phase difference because of that. However, there is a big issue here is that how to find 0. It means we do not have exactly, you cannot match the thing. So, you know that when they are exactly same, this is where will the fringe shift will be there. So, it was very, very difficult to know whether there is actually a shift on the fringe system or not. So, what he did? He essentially rotated the system. So, when he rotated the system, so one arm which was going this way will become perpendicular, then this arm will become parallel. Then whatever is the phase difference that you calculate, actually it will become twice. And then if you are watching in the telescope, you can really see whether there is a fringe which is shifting or not. And from the shift of fringe, you can find out whether actually the velocities whatever you have calculated are same. So, this whole thing was actually put on a big stone. And you know, the whole system was there. And this whole thing was, I mean, he put it in mercury. I know you can look at some historical book like Resnick's book. Now, see the thing is that, you know, entire system including this telescope, it's sitting on a huge platform, all right. And everything is made to move rotate. And the person sitting on the telescope is observing whether my fringe is shifting or not. That's the way this particular experiment has been done. Excuse me, sir? Yeah. Sir, I have one doubt, please. I always teach students about this, my cousin model experiments. And when I am saying that when we rotate this instrument by 90 degree, then the power difference will be double twice. So, can you please explain why this is twice? Okay. See, in this particular, I have calculated the path reference. Yeah. All right? Yeah. I rotate it like this somewhere. Okay. Somewhere it will become symmetrical. Path reference will become zero. Yeah. Okay. Then I move like that. Again, I have created the same path reference. So, as I move from this particular position to this particular position, I have created twice the path difference. So, overall we are rotating by 90 degree or? No, no. We are constantly keep on rotating it. We constantly keep on rotating it, okay? Let me just try to, let's suppose these are my two branches. Now, this is the. Okay. This is, this branch is parallel to it. Yeah. This branch is perpendicular to it. Okay. I am rotating it. I have come here. This has become a symmetrical situation. But the source is. Path difference will be zero. Everything has moved. See, all I have to see, the velocity is moving relative to V in which direction. I think we have to rotate it anticlockwise. Make it clockwise or anticlockwise. It doesn't make a difference. Okay. Okay. If you do this way, you can even do this way. See, the thing is that, you are starting from a situation which was asymmetric with respect to V. Okay. Okay. Here, this is along the V. This is perpendicular to V. Okay. Now, you come to a situation like this or come like this. Okay. In that case, whatever the component of this particular makes along the V, same along this particular direction. So, what happens? In this case, the path difference will be same. So, I have created a situation like this. Okay. Now, you are moving like this. This was my original branch, which was parallel branch. This is why you have perpendicular branch. Okay. Let us suppose we wrote in a particular rotation in a particular direction. So, let us suppose we come like this. All right. My V is supposed to be in this particular direction. Okay. This is symmetrical situation with respect to this and this. Okay. So, now path difference here and here will be same. Okay. It will not be under root c square minus c square, but you can calculate the velocities. It will turn out to be same. So, path difference, whatever I had started, the delta t or delta x, whatever you want to call it, it will become zero here. Now, as I move this particular thing back to here, I will again create the same path difference, but in a different direction. All right. Because here, let us suppose the time taken was more. So, now time taken will be more in this particular branch. So, my path difference is going from that particular positive plus point to zero to minus of that particular point. So, as I have rotated through 90 degree, my path difference has become double. All right. I always keep on rotating it. Okay. I am sitting always together. All I am trying to say that as I move every time by 90 degree, my path difference is actually making double. Okay. Because you are going from one particular direction, you are looking at path differences. Yes, sir. Okay. You have one particular path difference when I am going from this situation to this situation. I come to a situation when my path difference has essentially become zero. Then again, I rotate it further. Then my path difference, again, I create the same path difference, but in a different branch. Okay. And remember, my telescope is also moving along with me as I am moving. All right. So, what I will see that my path difference, whatever was the delta x, becomes zero and become minor delta x. So, overall path difference, as I go from this particular configuration to a 90 degree configuration, has become twice delta x. Right, sir. Thank you. So, then we observe the fringes. If the mirrors M1 and M2 are slightly inclined, they would create a gradual shift, and one would observe a fringe pattern. The time difference in arrival of the waves in two arms would cause an additional phase difference, which I just now mentioned. Now, as I said, they rotated these things in order to avoid the problem of having a zero. So, you always have overall rotation. And then see whether the fringe shift is moving, because it's easy to see the motion. But to see whether they have really shifted from some zero, it's very difficult. Because for that, you should know which corresponds to the zero fringe, which is not very easy. Sir, should we mention that the extended source is extended? Otherwise, with a single ray with inclination also. Yeah. The fringe pattern will not be formed. Yeah. So, should we end? Oh, yeah, that's always there. I mean, that's always assumed that's always extended. You never have a really point source. And I don't think that. So, this is what is the fringe shift, which we calculated. And this fringe shift turns out to be having this particular value. And in the original experiment, this I have been taken from Resnick's book. In fact, if you want to read a little bit more, there is a small book of Resnick by Special Theory of Relativity, a very, very beautifully written book, especially from the historical point of view, how things were rotated, how it was done. All those things are very beautifully written there. So, you can see the L was only 11 meters. That's not a huge long distance. The wavelength which was used was typical sodium wavelength. The velocities are this 10 to the power minus 4 C, as he said. You calculate the total fringe width, it turns out to be 0.4. He was reasonably sure, Michael Sinmorely, that they could measure typically about 100th of the fringe shift. You know, very, very sure. And 0.4 was definitely above their resolution, definitely above their resolution. They measured, they never found any fringe shift. Not only that, they measured, because you're not sure whether you're really aligning yourself in the direction of V, because you're performing experiment in a different place. They measured in different seasons during a different time of day, saying that, you know, things might have different, but the result was always same. There was no fringe shift. Experiment was performed in various seasons, but never gave positive results. Various unsatisfactory reasons were also floated. In fact, famous Lorentz length contract. In fact, the transformation is known, Lorentz transformation is not known as the Einstein transformation. Okay, because many of these transformations were actually evolved by Lorentz in order to explain the negative result of the Michael Sinmorely result, which were really taken in a much better theory at a much later time. In fact, there are also attempts, which were made later. Which was basically on the use of electromagnetic theory, where people sort of, as I said, try to see if I can have a particular particle and measure magnetic force on that, because anyway, Earth is moving relative to the ether medium. So therefore, V cross B, there should be some finite value of V cross B. So using that particular thing, also people try to do, but outcome was same that there is a failure. Okay, ether does not seem to exist. As you know that Einstein was a totally unorthodox thinker. You could think in a totally different directions. He has very, very strong beliefs on his convictions. He always believed that it cannot happen that mechanics and electromagnetic theory, which is part of the same nature, can show you different results. Different branches of physics have to be consistent with respect to each other. Probably there's something wrong in our dealing with the entire subject, but nature cannot be like that. Nature cannot be partial in that sense. So here comes the two postulates of special theory of relativity. Okay, very, very bold postulates. First postulate, laws of physics are same in all inertial frames of reference. No preferred inertial frame exists. There is nothing that you can think that there is one special frame in which physics will be different from any different frame of reference. All the inertial frames better be identical. Of course, then we have problem, as we have just now discussed, with speed of light. It means that he comes, the second postulate says that speed of light C is same in all inertial frames. So long your frame is inertial, you will always measure the same speed of light. It's not very certain whether Einstein knew about Michael St. Molder experiment. In fact, as all of you know, who have been doing research, that whenever we publish a paper, we always give reference, reference number one, you know, as such and such and shown, okay. Then they have observed this particular thing. Then, you know, we are doing something more beyond this particular thing. You always refer, because you always like to place whatever you have done in perspective of what others are doing in this particular area, okay. This particular paper by Einstein, 1905, did not have a single reference. It was a totally original piece of work. Yeah. Sir, according to the first, first postulate of spiritual theory of 100, okay, which says that the laws of physics are same in all inertial frame of reference, that I don't think it says that there is no inertial frame of reference existing. It basically states that there is no need of a inertial frame of reference. Well, I think this is more of a similarity. And secondly, sir, please, secondly, the velocity of light, C is not same in all inertial frame, velocity of lights in vacuum. That is same. Yeah, please go ahead. See, yeah, I must modify and I must correct myself. Whenever I have been talking about velocity of light, it always means velocity of light in vacuum, that I must say, because this expression, C is equal to 1 upon 0 to epsilon of v0, is also the expression in vacuum. I should have been more or less correct in saying that speed of light whenever I'm saying is sort of, is always in vacuum. But I mean, sort of whenever I'm writing the expression C, we will always believe you to be in vacuum. But I agree that this is my mistake. I should have told specifically that C has to be in vacuum. But generally, when you write C is equal to 3 to 10 power 8, it's always believed to be in the medium. In a different medium, it will be different. So this particular part, I could really agree that, but let's understand that whenever I'm talking C is always in vacuum. As for the second concept, I think this is a, first question is that this is more of semantics. What, I mean, whether you want to say that there is no need or whether there is no special frame, accordingly, they mean the same thing. Okay, I don't see any difference between this level, unless you have a special way of thinking, I'm not very sure. Okay, maybe your words are better than my words. Okay, but you know, basically what it essentially means that let's understand the philosophy behind it. Okay, philosophy behind it is that, that you don't have a special frame of reference in which physics will be different. That's already very interesting. I mean, it's true that, you know, whenever you do special theory of relativity, we can always evolve a special frame of reference for our own explanation. For example, when we define things like proper length, when we define things like, you know, proper time interval, okay? We always choose a special frame of reference, okay, with respect to which we define mechanics, okay? But it does not mean that if I would have chosen a different frame of reference, things will become different, okay? So, given a situation, I may always like to take a convenient inertial frame of reference. For example, a lot of things I may define with respect to Earth, even knowing very well that Earth is strictly speaking, not an inertial frame of reference, okay? So, I may always choose a special inertial frame of reference. That's correct, okay? And that may be special with respect to my point of view because it's easier for me to describe mechanics, okay? Looking in that particular frame of reference. But all that I'm trying to say, or all the first, you know, possibilities starting to emphasize, that if I was not sitting in that frame of reference and I would have been sitting in some different frame of reference, then things would have been identical, nothing, especially I have to evolve. I can apply the same layers, same mechanics, there also, all right? Well, in the earlier thing, that was not so because if I was sitting in either frame of medium in everything, I will measure a different speed of light and I'll find the forces to be different. But if I go to a different frame of reference, things may be different. So, there, the speed of light will not be given by the fundamental constants. See, there is another way of you can say that, okay, an epsilon or not, we not see, nothing is fundamental. I mean, that's another way of looking into it, okay? See, I mean, conservation of momentum, conservation of energy is not fundamental as of physics, okay? This is another way of looking. I mean, if you want to say, become completely bold, you can say, okay, nothing of that was correct. But let me, I mean, let me say that, that of what we believe today, okay? We do believe that these laws are fundamental laws of physics, okay? Situation may change tomorrow. Science always evolve. Things can become different. What we think is today very fundamental law may not turn out to be so fundamental. As you know that many things, I mean, even standard models, etc., people have been talking, which are not very sure, depends on so much of discovery and things like that, all right? So, but as we believe today, we believe that there is no need of having any, or there is no special frame of reference in which the laws of physics are different. So, all inertial frame of reference, I could have chosen, I could have chosen any one of them, and try to describe physics in that. I will apply the same conservation law, I will apply the same force equation, I will apply the same thing. Nothing of what we believe is fundamental would change, okay? That's what I mean by that particular statement, okay? So, I mean, as I say, let's not go by the words. Words, as I said, you know, different people may write better English and better, you know, more clearer language, I agree with that thing. But let's understand the psychology and the thought behind it, that I do not have, I mean, any special frame of reference, where the laws of physics have to be applied differently. That's all I mean. So long I am in inertial frame of reference, my laws which are in my hand are exactly identical to had I been in a different frame of reference. That's all I'm trying to say. And as I said, because this particular thing seems to be contradictory with speed of light, that's what is the second hypothesis. He says that speed of light C is same in all inertial frames of reference. What it means is that there is no ether, where the universe is filled with nothing, okay? In fact, you require something real in which you have to enact your frame of reference, then only you can talk in terms of velocities. You cannot talk, okay, this velocity, there's something somewhere, okay, with respect to that, the speed of Earth is that. It means I can never talk of absolute speeds. If I have to talk about the speed, I have to define my frame of reference. That frame of reference must be erected to some real body. Maybe there is a particle which is floating around somewhere in the universe, okay? Maybe you'll erect your frame of reference on that particular particle, and saying that with respect to that particular particle, the speed of this particular Earth is this, the speed of this particular moon is this, the speed of this particular galaxy is this, but you require something real on which you have to erect your frame of reference. The universe is filled with nothing. There's nothing like ether. That's what it means. This is what it implies, no absolute rest, no absolute velocities, no ether. Space is filled with nothing. We require something real to which we can attach our frame of reference, and only with respect to that frame, we can talk of velocities. It means velocity does not, light does not really require a medium to travel. Velocity, light, in its own cell is a fundamental quantity. It's a basic fundamental quantity which depends on fundamental constants. It does not require a medium to travel. So when Michael Schoen was predicting the velocity of Earth is 10 to the power minus 4C, so he assumed there is an ether with, ether with respect to ether, he defined the velocity. So now there is no ether. That's right. And where is the reference, or what is anything else? Whenever we are talking, I say we have to always choose a convenient, when we are talking of the orbital velocities of Earth, we always talk with respect to this, I mean to be more precise, the center mass of the sun and Earth system, otherwise with respect to the sun. So now we come back again, and we say there is no ether, and the reference is not good. Now there is no reference. Yeah, so when I'm talking of, where I see in a given a problem you may like to know what is the velocity of the Earth, but then you would like to know velocity of Earth with respect to what? My question, what is the reference now? That's precisely what I'm trying to say. Most of the time you will take the reference of the let's say Earth and Sun solar system, take the center of mass of that, or take Sun itself, because Sun is very heavy in comparison to Earth. So let's say we relate it to Sun, that's what I will try to say. See when we are talking of the Kepler's law, we always talk later velocity of Earth with respect to the Sun. Okay, when I'm talking of let's say velocity of a train, I'm talking of velocity relative to Earth. Okay, so if I talk, let's say velocity of Sun, I will talk with respect to let's say some center of our galaxy. So whenever we are talking of velocities, I mean it's true that many times we are not very careful in defining our frames of reference because it's supposed to be understood. See if I'm saying that my car is moving, I was moving with a speed of 100 kilometers per hour, okay, I will not say related to Earth. I mean it's presumed that in Newspaper we will not like to publish related to Earth, you know, it looks, I mean all of us understand that if the car was driving at the speed of 100 kilometers per hour, it has to be related to Earth. Okay, it's not related to Moon or related to Sun. All right, so similarly it's sort of understood when we are talking of velocity of Earth, okay, we talk related to Sun. So the truth is absolute rest doesn't exist. The absolute rest does not exist. That's what it means, that you cannot talk of, I mean if a body is here is at rest, this is at rest, at rest, related to Earth. Related to Sun, it's not at rest. Related to Moon, it's not at rest. Okay, similarly there may be a body in Sun or maybe on Moon, which is at rest, related to that. I cannot say this is at absolute rest, that is not. That's also at rest, related to Moon, this is also at rest, related to Earth. So whenever I'm talking of rest, it has to be related to the frame of the rest. Or to be more general, whenever I'm talking of a velocity, velocity has to be related to the frame of the rest. Whether the velocity is zero or non-zero, it has to be related to the frame of the rest. There is nothing, there is no question of absolute velocities. Are they? No, it is fine. But after that, is it implication of a postulate, that space is filled with nothing? What is that? See, I mean that's what we, I mean, okay, let me put it like that, probably I have tried to make a little more dramatic by writing it. What essentially it means that, like we always believed that medium consists of something because Earth, because the light has to pass through that particular medium to reach to us, okay? That particular thing does not exist. Okay? I mean, in the sense, let me paraphrase this particular statement. My sentence essentially, it means that there is nothing like a universal, as we believed Ether, was, it's a universal thing which is filled everything. It's possible that in a medium, there may be some particles, okay? And it may be filled with some particles. But like something which was as universal as Ether, which was supposed to be present everywhere, whether you're talking of galaxy or whether you're talking of any other thing, okay? That particular thing is not there, okay? If there is a particle there, I'll call there is a particle here, okay? If I call something moving in you, you know, sort of our galaxy system, I'll say, okay, no, this is a small piece of particle which is passing through our galactic system, okay? And then we'll erect our frame of reference and with respect to that, I can talk of the velocity or I can talk with respect to our, or whatever thing that we are talking. So what I need to say about that space is filled with nothing. I wanted to make it a little more universal that if I say, I mean, I probably should modify this statement, okay? There is nothing universal which fills this space, which is everywhere present, okay? It could be filled with something. It does not mean that, you know, it is filled with, I mean, absolutely nothing in that sense. So what actually it means that if you go back to this particular old example which I have given, that this observer, this observer, this observer, all three of them will measure same C, okay? So C plus U, C minus U, C, three different velocities expression which we have got earlier will not be valid, okay? This particular person, if he measures C, this all also measures C. This person which is moving away from C, this particular thing will also measure C. This is moving towards the source of C, okay? Still this person will measure C. This source could be moving this way. Still this person will measure C. This source could be moving towards him. Still measure C, okay? It means if both these things have to be valid together, we require certain changes in our way of thinking and that is what special derivative we did. Brought out certain changes in this particular thing so that eventually they fit into these two postulates. And most importantly, the basic velocity addition formula, C minus V, C minus U, that has to be challenged because I need a formula which makes C universal, okay? It means I require change in my mechanics laws, change in the way I add my velocities so that C becomes universal. I think I will stop here. We still have 10 minutes. So if you have questions, you are most welcome to ask questions. Any questions? I am having now idea that C is there. So in the derivation, if I want to do the my cursor model experiment and do derived theory, then I cannot write C minus V and C plus V. That is correct. That is incorrect. No, that is going to be identically such that. See, this direction is also in this direction. But in derivation part, that will be creating a lot of problem. No, there is no problem. See, only thing that all I am saying that. We cannot use C minus V, C without using that one also. Let us come to that. It is a very interesting question that you are asked. So let us go back to this particular thing. Now, we are talking of this particular expression. This particular calculation was done assuming my ether theory. If I am using my ether theory, then this particular derivation was totally incorrect. Which I agree with is totally incorrect. No, but we cannot write C. Let me complete it. What will happen? That here also it will be C, here also it will be C, here also it will be C, here also it will be C. That is the correct way. Therefore, time difference will be zero. If lengths are same. But without taking C minus V or C plus V, also we can calculate and we can get the same result. No, that is what I did just now. You do not get. You find the time difference. No, without C minus V. That is, we can assume that the speed of the light is same. There is nothing like C minus V and then we write C plus V. Same result that we will get in this case also. No, no, no, I am probably, I am not able to understand you. This is assuming C minus V and C minus U, assuming what I said that C is in ether and the velocity addition can take place like this. All right? No, without C that what my statement is there, without using the C minus V, C plus V, we assume C that is the C and we will get the same type of the derivation, same result. No, no, see that may happen in that particular branch, but what about this branch? See, remember what I am trying to calculate. I am calculating the time taken from here to here. Okay? I am taking time coming to here to here. I find the difference, important is the difference. All I am saying, what you are saying that instead of this, if I take this C and this C, you may get the same result of that. My might be, I am not calculating. If you have calculated, might be it's right. See that concept here is that we cannot use C minus V and C plus V, rather than we can calculate in this way, that time taken, let us suppose that this length is L1 for example, then we can take the distance travelled by the light in forward direction, C T1, T1 that is I am taking the forward direction, C T1 that is equal to L1 plus, it is moving in with this velocity V, so we multiply it by T1. And in the reverse direction that we can write C T1 prime for example, that is for reverse direction, that is equal to L1 minus V multiplied by T prime. So in this way, there is no controversy of C minus V and C plus V, but we will be getting the same result and we will be arriving the same conclusion. That is my statement. No, no, no. See, I will see your calculation. We can talk in the T time. See what I am trying to say, I am not calculating the only thing. I am also calculating this difference. No, that is also, that also we can calculate. So that is what I am trying to say. See, the thing is that conceptually, if this is also C, this is also C. And if the lengths are same, and this is also C, this is also C, the lengths are same, the time difference will be zero. I am not saying that it is, mathematically it is coming same, but the V that has been written, it is not going to be correct. One, this is my statement. It is not going to be C minus V, it is not going to be C plus V. It should be written in some other way, so that this controversy should not arise. And the way that I am writing is that, I am saying that this length is going to be L1. So C multiplied by the time taken by light, from going from that mirror to M1, that is C multiplied by T1 in forward direction, this is equal to this length L1 plus V multiplied by T1. Because within time T1, it is moving in forward direction V T1. Similarly in the reverse direction, that I can write C multiplied by T1 prime is equal to L2 the same distance minus V multiplied by T1 prime. So in this way, we will get the same derivation, but controversy of C minus V and C minus C plus V that will not arise. Or in other words, I want to say that we should not create this controversy here. No sir, you are mathematically manipulating, that is not correct. No no, this is correct, this is 100 percent correct. It is not correct. I understood it. I understood it. I am 100 percent correct. No no, it is wrong. It is wrong sir. No no, see. It is mathematical manipulation, purely mathematical. You can always get some result by somewhere, let me see your result, because I have still not been able to understand. See, what I am trying to do is basic physics. In one thing, I have assumed that C is related to ether. You are getting C minus V and C plus V. In that you get some time difference. Okay, now I am saying that according to the new postulate, this is also C, this is also C. No sir, that is correct. This is also C, that's all I am trying to do. That is 100 percent correct. What is given? You are saying that is 100 percent correct. But the way that we are deriving this, we can change this one. No, that's C minus V. Maybe you get the same result that I don't deny. That is that is it. That is possible that instead of... Sir, it is not important what result we are getting. If it is physically and mathematically collected, then only we can accept it. Sir, that's fine. Yeah. No, it is not correct. Anyway, why don't we discuss at tea time? I'll just see your derivation then we'll talk about it. Secondly sir, I want to say just one thing. Again, maybe the change of the words only. I do not think that this is the failure of Michael's and Molle's experiment. Basically, I think it is the sheet anchor in the history of relativity, which changed, totally changed, upside down change in the thoughts of relativity. Yeah, you are right. Probably, you cannot... I mean, see, let me put it like that. I mean, I agree that failure was a little too strong ever. Okay, what I meant by failure was essentially what he was trying to achieve. Probably, he could not achieve that particular thing. But let's agree also to the fact, and especially because we are all teachers and we always want to tell our students, we always say that from every failure, we learn something. Okay, I mean, you have not gone in one way, but you have gone in some other way. Okay, you know that this is not the way things work. And that's the reason. I mean, as I said, the transformation, we call Lorentz transformation. You know, we still don't want it because Lorentz was trying to explain the negative. Sir, there is a negative result. Sir, excuse me, sir. No, that's what he says. I mean, this again of semantics, you know, what word you want to use, you know, how strong word you want to use, whether you want to call it failure. See, it's true that, you know, sometimes I try to make things more dramatic and try to make little stronger words. Probably, those people don't deserve that strong words. After all, I mean, even for getting that negative result or whatever you want to call it. Okay, but people have worked and have they not worked it, probably we would not have a confidence on that particular thing. So, from everything, every failure in life, we always learn something. So, this is a very, very important aspect, you know. So, I mean. Sir, one more question, sir. I think this, there is one more explanation of this one. Yes, this was said. Yeah. One more explanation of this side for the contraction by the length in the direction of propagation by, as given by the Lorentz. See, the thing is that. That may be again, this is again Lorentz try to explain the negative result by assuming that one of the length gets contracted. So, we have to do. And see, but you know, as I say, these were all the after-effects of Michelson-Morley and trying to find out the result in the same origin. See, you remember Einstein proposed in 1905, Spirit of Relativity. When did Einstein get Nobel Prize? It was 1916 or 1917. I don't remember exactly. And that was for photoelectric effect, not for special thing. I think 1928, sir. I know not 1928 or so much later. Maybe 1921. I don't remember. I can check. But you know, the fact is that it was almost 15 years that Spirit of Relativity was not accepted. And what I'm telling you that forget about these things, all our brilliant students, so-called brilliant students of IIT Bombay when they come in first year here and you teach them, even after 110 years, they get a shock when you say time is frame dependent. The things were not easily digestible. Digestible. I mean, it was the things were extremely bold. And whatever you say, you know, we also work in our scientific life somewhat in Newton's law of motion. We don't want to change ourselves drastically. We always like to make things have, you know, as far as possible, work out in the same frame so that we will not accept a totally drastic idea immediately. So there are a lot of attempts that could explain the negative result of Michael St. Molden. In fact, Michael St. Molden experiment was repeated a number of times. And if you look at the residence book, he has given at least 10 different repetition of this experiment with much better and better accuracies. And every time the result was negative. But people still thought maybe there's something special, you know, okay, assuming time to be frame dependent is much tougher. Okay, why can't we assume that length has contracted? Maybe that will explain. In fact, the contraction formula, length contraction formula, which actually I will not be able to derive because we don't have time. Length contraction formula is called Lorentz length contraction because it was originally proposed by Lorentz, not with respect to Lorentz transformation. With respect to something different. Yes, yes. Historically, the ether is not needed was proposed after the radial or whatever they said. After the negative result of Michael St. Molden experiment. But if we see the derivation of Maxwell's equation and then getting the formula of C is equal to root over of 1 by root over of mu naught epsilon naught. In the derivation, never he assumed that medium is needed. That's okay. I agree with you. So, sir, why is it that historically it took another five or six years more to conclude that ether is not required? No, because people thought that, you see, there are two or three things which are coming together. And if you just assume one ether, you know, everything seems to be explaining well. See, first of all, it's true that Maxwell never assumed a medium. Okay. Unlike sound waves, you assume medium, which has elastic properties and things like that. You never assumed a medium there. Okay. But who thought after all, every wave that we know requires a medium to travel. So, what is so special about this particular life that it doesn't require a medium to travel? So, there has to be a medium. See, as I said, you know, we always in traditionally, I mean, we are all like that, we always are somewhat traditional thinkers. I mean, the way we have been, our thought process has been brought out. Okay. We have always been told that, you know, medium is required for wave to travel. Then suddenly you come across some particular wave, which doesn't seem to be having a medium. You think maybe probably there is a wave, probably we have not seen it. Okay. Probably there is a wave. Then it also explains this particular fact of earth motion. Also that, you know, all these controversies about, you know, being relative, you know, if velocity of light is different, indifferent frame of difference, what will happen? All those issues come. And they say, okay, if I assume, I'm comfortable. So, it was more to a, I mean, as I said, now if you look 110 years later, as I give you that particular transparency, when I had two options, you say that both these options are not acceptable to me. Okay. But if no other option was given to you at that time, people thought, ether seems to be a probably reasonable assumption. But eventually, one day it has to be experimentally verified. And that's where we failed. Small historical fact. Yeah. I was surprised to read in a biography of Michael's and Morley that Michael's and never believed that his answer was. Michael's and never? Believed that his answer was wrong. He always thought till he died that ether existed, that they are doing some mistake. It's possible. Yeah. I mean, it's generally believed that Planck never believed that energies quantized. He always thought that, you know, it was just by chance that, you know, everything matched. And, you know, so it's very likely. As I say, it's not very easy for us to change our ideas. Let's accept it. I mean, we know our nature. All of us, you know, I mean, forget about science. Even our daily life can we change our ideas so easily? We cannot change. We always brought with a particular set of ideas. Okay. Any drastic change in our ideas, it's not easy to accept. It's not easy to accept. Same thing is in science. Okay. We'll see you tomorrow.