All right, folks, we are back here this Tuesday morning for another fantastic edition of our weekly workshop, Traders Talk, great to have all of our students and members alike inside our live trading room. We have Joanna, we have Grant, Rod, Abdul, we have Alan, Eric, Brad, Ravina, great to see, great to see Charles and Gary who killed it on Tesla earlier, as happy as I am for my friends here inside our live trading room.  Tesla flew this morning. So we'll have a chance to cover that at least and then otherwise, great to have all this back collectively on social media at CybertradingU on X Twitter, Facebook, YouTube, et cetera. So, hey, first and foremost, folks, actually, just let me get that QR code popping up top on the left-hand side of your screen there. Just make sure that you scan that QR code at the end of this workshop if you're interested in joining our live trading room. Get the full rendition of this workshop and all of the previous recordings that we've done.  This thing looks like it's about a rip and run right away here, this ANGH. When I say right away, obviously, as you could see here on the chart, we've been following this for a little bit and it's not really right away. This thing has been more of a tease over the last hour, hour and a half than anything. So, you know, I just came off a coaching call with one of our students and we were looking at this for a nice move and we were patient enough to hold off on it. So I was very happy that it pulled back and like, oh, okay, well, no harm, no foul. But you know what? The more times that this test is this level in a shorter concentration, I'll even inch out the penny here, 251, because just before myself and my student Barbara, we saw a smaller little iceberg popping up out of nowhere at the price 251 on this trade for ANGH rather than 250 and just here is where we were thinking about it and it failed. So we'll make that price 251. If this could blast over 251 or the more times it nips at it, we should be getting a much more decisive move or reaction than just a mere few pennies going up. And even this, this is, you know, little move or a little mid-sized move, 20 cents. That's nothing big.  It's basically at this point in the day for this trade because we saw it move up earlier and pre-market held it, came back down. And from there, hey, our whole motto at Cybertrading University is to follow the big money. So of course you wanna wait for the break above that level, but the key is like I said from the top, you wanna have this test this level and nip and naw at it in a shorter concentration in a shorter timeframe. So from this level test to like this one, there's like a hour and a half that went by. So that's way too much time to just assume it's gonna pop and run again. Oh, it's trending on up here. Well, and if it were to make a very unexpected blast over that level at that time, then I would expect resistance to become support. But obviously that didn't happen yet and we're still waiting on this to retest. So, you know, throughout this traders talk workshop, folks, hey, we're gonna check back in on this ANGH trade. There's some news that came out on this company. I think they received like a $50 million investment or payment of some sort from a private company there and led to a nice pop and drop at first. And with this moving on up during traders talk here at the beginning of it, I was hopeful to see a better pop. Again, we'll come back to this and kind of go through. Now, with that in mind though, we have done a really well across the morning, not just on this ANGH, but we've done well across the board. Like I said, a few of our students like Gary killed it on the Tesla stock. So let's jump to that actually next. And then from there, we'll go through a couple of different emails. Watch, here we go, maybe not so fast. Hold up, trying one more time here. Watch, the second I turn over to Tesla, this thing's gonna blow the roof off. So I don't wanna get stuck watching this the whole time, but actually as we're looking at this live right now, you may have seen it on level three. It just popped up on book map right now too. You had to look at the 93,000 share iceberg that just showed up here 244. So as far as like, now or never, come on, let's see it. Oh man, if this breaks under this support level then I would say more likely than not game over, but this just popped up right now. And you don't even need book map to see this. This is, I believe, right on the NASDAQ here. It's on my matrix, it's on level three. So with that, let's see what happens. Could this pop? All right, so again, on top of this and on top of Tesla that I wanna jump to, for anyone that's new here for Trader's Talk, this is a weekly workshop that we do every Tuesday morning. We have a good chance to break down trades just like these, but more so questions that were sent in from Trader's from earlier, from like overnight from yesterday. I see, I believe I have one from Hamza here, from David S, from David W, from Allen. I'll take a look at that just a moment too, from Allen. Got one from Gary, but he was just telling me, yep, back in on Tesla there, it was from 1030 in the morning. Gary wrote me, so there you go, man, good catch. And I'm gonna read Gary's email there at the end too. But yeah, for right now, we'll just keep an eye on this for another minute, I reckon. Don't want the whole workshop to go by without this popping, right? But when you have a 96,000, 97,000 share order, just popping out of nowhere like that, you gotta keep an eye on this, follow the big money, right? All right, I'll tell you, hey, really quick, for all of us collectively, if you're new to our social media channels here at CybertradingU, or if you're an enrolled student or member of Cybertroup already, I've mentioned this already, but yesterday, actually, I was on BookMap's YouTube channel. They do weekly webinars, daily webinars of that, but a long list of presenters, Fausto normally is on their end each and every month and Fausto is away this week, so he gave me the keys to the castle there and I did a nice webinar, very similar to this, with Bruce Pringle and the fine folks over at BookMap. So definitely take a look at that too. You can just go on YouTube, look up BookMap on their channel, it's like one of the last videos from yesterday, but very similar situation actually where I was discussing a different trade. I took it off here, the CDIO, and out of nowhere, an iceberg order just popped up on the buy side and it's like, okay, well, hey, it's almost like they're listening to me here. So give this another like 30 seconds to a minute. If it smashes below this order and actually breaks this support, then obviously we'll just move on, but I wanted to see a lot more, a lot more exciting of a move than just this. So we'll come back, I reckon. Keep an eye on this though. So I didn't wanna talk about Tesla before that iceberg showed up. Obviously Tesla, speaking of a powder keg, this thing broke out once again here today. It broke out last week to fill a gap on the daily chart right there. So it ended up making another big move up this morning. It goes to show you folks, like A, and Fausto will obviously tell you this himself and myself included here right now, but we're not perfect. We're not catching every trade at the bottom, selling every trade at the top. And I know that everyone here knows that inside our room, but let's take this step further. I'm not catching every trade at the right time where I should be. I'm not lining up every stock that I'm semi-interested in. You know what I mean? So this morning, myself, I was more inclined to follow Spy at the minutes meeting here later on. It's a little wishy-washy market, but I was following Spy. I was following AMD. I didn't get the bounce I wanted there, but it's just Tesla. That was my third stock or third ticker that I was like considering. And I decided not to line it up. I said, ah, this might be too much work. Like, I like the two that I'm working off right now, this being in pre-market. Then add a nowhere as soon as the market opens up, this thing flew. So I want to go over this, how could we anticipate not just the pop-up, but where were the better levels on this trade? Where were the better levels to work off of? Because really going into the market open from 830 to 930 or from 8 to 930, trend of this stock is down, right? So at that, you should be anticipating a little bit more selling pressure perhaps. Let's take a look on book map here. We'll open up the heat map now. Okay, so for something this expensive, you can't just say dollar levels. That's kind of silly because you say that for a $20 stock, not a $240 stock. I would look to say every $5, if anything, to be a level, every $10 is even going to be that much more of a price on top, but you could say something like, oh, 235 could be a potential level to work with once the market opens, 240, 245, right? Those are assumed levels for Tesla.  So it's not every dollar and every $5, you could definitely assume you could, but specifically outside of the $5 incrementals, we have 240, 242, 245, we said, 246, and then 250. So we're not gonna plot every one of those, but I just wanna write them down, okay? So outside of that, there was a lot of volume filled here. Look at the CVP column. This is pretty much around the price, 236 and change, 236 and we'll say like 73 cents if you wanna round up to where the green is there, 236.80. And then lastly, the only other level that you would look to plot if you're following Tesla and this you only plot once the market does open, but it's the opening bell print. And conveniently enough, this is literally just at 235 the level. So it makes it that much simpler for us at least there. So we know it popped, we know it moved up, but how could you use the levels that we just spoke about to your advantage? You know, was there a key level that we could have used for an entry? You know, within the first five minutes, you don't really wanna just jump into something. So it's easy to tell you it popped here. If I did have my level set here, I probably wouldn't be taking this trade to just be very straightforward with you as much as I would wanna tell you, yeah, I would take it. Like it's still 933. You know, if we teach you in class the cyber clock, normally you wait till 935, maybe a minute or so after that, jump into something shortly from that point. So right here would have been a clean entry level, but it's still too early in terms of time for me. If it were to pull back there afterwards, that would have been, you know, a nice support test. We have the 23680 level that we said, that's from the CVP column from book map, basically right there. Well, you know, it breaks above that price, literally at 935, mind you. This is such a sharp pop though, that the same thing is kind of said there as it was at 235. This is just on a rocket ship, no pun intended deal with Elon, but you know, just took such a nice pop where on a pullback, that would be good support. Okay, like the more it pops from there on a pullback, that would be really good of a support level, right? Doesn't do that in hindsight. So what gives? Where can we find our real level to work off of? The next level I had set was not until 240. So are we gonna let it ride all the way up to 240 before we think about jumping in? Well, again, the same rules apply where if it breaks over it really nicely and pulls back, the first test of that level could be the best test, but to be transparent with you, in my eye, I thought this moved up so much without even giving me a single pullback at first where I said, you know what, let's just kind of wait at 240. I didn't take the straight whatsoever today. Gary was milking this for all it's worth for me, but you know, I didn't take this even at 240. I wish I could tell you, I jumped in eventually. Honestly, I'm happy I avoided 240 because this was very chippy around there. I think it was around, if I'm not mistaken, the VWAP price too. Maybe that was later on. Yeah, that was later on, okay. That was later on when it came back down to 240, but you know, right here at first, first test being the best test, that could be worth something. But I just thought that it popped so much without giving us really any inkling of a pullback that I wanted to wait here. And what happened was it dropped a little bit and at a deeper shake, I said, okay, well, let's get more. I was thinking that it would pull down closer towards where we had a little structure here around 237 and change, maybe like this little bump from CVP, VWAP kind of lining up right there too around this timeframe here. It just ended up bouncing back up, made higher lows and I'm thinking here, well, maybe there's a chance the more it kind of holds into this without breaking lower from it. It could go, obviously it does, but again, I didn't have like Uber confidence to take that trade right there. I wanted more of the VWAP and more of a deeper pull. So, you know, one thing that you could say here is that certainly your next level, 242, we had it from pre-market actually, that iceberg early in the morning, looks like it only got larger, 62,000 shares roughly there. The first test of this level, if we didn't get as deep of a pullback down anyway, hey, I'm not too interested at this stage, but this is where I could tell you, much like what we thought we had at 240 here, the more times that it tests this level in a shorter concentration, in a shorter timeframe, like our friend, A-N-G-H, you know, there's a case to see this to try and make that better reactionary pop, right? So, it took a few stabs at 242 and it kept going. It got the job done one more time, like, you know, broke over and under, okay, that's the first test, that's normal. You would probably expect for it to tank if it hasn't already, but it kept holding. And then one more test of it, just the next test, it's really just within a few minutes at that, couple of minutes at that, it led to the breakout higher, right? So, in short, that re-test in a shorter concentration is what I look for if I'm looking for continuation. I was just more hands off here though, and the spy wasn't really going much of anywhere at the time, it was very rugged, flat, you know, dropped off afterwards here, but with Tesla I thought eventually it would kind of come back down to planet Earth, but it took a little bit longer for that to happen, and even here at the VWAP, this would have been a really interesting test right here as support. You got the job done over time, but it still took a few minutes, and now we're kind of heading into sideways time of the day where things typically go flat or reverse and full. You know, a lot of times we'll tend to see the spy look to pull back a little bit, so not only that, we've got the Fed minutes meeting at two o'clock, so we'll see what comes later on this afternoon and see whatever they say. I don't think it's Powell speaking as much for this one, it might be the other Fed speakers out there, I think they have the minutes meeting as they call it. All right, so that's basically Tesla, unfortunately it didn't really make as deep of a pullback as we wanted it to. You know what, actually if I wanna poke at this for a second, just gonna play around, I might be incorrect with this, we'll just say. I have no idea, I'll find out. Obviously we had a gap fill on the daily chart, but if we're looking back from the last few days of the last few days on the daily chart, let's see, I just wanna see, is there any larger volume days that stood out? Like for instance, I mean we have a sharper closing spike here on the 14th, it's above that price right now live as we're talking, but it wasn't by the time the market opened up earlier, that was on the 14th, that was from Tuesday last week, kind of a random weekday, nothing really too special about that exact weekday, Tuesday the 14th, but it looks like you had a sharper closing bell spike a little bit larger than the others, so I just wanna take a look, what price was that at? Just wanna poke at that there. That was coming off the CPI report, right? So perhaps there could have been a larger print there for that reason, but that was at 237.41 cents, the price 237.41 cents. So let me just plot that there, I'll bring this back to a one minute chart. Was that a level that you could have worked off of? Obviously this kept pushing up throughout the morning, but it still didn't pull back that deep, I mean it came close here in this consolidation, broke over it, for as big of a print as you had there, perhaps that could be supported, still didn't even nip it, didn't even come as close to it as you'd wanted to, hovered above it, but if you're looking for that under and over, just kind of glides up, wow, it goes to show how strong Tesla really was today though, that's for certain. All right, so we covered at least the ANGH, let's go back to that, did it pop? It didn't, all right, so we didn't miss out too much of their live right now, at least looks like more of a rounded top here, so just turn back to that for the time being there, the ANGH because if it does make that move back up as I'm going through emails from students, then we'll definitely at least do an intermission, cut through, all right, so email time, for grant new hooded Jeff, all of our students, we always encourage you to send over any trades, any journals and email questions alike, right to josh at ctutrading.com, that's my email address, for anyone that's new to CTU or new to our streams entirely, then feel more than free to do the same, clear out a couple bogus emails in between. All right, so first question here, this was sent from yesterday afternoon actually, so this was from Hamza here, and he was asking, I signed up for the one week trial and I'm taking the course on learning the book viewer, NASDAQ book viewer, so level three, just as a quick heads up before I continue, that is the program essentially on the right side of my screen here on my platform, that essentially is what you can consider equal to the NASDAQ book viewer, so I'm gonna show this to you in just a moment here, Hamza and all of our new members here, so Hamza is referring to the NASDAQ book viewer program, this right here, and this shows you every buy and sell order that's out there at the current time for the NASDAQ, for any orders that are being routed across the NASDAQ ECN alike, you'll be able to see it pop up on this program, so if you don't have level three integrated into your platform, if you don't have book map, AKA level four, this really is your go-to, so Hamza was saying, you notice that the datastore.NASDAQ website, he signs any launches book viewer and signs out automatically after a few minutes, then book viewer also stops working, I also wanna know what I have to do so that it keeps working all throughout the day, it times out, I know it times out after like maybe an hour or so, if you check here just on your own, go through like click the help tab right there, you'll be able to see a little pop up just for the NASDAQ site, there's also right here book viewer facts, a little PDF that's on the datastore.NASDAQ website, so it'll give you all the deets with all the stuff going on with book viewer, but actually since you had asked just that, I mean I do wanna at least bring this up to show, a little demonstration of book viewer, why not? So this is the NASDAQ book viewer comparative to the trade station matrix here, one benefit of book viewer is that it has a lot more depth, you could actually go through like 120 different price levels here and see. Don't need to go that far out though really because not every stock is gonna make that big of a move to be transparent, so looking at where we have iceberg orders that are closest to where this stock is trading at, well right now there isn't really too big of an iceberg in general out there, there's at $2.13 here about 11,000 shares, that could be support, but looking at the size of a lot of these other orders out there, if there's something that is that much more significant compared to the rest of the field, that right there is something more compelling to make. If there is something that had a really large amount of orders in total at the price, instead of 20 here total orders at $2.50, even if this said 50, something that stands out that much to me, makes it a little bit easier on the eyes for me to call that support resistance. So you could detect icebergs and support resistance, not just from the shares column here, but the orders column tip, the orders column. Let's go through just a random stock right now, completely random, I have not Tesla, not A&GH, let's go AEO, I have this on my notepad, so not so random I reckon, but I didn't trade this today. It was on our morning list, AEO, doesn't really seem like it's shown a big iceberg right now. Yeah, this trade honestly, just I'm skimming it here, but very quickly I could just hint to you, there's nothing here that I would find respectable as a level, nothing. There's nothing, nothing, not at all. So with that said, all right, it's trending down a little bit off the last peak, is it possible it can make another drop? You know, it came off bad news this morning, so yeah, it's possible, right? It's anything's possible, right? Sky could be rainbow colored later on today, right? Who knows, just it's to say that without there being a significant iceberg level, I wouldn't really feel too keen to just jump in to jump in. That's all. Back to our friend A&GH just to check, haven't seen much going on on this lately, so that's all right. So again, Hamza, just with that, just go right back to the book viewer website, there's actually a little link on the book viewer website right there, I'll show it here for you. I don't think I showed it here, but book viewer facts right here, click that, and then book viewer user guide, it'll give you all the information that's preset for this. So it times out, it definitely does. For me, I thought it was like maybe every 30 minutes if it goes inactive or every one hour if it goes inactive. It's not just every few minutes, at least from my experience, if it is for you, then maybe it's a setting, but it definitely times out, but it probably got 30 minutes an hour, so it does. All right, might be wondering why I'm wearing a hat today. I forgot to get pomade when I went food shopping yesterday, so I'm looking like a golfer today, but otherwise, let's see what other questions we got right now. We got from David S, here we go. So David joins, he's going through the bronze classes. So David, perhaps being a cyber group, annual member has access to the phase one stock course, joining us actually really quick folks coming up next week. We got the phase one and two classes resuming once again. So if you're David or any of our new students joining us, definitely be on the lookout for that. I look forward to resuming the phase one classes again. We're gonna dig a lot further into volume and the meat and potatoes of really following order flow alike. So David going through classes and conveniently enough, watching the time and sales class from this past July, that's actually one of the classes I'll be doing next week. The question that keeps coming up in his mind is he's seen in traders talk and the class is how he should always, he should always have quite a small stop set. Let's say the level is 1850 and he gets in like around 1853. Well, he's basically what he's saying that I'm saying, which is true, not to really set too big of a stop. And the example David is referencing is like if he gets in at 1853, the price, a few pennies above 1850, they'll set a stop a few pennies under 1850. Let's say, you know, it doesn't go below 1847, right? Makes sense. That's exactly how I abstractly teach it, right? You wanna set tight stops, especially under your level. But when the stock approaches the level, it fluctuates above and below that range since you never know which nip will be the one to take off, I would just get stopped out if I, oh, so David, you're talking about, my friend, you're talking about not setting a stop to protect you, you're talking about setting a stop to enter. Is that what I'm hearing? Because I can go over that a little bit further here, more on a coaching call likely and more phase two probably there even. But what David is saying is, since you never know which little nip or break above the level is the one that will allow it to take off, a lot of times he would just get stopped out if he enters after the first few breaks and it's just not the right time, even if he thought it was significant there. David, my friends, this happens to the best of us, let me tell you. It's true, we can never be perfect or 100% with trading. If anyone says that they can be, they are lying to you.  But at least for those traders that I do see, they show full transparency where they take a loss because they took a false breakout and the stock pulled back, they had to cut ties with it pretty shortly afterwards. So a lot of times that will work out in your favor. And with saying that, if you're trading the stock, if you're even doing options, even more so if you're doing options because the leverage on it essentially, the volatility. A, as long as you're not putting all of your money in one position, certainly you can try and take another position shortly after you get stocked out the first time. So for me at least, when I look to take a trade, a large part of my confidence is based on timing of the day. So let's say Tesla, okay, when it popped at first, it was right time of the day, it was right within the first few minutes, first 15 minutes of the morning. But it moved up so damn much that you become a little bit leery of trying to take that trade, right? So you'd wanna pull back. Obviously this didn't pull back to where I thought it would, it kept going up more and more. All right, well, if you are going to take a trade on the stock, which I didn't, but if someone is going to take a trade on this type of stock, you wanna work off a rebreak, right? And that's what David already knows from class. He knows because he wrote it to me that way. But that's where I could just simply tell you here, David, we're like, 242. This was a clear level that we wrote down. I wrote this down as a level from pre-market. We run over 242. Our next pre-market level would not be until 245. So in theory, if we have a situation where we could anticipate a pop on Tesla here and it has the chance to make a three-point move, sounds good to me. Now that's where I could tell you, it broke under this price as support, right? Now I could just tell from David's dialogue, I could tell he knows the answer to the question I'm gonna ask. I want all of us to answer it though. When it breaks below, support here at 242, and it drops, and it takes about an hour, a little bit longer than that for it to move back up. Support should initially become what? There we go, right out the gate, Ryan, Rod, Mark, Charles, Sam, Allen, all saying resistance, absolutely. So it became resistance here, first test, best test, and basically this line held as resistance. Well, trend is up, and you know what? The more times that it nips and naws at it from this point forward in a shorter timeframe, we should be getting that more decisive reactionary move. That's my thought about this. So the first test here, I absolutely 100% would not be taken.  If a stock rips and runs without you, you're losing the opportunity to make money, you're not losing money that's already in your account. You know what I mean? Right? So how often do we see stocks like this just continue to make such a pretty run up right away? Not too often. Normally around 11, 15, 11, 30, 12 o'clock going forward, we typically see more shakes and pullbacks, false breakouts, lack of momentum. So that alone allows me to be more hesitant even on like the next test here. Now, obviously the more it nips and naws in a shorter timeframe, I grow more and more confident. So that's where I will tell you here. Okay, let's just say if I jump in, let's say if I set a stop over 242 and let's say I set a stop order to buy this stock over 242, so it pops above it. And let's say it fills you right away, you gotta make sure you set a pretty tight stop here, I feel. Because hey, this was a significant price from pre-market. Our next support is not until 240. So if it snaps below this level here, it's not a guarantee it gets to 240, mind you, but I don't wanna be held liable for a potential reversal. No guarantee it's gonna look to continue right here, right now, might take three hours for that to happen. I don't wanna be pulling my hair out for three hours. So if I do decide to jump in on this trade, I think how David had mentioned it was using a stop order to actually buy the stock. You could do that, but you gotta be prepared and have the level there for the taking. I don't always have time to set a stop to enter a stock to jump in because it might be too fast and I might just turn to it right when it's making the pop. I'll just use a regular old limit order. Let's just say right here, if you were to take this trade, if this is such a big level from pre-market, then we should be seeing a pretty good reaction off of it then, right? We saw a dollar or so move up earlier. This is a clean hold of resistance. This is a head fake where it didn't go anywhere at the time. So the more times that it's nipping that level, you should be getting that reaction. Whether it's a complete head fake and it tanks after or with trend, you're assuming obviously for that better move to be upward. So that's where I was saying, okay, trend at the time here is up. That helps, helps the cause. So at least you can anticipate a potential better move here coming up. Now the thing that's in its way here before getting to 245 is you have a new order that showed up at 243, about 75,000. We're not gonna be perfect here with figuring out the exact high of the day on the stock folks. If the market pops coming up here, then rising tide could lift all boats. But otherwise here, 243 definitely needs to get tested soon. Because if 242 is such a big level, then let's see it make that better run up there. Even if it gets to 243 and then drops, at least that's somewhat of a start. If it just kinda crawls up here for about 30, 40 cents and then drops, that's to me just like another false breakout. That's like a red flag. So where I tell you about setting stop losses to like protect you, you gotta make sure this holds above 242 for me here. If anything, maybe if you wanna base like off previous little dip points, maybe you can go as low as 241.75 or 241.85 here is a little dip point there to hold this little support. But this is a good example. I mean, hey, first test, best test right here as resistance, the more times it nips and naws at it in a shorter timeframe, you'd like to think that you can have potentially a much better move ahead. What's the closing print from the 15th year? No, it's a random weekday there, Wednesday, 242.84. Okay, so you know what? Yeah, there's gonna be a little turbulence here coming up and we hope that we could break right over this turbulence here, but it looks like the close price back from Wednesday last week, that's the highest close price from last week in full. That was a little bit under 243 and then you got the iceberg order that's there right now on the heat map. So it definitely needs to make a sharper move up there sooner than later. And it definitely has potential to do it. It's doing it in front of our eyes right now but sooner is always better than later. You don't wanna have your foot taken off the gas pedal. We made the little dad joke earlier when I did the morning meeting, but the difference between a stock and a car is that when you take your foot off the gas pedal when you're actually driving, car just coasts and then eventually stops and you take your foot off the gas pedal for a stock for an equity, it puts its foot on the gas pedal for you, shifts into reverse and all of a sudden you're going 60, 70 miles per hour the other way. So let's see this try and go, but even here we gotta see it break over this resistance sooner than later. Nice move. Nice move. Let's go back to our friend, A-N-G-H, did this pop? Nope. All right, that's good. Happy to miss that. All right, let's keep it moving. David asked if you have any follow up questions with that, at least if I didn't answer that question in full, please let me know. David asked to David W who, I don't check these emails actually before I begin here, so folks, so David W saying, thank you, Josh. I don't have any questions at this time. All right, keep moving. All right, I always get that every now and then. So this one is from Alan. So maybe not as much a question perhaps here, I'm just gonna read it out loud. So just learning a lot from phase two in the student portal to prepare for successful trading. I love to hear that. You know, I have the chance to speak to a lot or all of our new gold students as they enroll. You know, we always set you up with a quick phone call with myself initially, you're like five, 10 minute phone call and I hear from so many new students that join us and it's no rat race folks. It's no race, you're only competing against yourself but for like a student, let's say that joins on Friday, I would call them today and introduce myself. I did tell them, yeah, I'm on to phase two already. Like holy smokes, for our students to put in the effort to go through the recordings and all the classes, I really appreciate that. So thank you very much for students like David S, David W, Alan, Alan going through phase two. Okay, so yep, we got a couple of questions here. There we go. Is there a rule of thumb on how close, on how close you set your stock when trading long or trading short? There we go. So nice segue, that's for sure. So we covered it here on Tesla to a great level, to a great degree, right? Getting a bit of a pullback here, a bit of a dip here in the market right now, it looks like you wanna set a pretty tight stop, price dependent.  Got a stock popping right now and this stock I was actually gonna go over, Turing traders talk here, CDIO, this thing actually moved for us yesterday and out of nowhere, just now, about 12 minutes ago, 15 minutes ago, just popped once again. So let's actually cover this here briefly as an example. Point being, you wanna set a pretty tight stop because when a stock breaks through a big level, again, I don't mean to sound like one of those wind-up dolls you pull from the back, but when a stock breaks through a big level, we should be getting a much more reactive move. So here, although this broke out so nicely, this could have been a potential head fake. So where it breaks over the level 150, rather, it re-breaks over the level 150 because it was trying earlier and had a few headfakes. So that's where you even furthermore wanna say, you do wanna set a tight stop. Right here, let's say if it breaks above 150, you jump in at 152. I'd much rather get out at 148 here and really not have to worry and pull my hair and think about it. There could be other stocks making a better move here at the time. So I know it could be frustrating for new traders alike or traders that are new to Cybertrading University because if you're new to day trading, you might not be as accustomed to setting such a tight stop, but for the stocks we're trading at the times that we're trading them, we're trading them during high volatility. So the way that we teach it is if that's such a big level and we're risking the money to jump in and actually buy it, then much like Fausto calls it the 32nd rule, you gotta see this thing pop. You gotta see it rip and ride and really continue to go. Worst case scenario for me on a break like this is you'd wanna see it hold over 150 just flawless. If it just kind of doesn't make that move at first, but just holds over 150 perfectly, that's not my cup of tea. Literally, as I'm sipping black tea actually out of this mug, it is not my cup of tea where you wanna get that larger move sooner than later. So if it holds the level and then runs, I'll take it. This thing popped pretty nicely at first. It shook once or twice, but this didn't come down to 150, it eventually grinded on up. I wouldn't really call that flattening out as supportive much and trying to make the switch from unhealthy energy drinks to black tea, much cheaper and unhealthier too. All right, so Alan actually had a second question actually here on top, so my apologies. I think he had a second question here. He says those would be a couple of practices you can go over in your Traders Talk workshop today. So I think it was just in general Alan was asking just in general with going long and with going short. It's the same concept, just inverse. Like if I'm going short on a stock and it breaks under a big level, I'm expecting a much steeper drop like AMD today. Direction down, going into the market open and with that, it won't dropped off at first, support became resistance, it pulled back and it broke back under big support here at 120. So much like we were saying with a more expensive stock, something like AMD, I'm not as, I don't even like using dollar levels for AMD. I mean, I will if I see a reason to, but like every five, 115, 120. So here 120, definitely a big level for me and right away on the first minute, it snapped under it, big volume got filled. All right, the more times it nips and does here and breaks under it, we should get a much better move than just a few pennies here, like 20 cents or 30 cents this is for a $120 stock, this thing should be making a dollar or two move at least. So it's easy to say this tanked afterwards and made the move down, but when it re-breaks below this 120, you're not trying to set a stop like up top here. There is zero need to set a stop that wide in my opinion there. At that point with it already testing that level and it's breaking it again, I could use a catch, I could use a phrase here, not one of my catchphrases. I could use a phrase here, but it's rather blunt and not really meant for all ears here. It's just to say, let's see this make this move going down or otherwise it's gonna make another poppin and then break out higher and just there's no need to hold onto that. All right, Alan says I'm still in the process of setting up my monitor and laptop and getting a platform interactive brokers, he says and book map that is. Yeah, interactive brokers a great platform to use and you have a bunch of students in Canada that don't have access to trade station here or they don't have access to the actual thinker swim and interactive brokers is such a good platform, not just for anyone up North, but anyone alike if it's a great international platform. All right, so I had a question, I think from Abdul on the chat board here, just wanna cut in between going from top to bottom here really quick. So Abdul asking his book viewer part of book map. Nope, book viewer is right from the NASDAQ website. So I go over that in the phase one course where this is like the bare minimum version of level three. Like the matrix here, I already have integrated into my platform. So I use that because it's just easy. I have book map which is level four and if I have book map here then there really isn't much of a need in general for book viewer here. So for those that aren't using book map and if they don't have level three integrated in their platform then this is a must. Then this is your, you absolutely need this then. But again, if you have level four book map or if you have like trade station or interactive brokers interactive brokers platform has the book trader program which is like the matrix basically. It's integrated in their platform. So that right there is a go to. Marx says if you just hit go every 15 minutes or so on book viewer, book viewer does not time out. Well, that's more of a manual thing though, right? So I think Hamza, one of our members asking earlier is like why can't it just be left open like your platform is running over like overnight or into the morning. So I understand.  Maybe the settings here readjust you have to try and reformat all the column selection. That could take time from trying to jump into a trade. Honestly, so I understand Hamza's question there. Yeah, I think it's like 30 minutes or so and times out or so. All right, so folks current time is 1150. Let me just double check your across the board right now to see if there's any questions alike on YouTube, Twitter, X alike. Let me check my spam folder right now. I said I was going to do that. Sometimes you got one or two that somehow lands in there. Not today, that's good. All right, last one from Gary. He said this was not a question. No, he says just letting you know I'm back in now and continuing the training while he was away he did make some good long-term trades. Spaya 414, ooh, nice. And Gary had some long-term Tesla calls March 15th expiration. So definitely doing good there. Yeah, pretty nice Gary. Now, to at least add on top of that Gary and I'd made mention of this week after week now at this point really beginning from like probably late August. And I was wrong with it at first.  I'm definitely expecting a meltup in the market though. And we started to see it the last week and a half, two weeks. If you think that that's the end of it I believe that there's a lot more from where that came from. So if you are more bullish you don't need to be bullish. I'm not forcing anyone's hand-mine to you. I'm just telling you my own thoughts but myself, since I am bullish I'm gonna be looking for some more dip opportunities or breakout opportunities day to day. Not always gonna be there at the right time or the right day to take the perfect move. So that's where you gotta set tight stops. Now you're not always gonna get the right day or the right breakout. Abdul is saying I bookmarked through Bruce and CTU so I could have more than two trades to like. I'm not sure what you mean there Abdul but I have more than two trades selected. I just know that if you're saying if you have bookmarked then you're definitely set. If you have bookmarked here just like I have then you're good. You're good to go. All right so actually the CDIO. I was gonna go over this a little bit further. This was the one that broke out from $1.50 I believe from yesterday. It popped in the afternoon pretty nice. Looks like we had a ton of buying here at $2.00. Green so you know actually pulled back this morning there. This is a little bit of a 50-50 here and not too much of a surprise here for myself that it pulled back and it tanked. It broke below the opening print also green. It broke below two where we had a lot of green buying from yesterday. And it tanks. I 1000% would expect support to turn into resistance here. So when this moved up and it broke over the VWOP we weren't watching the stock at this very time right here but I would not have expected as clean of a breakout here at this time. So I would have expected a lot more of a fight at $2.00 or at least for it to pull back and like Tesla I see it pull back and try and become support. Well now at this stage let's just try and even see where the next level is. Not a whole lot in between the two level and $2.50. A lot of volume accruing here at $2.30ish. So the more times it can nip and naw at $2.30 there's a chance for it to pop but I'd still be a little reluctant here heading into like that garbage lunchtime of the day and such a quick pop though that this thing had. Yeah there isn't anything here that I could really use. There is nothing here to my advantage that I could really use. $2.20 maybe a potential volume level but right now $2.30 is looking more like that price here. So right now there isn't a whole lot that would lead me to say is it gonna make the move up to $2.50 definitely right now or is it gonna make a lower high and pull back down to $2.00 first. We'll figure that out soon enough but I'd say $2.30 is starting to become a price level here that you gotta keep your eyes on. All right so folks say we're gonna finish up perhaps a tad early here today but not too surprising we got Thanksgiving obviously in a couple of days here in the United States allow me to wish everybody in their family a very happy Thanksgiving going into Thursday of course and if you don't celebrate if you're not in the US don't celebrate have a nice day off at least at that. We got the market on a half day on Friday so we'll be open C2 here will be open in the morning I believe that I'll be doing the morning meeting as usual and we might do an afternoon meeting very like a quick small afternoon meeting with Richard like 12 o'clock markets will close Friday half day at 1 p.m. eastern time so just be in the know with that make sure that you're at all positions there before the weekends you don't wanna turn a day trade randomly into a swing especially coming off a holiday week. For all of us here otherwise on Facebook live LinkedIn, X, YouTube, et cetera all of our social media platforms at CybertradingU make sure that you're subscribed and followed there on top but any questions that you got for myself here just following up from this workshop feel free to shoot me a quick email Josh at C2Trading.com that's my email address right there and again just at CybertradingU use our social media stream and platform just make sure to follow us collectively. All right so from Margaret Lawrence, Grant Abdul and Alan Sam, Charles Rod and all of us here collectively I'll be on the horn back at 2.30 for the afternoon meeting and we'll go from there. All right folks see if there's any other stocks that can make a better move at that time. Oh last reminder we got the Fed Minutes Meeting ending at 2 p.m. So it should be kind of a choppy market up until 2 p.m. Who knows what's gonna be said during that meeting and which way the markets will break and hey going into our afternoon meeting at 2.30 we'll be reacting off of that at least so it could be a nice little afternoon to work with coming off that minutes meeting. All right folks oh and then yeah NVIDIA earnings after the bell so I would have mentioned that at 2.30 anyway but again from our friend Damon here in the chat reminding us NVIDIA earnings after the bell today so that's after closed but we'll definitely make another reminder of that later on. All right folks I'll talk to you all later on take care.


So, let us start with from whatever we had discussed last time. We had discussed two examples of what in classical mechanics are known as inelastic collisions. In the classical mechanics we are used to not conserving the mechanical energy at that particular moment of time we used to just conserve momentum when such type of collisions were discussed. However, we had discussed in our last lecture that in relativity we have to also consider conservation of energy along with conservation of momentum. Hence, we had to apply conservation of momentum which eventually led to increase in the rest mass of the combined particle from the sum of the initial rest masses. So, if we have two particles which collide with it with respect to each other and then they get stuck to each other then if this is m1 this is m2 then the combined mass becomes larger than m1 plus m2. This is because we are conserving energy and we say that effectively this type of energy is actually never lost and whatever was the energy probably has been converted to some different form of energy not really mechanical energy. So, these are the type of examples that we discussed last time when we said that even in the classical inelastic collision we will have to conserve the total relativistic energy. Now, let us go ahead you know in our last lecture we had introduced a concept of zero rest mass particle. So, let us go little bit ahead with this concept of zero rest mass particle and try to discuss in today's lecture little more about this zero rest mass particle. See we had said at that particular time that it is possible that this particular particle could have a finite or non-zero energy and a non-zero momentum but in that case this particular particle must move with speed of light. And if it so happens you know that this is the standard expression for energy to momentum this is the total relativistic energy e square is equal to p square c square plus m0 square c to the power 4. So, if m0 becomes 0 this relationship just reduces to e is equal to pc it means for a particle with zero rest mass the energy and the momentum would be related by such simple equation as e is equal to pc. Of course, this particular particle must be travelling with the speed of light. Now, let us introduce the concept of photon it was originally in the explanation of photoelectric effect that the concept of photon was evolved. It was realized at that particular time that the type of frequency dependence of the energy of the electrons which are released as a result of photoelectric effect can be explained only if we assume that light is particle light. So, in fact we discuss in photoelectric effect experiment that light has a dual nature it could show as a particle it could also show as a wave. So, photon was essentially the idea of photon was created with a particle concept of light in mind and that was necessary to explain the photoelectric effect. And this particular particle was considered to be having energy of h nu where nu is the frequency of the wave that we have been talking about. So, if there is an electromagnetic wave or there is a light wave with frequency nu we can imagine that this particular light consists of photons each one of them has a energy h nu and of course, this particular photon travels with the speed of light. Therefore, this photon qualifies to be called a particle with zero rest mass. So, this is what I have written explanation of photoelectric effect indicated dual nature of light and light could be imagined as consisting of photons having energy h nu. But we have just now seen the relationship e is equal to p c. So, we can find out what will be the energy of the what will be the momentum of the photon. So, this is what I have written in the next transparency photon is treated as a particle with zero rest mass the energy and momentum can be related by this particular expression because e we have just now seen from the explanation of photoelectric effect experiment that e is to be given a value equal to h nu and p must be equal to e by c from the relativistic expression that we have earlier considered for a zero rest mass particle it means the momentum of the photon must be given by h nu by c. So, whatever we are saying about special theory of relativity is correct and the way we have invoked zero rest mass particle is correct in that particular case a particle like photon must have a momentum also which is equal to h nu by c. It was generally known even in earlier cases that light carries momentum, but here we sort of get involved with a rather newer concept when I treat particle photon just like any other particle but travelling with the speed of light and having energy h nu and a momentum of h nu by c. Actually in the photoelectric effect experiment it is not really possible to test the momentum of the photon because actually the photoelectric effect has to be observed when the electron is bound inside an atom and therefore, quite a bit of recoil energy is taken by the atom or by the solid and therefore, it is not possible to really test that the photon has a momentum. In fact, in photoelectric effect experiment we only apply conservation of energy. However, there is another experiment which we call as Compton effect in which it is possible to really check and experimentally verify that this idea of photon is a realistic idea as far as particle of zero rest mass is concerned it can really be treated with a particle energy equal to h nu and a momentum equal to h nu by c. So, let us just describe the Compton effect experiment. So, Compton effect is actually required of a photon by a free electron. So, let us assume that we have an electron E which is at rest and there is a photon which comes here with energy h nu this photon gets scattered and eventually comes out in a different direction. This direction makes an angle theta with the initial direction of the motion of the photon and it comes out with a different energy the changed energy h nu prime and as a result of this scattering this electron scatters goes other way at an angle of phi from the incident direction of the photon with an energy E. So, this is just like a simple classical scattering problem which we are quite used that one ball coming and another ball coming hitting and one ball going at an angle and another ball requiring except that the particles that we are talking here one is photon and another is electron. So, what we want to do we will treat photon as really a particle of energy h nu and a momentum of h nu by c and would like to apply conservation of energy and momentum to this problem like we have been applying for any other particle that we have discussed earlier. And let us see what result that we get. So, what I will do in the next transparency I will write the energy conservation and the momentum conservation because that is what we are supposed to apply. Now, as far as energy is concerned the initial energy before scattering was the energy of the photon it does not have a rest mass energy because m naught is 0. So, m naught c square is also 0. So, the total energy of the photon is h nu. This particular electron which was at rest has only the rest mass energy which was equal to m naught c square. So, total initial energy will be given by h nu plus m naught c square. After scattering you have a photon which goes this way and it comes out with the reduced energy or a different energy in principle it will be reduced energy because part of the energy will be taken by the electron. So, this particular h nu prime is the new energy of the photon change the energy of the photon. So, the photon which comes out has the energy of h nu prime and the electron now also gets certain amount of kinetic energy and let us assume that it is total relativistic energy is E E. So, the final energy after the scattering must be equal to h nu prime plus E E. So, this is what I will be calling as conservation of energy. So, I will get one equation for conservation of energy. I have to also apply conservation of momentum. When I apply conservation of momentum, momentum being a vector quantity I have to consider both x and y direction. I have shown this as the x direction which is the direction of the initial motion of the photon and perpendicular to it is the y direction and I have assumed that this scattering has taken place in x y plane. So, I have to conserve not only the x component of the momentum, but also the y component of the momentum. So, we realize that as far as this particular particle is concerned the photon is concerned its initial momentum was h nu by C we have just now discussed that. This electron was at rest. So, its momentum was 0. This particular photon has momentum only in the x direction. Therefore, the x direction initial momentum is h nu by C and the final momentum in the x direction will be the momentum of this component of the momentum of this photon along x direction and the component of the momentum of the electron along this particular direction. In the y direction which is this direction there was no initial momentum. So, final momentum should also be 0. It means if I take the component of this particular momentum along the y direction and component of this momentum of this electron along the y direction that too must balance out. So, these are the equations that I am going to write. Only thing I will write the momentum of the electron as P subscript P, P subscript E. So, let us now write all the three equations which I am putting in the next transparency. Let me just show here my picture to make it clear. This was my initial photon. This was my electron. This was going in this particular direction. Make an angle theta and this was electron which was going in this direction making an angle of phi. So, my first equation says which is the conservation of momentum along the x direction. This is the initial momentum of the photon because initial momentum was only along the x direction which is h nu by C. Now, momentum of the photon which has been scattered is h nu prime by C. This is h nu prime by C. So, if I take the component along the x direction, it becomes h nu prime by C cos theta. Similarly, the momentum of this electron let us assume is P E. So, along the x direction this component will be P E cos phi. So, this is what I have written in this particular transparency h nu by C is equal to h nu prime by C cos theta plus P E cos phi. Now, we take the momentum along the y direction. If I take momentum along the y direction, this momentum must cancel out with this particular momentum. The momentum of the photon, outgoing photon in this particular direction is h nu prime by C sin theta. Momentum of this electron is P E and in the y direction it will be P E sin phi. So, I expect that h nu prime by C sin theta must be equal to P E sin phi. So, this is the second equation which I have written here, h nu prime by C sin theta is equal to P E sin phi. And this is of course, we have discussed is the conservation of energy which is initial energy, Rasmus energy of the electron plus the initial energy of the photon is equal to outgoing energy of the photon plus the total relativistic energy of the electron which of course means Rasmus energy plus kinetic energy. Of course, we are using symbol P E here and E, they are not independent variables because energy is always related to momentum. Therefore, we have a further equation which relates energy to the momentum which is written as E E square is equal to P square C square plus M naught square C to the power 4 standard equation with standard relationship between energy and momentum. Now, we have to work out with these equations and try to find out what will be the scattered frequency or energy of the photon or energy of the scattered photon. As we will be discussing little later in the experiment, it is not always very easy to know the parameters of the electron that is scattered. It is somewhat easy experimentally to calculate the energy of the photon whether it is incoming photon or whether it is outgoing photon. So, what we will try to do out of these equations, we will try to eliminate those things which are having relationship with the electron. So, first thing that I would like to relate, remember phi was the angle in which this electron got scattered. So, there is a cos phi here, there is a sin phi here. So, I will first like to eliminate this phi which is rather easy to do it because this P e cos phi, I can take this particular thing to the left hand side. So, this right hand side will become just P e cos phi. Here on the right hand side is just P e sin phi, I square and add of them, add the two equations. If I do that, I will get here P e square cos square phi plus P e square sin square phi because cos square phi plus sin square phi is equal to 1. So, I will just get P e square. So, that is the equation which I am writing in the next transparency. So, I am writing P e square is equal to cos square phi plus sin square phi which should be equal to P e square. This term was a term which I have taken in the first equation from the right hand side to the left hand side. Let me just go back. This is h nu by C and this was h nu prime by C cos theta. So, I have taken this to the left hand side. This is what is written here, h nu by C minus h nu prime by C cos theta. And of course, I have squared it because I have squared and added it. In the second equation on the left hand side, we had just this term h nu prime by C sin theta. So, I have squared and added up. So, this is what I have got after using the first equations and eliminating phi. Now, just to make these equations look somewhat simpler, what I have done? I have multiplied by C square from the both the sides. So, if I multiply by C square here, I will get P e square C square which appears here because I have multiplied by C square and there is already a square here. So, inside it will get multiplied by just C. So, when I multiply this by C, I will just get h nu here. When I multiply it by C, I will just get h nu prime here. When I multiply by C here, I will get h nu prime. So, I get this equation as P e square C square is equal to h nu minus h nu prime cos theta square plus h nu prime sin theta square. Let us open this equation and try to see whether we can still simplify it. So, I have to just take the squares and again try to manipulate the terms. This is what I have done here. Same equation which I have written on the last transparency, h nu minus h nu prime cos theta square plus h nu prime sin theta square. So, I first expand this term. So, I will get a square plus b square minus 2 a b. So, a square is h nu square which I put h nu square. b square is h nu prime cos theta square. So, it becomes h nu prime square cos square theta minus 2 a b. So, minus 2 into h nu into h nu prime cos theta. So, this becomes the expansion of the first term. The second term is just h nu prime square sin square theta, which I have kept just like that. We realize here that I have h nu prime square cos square theta and there is h nu prime square sin square theta. So, when I take these two terms into consideration together, I will get h nu prime square multiplied by sin square theta plus cos square theta, which again gives me one. So, these two terms together will just lead me h nu prime square. So, I go to the next step. This h nu square I just put it as h nu square. These two terms gives me h nu prime square. So, this I put as h nu prime square. This term I keep it as it is, which is minus 2 h nu into h nu prime cos theta. So, this is what I have got after elimination of the phi term in relationship between energy, sorry momentum and this particular theta corresponding to the energies of the incident photon and the outgoing photon. Now, this p square c square I can also evaluate from conservation of energy and as I said our idea is to eventually eliminate anything which has to do with electron. Here we have the momentum of the electron. Here on the right hand side, there is nothing which is relating to electron. This is relating to the incident photon. This relates to the outgoing photon. Similarly, these two terms. So, I would like to get eventually rid of this particular term p e also and there is easy way because I know that e square is equal to p square c square plus m naught square c to the power 4. So, what I will write? I will write this p square c square in terms of the energy of the electron. So, that is what I am doing in the next transparency. So, this was the energy and momentum relationship for the electron. I have just taken p e square c square on the left hand side and written this as e e square minus m naught square c to the power 4. Now, this energy I have taken from the energy conservation which I have written earlier. This was my energy conservation equation m naught c square plus h nu is equal to h nu prime plus e e. So, from this I can extract e e. This e e will be m naught c square plus h nu minus h nu prime. So, I know what is e. So, I will substitute this e e here. Then I will get on the right hand side everything in terms of h nu. This p e square c square I will eliminate from the first equation which I just now written. And therefore, I will get rid of energy of the electron as well as the momentum of the electron. So, let me write this particular equation which I have written here. For e as we have just now seen, I have written from this equation h nu plus m naught c square minus h nu prime. I just slightly reorganize these terms minus m naught square c to the power 4 which was here which I just brought here. Now, expand this particular equation. Now, we have a plus b plus c square.  So, let us do it. So, let me just take the square of this particular quantity. I will take h nu square which is here. I take the square of this quantity which is h nu prime square which is here. Remember there will be a positive sign here. Then there will be a square of m naught c square which becomes m naught square c to the power 4. And this m naught square c to the power 4 will cancel with this m naught square c to the power 4. So, I am not writing neither this term nor that term. So, I have written only these two terms out of the square terms. Now, I have to write 2 a b. When I write 2 a b, I write this as 2 h nu into h nu prime to m naught c square which I have written here. 2 h nu into h nu prime this a and this is b. So, 2 h nu into h nu prime because there is a negative sign here. So, this becomes minus 2 h nu into h nu prime. Now, this m naught c square has to be multiplied by this with a factor of 2. This also has to be multiplied by this and have a factor of 2. So, I have combined these two terms and have written here as plus 2 h nu minus h nu prime taking them together multiplied by m naught c square. So, I have just expanded this particular term here and using this particular thing I get this as the value of p e square c square. Let us see whether we can simplify it further. This is what I have written earlier h nu square plus h nu prime square plus 2 h nu minus h nu prime m naught c square minus 2 h nu h nu prime. This I am equating with p e square c square which I had obtained earlier for elimination from the conservation of momentum equation which if you remember was h nu square plus h nu prime square minus 2 h nu h nu prime cos theta. Let me just bring you back to that transparency. This is what we have written earlier p e square c square is called h nu square plus h nu prime square minus 2 h nu h nu prime cos theta. This equation was obtained by eliminating phi from the first two equations of the momentum conservation. The second p e square c square I have got by applying energy conservation. So, I can equate this right hand side to that right hand side which I have done in this particular transparency. So, h nu prime h nu square plus h nu prime square minus 2 h nu h nu prime cos theta from momentum conservation. This is from the energy conservation which I have written. You can see very easily that I can simplify these equations further because h nu square will cancel with this h nu square this h nu prime square will cancel with this h nu prime square. Here what I will be getting this two factor will also cancel and if I slightly organize bring this particular term on the left hand side what you have 2 is already cancelled here. So, you will get h nu into h nu prime. This being on the left hand side will give me 1 minus cos theta on the left hand side and only this term on the right hand side which is h nu minus h nu prime m naught c square. So, this is an equation which must be obeyed if whatever I am saying is correct which gives me the relationship between the frequency or the energy of the outgoing photon in terms of the energy or frequency of the incoming photon and the angle of scattering which is theta. This equation can be further simplified if we write in terms of lambda. Let us try to work out this particular example in a slightly simpler fashion. This is what I have written earlier the last transparency. Now I express everything in terms of lambda. The frequency of the incoming photon can always be written as c divided by lambda because frequency multiplied by lambda must be equal to speed and the speed of photon is c. Therefore, I can write nu s c by lambda which is the wavelength of the incoming photon. h nu prime I can write again as h c by lambda prime because nu prime is equal to c by lambda prime. So, this is what I have written as c by lambda prime. Remember in general we will find that nu prime has to h nu prime has to be smaller. It means lambda prime has to be larger into 1 minus cos theta which is the same term. Here also I express nu s c by lambda and nu prime s c by lambda prime writing this equation in this particular fashion. So, this h nu has been written as s c by lambda. This h nu prime has been written as s c by lambda prime. So, I can cancel lot of h c's. You can see there is an h c here, there is an h c here, but there are 2 h c's here. So, probably one of them will remain, will cancel one of the h c's. There is another c, here there is m naught c square. So, there will be one c which will be going away and the equation will turn out to be fairly simple. This was my equation which I had written here earlier. So, I get h c square because there are 2 h c's here. This is lambda into lambda prime which I have written here. Here I take h c. I just use this particular thing, simplify this, taking h c out. So, it will become lambda prime minus lambda. So, this is lambda prime minus lambda and lambda lambda prime in denominator which I have written in denominator multiplied by m naught c square which is this equation. Now, I start cancelling the term. I write this on the left hand side now, lambda prime minus lambda, this on the right hand side. This h c will cancel with this h c. So, there will be one h remaining here and one c remaining here. There will be m naught c square. So, one of the c will cancel with this c. So, there will be one h remaining here and on the right hand side there will be just a m naught c which will be remaining here. So, the equation which I get is as follows. Just like trying to write in a different fashion, trying to write on the right hand side, I get the standard well-known Compton effective equation which says lambda prime minus lambda is equal to h upon m naught c multiplied by 1 minus cos theta. It means whatever I am trying to say, the scattered photon will have an increased lambda and that difference between the original lambda and the increased lambda will be given by h upon m naught c 1 minus cos theta. Cos theta being always smaller or at the most equal to 1, either lambda prime minus lambda will be equal to 0 or will always be positive as I had expected because part of the energy of the photon must have gone to the electron. Therefore, the photon which is coming out must come out with somewhat reduced energy. It means reduced frequency and therefore, larger lambda. So, this is the standard Compton fact expression. Now, question is that can I experimentally verify it? If I really experimentally verify it, then I have sort of shown that my idea of photon as a zero-res mass particle with energy ash nu and momentum ash nu by c has a meaning and probably it is something which we can take forward. Now, it is very easy to say that you have a free electron and a photon comes and hits here, but where do I get when I want to perform an experiment, a free electron? It is not easy to get a free electron and perform this particular experiment when you want to do really experiment. So, generally in a Compton effect experiment, we use a metallic foil. When I use a metallic material, in metals, they are supposed to be very large number of nearly free electrons. I mean, I mean, strictly speaking, they are not really free, but to a reasonable approximation, I can treat them as more or less free. The other problem is that these electrons which are somewhat free, they may not all be at rest, but that does not matter. Let us, if you have to perform an experiment, we have to see that. So, what we do? We take a metal and allow frequency electromagnetic wave. In fact, as you will be seeing that this H upon M naught C turns out to be extremely small. Therefore, the change in the lambdas are very small. It is order of one tenth of an angstrom, which is very small. So, normally when we perform this experiment, we use gamma rays. So, this is the way we perform the experiment. We use free electrons within the metals for the experiment. And experiment is something like here. You have a metallic target. There is incident gamma ray beam which comes and hits here. And you have a detector which detects gamma rays. It is possible to obtain detectors which can detect and which can count, which can tell how many photons have come at a particular angle. So, if my photon beam is initially coming in this particular direction and I am collecting my photons in this particular direction by counting the number of photons reaching detector and I can measure their frequency which is also easy to measure, then I know all these photons must have come at an after scattering at an angle theta. Of course, this theta I can change and keep on verifying my experiment. So, this is what normally is done that you allow this particular gamma ray to be incident on metallic target. You have detector, fix at a particular theta, collect the photons, measure their energy, keep on changing theta, keep on going to different thetas. And at every angle, you keep on measuring the number of photons and keep on finding out their energies. When we do this particular experiment, we get something like this. The curve is somewhat like this. So, if we take the lambda prime which is the frequency that wavelength that we measure and find out how many number of photons are coming with that particular wavelength approximately. Now, in fact, you have to take a range between lambda and lambda plus d lambda. But let us not go into those details. We just take n versus lambda prime curve. You find two peaks. One at larger lambda, another at smaller lambda. This peak is generally having much larger width. Now, this original peak corresponds essentially to the original wavelength lambda which was present there. This particular maximum does indeed corresponding to the lambda prime that is expected out of the Compton scattering. So, you do expect, you do find experimental verification. Of course, there is a line width. I mean, we know that there is a natural line width which has to be always present. But here the line width seems to be broadened especially in this particular case. Also, we find that the original wavelength is also present. Now, this can be explained as follows. When the photons are coming and being incident on the atoms of the metal, not every electron, sorry, not every photon will get scattered only from the free electron. Some of these photons will also get scattered from the atoms. And if they get scattered from the atom, remember in the Compton effect experiment what was appearing was H upon M naught C. So, this M naught for the atom is going to be very, very large. In fact, you know, had it not been electron, but any other particle, this expression would still be alright, except that mass has to be different. Mass that you have to use is has to be of the mass of the particle that is scattering photon. And if that happens to be an atom, this M naught is going to be extremely large. Therefore, lambda prime minus lambda is going to be extremely small, which is essentially negligible. Therefore, you will not find any measurable change if the photon gets scattered from the atom. Therefore, you do also find the original lambda even though you are measuring or you are collecting photons at an angle theta, because the original wavelength is also present, because these are the photons which have got scattered from the atom and not just from the electron. Also, we see a larger line width and this particular line width is expected because not electrons are not really at rest. They are moving with different type of velocities and therefore, there has to be some amount of distribution of the photon energy that you are measuring. Therefore, this particular width is being explained because of larger number, a distribution of velocities of the electrons that you see in the metal. But basic crux of the issue is that you do really see that this particular experiment is just does prove that it is possible to get lambda prime minus lambda is equal to h upon M naught C 1 minus cos theta. This particular peak does satisfy that equation. Therefore, we can treat photon really as a particle with energy as nu and a momentum as nu prime as C. So, this I have sort of written in the conclusion of the Compton effect experiment. The original wavelength is due to the scattering from core and large line width due to velocity distribution of electrons. Now, once we have come to these issues of photon, let us try to discuss one or two problems based on the photon. All that we have said now that photon is like in relativity is like any other particle. Only thing special about the photon is that its rest mass is 0. Otherwise, as far as conservation of energy and momentum are concerned, they can be treated just like any other particle. So, let us take one particular example in which there are particles involving or also involving photons. So, this is my example. Say example is little bigger. So, let us try to slowly understand this particular example before we try to work it out. So, there is one particular particle which has a rest mass of 135 MeV by C square. See, as I have told you earlier that rest mass is often expressed in the units of energy. So, we can write this as 135 MeV, but actually it means is that rest mass is 135 MeV by C square. It is M naught C square which is 135 MeV. So, we will write in this particular expression the energy always in the unit of MeV by C square. So, it has a rest mass of 135 MeV by C square. I am sorry, I will write mass in the units of MeV by C square and is found to be 0.8 C. The speed of this particular particle is 0.8 C in a frame S prime. Normally, we have been giving in the frame S, but here problem is slightly different. So, this particular speed has been given in a different frame S prime and the speed of this particular particle as measured in S prime is 0.8 C and this S prime itself moves relative to S with the speed of 0.6 C. So, we have a frame S. In this frame, S prime moves with the speed of 0.8 C, I am sorry, S prime moves with the speed of 0.6 C and in this particular frame S prime frame, a particle moves with a speed of 0.8 C. Now, next part of the problem, all the motions are collinear and are taken to be along x direction. So, we assume that everything is moving in one line. In S prime, it is found that the particle decays into two photons. So, what is found that of course, if it decays in S prime, it has also to decay in S, but the final things are all given in the frame S prime. So, what we find that this particular particle decays into two photons. So, particle is no longer existing, but it has now become two photons. Two photons have emerged and the particle disappears, so to say. Now, it is found that in this particular frame of reference S prime, each particle makes an angle theta prime with the initial direction of the particle motion. Now, question is, find the angle theta prime and the frequency of photon in this particular frame. In fact, instead of frequency, I can just find the energy. Once I know the energy, I can always find out the frequency. Find the angle theta and the frequency also in the S frame. Though my experiment has been described in S prime frame, but I have also to find out these corresponding quantities in a different frame S frame. So, this is my picture which I have shown here. This was my S frame. This was my S prime frame. S prime moves relative to S with a speed of 0.6 c. I have shown everything in blue here just to match with this particular frame of reference. So, as far as the observer sitting in S prime is concerned, that particular observer observes that this particular particle suddenly disappears and two photons come and they make equal angle with respect to the initial direction of the motion of the particle. And this angle is theta prime. This is theta prime. This is theta prime with respect to the original direction of the motion of the particle. Let us assume that this photon has energy of E prime p1. Let us assume that this particular photon has energy of E prime p2. The question is, what is the frequency of the photon and other photons? And what is this angle theta prime? What has been given in this particular problem is only that this angle and this angle are same. Having now discussed conservation of energy and momentum and discussed the fact that photon is to be treated like any other particle, this problem is like any other simple problem of collision or scattering in which all I have to do is to apply conservation of energy and momentum, but relativistic equations have to be used. That is all. So, because the problem has been given in S prime. So, let us first try to find out before collision or before this particular decay has occurred. Let us not use the word collision. The decay has occurred. What was the energy and what was the momentum? So, everything is being written in the S prime frame of reference. Once I write in S prime frame of reference, the particle speed is 0.8 C. So, if I write S prime frame, the speed of the particle is 0.8 C. Using this particular U, I can calculate what will be the value of gamma U. And as we have seen earlier, gamma U corresponding to 0.8 C always gives out to be a comparatively cleaner number, which is 5 by 3. Once I know gamma U, I can find out what is the energy of this particular particle, because energy of the particle E is given by gamma U, M naught C square and M naught C square, I have been given is 135 MeV. Similarly, I can find out what is the momentum of the particle, which happens to be only along the x direction. So, I am not putting the vector sign is equal to gamma U M naught. So, this is what I have written in this particular transparency. Of course, because this S frame of reference, so I must use E prime is here also I must use U prime to be more precise, because everything is being observed and here also should be gamma U prime, because everything is being observed in the S frame of reference. So, let us look at this particular transparency. I have written gamma U prime is equal to 5 by 3 using value of U prime as 0.8 C. E prime is equal to gamma U prime M naught C square, which is 5 by 3 into 135, which is equal to 225 MeV, if you just calculate this number.  This particular value of M naught U prime, I have this particular value of U prime is 0.8 C. For M naught, I have used the value of 135 by C square, because M naught C square was 135 MeV. Now, what I have done here, I would like to express the momentum in the unit of MeV by C. So, one of the C I have retained here, one C cancels from this. So, there has to be one C in the denominator, because there is a C square here and there is a C. So, I cancel only one of the C, another C I have retained in the units. So, I have to just calculate this 5 by 3, multiplied by 135, multiplied by 0.8 and this C I am just taking as a part of the unit. So, if I calculate this number, I get 180 MeV by C. So, basically I have used these equations, which I have written here in this particular paper. Of course, this is M U prime, M U prime, gamma U prime, substituting these values, only thing expressing this particular quantity in the units of MeV by C. So, this is what happens in S prime before this decay occurred. Now, let us see what happens after the decay occurs. After the decay occurs, then what you are getting are two photons, one going this way, another going this way, making an angle theta prime with respect to each other. So, like before, like in the Compton effect experiment, I have to conserve initial momentum to the final x component of the momentum, I have to balance the y component of the momentum. That is what I am doing in the next transparency. If E prime P 1 and E prime P 2 are the energies of the two photons, the sum of the two energies must be equal to the initial energy that is available to me, that we have just now seen is 225 MeV. So, this is equal to 225 MeV. Along the x direction, I have to take, this is the energy. So, momentum will be this divided by C, because this is a photon, which is a zero brass mass. This is for the first photon.  For the second photon, you must have E prime P 2 divided by C cos theta prime. This must be equal to the initial momentum, because the initial momentum was only along the x direction, which was 180 MeV by C. As you can see here, it was 180 MeV by C. So, I am writing this as 180 MeV by C. In the y component of momentum, in the y direction, there was no momentum initially. So, final momentum must also cancel out. Therefore, E prime P 1 by C sin theta prime must be equal to E prime P 2 by C sin theta prime, because these thetas are same. Sin thetas have to be same. C, of course, have to be same. So, I get E prime P 1 is equal to E prime P 2. It means both the photons must have the same energy. And if they have the same energy, I know their sum is 225 MeV. So, the energy of each of the photon will be 225 divided by 2. So, I get immediately the energy of the individual photons. Now, I know the energy of the photon, which I can substitute in this particular expression. I can find out what is theta, because this theta is same. These two are same. So, I will get 2 into whatever this energy by C cos theta is equal to 180 MeV by C. So, I can immediately find out what is cos theta, which I am giving in the next transparency. So, as I said that E prime P 1 must be equal to E prime P 2, which is 225 divided by 2, which turns out to be equal to 112.5 MeV. And cos theta prime, in the right hand side, there was 180. See, this is equal to 225 by 2, but the two terms are equal. So, this becomes just 225. So, cos theta prime, this C cancels with this C. So, your cos theta prime just becomes 180 divided by 225, which is written here, from which you get theta prime is equal to 36.87 degree. So, approximately at an angle of 37 degrees, these photons will get scattered from the incident direction of the motion of the particle. Now, the question is that we have to find the same information in S frame of reference. What I can do? I have to use energy momentum transformation. I go back to S frame, find out the energy of the particle and do exactly the same thing as I have done here. So, that is what I am doing in the next transparency. I go back to S frame from S frame of reference. So, in S, transform the energy momentum of the particle before decay. And because I am going from S to S, I will be using inverse transformation. That is what is being shown in the next transparency. If you remember, this was the equation of the momentum transformation and I have put a plus sign because I am talking of inverse transformation going from S frame to S frame. So, P will be equal to gamma P prime plus V E prime by C square. So, I know what is P prime of the particle before a decay. I know what is the energy of the particle before a decay. I substitute in this particular expression. I should be able to get the momentum of the particle before it decays in S frame. Of course, gamma that I have to use is between S and S frame and their relative velocity is 0.6 C and not 0.8 C and corresponding to 0.6 C, we have seen many times earlier gamma turns out to be equal to 1.25. So, this gamma is 1.25. Momentum P prime was 180 MeV by C. So, this unit I have retaining here plus V which is 0.6 C. So, there is a 0.6 and there has to be one C will cancel with this C, another C will come out in this unit, this is 225 MeV. So, this everything becomes in the unit of 225 MeV by C. So, if I calculate this thing, I get 393.75 MeV by C. So, this is the initial momentum of the photon, sorry momentum of the original particle before it decays in S frame. Similarly, I can calculate the energy. For energy, I have to use energy transformation. Again, I have using a plus sign because I am talking of inverse transformation. So, E will be equal to gamma E prime plus V P prime, gamma is 1.25, E prime was 225, P prime was 185 MeV by C and there was a 0.6 C which is the speed. So, this C will cancel with this C, everything becomes in the unit of MeV. So, I get 1.25 multiplied by 225 plus 0.6 multiplied by 180 in the unit of MeV. So, my energy, if you calculate this number, turns out to be equal to 416.25 MeV. So, now problem is exactly similar of what we have discussed earlier, except that now the initial particle energy is 416.125 MeV and its initial momentum is 393.75 MeV by C. Then we apply exactly the same way transformation and conservation of energy and momentum and get the new angle, get the angle in S frame. So, that is what is being done here. It is just exactly the same equations that I had written in S frame except that instead of prime, I have removed those primes and the numbers that I am using are those numbers which correspond to the energy and momentum in S frame. As far as energy is concerned, S frame is 416.25. So, this I have written here. As far as the momentum is concerned is 393.75, which I have written here. I am not using prime because this is everything is in S frame and otherwise all the equations are exactly identical. Once I write this particular equations, exactly the same way I will solve, I will get E p1 is equal to E p2 and therefore, the energy will turn out to be half of the energy. I substitute it back and get the new cos theta. So, I get just E p1 is equal to E p2. That number divided by 2, we get 208.125 MeV and cos theta turns out to be 393.75 divided by 416.25, which is equal to 18.92. Now, we can verify these numbers. In fact, what we have done, we have used transformation before the particle got decayed. I could have even used the transformation after I have obtained the photons because their energy will also be transformed, their energy and momentum will also be transformed when I am going from S frame because for us, photon is like any other particle. So, I can use exactly the same transformation equation even for photon. So, that is what I am going to do next and show that I get the same result. So, I said verify, we can verify the results by transforming the photon energies and also momentum. So, let us look at photon 1 in S frame of reference. This is what I had got its energy 112.5. This is what we had calculated earlier. Now, let us calculate its momentum. This particular particle was moving at an angle theta prime from the incident direction. So, if I take the x component of the momentum, this was the total momentum of the photon multiplied by cos theta prime, which I had already calculated as 180 divided by 225. This was the energy, this C I take in the unit of the momentum MeV by C. So, the x component of the momentum, if you calculate this number, turns out to be 90 MeV by C. The y component of the momentum is this momentum multiplied by sin theta prime. If I do that particular thing, I take this particular value is 112.5 and take sin theta prime, this turns out to be 0.6 and I get this number as 67.5 MeV by C. So, I have found out what is the x component of the momentum, what is the y component of the momentum. Now, transform these things back to S frame. So, I calculate P1x, which is the momentum of this photon, x component of the momentum of this photon in S frame of reference. You see in transformation equation, there is no difference photon is just like any other particle. So, I write gamma times P prime for the first particle x component plus V for the first particle divided by C square. Gamma has to be 1.25, because I am transforming from S prime to S, exactly similar equations. This momentum is 90.6 multiplied by V is 0.6 multiplied by 112.5. You calculate this number, you get 196.875 MeV by C. Now, as far as y component of momentum is concerned, there is no problem, because they are same. So, I just write P1y is equal to P prime P1y, which is 67.5 MeV by C. Of course, I have taken the photon, which has a positive component in the y direction. If we take the other photon, that will have exactly the same value, but will have a negative component in the y direction if the photon was coming down rather than going up. So, otherwise this particular expression will be valid, this number is valid for both the photons. Now, I transform the energy of the photon. If I transform the energy of the photon, I get energy of the photon in S frame as gamma multiplied by the energy of the photon in S frame plus V multiplied by the x component of the momentum of the photon in S frame of reference. So, this gamma as we have seen is corresponding to value of 0.6 C, which is the speed between S and S frame. I substitute here 1.25. E prime P1, you know is 112.5. This V is 0.6 and this was 90. This is 0.6 C and this P prime was in the unit of 90 MeV by C. So, this C cancels out. I get everything in the unit of MeV. So, if I calculate the energy of the photon in S frame of reference, this will turn out to be 208.125. Now, I have to find out the angle in S frame that I can find out because I know the y component of the momentum and I know the x component of the momentum which is here. So, that is what I am doing in the this particular transparency. This is the value of the x component of the momentum. This is the value of the y component of the momentum. I just take 10 theta. This divided by this, this gives me the value of theta, which I get exactly same as 18.92. Of course, I have also found out the energy of the photon in S frame and what has been asking the problem is the frequency, but as I have said that if you know the energy, I can always find out the frequency by dividing it by h. So, essentially the problem gets solved. The basic idea of this particular problem is just to tell that like we are applying energy momentum transformation for any other particle, I can apply also for the case of the photon. So, in the end, I will summarize whatever we have discussed. We had introduced the concept of photon as a particle with zero rest mass. We gave an example and saw that photon momentum and energy conservation have how they have to be applied. Thank you.