A fiery horse with a speed of light, a cloud of dust and a hearty high-o silver, the Lone Ranger. In the early days of the Western United States, the masked rider of the planes not only fought crime and criminals, but also the enemies of justice who worked within the law. No one could match his strength and courage, and his daring and resourcefulness made him the greatest champion of justice the West ever knew. Return with us now to those thrilling days of yesteryear. I'm out of the past from the Thundering Hoof Beach to the Great Horse Silver. The Lone Ranger rides again. Come on Silver! We're heading for the Hill Camp! The Lone Ranger and his faithful Indian companion, Tonto, rode toward the small settlement that sprung up within a mile of the great Eureka mines. Sharing the Masked Man saddle was a young girl, a child of five or six. The Masked Man pointed to the neat cottage they were approaching and... Now then young lady, is that where you live? Uh-huh. You think your mother's worried about you? I don't know. Well, I'd be surprised if she isn't. Young women your age should stay close to home. Do you think you can remember that? I wasn't lost. Weren't you? Uh-uh. Then you possibly would have been if you'd gotten much farther. Here we are. Hoof, Hoof, Silver, Hoof Count. All right, young lady, down with you. Wee! Hello, Mommy. See the Night Horse? You never mind the Night Horse. Where in the world have you been? Just walking. It's not only I found her near the swamp. We were afraid she'd get into trouble so we brought her back. The swamp? Oh, good gracious. Nancy, I told you never to go there. I wasn't afraid, Mommy. I just bet you weren't.  I've looked everywhere for you. And that dress. Mud from head to foot. Now you run in the house. You're gonna have a bath. But I like mud. Don't I know it. Go ahead now. I'll be in a minute. Bye, Masked Man. Goodbye, young lady. Thank you very much for bringing me home. You're welcome. Isn't she awful? Today I think I owe you some thanks. Does she wander away often like this? No, thank goodness. Usually I got time to keep an eye on her. But I've had so much to do today. Packing our things and getting tickets for the stage and washing. I just lost track of her completely. Looks as though you're moving away. Yes, at last. Your husband must work at the mines. He did work there. This is his last day. And what I've heard recently, he's fortunate. How soon do you expect him home? Well, I don't know. Almost any time now. Why? Has he been employed at the mines long? Over a year. Then perhaps he could give me some information. The stories I've heard have all been at second hand. I'd like to talk to someone who's actually worked in the mines. Oh. You've heard about the accident. Yes. I am. Well, after all the ants, there was a trouble to you. Well, I don't want to seem curious, but just why are you interested? Don't be misled by my mask. My friend and I are not outlaws. Oh. We're interested because they say the accidents could be avoided. And that's true. Why aren't steps taken to prevent them? No, I can tell you that. Yes? Meakin. Jim says he's taken over a million dollars out of those mines, but he can't afford to spend a few thousand to protect the lives of the many employees. I see. He must be the greediest man ever lived. How can he get workers? Oh, there's always plenty of men needing jobs. Jim did when he come here. But he doesn't have to work here any longer. We'll leave him here tomorrow. Fine. We've saved half of everything he's been paid. We're going back to Kansas, where Jim can buy a little business and work just for himself. I'm so happy that he can get away. I scarcely know what I've been doing. I don't blame you. If you just knew what it's been like. Wondering every morning when he leaves, if he'll come back home safe. Going almost crazy every time there's another cave in till I know he's not been caught. See, and the other women have had their husbands crippled or lost him. I can understand. So this is the first day since we come here. I've had any peace of mind. Here come Pellar. And this must be Jim. Oh, no. No, it isn't. It's his foreman. Well, if they're making him work overtime today, I... Perhaps Talonide better be going. No, wait. What is it? I don't know. It's just suddenly... I'm afraid. You don't think... Wait, please. Oh, fella. Oh, I... Ma'am, I... I hate like sin to have to tell you this, but there's been a cave in. Jim had just knocked off and was getting ready to leave. Ma'am, it... Come so suddenly, he never had a chance. No! No! The Lone Ranger and Tato made camp fairly close to the mines and two hours later. Tato, I never want to see a thing like that again. For a year, that poor woman and her husband had saved so that they could leave. They had enough money. He'd gone to the mines for the last time. And he's killed. That heatbans. It's no less than murder. He lived his life in the mines in just the last six months. With no honest excuse for it. Old, rotted timbers used over and over again to shore up the tunnels because it would cost money to freight in the kind of lumber that's needed. The men forbidden to take the time to make the tunnels safe because it would cut down on the time spent bringing out ore. Cheap, undependable blasting powder.  He lives back in the hills he bought when the mines were first opened up. Him heap band-puller. No one can touch him. Short of going outside the law. Not right. Well, if the law can't make him protect his men, perhaps there are other ways. Here's over. You'll ride. We both ride. Here's scouts. Where we going? This either man responsible for all this. See meek in himself. Come on, so... When they tumbled down old house where the mine owner lived, meeken had already been accused of criminal carelessness. His son, Dave, glared at him. Pa, this is the finish. I'm fed up. You send me to school. You have me taught everything I can learn about mining and then you refuse to listen to anything I say. You telling me my business? I am. You're just a fresh young sprout. Do you realize how many men have died in those mines since they were opened? You don't have to tell me. Over 30. I'm sorry for them. Sorry, sorry. Do something about it. Why not? Ain't practical. You mean it would cost money. No such thing. That's exactly what you mean. If you meant anything else, you'd listen to me. I could show you a dozen ways to make those mines safe. I have shown you.  Nobody has to work for me, do they? Is that an excuse for criminal carelessness? I ain't breaking no laws. Never broke a law in my life. Needn't said it either. And you don't feel any responsibility for those men. Why should I? Do they feel responsible for me? They do their jobs, honestly. Well, we won't argue that again. We've been over it too many times before. I'm just here for one reason. Since I've left school, I've learned just as much practical mining as you have. Besides that, I have my training. You could put me in complete charge of those mines. Let me run them absolutely on my own, and I'd guarantee to show profits as big as yours or bigger. I'll call it anything you want. I know it's so. Look, I'll make you a proposition. Let me run the mines for a year, and if my management doesn't show as good a record as yours, I'll turn them back. Suppose you'd spend cash on all them fancy ideas. Are yours for the tunnels, huh? I would. Well, I won't have it. Very well. In that case, I'm leaving. Huh? Leaving? Today, right now. Oh, hard. I can't stand to see any more men die without cause. Dave, you don't mean it. I do mean it. And you can't. You can't leave me. Am I to be manager? Well... Am I? That's nonsense. I won't do it. All right. Then that's my answer. Goodbye. No, wait, Dave, boy. You can't. James, do you mind? Well? I can't do it. You'd ruin me. Bye. Davey, no, come back. Wait, Davey. You can't leave your old boy, please. Davey! Davey! Come back, Davey! I can't hear you, Meakin. What? I heard your quarrel. If you won't listen to your own son, you won't listen to me. You! But I'll make you a promise.    Come on, sir. Get him out. Get him out. There's Dave, tunnel. Just going over that far rise. Uh, Mr. M. You think you can overtake him? Uh, good. Go after him. Get him and bring him to our camp. How to do it? I'll meet you there. Uh, get him up, Skull.  Come on, Silver! Hey, oh, Silver! Away! Night had fallen, and the lone ranger had built a small campfire. At last, he heard Tonto approach. So you're the fellow that sent this Indian after me? Yes. Hi, Arthur. He pulled a gun on me. He refused to go with him. What if I did? I don't know. They're not so fast. If you'll hold on to your temper, I think you'll find that we're on the same side. What do you mean by that? Tonto and I rode to your father's place. We overheard your quarrel. Well? Unless I'm mistaken, you're as anxious as we are for those minds to be run as they should be. As anxious as you are? What's it to you? We were at the Edwards Cottage when the news arrived today. Oh. I doubt that anyone could have seen what that news did to Jim Edwards' wife and will not wish to do something, anything, to make it impossible for such a thing to happen again. But you're an outlaw. No. Well, that man... I wear for reasons of my own. Now look at this. A bullet. For what? A look again. Silver. Well? Wait. I've heard something. Somewhere, I've heard... My friend's name is Tonto. I've named my horse Silver. Tonto. Silver. I've got it. Yes? A lone ranger. You still think it's impossible for me to be on your side? I didn't know. I never expected this. Dave, listen to me. Yes? I suppose you were telling the truth when you told your father you were confident that you could run the minds. I know I could. That's all I've been hoping for, to get the chance. And if you did get the chance, would you make it possible for man to work for you in safety? If you heard as much as you say you did, you must know that without my telling you. Then you'll get your chance. It can't be done. No? There's no way to argue my father into it. I believe there is. How? When I rode your father's place, I had no plan in mind. What I heard and saw there suggested something. Suggested what? Your father seems to think quite a bit of you. Oh, he does, yes, but he doesn't think anything of my ability as a mind manager. Well, that won't count. Well, what? You agree, Tonto will prepare disguise for you. Disguise? What in the world for? So that you can go back and work for your father. Huh? In one job, he'd never expect to find you as a common minor. The curtain falls on the first act of our Lone Ranger story. Before the next exciting scenes, please permit us to pause for just a few moments. Now to continue our story. When three days had passed with no word from his son, Mekin could control his fear no longer and summon the sheriff to his home. Want to see me about something, Mekin? I did.  What's the trouble? Something's happened to my boy. Yeah? He must have been hurt or something. Well, now that's too bad. Dave's all right. I always liked him. What do you think has happened? I don't know. That's why I sent for you. Well, what I mean is if you figure something's happened to him, you must have some kind of an idea of what it is. Well, I ain't. No? Then why are you worried? He's disappeared. Oh. He ain't... He ain't heard from the boy in the past three days. And that's what's got you upset? You trying to tell me I shouldn't be? Well, Chuck, you're his paw. From what I've seen before, you set a heap of store by the boy. So I can serve you while you're bothered. But I don't think there's any real reason for it. Why ain't there? Well, I've heard of other young fellas not being seen by their folks for that long and nothing serious come of it. I ain't no joke. Well, I didn't mean it to be. And you find the boy. Do you hear me? You find him. Sure, I'll try. I didn't say just try. I said find him. All right. You got any notion how to go about it? Any idea where he might have gone when he left here? Seamus told you I ain't good, didn't I? Then you're asking me to carry out a pretty tough job. Too big for one fella? Well, after all, I got other things to look out besides your... Then hire some fellas. Hire all you need. Scour the country. Look everywhere. Who's to pay? I will. All right. Fair enough. I'll tell it to you, straight sheriff. There ain't but one thing in this world I give a hoot about. Don't care much for the mines. Don't want no friends. Don't even like myself. Very special. But I won't have nothing happen to Dave. You understand that? I won't have it. Sure, I understand. You'd better. I... Because if that boy ain't found, you're out of a job if it takes every dollar I got to do it. The sheriff heard it done by Meakin and back with his money and listed a dozen men to make inquiries as to Dave's whereabouts. Never suspecting that Dave was working in the mines. It was a week later that the young man slipped away to ride to the secret camp of the Lone Ranger. Whoa, whoa, boy. Whoa there. I've been expecting you. Have you seen my father? Tonto and I have been keeping an eye on him. Haven't you? He scarcely ever goes to the mines. He has an office at home. I think he's afraid of the men. I see. Does anyone at the mine suspect who you are? I'm sure no one does. Good. What have you done so far? Everything's ready. Yes? I've found exactly the right tunnel. It can be done easily. Fine. But how soon? Not for a while yet. Oh, why not? Everything depends on how badly we can worry your father. The longer he goes without a word from you, the better chance we'll have to handle him when the time comes. Yes, yes, I suppose. Don't worry, Dave. Trust me to get word to you at the right time. I am trusting you. Then there's nothing more to say. Get back to the mines. Watch for Tonto and I'll keep in touch with you through him. Very well. I can tell you this. You've done most of your waiting already. Another week went by and then... Oh, this'll be... Oh, boy, oh. Tonto. Uh-huh? I saw the sheriff on his way to report again to Meakin. I think when Meakin learns his son still hasn't been traced, he'll be ready. Ah, that heap good. I'm going to get rid of this mask and wear this skies. He picks them. And when you finish, ride to the mines. Hmm. Find Dave and tell him to go through with our plan. The sheriff found his report to the mine owner. An unpleasant task.  I'll wait, Mr. Meakin. Dave gave you a case to hire all the fellas you claim you needed. You've had time to search between here and the next state. And you ain't found a thing. Mr. Meakin, you don't seem to savvy. Well, we know maybe Dave cleared out of the district complete. Might even have gone back east. Checked with the stage lines, ain't ya? Yeah, but I... Checked every trail out of here, too, didn't ya? Sure did. Then he's still around. If you ain't found him, it's cause you don't know your business. Take it from me, sheriff. If you get into office next election, you're gonna be a mighty lucky man. Well, I've done the best I could. I know it. That's what I'm complaining of. Your best ain't worth nothing. Who's there? Hey, Mr. Meakin.  I'm busy. Bastard, didn't you hear me? Stay away from here. Mr. Meakin, I'm sorry, but this is important. Now, but ain't you are fired? There's been another key, then. What? It just happened. I got over here as fast as I could. Meakin, this has gone too down, gone far.  Who's hurt, anybody? Well, there's one fella. Killed? I don't know for sure. Tramped, anyhow. It happened in one of the tunnels that's been worked out. Don't even know what this fella was doing. Then serves him right. But ain't you coming over to see what can be done? Can't you handle it? For sure, but... Then get back and do it. Get your job in it. Or don't you want to work for me anymore? All right. I'll do what I can. No, wait. I'll ride over with you. Oh, sure. I'll meet you.   Confounded impudence. I'll teach that lawman. Show him he can... For you. You most likely wouldn't know if I told you. Who gives you the right to walk in here without knocking? I've got news for you. News? News? That's all I get. And all of it bad. This is also... Well, let's have it. You've been searching for your son. Sure I have. You mean you know where he is? I do. Well, tell me. I'll pay anything. Just tell me. That's your man. He's been working there. It's a lie. He couldn't have been. If he had, I'd have known it. He's disguised himself and hired out under another name. You're telling the truth? I am. Your foreman was just here. He probably reported that one of your miners was caught in another cave-in. He did it. Yeah. You don't mean... I do. That miner was your son. Driven frantic with fear by the Lone Ranger's announcement, Mekin hurried to the mines. Arriving there, he found that most of his employees had gathered outside in sullen groups. Following the main tunnel, Mekin at last found the place where it branched to form the tunnel where the cave-in had occurred. His foreman and half a dozen miners stood looking at the piled-up rock and gravel. What are you standing there for? Why don't you do something? Get him out of there!  Well, hold on, Mr. Mekin. That's my boy in there. Why? Well, that can't be so easy. It is. What? I've already explained to Mekin here. This guy is himself and was using a different name. Oh, come on. Well, get shoveled. Start digging.  Look, Mr. Mekin, we can... Can't you see for yourself what might happen if they started digging? The whole thing had likely cave-in. Oh, what's this? That's the only entrance in there that wasn't covered up. Have you talked to Mekin to it? Well... How many have you? Well, at first we did, then... Then he quit answering. Maybe. Maybe he's died. No, I wouldn't say that. Why can't he answer, then, if he ain't? Maybe he's dead already. Davey! Dave! It's your Paul. Can you hear me? Davey! Say something. You see? I'm climbing through there. No, you don't. I'm gonna go. I'm going in there. No, I'm not. You want to get yourself cute? You couldn't squeeze through that hole a thousand years. No, still. But we've got to do something. You there. Well... You could make it a hundred dollars if you would go in there and bring my boy back. Not me. Five hundred dollars. A thousand.  Then how much could it be a thousand dollars? You make it.  You never cared anything what happened to our son. I'll pay anything. Anything. Save Davey. Please. Name anything. I'm afraid that it won't work, Mickin. There are no cowards working in these mines. No coward risks his life day after day for the kind of wages you pay.   What do you think the families of the men killed in these tunnels have felt? You think they cared any less for their men than you do for your son? The raises were the raises with everything. I'm going in there. These men wouldn't let you if you tried it. I have another suggestion. You could save him. Perhaps. How much do you want? Perhaps more than you're willing to give. Just name it. Davey wanted to take over the money. It's one of these mines. He's always favored the men. Moreover, he's had the training and the handling job like that. What's all I've got to do with being trapped in there? I'll get him out on one condition. One condition? If he comes out alive, you'll retire. What's that? I think you understand me. You'll retire and put Dave in full charge of the mines. I don't know such things. Very well, then. I'll give you five thousand to go in there. I'm not after your money. You're the only condition that's acceptable. I couldn't. Why not? Dave, Dave would ruin me. Nonsense. He'd probably make the mines pay twice as well. You've been using outdated methods here for years. You've reached the age where you should be glad to rest anyhow. Step aside and give your son the chance. No. No, I just couldn't. None of you will make the try. None of you will make the try. And it looks as though Dave will have to remain here. Wait. Wait, don't go. No. Dave, if I promise you, you will save him. Accept that condition and I'll give you my word. He'll not be left in there if he's still alive. Oh, it's hard. Remember that these men are witnesses to anything that you may promise. He won't go in there for anything else? No. Then I guess it's got to be. You'll retire? Yes. I warn you. You go back on that. I'll see to it. You'll regret it. Folks have said lots of things about me. But never that I went back on my word. Dave, you hear me, Dave? Come out. It was a trick. Yes. It wasn't ours. Why wasn't it? You didn't have to go in there. Think back and you'll see that I never promised I would. But I... I promised only that if Dave was still alive, he'd not be left in there. Well, he hasn't been. Here he is. You'll have to admit it now. If you do break your promise, this time we're finished for good. You don't mean that. I never meant anything more. But... Call me and see. What in? He did kind of out flicker me, didn't he? You admit it? I'd be glad to see it. Maybe it won't be so easy. He took advantage of it after all. And you're retiring? Mine as well. I reckon maybe that fellow who took charge of things was speaking true and it's time to do it. Son, you were right about me in the way I've been acting. I am so dependent on you, Dave, to make up for your Paul's mistakes. I'll do the best I can, Pa. Thanks to the Lone Ranger. I'm sure you have just heard as a copyrighted feature of the Lone Ranger Incorporated.


Freedom! Today I want to talk to you about breaking news! We just got two brand new condos that are set aside for a couple of people who have come to the Philippines. Not saying who, but I do want to show you the two condos. One of them is a fully furnished condo. It comes fully stocked with furniture. It comes fully stocked with two bedrooms. One master, one small bedroom. It comes with three bedrooms. It also comes with a nice little laundry room, nice kitchenette. We also have another one. This one is unfurnished as you can see behind me of course. This condo is entirely up to your imagination depending on how you're going to set it up. Freedom has acquired these two extra condos that are just kind of sitting waiting for somebody like you to take possession. That is, if you want to, if you have some skills, some idea that you think that is worth coming out here to the Philippines, we would love to hear it. You can fill out the application and the information on what you think you could do for us down there in the description down below. And hopefully I'll be able to hang out with you or someone like you here really soon as we build our team here in the Philippines. Sorry about my somewhat disheveled appearance with the shirt and the gamer glasses. I was actually in the middle of a game and figured that since we just got these, I would want to make a video as soon as possible about this and get it out to you because these are beautiful. They've got great views. I am floored by these. And did I mention they're on the same floor? So if you have a friend and you'd like to build something with that friend, maybe you two could be on the same floor. Chill, hang out, be awesome. Let us know in the comment section down below what would be important to you in a living space. I'm always interested in hearing what you have to say. I'd like to have a discussion with you about it down there. Till next time, I'm Anthony. Like, subscribe, comments please.


So very very commonly we see the children in their early years of life say one year, two years when they start walking and they keep running around. So children are always more prone to injuries at home. So right now I will try and focus on how to manage these injuries at home the first aid before you take the child to the doctor. So my purpose is not that everything can be managed at home but at least minor injuries or first aid should happen in the right way at home and it makes the work of the doctor also a little easier. So let's talk about say first we take an example of a fall and followed by a head bump or a head injury. Now it is very very important this is one situation where parents tend to panic a lot. The child fell from the bed or fell from the stairs and there was a small bump on his head and there was a cut from which he was bleeding. Now remember this is very very important if there is a bump on the head or if there is a swelling. So the way to reduce the swelling is only one that is pressure. So if there is a head swelling, the child has fallen, there is an injury, you have noticed the swelling, so at least put a pressure bandage. So we can tie it tightly with a hen and tie it with a bandage and put a tight bandage on the head so that the swelling does not increase. In the olden days people used to say that if it is hurt then apply turmeric and hot oil on it. Now it is very very important to understand that wherever there is a wound or swelling, it is underlined in the skin. There was some breach, some bleeding, it was small. For example, the needle fell, the needle fell is bleeding under the skin. So the only way to reduce it is not warm compress or hot compress, it has to be ice packing. We say that it should be cooled and cooled so that your swelling will be less on the forehead. The more we will teach it with heat, the more swelling and chance of increase. Second, if there is a cut on the forehead and head and it is bleeding somewhere. Most of the times what we see is parents bring the child and the child is actively bleeding. Which by the time the child reaches the hospital or the emergency, there will be significant blood loss. So the only way to stop bleeding is pressure. Wherever there is a wound, by keeping any clean cloth or cotton pad, I am stopping the bleeding by giving pressure. For 5 minutes, if we press that area, bleeding tends to stop. If we keep looking at it, bleeding will continue. The same process happens when there is nose bleeding. Now in nose bleeding, commonly we see that the nose is bleeding and parents bring the child to the hospital, they get worried and tell the child to go back. So that the blood will not come out. Now again that is wrong. If there is nose bleeding which is happening, which most commonly happens because of trauma. So the children will stab the child in the nose, or they will do anything which causes bleeding. Bleeding has to be stopped by pressure. So we have to pinch the nose so that, and press it for about 3-4 minutes so that bleeding stops. Second, if bleeding is happening and you have pinched the nose, then the child will have to go back and not lie down. Because all that blood from the nose will travel through the throat and into the stomach. It will irritate the stomach, the child will vomit and then the child will see blood in the vomit and parents will panic. So best thing is, the child's head should be front, nose pinched and that will take about 3-4 minutes for the bleeding to stop. The next point is, once the bleeding has stopped, where the bleeding happens, there is a crusting. And the moment the crusting happens, there will be irritation, the child will vomit again, and then the chances of bleeding increase. So wherever the nose bleeding happens, we put saline drops in the nose so that the nose gets moisturized so that the bleeding does not get irritated and lessens the chances of bleeding. So these are important points which we need to take care as far as the nose bleed is concerned. Third important thing, suppose the child fell down and got hurt in an arm, fractured. You can see that it is obvious deformity, the child is crying in pain. So it is very very important, if there is a bone fracture, if the bone is broken, then as much as we can immobilize it, we can manipulate it as much as we can. We don't have to manipulate it. Just keep any hard thing around it, and if we tie a cloth or bandage on it so that it becomes immobile, that is more important before we take the child to the hospital. Second, again on the swelling part, cold compresses, so we can put ice pack so that at least the child gets less pain from there. We can give a painkiller in which paracetamol is the safest painkiller to give to a child at any given point of time at home. Fourth common injury what we see is burns. Now it is very very important, if a child has a hot water or tea or milk and a significant area is burned, the best thing to do at home is put lots and lots of water. Commonly you have seen that people will say apply toothpaste or apply this, it will give a soothing effect. All these will tend to cause more injury to the overlying skin. The more we wash it with water, the less the effects of the injury would be less severe. Which burn is minor, which burn is major, that only time tells. So right on the first go, to predict which burn is severe is very very difficult. We have seen a number of times that an ugly looking burn turns out to be a minor burn whereas a minor looking burn turns out to be a major burn. So best is to put lots of water, cover it with a clean cloth and get the child to the hospital as early as possible. We can give a painkiller again for which paracetamol is the safest painkiller to give.


So, last time we saw the basic motivations for why we have to treat gauge field theories carefully. So, as we know the quantization goes through canonical structure and we saw that pi 0 a are all equal to 0 for any gauge field. So, right in the notation in the notation that the gauge potentials are written as a mu a T a and T a are generators I think no. So, this pi 0 just means that for the conjugate to a 0 are all 0 all the internal group index in the adjoint representation. We also saw that in many a sense the a 0 are also 0. So, a so called Coulomb gauge the Lorentz gauge is almost always imposed and it is a class of gauges which is simply that d mu a mu equal to 0 and here we would have to say a covariant derivative that is right. So, in the electromagnetism we said this equal to 0 and in non-Abelian case. So, this is a covariant gauge and within it one further puts the restriction that a 0 are equal to 0. So, the Coulomb gauge which is a subclass further imposes that a 0 a are all equal to 0 equivalently a 0 equal to 0 which leaves behind d i of a i equal to 0. Now, this we can see is a essentially a space derivative there is no time involved except that it is a differential condition it involves derivatives of fields it is there only space derivatives. So, it is at a particular time. So, if you actually think of taking derivatives as taking difference of fields at nearby points it is just a condition on values of fields at a on a particular time like surface right. So, if t is going this way we have some domain in the space like part and we are just saying that this has to be imposed here on a particular time like slice. So, you code in principle invert this and find out and just replay. So, you can solve for this and put it permanently in the dynamics and not have to worry about it later. So, in principle can be solved not that you will do it in practice well actually it is done also I should not say. So, in, but I do not want to get into too much of the detail formalism can be solved for a i in terms of space like Green's function for the Laplacian this is of course, a covariant gauge covariant Laplacian thus retain only physical degrees of freedom. So, I will give this as exercise that is one way, but it is a bit cumbersome and ultimately it has to do with very specific gauge. So, the general approach is to recall what we were doing last time that there exists. So, what is the general lesson we had that there are some coordinates that can be superfluous further there can be also space like differential conditions on the fields. So, we note that there are constraints in the phase space which can be taken care of by imposing gauge conditions. So, we say that C A of q p equal to 0 are conditions are constraints and some gamma A of q p are gauge conditions. The requirement that the imposition gamma A takes care of the condition C A and leaves behind only canonical independent set. So, we went through this last time. So, recall from last time things like what did we say C A new canonical variables which are you treat the C A as some coordinates and then q star q n minus n star as the coordinates and some p 1 p 2 p n and then p 1 star p n minus n star as the conjugate momenta where p i are found by inverting gamma A of written in this language right new variables. So, you have to invert these and find from them the p 1 2 p n there will of course, be A equal to 1 to n there will be as many conditions as there are constraints and that will be that many constraints. So, A runs from 1 to n here not to be confused with the A of the gauge fields, but they are going to become the same in the end. This is more general discussion right. So, this is sort of formal we do not know how exactly you are going to do it, but we assume that it is doable. Then we know that then the true we can construct physical vacuum to vacuum amplitude as a path integral only over the true variables well. So, put a j there and then we can say i s plus integral of all the dynamical variables right q star times j is keep it simple. So, that would be the vacuum to vacuum amplitude. So, you would modify it appropriately by introducing sources and so on. So, but this does not all I mean because the detail is not my point what we are going to do is in practice this is not what we do. So, what we do is right. So, I think we were writing the external current language only for phi version without the pies having been integrated out. So, that is why got concerned about the notation, but here we want to written both phi and pi. So, what we do is we. So, let me return to phi pi language or well we can continue to write this. So, we write omega plus omega minus as integral over all the d q's and all the d p's, but what we do is introduce a delta function of the gauge conditions and we also need to restrict the p's. So, we want to restrict the p's such that the gamma a are to 0 times x i s of some q's and p's. Now, there is a simple argument that says that the imposition of gamma a is as good as saying. So, yeah. So, we in fact, write this is integral over the q star p star then d of c if you like. So, we pretend that we made this canonical transformation from the old q p to the the symbolic ones and the the formulae p minus f is whatever you get from inverting the statement gamma a equal to 0. So, call this thing as we already used star somewhere, but so this is so this equation f a equal to 0 is a rather sorry. So, this equal yeah. So, p a equal to f a that is what this p a equal to f a of all these fields there is c and there is gamma, but gamma is equal is being set equal to 0. So, think of this as the formal inversion of the conditions gamma a equal to 0 I think this is enough to write. And so, we are imposing that here. The thing to remember now was that in order that this transformation does actually distangle the constrained and the unconstrained things correctly is that the Poisson bracket of C a and gamma a has to be non-zero. So, in a sense they remain they would after due rearrangement of the gammas into p's into this p equal to f a the f a would become conjugate to the C a. So, that requirement was that the gamma a and C a have a non-zero Poisson bracket. So, we are equal to 0 in non-equal to 0. So, that they remain the as a matrix treated when treated as a matrix, treated as an array labeled by a and b or in other words the determinant of this should not be equal to 0. So, this is same as yeah. So, being the same as determinant of well you can work out this Poisson bracket it is same as d gamma by d p equal to 0 what is happening to me yeah right. So, that for the invertibility the inversion requires that this has to this determinant has to be non-zero and which ties in with our need that they become canonically conjugate to each that some combinations of them can be made into mutually canonical. We now argue that the d d p d delta function is the same as an equivalent delta function integral over the gammas well this is not what we. So, we stipulate that that this that because the p's are found from just inverting the statements about gammas. So, this would be true up to this is in the functional space it would be true up to some overall constants right which are not important. So, you can take it as a stipulation where we assume that the gammas can be normalized correctly or some overall norm so that this can work out correctly ok. So, up to a the point is that whatever that adjustable factor is not dependent on the phase space ok. So, let me write it here. I should tell you though that all this is all this is a way of justifying to oneself what one is doing and some of these things may have strange flaws these arguments are slick, but they may have flaws and in fact, there is this thing called gribo ambiguity which you should try to read on your own. So, they may not always be quite correct, but turns out that so people do identify them then fix them later and so on, but for the time being we assume that this works. The gribo problem by the way has never been completely resolved, but people just live with it yeah. So, this is if we assume this stipulation then we claim that this delta of P a minus F a can then be taken to be times this determinant d gamma by d p the Jacobian right transferring the measure here. So, we can equivalently think of this was some measure times some distribution. So, equivalently we take this to be the Jacobian of the transformation. So, this logic is correct right that I have C a equal to 0 emerging from analyzing the equations and I realize some of it is not dynamical. So, I say that oh that means, have to put this constraint and then to say that. So, the gauge condition is something independent of it. So, this is the picture I tried to draw last time and failed I do not know that I will succeed this time. So, there is some constraint surface and what we want is that that genuine path integral does not end up traversing this surface because if you in integral because these are all equivalent only one of them is a representative member. So, you somehow want to impose a gauge condition that picks out at trajectory that cuts this only once. So, at least in this way where although I have fashionably drawn many axes restricted to three-dimensional. So, it would have to be the co-dimension of the C a. So, this is the condition gamma a. So, if the condition gamma a such that it cuts this C a only once, but does cut it which is what makes the determinant non-zero then they are not independent then it will be. So, this is the geometric picture. Now, that you have the picture you do this clever set of arguments to convert these into canonical variables mutually canonical by finding F a which invert the gamma a and then declare them to be the conjugates of this q's yes. So, the identical copies are perpendicular to this. So, there are lot of these which are the redundant ones. So, that equal you could have set instead of 0 you could have set 5 or something which would all be equivalent and one has to write. So, let us think of specifically we said. So, if I had the amuse let us just say there is a 0 a 1 and a 3 a 2 and we said a 0 equal to 0 it means that I am restricted to remain in the a 1 a 2 plane. To do that I well in this case of course, it is trivial, but in principle what it requires to do is to impose the gauge condition that sorry because this is not a constraint this already is the gauge condition. We have to say divergence a equal to 0 gauge transformations take you within a particular set of that is what I meant here that gauge transformations would leave you within this. I think this is correct picture, but we can discuss it later because right now I mean the another flow of thought. So, but I just want to answer at least algebraically without the picture which I right now do not remember how it works, but that we are trying to convert the existence of constraints and the gauge conditions we place to repair them. Yeah. So, the gauge condition was divergence p equal to 0 pi or which is same as divergence e equal to 0 and to take care of that the gauge condition was divergence a was equal to 0 within the Lorentz gauge. So, these are the two things that are proposed to be made mutually canonical. So, there is a geometric picture of what the constraints and the gauge conditions are and then there is the canonical picture where you try to move from the geometric picture to the canonical picture and in the process you claim that imposing the delta function for these formal p's that were meant to invert gamma. So, the great advantage of this is that we actually get rid of the p's completely in the end. So, we now answer that this is same as the determinant of the Poisson bracket and we thus get rid of the superfluous p's which were placeholders to think through this thing. We need the matrix m a b which is variation of the gauge condition with respect to the gauge transformation that is what this boils down to. So, for example, what is the idea? For example, we had the gauge condition divergence e equal to 0 and, but under gauge transformation e tilde equal to old e minus da dt we are talking about transformations of a. So, a tilde are equal to old a minus d lambda by dt. I can only remember the covariance statement. So, a tilde equal to a mu minus d mu lambda. And for the non-Abelian case it is d mu. So, let me write the Abelian case and then the non-Abelian one as we struggled and realized one day delta a mu is equal to d mu of to the leading order is same as d mu of lambda a.  So, even the infinitesimal one has the imprint of non-Abelian gauge transformation. Actually, this is why this gribov ambiguity arises.


You either stay the villain, or you grow up, to see yourself become the hero. You're at the best place, for your vengeful needs. There's something about childhood friends, that you just can't replace. As we grow older, this friendship stays fruitful for some. For others, it could lead you to places that taint your soul. In this episode, a rebellious boy likes to cause trouble with his friends. But as they keep pushing the borders, one of the friends comes up with an insidious and unthinkable plan, which will hurt an innocent girl. When spark of doubt enters his mind, it causes an inner conflict, forcing him to choose between two life-changing outcomes. A wise man once said, It takes a great deal of courage to stand up to your enemies, but a great deal more, to stand up to your friends. Before we start, hunt the like button down, and be sure, to avada his cadavera. Let's dive in. Naturally, viewer discretion is advised. This revenge story, might be disturbing to bad friends. So, to put it simply, I was a real bad kid. I used to steal from stores and family, swear and throw things at random people walking down the street. I was smoking from the age of 12 and didn't give a doodoo's fart about anyone but my friends. They were my real family, or so I thought, and the group of all five of us would cause trouble every single day. My parents, though in my later years have told me they should have been more effective in their discipline, really weren't to blame. I was just a mixed-up kid. I used to think that doing all this stuff made me cool. I can't really describe how superior I felt when I made grown adults afraid of me, but it made me feel powerful, and power was something I craved when I was younger. I could go on and on about my sins but the fact is, I was just messed up in the head. I've made amends where I can to who I could but you're not here for self-flagellation, you're here for the revenge. So long story short, let's get into it. When I was 16, my parents finally had enough, and despite all my tantrums, screaming and even some physical violence against my dad, they decided to put me in a school for troubled youth. I call it a school, but what it really was, was a military institution that taught discipline in the most brutally effective ways, while throwing in some literacy and numeracy classes along the way. Without going into too much detail I'll say that this school changed me. While aggressive, violent, cocky and near homicidal when I was first dumped on their doorstep, the men who ran this camp broke me down. I was there for just over a year. No phone calls, no visits home, no access to the outside world. For one whole year, I had this camp and these counselors, these real life hardass men teach me just how much of a stain I really was. By the end of my second summer, I was a changed kid.  These men taught me that real men simply don't act the way I did, and that the type of path I was headed down would lead me either in jail or dead. They were brutally honest about it, especially this one counselor J. By the end of my stay, I considered J a second father. Though I hated him at first for making me feel inferior, he really did me a favor teaching me how toxic my behavior was, and to this day, I still think of him as something of a hero. He was the main person who deemed me ready to return home. But the backstory is getting really long, so let's get to the real story. When I returned home, I had changed from an abusive little prick to a somewhat civilized young man, ready to take on my last year of high school. I was nervous to go back, since I had adapted to the disciplinary school lifestyle, but I was also excited. I missed my friends, and hoped they would just accept me back despite the fact that I hadn't spoken to any of them in over a year. And to my relief, I was accepted back with open arms. One of my closest friends had moved states since I'd been away, but the other three were ecstatic to see me. Over the next few weeks I settled down, I didn't spend a lot of time with them outside of school. My parents were kind of testing how much I'd matured since returning, and were setting boundaries on when I could go out, how long I could stay out and where I could go etc.  All of this is relevant, because of what happened next. I had joined the school football team all three friends were a part of, and one evening after practice, all my teammates were in the gym, sweaty and dirty but pleased with ourselves. I was laughing and chatting with my three best friends so much, I didn't really notice that we were the last left in the gym. But that's when the conversation started turning bad. One of my friends, I'll call him F1, friend one, for simplicity, started telling me about a college party they were all planning on going to, and how they'd been crashing college parties for a few months now, since it was easy access to girls and booze. I was hesitant about it because I didn't think my mom and dad would agree to let me go, but then F1 started talking about this girl he was planning on inviting. A girl who went to the same school as us, but not one I thought F1 had any real relationship with. I knew her, but I didn't know her. He started to tell both my other friends, and me, that he'd been trying to get her into bed for a while and she kept making excuses, so he planned on taking her to the party and finally seal the deal. When I asked him, in a joking way, what makes you so sure she won't reject you again?  I'm just gonna slip something in her drink. It'll loosen her up, no problem. At first, I just kind of awkwardly laughed, thinking it was some twisted joke, but they weren't laughing with me. When I asked him if he was serious, he told me he was sick of her games and knew she was just stringing him along, and that the pills would just make things easier. I could not believe my ears. I excused myself from the conversation pretty quickly and practically bolted home, most likely driving through several stop signs but I really don't remember. I spent the whole night convincing myself my friends were just messing around. A few more days pass and the conversation in the locker room is all but forgotten, though they hadn't shut up about the party, and kept insisting that I just sneak out and join them.  Then the doodoo finally hits the fan. During yet another, after-school training session we all end up as the last ones in the lockers. And F1 does something I never would have expected in a thousand years. All three of them have been talking about the party this whole time, then F1 starts rummaging through his gym bag. He tells us all to look at what he has and tosses F2 a small bag of little pink pills.  It's really hard to describe what I was feeling when F1 started going into detail about how he planned on inviting the girl to the party, slipping something into her drink and making use of one of the frat boys' bedrooms for a few hours. I felt sick. Literally could have hurled everything from my stomach all over the floor, as I listened to all three of them talk about how awesome the party was going to be, after just describing what they were planning to do with the girl. I couldn't take it, and again I ran off. I actually did end up puking later that night, going over and over in my head what I had just witnessed. I almost couldn't believe it. These three boys had been my friends for 15 years. I thought of them as my own family, thought I knew them better than anyone, but one year away in this? I'll tell you honestly, that I actually broke down crying that night. I'm not ashamed to admit it. What I am ashamed of, is how long I took to actually get a grip and handle it. I knew I should have told someone, but in some twisted way, my loyalties were still screwed. Don't crucify me for it, I know now what I should have done, but I was 17, and these were my best friends. I didn't want them to get into trouble, but at the same time, I knew I couldn't let this go down, so instead of reporting all I'd heard to an adult like a normal person, I decided I'd sort it out all on my own. So I went to F1, and told him not to do what he had planned.  He didn't even blink. He got right in my face and told me that the school I got sent to, had turned me into a weakling. That he hated how much I'd changed and had been trying to change me back with F2 and F3. Even told me how they'd been talking about me behind my back, and how they'd planned to surprise me, by letting me participate once F1 was done with her, just to show me what I was missing out on. Then he said something I'll never forget. He told me, word for word, I'm doing that skank a favor. She's a virgin.  I punched him. We fought, and we both got sent home on suspension for fighting. I couldn't believe it. I was seething. My best friend had said that to me. My best friend had told me he was going to do this to an innocent girl at a party, and I was a weakling for not wanting to join in? I was disgusted. Sick into my core. And I was done with him. My parents were disappointed I had gotten suspended so shortly after coming home. That night at home, I just sat there quietly while my mom cried and my dad screamed at me. I know now that I should have told him, but after what F1 said to me, I had this insane notion in my head that I was going to get him back all on my own. And now, to the revenge. After a weekend of being grounded, I went back to school, and the first thing I did was seek out F1. He was about as bashed up as I was, but he was sporting a nice black eye from where I'd hit him in the face. F2 and F3 were standing with him, and they all glared at me as I approached them. Then I did something that made me feel sick. I apologized to him. I told him I was sorry I hit him, and that he was right, I had changed, and I hated what that school had done to me. I wanted to go back to being the old me again. Surprisingly, they all bought it. F1 and I even hugged it out, and I put the cherry on top when I told them I'd be coming to the party.  First, I started recording them whenever we were alone together. I wanted to get everything they said about the party and the girl that were planning on victimizing on tape. I knew I needed some kind of proof, or it would just be my word against theirs. And after a few days, I had gotten more than enough. But I wasn't done.  So the next thing I did was track down the girl, take her aside, and tell her everything. She was pissed and scared, but I begged her not to go to the police or tell anyone.  I had a plan.  So I told her to tell F1, that she was going to meet him at the party, but to just stay home, so she could stay safe. Later that day, F1 started bragging about how the girl had accepted his invitation and everything was going according to plan.  Then the night of the party finally rolls around, and I sneak out because, you know, I was grounded. I think it's worth mentioning that I wasn't filled with vindication and self-righteousness throughout the whole night. I was second guessing myself, I had doubts, but in some strange way, I felt betrayed.  What messed me up in the head even more, was the possibility that I might have been just like them, if my parents hadn't sent me away. It was a strange moment of realization to come to, in the middle of a crowded frat house surrounded by drunk idiots, but you take what life throws at you. So the night goes on, and F1 is getting steadily more frustrated that the girl he invited hadn't shown up. I've made sure to keep him in my sights for the whole night, not wanting him to decide that any old girl would do, if he couldn't take the one he wanted. I kept an eye on all of them, watching as they drank and drank while I stayed as level-headed as possible with some water and a beer can. When midnight came, all three of them were plastered, and I knew that all the girls at the party would be safe by then. By this time the crowd was dying down, and a few people who couldn't hold their liquor were already passed out around the house. The moment arrived, now was my time to shine.  Here's where I did something I'm not particularly proud of, but I'll tell you anyway. I slipped one pill into three beers each and handed them to my friends, and then waited. It didn't take long before all three were passed out on the floor, along with quite a few other party guests.   This couldn't be it, what they were planning was insidious and a next kind of evil. So I also took pictures and immediately uploaded them to our school's Facebook page. So everyone who attended our school would see. Admittedly, I didn't really think this part through, since I not only did this in full view of every other conscious person at the party, but also knew the photos wouldn't last long on the school site before they would be taken down. But since it was a small school, in a small town, I didn't doubt that a whole bunch of people would see it before a teacher removed the photos, and that's exactly what I wanted. Next came the recordings. When I got home, I got a verbal bludgeoning from my parents for sneaking out, but they stopped when I finally told them what had been happening. They were both shocked, and a little disbelieving, but when I played them both the recordings I'd saved on my phone, they were just as sickened as I was. I was silent in the car as my dad drove me to the police station, receiving a lecture about how I should have just come to him in the first place, and what I'd done at the party wasn't necessary. But I truly felt like it was at the time though. My phone had already blown up with other students commenting on the pictures of my three ex-friends, condemned and crucified with the word I wrote on their foreheads. And while a lot just laughed at them, many were questioning if there was any truth to it. This was exactly what I wanted. I wanted everyone to know who they really were, so they had nowhere to hide. The hours at the police station were admittedly very scary. I was still debating with myself whether or not I did the right thing, but my friends had chosen their own fate.  Long story short, the recordings were enough to get them all on charges of planning to commit a crime. Since the girl had been named in the process, her parents were understandably furious, and demanded all three of my ex-friends be arrested. I would have been too, were it not for the girl telling her parents, and the courts, that I had warned her to stay away from F1 and the party. I was charged for my use of an illegal substance, since I admitted to using the pills on my three ex-friends, and also for battery, since the permanent marker was seen as a form of assault, but luckily I never got jail time. I did get a boatload of community service though. All three of them were tried as adults in a case of attempted rape, but only F1 got actual jail time, since he was the one who'd gotten the pills and was the only one who admitted to wanting to use them. The other two only got probation and community service for being accessories, but were completely shunned in our town. No one would ever let them forget. I was prepared for the backlash, ready to be jumped by them or something, but strangely enough, I think seeing F1 go to jail for what he did knock some sense into the two of them. They wised up enough to actually get into college without football scholarships, since they were both kicked off the team. They never came anywhere near me again, which surprised me, but I no longer cared. In my mind, my friends were dead to me long before all of this went down, and by the time I moved away to college, it was all behind me. I'm in my final year of college now and I still think about those three sometimes. I think about how, if my parents hadn't sent me to that special school, I may have ended up just like them. Oddly enough, I do miss them at times, but I know it's the memory of the kids I miss, not the men they turned into. I thanked my parents continuously for sending me to that place, and even got some approval from Jay when I felt man enough to tell him what happened. I don't know what will happen to F1 when he gets out of jail, but a part of me hopes he learns his lesson and moves on with his life, like I have. Jay called me a few days ago, just to check up, and I told him this whole story, which is kind of why I'm now telling the internet. I guess the moral is to stand up to your friends when you know they're doing wrong, but maybe not in the stupid way I did it. Always involve others more qualified to deal with situations you're not sure about. Even if you're a headstrong, stubborn teenager who thinks you know everything. I'll answer some questions that I've received. For everyone curious about Jay, well he's great. A great man who's gone through a lot in his life too. He lost his son to drugs, which is why I think he made it his job to look out for boys like me, just to make sure no other parent goes through what he did.  He's also told me that he'd like for me to come and speak at the school next summer, just to tell some of the new boys coming and how bad things can get if you refuse to change the way you live. If I ever strike it rich, I'll be giving that school a massive donation. To all of you asking if the girl in the story and I became friends, well, sadly, no. We talked a lot during the court case and after, but we never really developed a friendship. I think we were both too embarrassed over everything, so we just won our separate ways and remained civil in school. For everyone questioning why I sound British, all I can say is wow. I'm used to people picking up on it in person, but not through writing. Some of you guys must be secret geniuses. My father is British. His whole family lives over there and we visit a lot. And his family is about as British as they come. And a little piece of side information, I was actually born in Britain, six weeks premature, but I was raised in America. For everyone asking where this happened, for the sake of everyone's privacy, including mine, I'm going to have to keep that a secret. All I can say is it was a small town, with a small population, which is probably why the whole thing wasn't plastered all over the news. But I'm paranoid, so that we'll just have to remain a mystery. For everyone suggesting I tracked down my friend that moved before I got back home, while I'm kind of on the fence about that. Call me a coward, but I think I'd prefer to remember him as my childhood friend, without all the memories being tainted the way they are with all the others. If I went looking, I might not like what I find, and even though it's possible he changed too after being removed from such a toxic environment, I just don't know for sure. I guess I'd rather live with the ambiguity. For those of you wondering what I would have done in the situation if I'd never gone to that school, well, for obvious reasons, I can't really answer you. I'd like to think I would have stood up to them all the same, but my mind was seriously twisted back then, so I'd prefer not to think about that. For everyone questioning what I'm doing now, I'm studying aerospace engineering. I love planes, and through my course, I've gotten to tour the underbelly of both planes and even some aircrafts that have been in space. I don't want to sound like a dork, but seeing all those components fit together, actually knowing how it all works, what everything's called and how to identify everything, is seriously epic. I just hope I pass the course with a good enough grade to make a career out of it. If there are any other questions I missed, feel free to ask me. I don't have a lot of free time so the responses might be late but, by all means, ask. Thank you to everyone for your kind words, and for the surprising lack of people calling me a dumbass. I appreciate that. You stay till the end, which means you're the one I make these episodes for. I want to take this moment, to thank you, I really appreciate you, because you bring me a great amount of joy. Subscribe for future uploads and show your vengeful devotion, by tickling the like button, without mercy. Do you have any experiences surrounding the topic of this episode? Share yours below, I'll join the conversation. And I'll be seeing you, in the next one.