Bono Vox, the lead vocalist and primary lyricist of rock band U2, became a gust of honor at this year's 27th Sarajevo Film Festival on Sunday. The festival kicked off on Friday in the capital of Bosnia and Herzegovina. It featured a special award for famed director, Wim Wenders, and five movies rather from Turkey's national broadcaster. Bono was seen with Wenders walking on the red carpet at the National Theatre. Hello, hope you enjoyed the news. Please do subscribe to our YouTube channel and don't forget to hit the notification button so you get notified about fresh news updates.


The provision of safe drinking water and adequate sanitation in developing countries is essential. Current methods for ensuring the safety of water for consumption face high costs, complexity of use, and inability to function on-site or in real time. Microbial fuel cells, MFCs, which utilize bacteria to generate electricity, offer a promising alternative for rapid and simple water quality monitoring. MFCs are easy to produce and maintain, and can be made cost-effective depending on the material used. Research into MFC sensors for water quality monitoring is advancing rapidly, with many applications already being tested in developing countries. This article was authored by John Choller and Mirella Di Lorenzo.


Hi, this is Karen Alexander Banks and I'm so excited to tell you some information about an upcoming program at the Cougar Center. We are so pleased to sponsor the 2020 Legends of Concert this year featuring people Bryson and Stephanie Mills. The event will take place on February 21st, 2020 at the Cougar Center for the Arts and you can get tickets at www.antecaren.org or call<PHONE_NUMBER>. The silent auction takes place from 6 to 7.30 and we have over 75 items for you to bid on. Proceeds from the Antiquarian Foundation benefit our programs. We have several. We have the artists in the schools where it's called Artpreneur where artists teach their skill sets to kids across the state. We have our free television show which is on South Carolina ETV, knowitall.org. And then we also do our annual Young Entrepreneurs Conference. We are in our 18th year of doing that event. So your support of the Legends of Concert allows us to do programs like this that benefit not only kids in South Carolina but kids across the globe. So we hope that you enjoy us on February 21st. Legends of is our annual tribute to music legends. This is our 16th year presenting the event. In years past we've had legends such as Gladys Knight, Chaka Khan and Al Jarrell. We're so excited to welcome these two music legends to Columbia, South Carolina. So please consider joining us on February 21st at the Coker Center for the 16th Legends of Concert and Silent Auction featuring people Bryson and Stephanie Mills. See you there.


again and just having a great time. Hope you're having a beautiful summer. We're into August now and we're just floating along here and I thought I would come on and share a little bit some of the thoughts I've been having recently. I'm down in Mexico here in central Mexico but I am heading up to the United States the beginning of next week and I started to have the thoughts about maybe Spava and I taking a spontaneous trip perhaps somewhere around the middle or a little bit later in the week driving down to the southeastern part of the United States. So I was thinking you know the states that were coming to mind was Kentucky and Tennessee and Georgia and Florida and the idea was maybe to come down along the route of I-75 you know moving through New York by Lexington and then have some friends in Knoxville, Tennessee at the Oasis Institute and yeah then just heading on down to Georgia and then through Georgia down 75 towards the Tampa Bay area. So it's been a while since taking one of these spontaneous trips but Spava just got a like a Bose speaker with a couple of jacks and we've got some microphones and our iPhone and you know some some background music and I think Spava will probably bring her guitar but it just feels like one of those spontaneous trips maybe some visit with friends perhaps some house gatherings if there's some stops along the way just to come and share the joy and happiness and and have these like spontaneous gatherings and visits. So that's just been on my mind today and yeah I recently had a call too with a friend in the Tampa area and she said oh yeah her inner partner would love love to have us come down so that kind of got me open to that idea to that possibility. So it's always fun to hit the road and it's always fun when there's kind of an openness to it when there isn't a set schedule so we can kind of float float along in a car it's great too because you can just throw some luggage in there and throw a few supplies and things and then just hit the road. Reminds me a lot of the road trips that I've taken for many many years starting back around let's see around 1990 actually around 1989 I took a a little road trip up to Monroe Michigan to see a Course in Miracles teacher from India who who came from the Sikh background Tara Singh and then 1990 I was on my way up to Roscoe New York Lake Tanana to visit Ken Wapnick and his wife Gloria and lots of translators and what would turn out to be lots of dear friends from from the Foundation for Course in Miracles up there in the Kesco Mountains wow was that a trip uh mind-blowing opening hearts hearts breaking wide open as the as the song says under Christ control so it just feels exciting to be open to the possibilities and I thought I'm going to come on and do a live and just fling some seeds like Jami Apple seeds used to do this fling some seeds the seeds of possibility just open to traveling and stopping no particular time frame in mind other than maybe starting around the middle or or or the later part of next week and then and then taking off and seeing how it goes and and just being open to invitations to come I know Saba and I have done some beautiful retreats down in the St. Augustine area with Igor and Katerine and and then we have friends down in the Cape Canaveral area and really some really dear friends that are kind of sprinkled around Florida so yeah even our our friend Stephanie is down more towards the bottom of Florida but but you know we just would open the car and and throw some things in the car and go and see how it goes so I thought I would give you a popped open here to a little message from Jesus always like to see the message from Jesus just resonates and shines and and just percolates in our hearts and and lists us lists us up so I'm just going to read a couple paragraphs here from chapter one and this one is called the meaning of miracles it starts with paragraph five whatever is true is eternal and cannot change or be changed spirit is therefore unoperable because it is already perfect but the mind can elect what it chooses to serve the only limit put on its choice is that it cannot serve two masters one rule cannot serve two masters if it elects to do so the mind can become the medium by which spirit creates along the line of its own creation if it does not freely elect to do so it retains its creative potential but places itself under tyrannous rather than authoritative control as a result it imprisons because such are the dictates of tyrants second about the ego obviously to change your mind means to place it at the disposal of true authority as God is our author so the true authority is is God and the the voice for God the Holy Spirit and in Jesus that's true authority the miracle is a sign that the mind has chosen to be led by me in Christ service the abundance of Christ is the natural result of choosing to follow him all shallow roots must be uprooted because they are not deep enough to sustain you the illusion that shallow roots can be deepened and thus made to hold is one of the distortions on which the reverse of the golden rule rest as these false underpinnings are given up the equilibrium is temporarily experienced as unstable however nothing is less stable than an upside down orientation nor can anything that holds it upside down be conducive to increased stability so of course as we answer the call of our heart as we answer the call of God things get the stirred up you know the status quo gets stirred up the the apple cart gets tossed over the we experienced some feelings of of instability of of at times there's there's an anxiety there there's a fear and it's just that our upside down belief system which believes in the ego is being turned right side up to a holy spirit inspired perspective and that perspective is is a spirit of joy it's a curriculum of joy it's a spirit of joy it's a spirit of Thanksgiving it's a spirit of extending love extending and that is our calling to know our creators will for us to know true happiness to know true love so yeah I hope you enjoyed that little snippet two paragraphs and yeah I think I will put this up on a number of different social media platforms some youtube channels and facebook channels twitter and pass it around here and there just because you or maybe some friends that you know who live in the pathway I was talking about running down through Kentucky and and the eastern part of Tennessee around Knoxville and then of course Atlanta Georgia and then on down to Florida if you or anyone you know is on that route and you want to forward this link then yeah feel free to contact me in fact I'm going to put up the oh there it is my facebook messenger it's my name and you can just message me on facebook messenger just send me a message and also if you would like rather email me then I'm going to put that up there's the email address mystic spirit one at yahoo.com so just drop me a message drop me a line drop me a note if we take off next week for example and start heading down through those states and working our way down to Florida then we'll have our of course our cell phones and we'll be able to receive messages and who knows maybe do some facebook lives or something like that along the way just sharing our happiness and joy and yeah if you'd like to meet with us or host us maybe somewhere along the way that happens to be along the route could even be just meeting in a restaurant or a cafe it could be taking a walk along the beach you know getting a bed and breakfast I've had some amazing trips over the years down the same route down to Florida with all my friends in in Knoxville Tennessee and in the land of Georgia area and then also many many friends in central Florida and the panhandle and the both coasts the east coast and west coast of Florida it's just been a lot of fun I've had a lot of these kind of kind of spontaneous trips anywhere from like a couple weeks to anywhere to six weeks I think I've I've gallivanted around around Florida and met a lot of friends and I occasionally pop into like a unity church or yeah just so many friends like a little spiritual center over near Orlando Tampa lots of friends in St. Pete lots of great joyful miracle memories from from all the years of traveling along there so I actually hope to see you along the way Svava and I are yeah preparing for a nice little trip just pack up the car put in the Bose speaker and yeah put in some clothes and and take off with our with our mobile phones ready for some action some joining some holy encounters so thank you so much for joining me for this live and I love you and I share my heart with you and you're in my prayers and in my thoughts and thank you God all glory to God for creating us with all this love in our hearts that we may open up and give it away and feel it giving and receiving are the same as you so so shall you reap I think it says yeah in the bible so let's let's do lots of that all right lots of love


Greetings, I will begin unit 3, which is a very fascinating topic. Relativistic quantum mechanics of the hydrogen atom. So, we obviously have to use relativistic formalism together with quantum mechanics. And I will be using predominantly these 2 books, both have the same title called relativistic quantum mechanics. One is by Bjorken and Drell and the other is by Greiner and these 2 are very good sources for much of what I will be discussing in this particular unit 3. Now, again you would have had some exposure to some relativistic effects in atomic spectroscopy from your earlier courses in quantum mechanics or atomic spectroscopy or whatever the courses you have taken. Are there various questions that may have been raised? For example, you would have seen this term possibly if you have seen it that is what I am referring to. If you have not seen it, you are going to meet this term in this unit and a dominant effect, a dominant relativistic effect in atomic spectra is the spin orbit interaction in the atomic structure and spectroscopy and collisions and all the atomic processes. This is the spin orbit interaction. It has this form which you may or may not have seen earlier and if you did, the question that would ask itself is where does this form really come from and we are going to figure out how exactly you get this term. You also may have seen the Dirac equation which we shall introduce and discuss in some detail from first principles and you will notice that this equation has got a matrix structure alpha and beta are 4 by 4 matrices. The wave function has got a number of elements and then you also know that there are questions about negative energy solutions, anti matter and all that. Now, we do know that electron spin requires 2 components, but you see in the Dirac equation that you have got 4 components. So, what is all this about? These are some of the questions that we shall tackle in this unit. So, before I get into the main subject of discussion, I will spend some time in today's class which is the first class first lecture on this unit on brushing up the transition to relativistic dynamics. So, before we get into quantum mechanics, relativistic quantum mechanics, I will remind you of what is involved in the transition to relativistic dynamics as opposed to non relativistic classical mechanics. So, I will spend just some time recapitulating those ideas, I am sure that you are aware of that, but this will be just a quick brush up. So, let us look at phenomena seen by two observers, one in an inertial frame of reference which is this red frame and the other also an inertial frame of reference. The second observer in this blue frame is also in an inertial frame and inertial frame is one which moves at a constant velocity with respect to another one. So, the second observer is moving at a constant velocity which is this u with respect to the first observer and let us say that these there are these two observers whose observations we are comparing and the first observer looks at an object whose position vector in his frame of reference is this r, this is the instantaneous position vector at time t. The position vector of the same of object for the second observer is r prime t, this is the prime frame of reference, this is the unprimed frame of reference. And from the triangle law of addition, you know the relationship between these two vectors, the difference is this displacement of the second frame of reference, we assume that the x y z axis of both the frames lied on top of each other at t equal to 0. So, the displacement in time t would be this velocity times t and this is the relationship between the two position vectors. Now, if you took the time derivative of this relation d r by d t, you get the velocity of this object in the first frame and d r prime by d t gives you the velocity in the second frame and these two velocities are obviously not the same because you must add u c to this to get the velocity in the first frame. Now, essentially this is the relationship between the velocities of an object in two inertial frames of references. Now, this is Galilean relativity, this makes a certain assumption that the speed of light is finite and all of these conclusions are consistent with this assumption and as long as you do not question this assumption you are ok. So, the relative velocity between as seen by two observers depends on the relative motion that is the essential point in this and I like to show this little video of this kid. Let me see if it comes up yes it does and I really like this video and what you see is if you ask the question as to what is his velocity is it positive is it negative is it going forward is it coming backward does it does his velocity even have the same direction and it really depends on what the frame of reference is that is something that you must really ask it is nice fellow he makes it this I downloaded by the way from the YouTube and I have given the reference here. So, this is the full reference you can also view it if you like and our conclusion is that whenever you are looking at the velocity of an object you must ask velocity with respect to whom now is it this car or the other car and with respect to whom is it with respect to somebody on the road or is it somebody who is sitting in one car or the other. So, these are the questions of immediate relevance whenever you are looking at any object and ask how fast is that object moving. Now, it turns out that if the object of your interest is light you are not looking at a car or you are not looking at this little kid on the treadmill. If you are looking at light a pulse of light is fired then what kind of considerations are involved. So, let us actually see what we are talking about. So, here you have got a light source a laser gun if you like and you fire a pulse of light and this light goes from the left to the right in this frame of reference and you have got an observer in this frame of reference and this is our observer. Everybody is getting smart these days so younger and younger people do more and more challenging things. So, you have your observer over here who is looking at this pulse of light and this observer would measure the speed of light in her frame of reference. You have another observer who is moving in a another frame of reference which is also in inertial frame of reference and he is going at a constant velocity with respect to the first observer and he also measures the speed of light. You can think of another experiment in which light is fired from a different gun in the opposite direction and now you have these two observers who are measuring the speed of light. Now, what is interesting is that no matter which observer is measuring it and no matter which light you are talking about if it is the light which is going from left to right or the other one from right to left. All the observers get essentially the same answer which is root of 1 over mu 0 epsilon 0 which is the permeability of light permeability of vacuum and electrical permeability of vacuum. So, the speed of light is determined by properties of vacuum and it makes no reference at all to which observer you are talking about. Now, this is very strange thing because this was not our experience when we talked about the velocity of the child that we were looking at. If you were the child it would be fun, but the speed would always be 0 whereas, if you were standing behind him or in the trade mill it would be different for all the different observers. Same thing with if you are looking at a car which is moving, but the speed of light does not make any reference to the observer. It is always the same no matter which observer you are referring to. It is always the same value in every inertial frame of reference and physics has to reconcile with this. This is a result which physics was not really prepared for and this is a result which Einstein was the first one to see and not just from the Michelson-Morley experiment, but from many other considerations and I will not go into the history of the special theory of relativity which is very fascinating because in this course I just want to refer to some of the main conclusions to lay the foundations for our discussion. Now, this is what I would call as counter intuitive because if our intuition was built on our experience with regard to our conclusions on our observations about the child's walk on the trade mill or looking at a car from one frame of or another, then we would think that it is counter intuitive, but intuition is a function of education and then if you get educated and build your intuition based on further knowledge of the laws of nature, then you might find that this particular conclusion would completely meet the expectations of your intuition. It is a result which once you understand the implications of the special theory of relativity, you would find that this is precisely what you would expect. So, now the reconciliation comes from the fact that the laws of transformation between the coordinates in one frame of reference and another frame of reference are no longer Galilean, they must be modified and they are what are known as Lorentz transformations. And these transformations transform not just the space coordinates, but also the time. So, time is no more to be treated as absolute. This is one of the offshoots of the special theory of relativity, we always think that time is absolute and we do not connected to the state of motion of the observer himself, but that is something that we have to reconcile with. And these are the Lorentz transformations, you go from x, y, z and t to x prime, y prime, z prime and t prime through these transformations gamma is this ratio and v is a constant velocity of the second observer with respect to the first observer along the x axis. So, that is the coordinate system that I have chosen over here. Now, what are the consequences there and then again I am not going to spend any time you know discussing these consequences, because that will take us into specific discussion on the special theory of relativity, which is not my intention, because we want to get into relativistic quantum mechanics. But I will just remind you that time is not absolute not a space. So, what we think of a space interval you know the interval between two points in space or the interval between two events that we talk about between you know the time it took for you to come from your hostel to the classroom or whatever. These intervals neither the time interval is absolute nor is the space interval absolute and they depend on the state of observer and it leads to what is referred to as time dilation and Lorentz contraction. So, both time and space intervals we have to modify our perception of time and space intervals, this is guided by a reconciliation with our notion of simultaneously. What is simultaneous for one observer is not necessarily simultaneous for the other and then one needs to ask that if neither space nor time intervals are invariant under Lorentz transformations, what is it that is invariant and that is the quantity of interest. So, this quantity is of interest to us, because our interest in quantum mechanics is the following we deal with the Schrodinger equation in quantum mechanics the non relativistic Schrodinger equation. You have got the dynamical variables position and momentum, you have the time derivative involved when you take the time evolution of the state function or the state vector and the space interval that would go into the potential function for example, even in a simple problem like a one dimensional potential barrier problem if you like. The distances that you are talking about these are no longer to be considered as invariant and you must take into account the state of motion of the observer to analyze these dynamical variables. So, the distance l is not Lorentz invariant and then we should therefore, ask that the Schrodinger equation since it cannot be Lorentz invariant, how do we get a relativistic equation which is consistent with the Lorentz equation with the Lorentz transformation which reconciles with the fact that the speed of light is finite. So, this is the question that we must ask and again this comes from non relativistic classical mechanics that you need to extend your idea of space to four dimensions and this is an extension into a four dimensional space which includes time, this is sometimes referred to as the Minkowski space time continuum and then an event in this space is characterized by four variables these are the x 0, x 1, x 2, x 3. So, I will quickly remind you of the notation I will not spend too much time working this way up, but just to quickly remind you and then introduce the invariant quantity which is this scalar dx mu dx mu this is the quantity which is invariant under Lorentz transformations. Now, how do we know that this is invariant? Now, first of all the way that you get it is through this lowering of indices as it is called through the G metric and this G has got a certain signature this is a 4 by 4 matrix which has got these diagonal elements which are given by 1 minus 1 minus 1 minus 1 all the remaining elements in this 4 by 4 matrix are 0. So, I have not written them out and there is a specific difference between the interval in a four dimensional Minkowski space which is referred to as a pseudo Euclidean space as opposed to a Euclidean space and the difference is in the signature because d s square is defined as this particular summation of these quadratic terms, but the signature 1 minus 1 minus 1 minus 1 of the G metric assigns these specific signs whereas, if the four dimensional space was Euclidean if it was an ordinary extension of how we go from a two dimensional flat space into a three dimensional Euclidean space that is a straight forward extension this is different. This is why it is called as a pseudo Euclidean space and in this pseudo Euclidean space the signature of G is particularly important and special theory of relativity is built on this pseudo Euclidean space in which all events all physical events are described to take place in this particular pseudo Euclidean space. Now, this is the signature of the pseudo Euclidean space and what you can do is look at this invariance criterion because we expect if our contention is correct that d s square must be exactly equal to the square of d s prime and we can very easily verify this by subjecting all of this t prime x prime y prime z prime to the Lorentz transformations plug in the corresponding substitutes and do some simple analysis which I will not spend any time on working out for you this is something that you will do very easily. And if you just do the substitution and simplify the terms your conclusion will be that this d s prime square is exactly equal to d s square which is how you demonstrate that this is an invariant quantity and the Lorentz transformations fine. So, this is our invariant quantity it is a measure of the what we call as an interval between two events and of course, because each quantity is a square of a number and the first term is positive and the other three terms are negative this quantity can of course, be either positive or 0 or negative and depending on what it is it has got different names it is called as time like light like space like, but we are now interested in quantization. So, this is our machinery this is our tool and our interest is in quantizing the system we know what quantization is we have discussed this at length in unit 1 that you must abandon the dynamical variables q and p and replace them by judicious operators. And dynamical variables which are functions of q and p get expressed as operators which in turn are expressed in terms of the position operator and the momentum operator. Now, this was our notion of quantization and we expect something similar to be needed to be done in relativistic quantum mechanics. Now, let us see how we would go about doing it now momentum is obviously, a quantity of specific interest it is one of the dynamical variables which specifies the state of a classical system its quantization is fundamental to what else we do in quantum mechanics. So, let us have a look at momentum which to begin with we define as mass times velocity although we have better definitions like the derivative of the Lagrangian and so on, but if you look at the mass times velocity that this velocity is a ratio of space to time in the limit that the denominator time interval goes to 0. And our concern here is that the numerator space interval and the denominator time interval neither of these two quantities is invariant under Lorentz transformations one undergoes dilation time undergoes dilation and the other undergoes contraction. Now, these are the up shots of special theory of relativity. So, obviously we are going to need some special effort to deal with this quantity which is the velocity and then it will have consequences on how we define the momentum and further more on how we would quantize. So, in special theory of relativity what you do is to construct a ratio of space to time, but you do not take the space and the time in the same system of frame of reference. You take what is called as proper length and proper time and these two are different and you have met these quantities in your earlier course on a special theory of relativity. So, I will not define them I will not spend too much time discussing it. You need to introduce this proper velocity which is the ratio of these two quantities and that is what that goes into the special theory of relativity. So, this velocity is now not just d r by d t, but d r by d t times gamma where gamma is this ratio which includes v square over c square and this is not 0 because the speed of light is finite. So, this is now your proper velocity and I have discussed this at some length in another course which happens to be available on the internet. So, if you want you can look it up it is available in the NPTEL library it is also available in the YouTube and I have dealt with some of these ideas including the idea of time dilation and length contraction and some detail in those lectures. So, I will not repeat any part of it over here. So, this is our introduction to what we will call as the proper velocity. This gives three of the four components because event is described by four components you have got four vectors. So, velocity will also have four components and the fourth component is the natural extension of this. So, the first three components which we get from this relationship are this eta 1, eta 2 and eta 3 which are gamma times the corresponding components in non-relativistic mechanics and eta 0 which is the fourth component is given by the ratio of d x 0 to this quantity over here. So, essentially you rationalize the whole thing in a consistent fashion this is the natural way of doing it and this gives you the four vector which constitutes the proper velocity. Now, that you have got the proper velocity you can ask if it is invariant. So, you construct this scalar and all you have to do is to plug in these numbers and determine what this quantity is and it turns out to be the square of the speed of light. So, obviously it is invariant because we know that the speed of light is invariant under Lorentz transformations it is the same for every observer which satisfies us that our rather unorthodox way of defining velocity which is to take the ratio of proper length to proper time this unorthodox way of defining the velocity is well justified and very well rationalized. So, this is an obviously invariant quantity in every inertial frame or we define the proper momentum as mass times proper velocity which is again a straight forward extension of the classical idea. So, you have the proper velocity you multiply each term by m and you get the proper momentum which is again it has four components and the first component involves the speed of light. So, this is your description of proper momentum again you can ask if it is an invariant quantity and you construct the scalar and you find that it turns out to be m square c square which is again invariant although one must be careful about how you define mass and you will see why it is important to define mass carefully. So, I am use a mass which is invariant to Lorentz transformations it is the same mass in every frame of reference and this is m square c square. So, again this is a manifestly invariant quantity in every inertial frame of reference. Now, if you look at this expression it has got two terms one is the quadratic term in this velocity and the other is the quadratic term in the speed of light and if you take the difference essentially this is e square by c square minus e square. Now, what I made use of is a certain relativistic well known expression and now we have the dynamical variables with us we have the momentum we have got the energy and we can proceed to find how to go about quantizing this and then how to describe a state vector and how the expression is evolution of that state vector is to be described because we know that the fundamental problem in mechanics whether it is classical mechanics non relativistic quantum mechanics or relativistic quantum mechanics is essentially the same how do you describe the state of the system and how does the system evolve with time. So, these are the questions that we are going to discuss, but before we proceed I will like to remind you alert you to what exactly we mean by mass because mass obviously appears in two of the most famous equations in physics one is f equal to m a and the other is equal to m c square I do not think that anybody would argue that there are any other relations in physics which are more famous than this including perhaps the Maxwell's equations good, but this one is not right. So, first of all I like to discuss this because you must understand exactly what you mean by mass because the correct way of writing this expression which establishes the equivalence between energy and mass this whole relationship between energy and mass is about establishing the equivalence between energy and mass that is what helps you make a bomb right. Now, you and I may not be interested in making a bomb although some of you may be who knows. And you have written a mass the rest mass, but if we write the variable mass as m then is equal to m c square. No I am going to explain this I am going to explain this there is a good reason why I raise this you will see it very soon in the next few minutes it is not the same because the whole idea of introducing energy and mass and writing this relationship is to be able to convert mass into energy and vice versa is to establish the equivalence. And if the two are equivalent you cannot be required to introduce a relativistic energy and a relativistic mass just one will do that is the key to understanding this, but you will I will explain this further. Let us look at this expression this is the correct expression equal to gamma m c square rather than equal to m c square this is the correct expression and write this as m c square into this factor gamma which is one over the square root factor go ahead and expand this 1 minus x to the power minus half which the little kid on the trade mill perhaps would do. And you have various terms and if you look at the first term that is what gives you m c square if you look at the second term you get the non relativistic kinetic energy which is half m v square and then you get corrections of various orders which go in multiples of v square over c square. So, with that factor those subsequent terms become weaker and weaker and you can truncate it as you like and depending on the level of approximation even the first term which is the half m v square would be of interest m c square would not count because you are going to measure only changes in kinetic energy. So, it is a constant quantity for any mass. So, it really does not matter and this in fact is the correct expression for the equivalence between energy and mass not equal to m c square. So, equal to m c square would give you only the constant term in this complete expansion. Now, the m c square itself does not really matter very much in our observations I will like you to note the third term which is the leading term which is the leading relativistic correction to this goes as the fourth power of velocity or the fourth power of momentum. I am going to come back to this much later but I want to draw your attention to this because it will be of some importance at a later point. Now, look at the expression for this energy gamma m c square if you are looking applying this relation for a photon. Now, the photon is a massless particle which moves at a speed of light it always does if it exists it moves at a speed of light. So, v is equal to c for the photon. So, this is 1 minus c square by c square. So, the denominator goes to 0 the numerator m goes to 0 because it is a massless particle. So, you get 0 over 0 that would make it impossible to define energy for a photon, but the photon has energy you know it. In fact, you and I live because we get this energy from the light we get from the sun. So, photon has energy and this expression would give you 0 over 0 which is indeterminate. Now, it turns out that the question of whether the photon is a massless particle or not is intimately linked to how well we know the coulomb's law the inverse square law. These two are the same questions consider this look at the coulomb potential the inverse square law tells you that the potential goes as 1 over r. The 1 over r potential is what gives you the inverse square law take a different kind of potential like the Yukawa potential. Now, I have constructed a numerator here and I have chosen an exponent to include the mass the speed of light and the angular momentum. So, that the dimensions are m c over h would cancel and you get a number and if you let this mass go to 0 you would get the coulomb's law. Now, what is interesting is that the mass going to 0 is linked to the coulomb's law. If one or the other was different you would find some incompatibility between these two relations and this is what I implied when I said that the question of rest mass of a photon is intimately linked to how accurately we know the coulomb's law. If it was any different then it would require a mass which is non-zero. So, for if we were to apply this relationship to light we would get an indeterminate quantity for the energy of the photon, but that is not a worry because this relation that we got from the invariant scalar constructed from the 4 momentum it still holds with the difference that now we should allow m to be 0 no problem, but let us define the momentum using the de Broglie wavelength because if you used p using the de Broglie wavelength you get e equal to p c which is h c over lambda which is h nu and then you do not have any problem defining the energy of a photon. I have highlighted this because you could also write this e equal to c p, but I prefer that you write e equal to p c because then it associates energy with my initials. I do the same with the c p t theorem which I always call as the p c t theorem and this brings me to the other relation why it is not appropriate to define a relativistic mass which some books and some literature actually do because you really deal with only one mass and you need to deal with only one mass if mass and energy are equivalent and they are. So, it becomes pointless to introduce another mass which is gamma times m they may be mathematically or ethnically equivalent, but this is completely redundant and then you must define e equal to gamma m c square the only mass that I will always refer to is the rest mass which is what makes m square c square invariant in all inertial frames of references. It is a conclusion that we are going to base our formalism on and it also means that e is equal to gamma m c square rather than m c square. So, we will proceed with this and now what we want to do is to quantize the system. So, we have got the momentum and what we did in on relativistic quantum mechanics is to quantize the momentum replace the momentum by the gradient operator we discussed why you need the gradient operator. So, we expect something similar we do expect the gradient operator after all non-relativistic quantum mechanics is not absurd it has given us excellent results. So, it is something that must be corrected for there is no doubt about it because it did not take into account the fact that the speed of light is finite no matter how large it is huge, but it is finite. So, it must reconcile with that and we can borrow many things from non-relativistic quantum mechanics, but not everything. So, we are going to be guided by our method of quantizing momentum by expecting a gradient operator, but we have to be prepared for some modifications and we have to look for quantization of this 4 momentum rather than the 3 momentum that we did in non-relativistic quantum mechanics. So, this is our 4 momentum and this is how we quantized it in non-relativistic quantum mechanics. So, now our 4 momentum and this mu will take 4 values 0, 1, 2 and 3 these are the 4 values of the index mu and there is a gradient derivative operator for each one of them and this is what the operators are this would be a natural extension of what we did in non-relativistic quantum mechanics. This is the covariant one, this is the contravariant one and you have a minus sign here, but a plus sign over here and this you know comes from the fact that the signature that we have been using is this plus 1, minus 1, minus 1, minus 1. So, it relates to that and now we have the operator p 0 for which the quantum operator would be I cross del over del c t you take the corresponding variables and this is your complete quantization prescription. Now, this is how we would go about quantizing it and then we are going to have to ask does it lead us to satisfactory physics. We have followed we have taken some guidelines from non-relativistic quantum mechanics, we have taken guidelines from the special theory of relativity as introduced in classical mechanics. We have put it together and we have come up with a scheme for quantization, but then we have to proceed because we have to describe the state of the physical system and see how this system would evolve with time. So, quantization would require these operators, these would need to operate on the state vector of the system or the wave function and then you come up with a wave equation. So, this is the wave equation that you would get. So, this is the quantization scheme. So, far so good looks fine and when you put in all of these operators in this relation you get what is called as the Klein Gordon equation. All we have done is to put these operators in this relationship over here which comes from the Lorentz invariant quantity. So, this is the Klein Gordon equation and this is the relativistic equation relativistic quantum mechanical equation and I am going to conclude today's class over here. Tomorrow we begin from here I will mention certain difficulties with the Klein Gordon equation and quickly go over to the Dirac equation which is the one of interest to us in atomic physics. It is the Dirac equation which would describe the electron in an atomic system. So, that is what I would introduce tomorrow. If there are any questions I will be happy to take. Klein Gordon equation is the improvement of the non-relativistic certain the equation relativistic quantum. It is and it serves well to a certain extent. It also creates some difficulties I will mention some of it. I would not spend too much time on it because the relationship of specific interest to us for our interest in atomic physics is the Dirac equation rather than the Klein Gordon. So, I will very quickly go over to the Dirac equation. This kind of things can be explained by Klein Gordon. Also by Dirac I will discuss some of these things in the next class. Any other question? If not, goodbye for now.


Welcome traders to another tickmail chart here with me, Patrick Munley, I want to draw your attention to the developing opportunity in the Euro Yen, one of the daily time frame. So we've been trading in this sending trend channel, broke out through that 127 resistance and have pushed higher here. What I'm looking for now is a test of the 161 extension of the last swing to the downside which coincides with the monthly R3 at this 130-40 area we have projected ascending trendline resistance 130-60. So watching the bearish reversal patterns in that 130-40 to 130-60 area, setting short positions, initially targeting a move back down into 128-47 on route to an ideal test of the ascending trendline support back down to 127-40 before starting the next leg higher. As always traders, plan the trade, trade the plan and most importantly manage your risk. Until next time, thanks very much.


Hello, everyone. Welcome to Options with Doug, streaming live daily on Bookmap Discord and the Bookmap YouTube channel at 1.30 p.m. Eastern Time. Before I get started, I need to go through the general disclosure. All Bookmap limited materials, information, and presentations are for educational purposes only and should not be considered specific investment advice nor recommendations. Risk disclosure, trading futures, equities, and options involves substantial risk of loss and is not suitable for all investors. Past performance is not necessarily indicative of future results. The focus of my presentation and the focus of the Options-Doug chat channel in Discord is options, order flow, the impact of options markets on stocks and futures, and the influence of market maker hedging flow on price action. I have a two-step process for trading and the first is planning, and I use positional analysis. I look at how traders and market makers are positioned in the options market and how those positions change from day to day to develop a thesis regarding the expected trading range and volatility for the day as well as a directional bias. And the second step in my process is execution. I look at real-time order flow in Bookmap and real-time market maker hedging flow in Spont Gamma Hero to confirm my thesis and for setups for entries and exits. And when I talk about setups today, I will be talking about setups in an underlying asset. Setups can be taken with futures, shares of stock, or options. Questions and comments are welcome and I will be watching both the Options-Doug chat channel in Discord as well as the chat in YouTube for your questions and comments. So please feel free to post. And Victor Ben, glad what I'm doing is helpful. That's great. That makes me very happy to hear that. Keep up the good work. And Karm FX, hello to you. Welcome. Glad you're here. All right. My agenda for today, what I want to cover is news items for today, the rest of the week, economic data events, earnings. Then I'll go through my positional analysis. Then I want to review some setups from this morning. And then we can then I'll talk about the live market. And when I get to the live market, if anyone has had any stocks, they want me to take a look at, please let me know. All right. So first of all, economic data. Apparently, there was another downgrade today. Sometime, I don't know if it was overnight or this morning, Moody's downgraded the credit rating of 10 banks. And that might have been somewhat of a reason for the move down this morning. All right. So that is today. And then for the rest of the week, the key high impact data. First of all, CPI data comes out on Thursday at 830 a.m. Eastern time. And then PPI data comes out at 830 a.m. Eastern time on Friday. And then on Friday, Michigan consumer sentiment is out at 10 a.m. All right. So those are the news items. Now let's let me get started with positional analysis. I'm going to go start with the SAP 500. This is the ES futures in book map. And before I take a closer look at this chart, I want to take a look at a larger time frame. This is SBX, a 30 day one hour chart showing key levels and also the the trend of price again over the last 30 days. Let me zoom in on this chart so we can see the current price a little bit more clearly. So this is showing the kind of the break of the uptrend last Wednesday. That was the Fitch downgrade of US debt. And the downtrend continues after that downgrade. Let me point out the levels on this chart. First of all, the dash purple lines are showing the lower and upper weekly expected move. And SBX is trading still within that range above the lower and below the upper weekly expected move. The dash blue lines, not the same case here. Dash blue lines show the daily expected move. Both of these are based on just come from the options market. And note that SBX is trading below the lower daily expected move. Again, shown with the dash blue lines. And there are also some key spot gamma levels on this chart shown with the dark red horizontal lines. And the first is the 4500 level. That's right here. And that is the poop wall that is spot gammas support level. The poop wall is a strike with the largest net negative gamma that can be expected to act as support. That's a key level. That is also the absolute gamma strike. And that is the strike with the largest absolute gamma positive and negative. So 45, a very key pivotal level for the SBX and SBX is trading below that level now. Then the next level up is the volatility trigger at 4520. And that is spot gammas proprietary gamma flip level below that level. Market makers position on the gamma curve is negative in a negative gamma environment. Market makers have to trade with price to hedge their delta exposure. And that tends to enhance or increase volatility. And I'll show you a graphical representation of that in a few minutes with the Vana model. So right now SBX is trading below its volatility trigger in a negative gamma environment. And then on the other hand, above that level, market makers position on the gamma curve is positive. And in a positive gamma environment, market makers have to trade against price to hedge their delta exposure. And that tends to subdue volatility. And then finally the call wall is at 4600. That's the strike of the largest net positive gamma. And that can be expected to act as resistance. So the key points here are the SBX is trading below its lower daily expected move is trading below its put wall and below the volatility trigger. And note, there were a few shifts in levels for the SBX and spy, both the volatility trigger triggers and put wall shifted higher. All right, let's take a look at another another SBX chart. Just to get a closer look at the levels that are in play for today. This is SBX in a one day, one minute chart. Let's just zoom in on this. So you can see here that SBX is trading below the volatility trigger in negative gamma environment. Also below the put wall, the key 4500 pivot level, and also the lower daily expected move. And one other thing that I should point out on the larger timeframe here, note the large gap in gamma levels from actually this 4500 combo L five level all the way down to 4400. Very large gap in gamma levels. And what that might mean is that I think that opens up the potential for a fast move down to 4500 before the next level of support. And know that is that slightly below the lower weekly expected move. All right, let's go back to book map. Now in a book map, I have my cloud notes here. And I'm showing the SBX levels as well as spy levels. So here's the spy 447 put wall. And now the SB 500 is trading above that level. Trade a blow it earlier today. Note the zoom just a little bit here and note the spy 448 level. That's a combo three level. Combining SBX and spy gamma into one level. That level did act as resistance earlier today. And then price moved down to just above the spy 445 level. That's a large gamma four level. Alright, so those levels in play again. Here's the spy 447 put wall. And if I zoom a little bit, so right here, this is the spy 451 volatility trigger. And I have their two lines there, the SBX volatility trigger is just about at that same level. Alright, so those are the levels in play today for the SB 500, both SBX and spy levels. And we'll talk about setups in a few minutes. All right, let's take a look at NASDAQ. So again, remember shifts for levels for the SB 500 volatility triggers and put walls shifted higher for the SB 500 SBX and spy. Let's take a look at NASDAQ. This is in Q futures. I'm going to take a look at a QQQ chart first, just so we can take a look at the the key levels and note that the 373 level. That's not a gamma level did act as resistance earlier today before the cash open. Here's the put wall at 370. And now QQQ is trading above that level after apparently finding support at the 369 level. Again, not a not a spot gamma level, but a round number QQQ round number. Alright, so those are the QQQ levels in play for today. And I'm showing those on my chart as well. And note, this is the right here. I have two white lines. This is the label for the NDX 15,192 combo to level just below the 370 put wall. Note that in Q is trading below its lower daily expected move. And again, there's the 373 resistance and the 369 support. And again, we'll talk about setups in a few minutes. So there were really no shifts in levels for the NASDAQ NDX. Volatility trigger did shift lower by 10 points, which is not not significant. Alright, so those levels in play today for the S&P 500 and the NASDAQ. And for NASDAQ, mainly QQQ round numbers in play. Alright, let's take a look at gamma notional now. We'll take a look at gamma notional, see how market makers were positioned in the options market at the beginning of the day. So I'm looking at gamma notional for SPX, SPY, NDX and QQQ. And what this is showing is that market makers position on the gamma curve at the beginning of the day was negative for SPX, SPY and QQQ. And I generally don't pay any attention to NDX. So these numbers did shift higher. They are less negative than yesterday, but all still negative. So at the beginning of the day, market makers position on the gamma curve was negative. This indicates that in this portion of the gamma curve, traders are long puts, market makers are short puts, and they have to trade with price to hedge their delta exposure. So if price drops, they need to, and implied volatility increases, they need to sell futures. And then on the other hand, if price increases, they can buy back their short futures. So again, all these numbers negative, but less negative than yesterday. All right, let's take a look at the Vana model. Now, we can see an illustration of this. Let me take a look at, go back to one thing here. We'll start with SPX. So we see the lower the day for SPX was around 44.64. All right, so I'm going to open up the Vana model and note the gamma notional for SPX was mildly negative. So this is, this Vana model curve is typical of a, you know, I guess a slightly negative to neutral negative gamma. So what this chart is showing, gamma position, I'm sorry. So what this chart is showing is delta notional, market makers delta notional and the vertical axis price for SPX on the horizontal axis, there are two curves on this chart. The light gray curve is showing how market makers delta notional changes with changes in price only. And then the purple curve adds implied volatility to the equation. It is showing how market makers delta notional changes with changes in price and implied volatility. And that change in delta with a change in implied volatility is the Vana effect. That's a second order Greek. So what the chart is showing is if price decreases, market makers will need to sell futures to hedge their delta exposure. Their delta exposure increases, they want to remain delta neutral. So they have to sell futures. And then on the other hand, if price increases and implied volatility drops, they can buy back their short futures. Alright, let's take a look at, first of all, SPX traded down right around 44.64. There's 44.65. So in the low of the day, market makers position on the gamma curve was firmly in this negative region, this left skew where they are, they are selling futures as price decreases and buy back short futures as price increases. Alright, SPX right now is trading around 44.80. Alright, so still firmly in the negative portion of this Vana curve. So again, in a negative gamma environment, on this portion of the Vana model, we're expecting larger moves enhanced by market makers trading with price. Alright, so that is SPX. We'll take a quick look at SPI. So right now SPI is trading right around 44.47. So trading above the low of the day, but still firmly in the negative portion of the negative gamma portion of the Vana model here. So again, expecting larger moves market makers trading with price. Then finally QQQ, this curve of Vana model again very characteristic of a negative gamma environment. A sharp skew to the left, QQQ trading right around 370, 370.50 just above the put wall, but well below the volatility trigger at 376, 376 volatility trigger. So firmly in the negative gamma portion of the of this Vana model here. One thing to point out is the news that I mentioned, news items coming out later on in the week. CPI data and PPI data. So if this negative gamma position persists into Thursday and Friday, I would expect a large move similar, somewhat similar to last year in a persistent negative gamma environment. There were often very large moves after the CPI reports came out every month. Often not as bad as expected or better than expected and price would rally implied volatility would drop and market makers could buy back their short futures contributing to a sharp rally after the CPI reports. So that would that's something that you want to look at look for in a negative gamma environment. A larger move after key data like CPI data. Alright, so that's the Vana model. Now let's start with actually so my thesis for the day was really looking for higher volatility. That was essentially my my thesis for the day based on the negative gamma positioning. Alright, let's take a look at some setups. Now review some setups. Oops. So I'm going to start with the SV 500 and I'm going to start with this hero signal here and we'll see what options traders have been doing today. And by the way, remember from yesterday that options traders were taking negative delta positions pretty much throughout the day. And it looks like they they really excuse me, they really didn't get paid yesterday, but they are getting paid today or at least they were earlier in the day. So this is the hero signal. This is provided to spot gamma subscribers. Hero stands for hedging impact and real time options. This is showing price for SPX that show more the white line and then market maker options trades traders options trades and the corresponding market maker hedging activity for a combined signal for SPX spy XSP and ES futures. So if you trade any form of the SAP 500, whether you're trading ES futures, spy share spy options, or SPX options, this is generally the signal that you want to take a look at the combined signal. So when traders are taking negative delta positions, market makers are taking the other side of those positions. So there they have to sell futures to hedge their delta exposure to remain delta neutral. All right, let's take a closer look at this now. I'm going to zoom in. So note the hero signal was trending down this morning, really making lower highs up until about several between 11 and 11 30. So let's go take a look at book map now. And of course, the the setup for this morning was to go short. Gonna zoom in. We'll look at data from around just after nine nine a.m. to to noon. So remember, from the open options traders were taking negative delta positions. So let's look at order flow now. So first of all, we see the kind of a double top that to test of the spy 448 level that acted as resistance. And after the second test note, the aggressive sellers coming in that was right after the the cash open that shown by the pink volume dots or the magenta volume dots showing aggressive sellers those the market sell orders selling as price tested that 448 level and that bearish order flow really continues almost down to spy 446 before a few aggressive buyers come in and note the large option traders were were buying with iceberg orders that shown by the rising light blue line there. And that is pretty typical behavior for larger traders buying weakness and selling strength with large iceberg orders they used to hide their size. And then on the other hand, you can see the following cumulative volume delta as well as the following yellow line showing cell stop orders fueling the move lower. So here's some of the cell stop order shown by these right bright red dots helping to fuel the move lower. Alright, so the target would have been the 445 level the spy 445 level and price did not quite make it down to that level. Alright, so that was the the obvious short set up this morning. And now it looks like price consolidated for almost two hours just around and below the spy 446 level before finally moving higher. So the larger traders with their iceberg orders are finally starting to get paid. Alright, let's take a look at NASDAQ. So let's go back to hero. So we know that options traders were taking negative delta positions. And really that so that slowed down from about 11 to just after one o'clock and then it is that they're starting to take negative delta positions again, the SB 500. Let's see what they're doing. So the rising orange line and the positive value here, positive notion of value shows that traders are buying calls. That's very typical behavior. In an index traders buying calls and buying puts that shown by the falling blue line and the negative notional value there. And so far the put buyers are more aggressive than the call buyers minus five billion versus positive two billion. And for most of the morning, the put buyers were rewarded until again around noon when price started to move higher as aggressive buyers came in. And let's go back to the total signal. Let's see what zero DTE traders are doing. So zero DTE traders looking at notional value here for the green line, that's about two billion versus the purple line, which is all expirations. That is today, tomorrow, Friday, next week, next month, all expirations. So today, the zero DTE trades that options that expire today, that is making up about two thirds of the total notion of value today for the S&B 500. Alright, let's go on to NASDAQ now. And we'll take a look at the live market in a few minutes. Let's go to NASDAQ and not as clear a signal to me for the NASDAQ as there was for the S&B 500. Definitely for the morning. Let's we'll zoom in on this. So this is a combined signal showing options trades and market maker hedging activity for NDX and QQQ. So for the first few minutes in the morning, up in first 20 minutes, there was a confirmation and then some confirmation short. And then trader started coming in and taking positive delta positions.  So for me, hero was not nearly as clear and helpful for the NASDAQ. That's not always the case. But for today, as the S&B 500. So let's go take a look at book map, read, do a quick read of the order flow. And here's the reversal before the cash open that I mentioned at QQQ 373. And then price broke below the lower daily expected move. You can see the aggressive sellers coming in there. And price moved down all the way to the 369 level. And note here, the larger traders, first of all, looking at the falling light blue line, larger traders were selling with iceberg orders. So they were on the right side of the trade this morning. And this is the falling yellow line showing sell stop orders. So there's the sell iceberg. They're also buy iceberg orders there. The sell stops, all helping to feel the move lower. And note that aggressive buyers did start to come in right around here. But it took couple of hours and pretty substantial move lower before they are being rewarded. And note the cumulative volume delta line is rising, starting around when these larger buy volume dots come in. Right. So that is the NASDAQ. Let's go back to hero. And let's just check and see what zero DTE traders are doing in NASDAQ and making up a pretty large portion of the of the hedging flow today up until about the last 15 minutes or so. Now it looks like just comparing notional values zero DTE at the current time is about half of the water flow of the hedging flow today. All right, let's take a look at some stocks now. I'm going to start with Apple. Let's just zoom in on the morning here. Note the this is a nice divergence long in Apple. Note just a few minutes, maybe three, four minutes after the open traders options traders start to come in and take positive delta positions. Let's go take a look at book map. Let's go to Apple. So here's the first divergence long and price move down. Let's go take a take a look at hero again. And this next long was not really confirmed by options traders as hero continued after about 1120 to move down. Right. So that is Apple. Let's take a look at AMD and Karma FX. Yes, I will definitely take a look at Tesla today. So really the interesting thing about AMD here is the this large a couple of large block orders that shown by the vertical line here in hero. So these are bullish options trades in AMD. And let's see if we can figure out what they were. So first of all, we'll take a look at puts and calls.  All right, let's see what. Let's take a another another deep dive into this and we'll separate out zero the next expiration, which in the case of a stock would be a Friday expiration next expiration. So they're for single stocks, there are no zero DT except on Friday. So there are weekly expirations. All right. So the the next expiry for puts is shown by this kind of light blue line there. Cyan maybe I'm not sure. And then call shown by the green line. So what this is is options that expire beyond this week. That's all that's all we know there. So longer term position. So somebody is taking more of a longer term position in AMD selling puts. We'll take a quick look at book map. So really that had no no impact on AMD today. So overall still pretty negative bearish water flow here for AMD. And one other thing I want to take a look at is let's go back to hero. I'm going to jump down to IWM. I don't have IWM in book map. But this is interesting that let me take a look at one thing. All right. So the RTY we'll just compare IWM with QQQ. So IWM down about 0.93% versus QQQ 1.2%. So IWM still down for the day. But not down as far as the QQQ. So a little bit less bearish for IWM today. But options traders are definitely taking positive delta positions and IWM today. And that helped to set up a nice divergence long as options traders were taking positive delta positions and the price reversed higher right around 1020 or so. All right. The next is meta and note the 310 is the key gamma strike. It looks like around that level did act as support. And in the morning options traders were taking negative delta positions confirming a short setup in meta. So meta there were multiple. I'll just draw that with this tool. So multiple Pavex for shorts to VWAP to the 315 level to the 314 level. And on with the target price didn't quite make it to that 310 key gamma strike. And note all the liquidity in that level acting as a magnet for price. Liquidity that comes in at the cash open. That's pretty typical of stocks. Nice target there high liquidity also the key gamma strike. And then the put walls down below at 307.50. All right. Microsoft also confirmation short strong correlation between options trades hedging flow and price action and multiple short setups. There's the first if you missed that entry at 326 325 and note the shift in order flow here. I normally don't look at CVD and with single stock some sometimes it helps. I think it just helps to illustrate the shift in order flow here. Note the all the green volume dots aggressive buyers start to come in and the shift higher and cumulative volume delta. So nice short setup here in Microsoft this morning. Let's go back and take a look at hero. So traders were selling calls. Let's just zoom in. So up until around 1030 they were selling calls and buying puts and then around 1045 they stopped buying puts and start selling puts. And that's shown by the rising blue line there. So it's aggressive buyers came in. Well at first of all the sequence traders started stopped buying puts started selling puts and then they stopped selling calls that activity leveled off and then remember the shift in order flow aggressive buyers start to come in and so far that has not really led too much of an up move maybe now but it certainly halted the move down. Now it looks like a large block trade here positive delta. All right let's go back and take a look at book map and Microsoft trying to move higher. All right the next is Nvidia very interesting day in Nvidia. Let's start by looking at hero to Nvidia. Zoom in on this. So first of all I'm going to go to the portion here before the news came out. So in the morning hedging flow options trades definitely negative confirmation short. Note that level levels that activity levels off and price consolidates. All right let's go take a look at book map that's up to about 1120. It's right around here. All right so as options traders were taking negative delta positions price breaks below this early wedge pattern this morning at VWAP and the 450 level moves down several points toward the liquidity target at 445 scroll over here and as far as I can tell this was this was news something about a new grace hopper super chip platform so the news bots algos that read the news saw that and initially reacted very bullish. Note the buy sweeps that shown by the small green dots all also the aggressive buyers shown by the large volume dots buy sweep up to 451 and then price reverses sharply lower down to and note all the sell sweeps shown by the bright red dots down to 441. So a quick nine move point lower nine point move lower big gaps in volume there not much liquidity it was such a sharp move lower and then aggressive buyers start to come in. So let's go back to hero and right around 1150 aggressive options traders or options traders started taking positive delta positions moving price higher and note again here's a large block block order institutional order positive delta all right let's take a look at Tesla. So Tesla there is very often a very strong correlation between options trades hedging flow and and price action so the initial trade this morning was short up until about 950 and then options traders started taking positive delta positions setting up that divergence long let's take a look at that. So here's the first divergence long in Tesla this morning and then there was another one just looking at these trend breaks pull backs and another nice divergence long right around 1145 that was the second one that I had shown on the chart as traders started taking positive delta positions let's go back to book map so here's the second long note the trend break pullback as options traders were taking positive delta positions and let's check for gamma levels so the hedge wall is at 252 50 250 is not a not a gamma level but it is a high liquidity level note these sellers these orders were consumed earlier today and they were again just a couple of minutes ago let's just zoom into this more closely so now it looks like well maybe they may have pulled no it looks like those orders were most likely filled and no then they came in and with buy orders limit buy orders and you can see the absorption indicator showing that that's what that light blue square means so orders here these were sellers at 250 those orders were consumed and then they came in and were buyers at 250 that's a flip of the order book and then those orders were were consumed all right so karma FX says the 268 level feels real to me like it's headed in that direction I'm just unsure of when and how long so let's take a look at certainly not today not in play for today and let's see what the the gamma structure looks like a little bit further out in time so I want to go to let's go to equity hub take a look at my watch list we'll take a look at tesla so this is the composite view chart showing that throughout the price range shown on this chart the usual price range that is all put dominated that's the and it's kind of a moderate moderate level there let's take a look at this put call impact chart we can zoom in on this so here's the two 270 level 267 below that two so 270 is the call wall all right so the this level the call wall is a i'm sorry the key gamma strike and the call wall are both at at 260 but there is a pretty significant gamma at the 270 level so the key gamma strike and call wall are 260 10 points below so karma facts if tesla is going to make it up to 270 it has to get through the 260 level first that is again the that so that should act as resistance so it's important to note there you can see all of the the high amount of gamma at that level again that's the call wall that is expected to act as resistance so to get to 268 tesla is going to have to make it through the 260 level first and let's take a look at one other thing here let's go to history and see what the how the levels have shifted today so first of all the call wall shifted significantly lower from 300 to 300 to 260 all right so that is bearish and then also the put wall shifted lower from 250 to 240 also bearish but i would interpret this shift lower in the call wall as more bearish so we'll keep an eye we'll keep an eye on this tomorrow and see how these if these levels shift keeping in mind that the order flow and hedging flow for right now for tesla are positive right so again the key point there is to get to 268 tesla is going to have to get through the uh 260 level first let's go take a look at book map all right so it looks like uh tesla is having some trouble at the 250 level all right let's take a look at uh the broad market let's go back to the s and b 500 s and b 500 making its way back up to the the high of the cash open the 448 level let's see what options traders are doing so right now for the s and b 500 options traders are taking taking the opposite taking negative delta positions and price continues to increase there was a strong correlation this morning that's pretty typical and then that is um that relationship really is no longer holding this afternoon this is one reason i uh really enjoy trading uh equity single stocks versus the index is there is often a very strong correlation between options trades hedging flow and price action throughout the day much easier to read and interpret all right let's take a look at the nasdaq and pretty similar situation options traders fading the move maybe this will take longer to play out uh maybe tomorrow options trader taking options traders taking negative delta positions and prices still starting starting to move higher let's go take a look at book map all right so the s and b 500 this afternoon is a little bit stronger than nasdaq remember the s and b 500 is making it has made it back up to the uh around the opening print and uh at the cash open and uh nasdaq so far has not done that all right let's take a look any uh i've got a minute or two left anyone have any stocks they want me to take a look at before i wrap it up here let's take a look at invidia see what it's doing so invidia continues the uh the move higher aggressive buyers coming in trim break pull back long entry multiple long entries on the way up let's go back to tesla and see how it is resolving with the test of the 250 level so now the sweeps indicator is showing there was a buy sweep shown by small green dots up to the 250 level then a sell sweep down remember we saw the the flip of the book there options trader traders coming in with limit buy orders those were consumed with the sell sweep and we can see the absorption there and now aggressive buyers are starting to come in and let's see what options traders are doing and see if they're supporting this move let's go back to tesla and so far tesla um options traders continue to take positive delta position and i would i would definitely be looking for uh along here not a recommendation by the way so options traders taking positive delta positions so they are buying calls and selling puts both notional values are positive buying calls selling puts market makers take the opposite side of that and they have to buy stock there's their delta exposure so we'll take one last look at at book map so now it looks like some sellers have come in at 250 so tesla may struggle at that level a bit consolidate just like it did at the around the 249 level before resolving higher all right rs says uh great stream uh thank you thanks for the compliment thanks for your kind words all right that's all i have for today i want to thank everyone for watching thank you for your questions and comments and i will see you tomorrow thanks again bye