MIT IAP Animating New Physics Day 2: Quaternion Quantum Field Theory Demystified

Transcript

[Music] All the girls in the classroom think he's hot. He shows up wearing the sandals with the white socks. He hears some gig man while he's got his back to the class. He thinks he's got an eraser mark on his ass. And all the girls from the hall show up to hear him talk.

Even though most the time he's covered in chalk. Math prop rockar. Math prop rockar. Oh yeah. Math prop rockar.

What's amazing is these these lectures are actually pretty darn independent of each other. Um except for that little thing, the one thing to know and that is what the aquatronian product is. It's just the the scalers multiplied together. the dot minus the dotproduct like like happens with complex numbers and then the scaler times a vector vector times a scaler and then the cross and that's it. Okay.

So uh we're going to do a little uh speedy review of what we covered uh yesterday. Uh what I said yesterday was that I was a lunchbox physicist and it says oh how beautiful and simple it all is. How could we have missed it for so long? And claim that what I was really trying to do was was to put time and space together. Now, I'm going to give you something new out of that. Like, there's a big problem out there with the arrow of time.

Actually, it's it's not a new problem. It was around since Boltzman's day. And um to me the question is posed incorrectly because if you have a problem with time, I'm going to go buy you in a in a spaceship and I'm going to have now a problem with space time because time is going to rotate in space and now it's no longer a pure question of the arrow of time. It's the arrow of spaceime. And so is there a problem with an arrow of spacetime? And it's like well the space part has got point fingers to it.

And I can actually get a little bit more technical than that. I can show you the look. Well, actually this is so small it's it's easy to do the the the Lent transformation for doing that is got it looks like this. And you know it doesn't matter how many times you hit things back and forth it it'll it'll still be the same matrix. You'll still get the same results.

You can play pingpong back and forth with flipping time forever. That's their arrow of time problem. Okay. Now if you try and do the same thing with the quaternian and ever so slightly little bit of the cross productduct creeps in that's the handedness and that solves the arrow of spacetime which as I say is a diff different from the arrow of time problem but that's because I think the arrow of time problem is u is not the way to go. Okay.

So, um, now we'll we'll kind of, uh, step through the slides, uh, and we'll start with a, an executive summary. So, we make this very simple. Executives like simple. Oh, great. I forgot.

Uh, let me go back. I I've got to have my amp on for you guys to hear this. Okay. So, what we did was we went we went over numbers, you know, thinking about querians in terms of numbers. We showed you the little bit of algebra.

Uh we did a lot of equations and I did have uh a few words uh few words to say about it. Okay, so um let me just make sure something's going on. Okay, that's great. Um, no, we don't want to hear it twice. Okay.

All right. So, now we look at the um the linking of the math to the words and we've got Oiler Lrange somehow getting us from uh the back what's written on the back of the t-shirt to the front of the t-shirt. Um, I do have these little index cards uh that I'm trying to give away just because if you do happen to wear the shirt, um, it might be a little frustrating. I've been in the situation where I say, well, you see that it doesn't work. Um but if you had a card you can say well this little part here is about the symmetry of uh uh of light and the weak force and the strong force and you know anyway so this is really an aid uh if you if you decide to wear the t-shirt and hope to try and explain things.

Okay. So um then it was the idea of merging complex numbers, scalers and vectors using both i^2= positive1 and i^2= minus1 for um for hyper complex and and complex numbers uh respectively or I should say quitterians. All right. So in these this was the graph theory that I came up with for uh quitterians and hyper complex numbers uh where the the little clay balls are vertices and the edges are labeled um and and they've got to go like I and minus I to kind of uh get back and forth and then the plane is where it gets uh confusing because it's the it's the crossroduct but hyper complex is is easier and simpler. uh and that's related to gravity.

So then we uh went ahead and derived uh the oiler lrange uh equation and I don't think the person who corrected me is uh returned but uh I corrected the notes. I just wanted to thank her. Um and even though that looks really really scary uh we notice patterns like the dadz going straight across there and we've got all these duplicate sorts of things. So maybe we can deal with uh all those terms. Uh we looked at Lorent and variance and I identified four that are on the back of of the t-shirt and then we went ahead and derived in the the right way uh all four maxwell uh equations.

Uh the first column is for E.B. and it gives us the u the no monopoles and Faraday's law. And what's kind of neat about this graph is you can almost kind of think about how each one of those terms is used. It's one of these things like, oh, this must in Faraday's law, this must be the the e term and this must be the cross term. So this this example must be for uh x, this must be ex.

And then we'll have have this thing shift down for y shift down. And then those other boxes will shift around and we'll cover everybody. So this is another way I'm trying to communicate the completeness of what Maxwell has done. Uh and then we've got um Gaus's law which uses this B ^2 minus E^2 Langian where the B's are separate from the E. So they're not mixing together and crossing each other uh stamping each others out.

Then we went ahead and did um did the what I calling calling the G field. This is only about gravity where everything flips signs in this lron density except the cross terms and we end up with uh with Newton's law down there um row equals you know the lassing of of scalar field and a time dependent one and that's very very vital uh because it means that the time dependent change in in the mass density has time to propagate and be consistent with special relativity. Then I moved on to what's covered on the t-shirt. That would be the the gem field equations. Uh and I called it an uber modern uh Lelass's equation.

So we are trying to do so much more than just say well it's just this one one thing going on. And the math is actually easy which is kind of nice. Okay. So then I gave you a a flavor of group theory. Um and this one here has I claim uh U1 symmetry, SU2 symmetry, SU3 symmetry and in a certain way it's really about um uh about unit spheres in space.

We even made it out to the issue of spin uh which is somewhat remarkable. Um, and I was able to uh at least show you uh and give you a a sense of um the angular momentum spin projection operator if I use jargon. And if I don't use jargon, I just said I got a zero for the imaginary part because my two things cancelled. And if you look at the coefficients, one of them had a bunch of ones. Uh another one they added up.

And the the ones that add up or spin too. Uh and that's that's the natural curl. The ones that kind of look like they're cancelling each other, they they're only ones involved. And uh that's curl and uh that's connected to VM. And then uh sprinting hard at the end.

Uh we said that the uh exponential metric um was was a solution to uh my uber modern uh field equations. And um I think it's prettier because it is exponentials and exponentials seem to dominate the world because they're they combine both doing absolutely nothing and doing a little bit of oscillation. And that's actually been an important uh kind of philosophical change that I've had is I've always thought about physics as doing a lot. But it's like you know the universe uh is like 13 billion years old you know and if something is around after 13 billion years it must be like basically doing almost nothing. And the key is what is the smallest possible step from doing almost nothing.

And I think that's what fundamental physics is is really studying. So that is the review of what we covered uh yesterday. So I wasn't here, but can I ask one question? Absolutely. And by the way, anybody should do what this man's doing right now. So on the shirt it says no stinking hesitates, which implies that that you've got SU2 and SU3 in there or SU2 in particular.

Uh can you go over that again because I didn't see the SU2 symmetry? I did not review that. Uh, no, I I I had SU2 symmetry in there. No, the the no sticking higs was that um was because there's a gauge field in this. Oh, I need this. I need this card.

Actually, I need a t-shirt. Unfortunately, I have a few. Okay. Um it's better than all right. So um the no stinking pigs is is is a is based on a an essential trick that happens in the standard model.

You've got three symmetries u1 su23. In a certain sense you need to preserve those. If you don't preserve them what it means is that those charges are no longer conserved. If those things are no longer conserved, then some experimentalist is going to show you wrong. Okay? Because they actually do have experiments that show electric charges conserved to a super huge uh degree of accuracy.

So the way standard physicists do it is they say that vacuum that vacuum is a false vacuum and when I break symmetry from that that's how some of these particles gain mass. Okay, I use a uh I don't use that technique. Okay, my vacuum is completely real. There's nothing false about the vacuums that I work on. I think a vacuum really accomplishes nothing.

Okay, which turns out ironically enough to be radical these days because everybody uses the the vacuum to get stuff done that they don't understand at this time. I am going to hold the position that if I don't understand it that's fine but the vacuum will never explain anything in the universe other than like like the um volume shift. Yeah. Sorry. How do you explain electros? Uh I don't think I do at this point.

I what I do what what I what I do what I do on the t-shirt what I do on the t-shirt is say um this this term right here this holding a t-shirt. So you're adding a gauge to explain why no no this is what I'm doing. It's a it's a slicker trick than that. um this this stuff with the with the um with a hyper complex product that has a gauge field. So So this thing has a gauge field.

I think this is related to things that are that that deal with gravity. This thing also has a gauge field. Okay. So this also applies to things with mass, but but but this is a plus and this is a minus. So the two gauge fields exactly cancel.

I see a question how you explain how you can justify justify all the No, what I'm throwing out No, the one that I'm trying to throw out is the hits. There is no data for the hits. No, but I know and I'm consistent with that because this equation has uh has a gauge field. Okay. Sorry.

It's just that this gauge field exactly cancels that other gauge field. It's that I have two gauge fields. One for the standard model stuff and one for gravity. That's probably where I bring it in. There's a gauge field for gravity.

And it's the gauge field for gravity that cancels the gauge field for the other three forces. Is that closer? Is it closer to making sense? Okay. All right. So um what we're going to do now is uh try to address the question why quantum mechanics uh is weird. And there are a variety of schools for for for this.

Um and in fact I went to a talk by Max Tedmark where he took a vote on what people preferred which is kind of funny right to me that's a sure indication that physicists haven't settled on an answer. Okay. And in fact in this group it was at Harvard University um it was um the Copenhagen got no votes. It was, wow, the Copenhagen interpretation really uh is is not popular. Oh, who was it? Who was who was the other guy? Oh, my friend's going dry.

What? Yes. Yes, Everett got a lot of votes. Um and uh so did Oh, who was the other person? Anyway, um but it was kind of curious that Copenhagen got no votes. But but we're so physicists still are not at peace. And I I I said I do have a different answer.

Uh and I'm going to go through uh the logic of my my thing and the what it is is that if you do quitian calculus correctly uh that I think that provides a new answer uh to why uh to this old question. Uh so is quantum mechanics weird? These are probably the most famous quotes out there. I don't know maybe I will read it just whatever. So from Neil's Boore it says for those who are not shocked when they first come across quantum theory cannot possibly have understood it. More modernly uh Richard Fman says I think I can safely say that nobody understands quantum mechanics.

And then Albert Einstein said something like, you know, God does not play dice with the cosmos. And Neil for retorted, do not presume to tell God what to do. And Groucho March even had a comment in there. Very interesting theory. It makes no sense at all.

Uh so I thought we thought we'd go a little deeper in a Richard timing since I have so much respect for him. uh we have always had a great deal of difficulty understanding the world view of quantum mechanics represents at least I do because I'm old enough man uh that I haven't gotten to the point where the stuff is obvious to me okay I still get nervous with it I don't I uh you know how it is always is every new idea it takes a generation or two becomes before it becomes obvious that there's no real problem. I can't define the real problem. Therefore, I suspect there's no real problem, but I'm not sure there's not a real problem. So, I think that's nice because it shows the tension uh in his mind.

And let's face it, this guy won a Nobel Prize for QED. So, he was good at quantum mechanics. And yet, there was there was like a pee under this aisle of mattresses that he was sensitive enough to still feel at that age. and and based on uh I don't think we've solved it uh to this day. So the problem just to define it is the um non unitarity of quantum collapse.

Is that fair? I would say that's uh probably too technical an answer. I mean it it maybe that's a way to look at it. Um I think it's like things like the uncertainty principle. It's like how how does that really work? Why why is that there? I think it's almost as simple as that. Uh but if you start to get into direct equation, you go what's a creation and an annihilation operator really doing.

Explain that to grandma. I might explain it to a graduate student in physics, but not grandma. Okay. So, um I'm arguing basically that quantum mechanics is still weird uh today. Um Einstein I I think his views are everybody wants to say Einstein thought just like I did.

It's like no no that's not the case. Um I I read a very very good uh uh the subtle is the Lord is a is a wonderful book um about Einstein and his philosophy in actual science and and he was he was impressed with what they did. You know the the bore atom was was just spot on. Um but Einstein thought a lot about causality. Why did this happen? How could this have happened? And that's I think I think that's the the key under his collection of of mattresses is what is different about causality for quantum mechanics uh than than classically.

I mean classically A happens then B happens and C happens. Okay. Um well this is a little picture of uh of what goes on. uh that only the sum of all possible histories says what happened in quantum mechanics. So there's this guy looking at the moon.

It's bouncing off of a lake. And um if you actually decide to to focus on just one path, you'll get that signal. No matter very often, but it will happen. But if you go ahead and calculate what happened, what you need to do is out of every single one of those, you'll notice that one of those actually happens a lot more often. It's uh it's not destructive sort of thing.

Um but you must include them all and that in essence is kind of odd. I gave this one kind of its own space and that is that the math of quantum mechanics is flawless. It's used to make the most precise calculations out there. So, I'm not challenging uh that issue because it's not an issue. It's great math.

And it's like now when we get away from the philosophers, you know, we just say we got to do these calculations, everybody's uh with the program about how it is done. So, my list of the largest Two new math ideas generated over the entire history of physics is calculus by Newton and spacetime by Einstein. And I probably should give Mowski credit because he was the guy who he was his math teacher and said, you know, you're really rotating time into space here. All right. So, I'm going to try and smash the two biggest ideas together to make space-time calculus.

And I take this right out of my my calculus book from uh from from the day. And it just doesn't work. It doesn't work because quitterians do not commute. So should I write that dq on the left or should I write it on the right? Now there are professional math wonks who work with quitterian derivatives on the left or maybe they do it on the right. I don't know which is actually more popular in the literature.

But either one I consider a disaster because for technical reasons they can't show that q ^2 is analytically q and it's like well then why bother? If you can't if you can't figure out the polomials, you can't figure out anything. If you can figure out the polomials, you can figure out everything. So, um I consider a complete train wreck. And um so I thought about an alternative. Um it's it's basically the three vector part of the of the differential element um that goes in the cross productduct.

It's the cross productduct that makes it not commute. So why don't I just make that go away by being clever here. I'm going to take two limits one after the other. I'm going to first let the problem child go to zero and then I'm going to let the time go to zero. Okay, that's a well-defined sort of animal.

And it's kind of it's a variation on Waspal's rule which I always consider a little miracle when I first learned it about taking two two limits in order to get something that actually is valid. So after after dr has gone to zero dt the dt part commutes and so maybe it doesn't matter if I write it on the left or I write it on the right as long as I use two limits just like this. Um so we're going to test it. We've got this function uh Q ^2 and we're going to use that uh the limit definitions and I don't know if you uh remember those calculations from uh I don't hopefully you did those in high school or something uh but uh it it's kind of fun to see them actually kind of work out. So the first one uh first line I just say okay I've got Q and I'm adding in my DT my my differential element I'm divi and I'm subtracting off the Q without out the differential element um and I'm dividing it maybe on the left or the right um that wouldn't make a difference at this point um but now I just kind of crank through that multiplication and I've got Q the differential element and then the differential element Q at this point they are different and then when I let the R actually go to zero then um it that that this guy right here it doesn't matter whether I write him on the left or the right because he's just a real number and since he's the inverse of that he's going to cancel that one he's going to cancel that one I'm going to end up with exactly dq um 2dq um and a differential element and so one dt goes to uh zero I just get dq that's that's what you expected okay but it required this two limit trick if that two limit trick isn't there it does not work okay so with our physics hat on okay we say if if dr really being a change in space is less than cdt then things are traveling at less than the speed of light.

Okay. And so in a certain sense I I think of mathematical physics as being a little bit more constrained than than math is. Um it well because yeah that's that's a more philosophical sort of thing. Um, and I I call this a timelike derivative. And only by me, this isn't like I I know I've had some people who who do uh we're doing reviews of quitterian derivatives that are out there in the journals and uh actually twice people have said, you know, I I happened to stumble upon your definition and I I really liked it because it was really simple, you know, and it seemed to work.

Um where those things got published I have no idea. Um but I yeah anyway so so that's that story. Uh but then you go um well what how about the other case? What happens if the change in space is larger than your changes in uh time? Then don't I like have a problem? It's like yeah you do that guy. what can I conceivably do with that that's still going to have this uh this this cross productduct problem okay uh that doesn't shouldn't shouldn't nature also use that situation and I think the answer is yes okay but how does it use it and this was my idea to say that the norm actually does not depend on the cross product doesn't show up there okay so if I take the norm of these derivatives that is well defined. If it's written on the left or it's written on the right, the norm will be the same.

So you may not have dealt with norms of derivatives back in high school or even in college, but I mean it should be okay. You're going to get less information though, right? You're just going to get the size of that change. Uh you're not you're not going to get a sense of its direction. But this is all you can do is is my perspective. So uh we'll test on the same function.

Okay. Now the first two lines there's really no difference except the order of the the limits. Okay. Then you write it out and you go oh okay. So now I don't have time around anymore.

I just have um these these sorts of uh these these terms here. And he's like, well, how did you get go from line three to line four? The way I did that is I said, well, I'm just dealing with norms. And way norms work is the norm of one uh times the norm of the other just equals, you know, the product of those two. It's just really really that simple. So I'm taking the norm of that uh the the the one over uh r thing and when I take the norm it will just be a real value.

It will just be uh a a a scalar value. So I can commute the norm of that that thing. And if I commute the norm of that thing then um then I'll I'll be able to get a one out of there, right? I'll be I'll be dividing I'll be dividing the norm of this by the norm of that. Well, that'll be one. And so one times that I'll get just get the norm of that.

I'll just get the norm of that or 2 * the norm of that. And so that's that's the result there is that that it's the square root of 2 uh Q star Q in the limit. So um the timelike derivative and the space like derivatives of the same function uh actually give you different results which isn't that surprising right because uh um oh different well I don't know whether you're surprising or not but um what I'm thinking here is that classical physics is is the normal derivative where where you you you let space go to zero first and then time go to zero whereas whereas quantum physics has all these norms showing up because you have to take the norms of all these differences. Um, and as I say, I don't think there's a testable difference um with this definition uh of of of these issues. And so that's why I don't like get up on a soap box and bang on it.

Um, I mean, I feel warm and fuzzy about it. uh but if I don't have an experiment where I can say hey if you do this it'll give this you this different answer. Um actually what I did do was I I went to that talk by Max Tedmark and um warned him that I was coming with my own approach to it and uh tried to do the uh tried to do this calculation on a piece of paper. He asked me to actually do it and I I wasn't able to to spin it up. So um so and in fact one of the things I'm most pleased about from this whole lecture series was uh was figuring out not only that one but uh but the uh calculation there uh that was a new calculation for me.

Uh all right so um and uh and and we'll actually get some visuals of this uh amazingly enough. Um so so why haven't we why haven't we heard about this particular idea? Uh because it's a mashup of complex numbers uh vectors and the limit div uh definition of uh derivatives um and that's a lot of things to mash up and not enough people work with quians in the first place to be that worried about the definition of a quitterian derivative. All right. So now we uh move on to uh quitterian uh quantum field theory demystified. This is actually a uh book uh available on Amazon.

And um my uh my good friend uh lol uh who's kind of doing research with me uh he said you should read this because it's kind of your style of heavy equations a few words summarizing what it is and then the next equation and then the next equation and um so I was able to uh read this in about a week or so. I had taken a full graduate year level uh class in relativistic quantum field theory. So it was like familiar but it's like I hope I don't have to answer all these questions because I I'm probably too rusty. But they were all familiar issues for me. And then I went back and said okay now if I was to do this with fraternians how how the heck would I do this and what would my approach be? And it took me three weeks to get through three pages.

I don't feel bad about that because by that time he'd already done the uncertainty principle. He'd done uh uh Klein Gordon. He done the Schroinger equation. Uh he had to wrap. So those are really core equations to quantum field theory and we're going to show you basically uh that sort of stuff.

Um so I read slowly but um it was it was a productive process and um all right and and out of it came what I'm calling the method uh if I can just switch over modes. Okay so new methods really rewrite everything that was done in the past. So special relativity which applies if if things really are are moving very quickly. Um you've got time and space there they're they're four vectors. Energy and momentum are four vectors.

Uh and in quantum mechanics which applies to things that are really super tiny. Uh you've got the correspondence principles. So you can connect stuff that happened in classical physics to quantum mechanics. You've got these complex amplitudes. You have real observables.

All sort of stuff. um that works if and only if things are really small. And so I was saying to myself, well, let's get rid of those, you know, if and only if sort of situations. Let me just write it once and use it whether things are going fast, whether things are going small. I don't want to rewrite anything.

Okay, that was my attitude. Um so, uh the method as I'm calling it um has just four rules. um to rewrite all equations in field theory. Uh or I maybe I should just say in physics. I probably should just say physics.

And I I nothing is really radical except being this consistent. Um and we don't really tolerate breaking rules. And um not being flexible is actually pretty easy. You just say, "Well, I didn't do this, so I I have I have to keep on I redoing things until it's consistent with my rules." Because nature appears to be this rigid, right? It's like, I'd like to not, you know, deal with gravity today. It's like, no, you will always deal with gravity.

Uh nature will never allow you to take a step outside. So, rule number one uh is to keep all four vectors together uh as quatronics. And I uh okay so examples would be spacetime okay got this the time element and the space part and they're together and for momentum be energy and momentum together and differentials okay turns out that the this that's a very simple statement to make there's nothing apparently radical and believe me I'm not going to get along with all the books I've recommended people like think about energy and not concerning themselves with momentum or if they do they'll put it on the other side. That happens all the time. Um it will be resisted and in some ways I think this is somebody said what it's it's I'm not remembering the quote exactly maybe uh quote exactly but it's something about is it aren't we lucky that math and math is gets along so well with physics.

Um but is there any tension there? And I would argue actually after th this kind of talk that there is some tension. And the tension is that because we're so used to the equal sign, we're so used to saying I'll put this on the left side. I'll put that on the right side. And do you have any criteria for doing this making this decision? It's like criteria. I don't need any criteria.

It doesn't matter. Okay. And I think that maybe it does in a certain sense. um because it's a deep lesson of of special relativity. Um people like to focus on energy and ignore momentum.

You know, it's like well I'll deal with that or I have to. It's like no, you have to because somebody in a rocket ship is going to look at your equation and they're going to see the energy part. They are going to see the momentum and if you don't have it written out explicitly, rocket ship man is lost. Okay. So that message from special relativity says I can't do a calculation that only involves energy.

Well, a vast majority of what goes on in in these books are calculations that just involve energy. And um that little thing uh bothers me. Okay, rule number two is very easy. Drop all factors of I. and factors of I are rather popular in quant quantum mechanics books but because I'm using quitterians it's got an I built in it also has a J built it and has a K built in so it's nice to have these these things built in um and what I do is I really no longer try and I stay away from the word imaginary the the word imaginary came about as an insult right that was when people were fighting over whether complex numbers should be used by anybody.

Okay. And as we know complex numbers one out but in the meantime that you know that the people trying to knock them down those are imaginary. There's nothing imaginary about space. There's nothing imaginary about momentum. There's nothing imaginary about that kind of spatial derivative.

Okay. So it sometimes language helps um if you step away from language that was uh insightful. I should say maybe a as a kind of correlary to this uh quitterians some people thought they were really going to be important and they got into the same kind of super nasty fight just quitterians lost. So that's why it's not mentioned in any of your technical books except those that have to deal with 3D spatial rotations uh which would be either for rocket scientists or game designers. uh those are the only two technical books that will have quitterian an index element to it.

Okay. I in fact only had one math book that mentioned quitians once and I read that I know in 1988 and I came back to it in 1997. Uh so that's the that's the only reason I'm giving this talk today is it was mentioned once and uh this is the this is what's come out uh since that time pretty remarkable. All right. So, rule number three, keep all those constants.

Uh, write all those factors of, uh, C, H, and B. Uh, find one was actually a big fan of this. And people today say, "No, I'm going to use natural units. I don't have to write it out." Okay. So, um, so that's a kind of difference in in um in attitude.

Um, but I think that that the constants actually give you a handle on what's going on. Okay. Um, you know, if there's not a factor C in there, well, then you can't be really relativistic. If you got an H bar, hey, maybe you've got quantum mechanics going on. Uh, quantum uh, gravity, uh, relativistic quantum gravity has a G and an H bar and a C like like uh like the t-shirt has.

So, rule number four is uh that all equations must be made dimensionless. So, um, this is really I I don't want to deal with the French. That's the whole my whole, you know, they've got the kilogram defined in Paris. Okay, I love Paris. I love the city.

I don't want to go there to find out about the kilogram. Um, so the way you execute this is that you put in only dimensionless things and they're going to stay that way. Okay? You're still dimensionless. They're still dimensionless. You see, and this is one of these kind this is actually a little dividing line between physicists and mathematicians.

Mathematicians, they're always dealing with dimensionless things, you know, everything is this is a set, you know, and it's got these, you know, collections of numbers. They're always dealing with dimensionalist things. That's one of the strengths of their their the hand they play. So, we should copy that if we're coming at it from physics. Um, and it's a nice check on things that are done.

Now I have yet to really commit all of a different way of saying this was I'm using plank units uh for everything or dividing by plank units for everything. So so that would be one over plon time that would be one over plon energy that would be uh that would be plon um oh yeah look that's the inverse that must be plon time on the end. Okay. And um so you end up writing more uh and having to look at that wiki page that tells you how to convert all of these uh units to to planking units. Um but so they're they're in the set of rules.

The only one I think that's truly uh a little odd is the the thing about using quitterians in the first place. Okay. But once you accept that then dropping factors of I keep all the constants making them all dimensions. That's all we're going to do. So, who are we gonna who we're going to subject to this sort of thing? Why not start out with Sir Isaac Newton? He's the one who started it all.

Okay. So, um what makes Newton's second law just so darn classical and so darn relevant um to our local world? Um so, here is that second law. Nothing's moving fast, nothing's small, nothing's amazing. We've got, you know, father equals mother sort of thing. But I was just wondering, uh, in your own opinion, uh, why do you think that equation is just so important? Do you have kind of a a reason why you think it is? All right.

Um, you know, it's like, well, it was the second law. He was starting out. It was the thing that that kind of told us about inertia, about how you change inertia around. It seems really basic, but but can you make it kind of more concrete? Uh I certainly didn't know how until I did this exercise. Um and that is I just used the method.

And so I've got a time operator acting on mass times velocity. Okay? And I made each one individually dimensionless. And I multiply that that whole thing. And I think the reason it's so relevant um to our world is that there's this zero in every single term. You know, I wasn't taking time derive and a space derive.

I wasn't dealing with velocity and what whatever would go in in the front of that. uh and then I just multiply that out and I do get the uh the rocket uh riot rocket science term out of that um which of course should formally be included but most people don't want uh don't do rocket science um and I also think that um there's there's nothing relativistic going on here you know because otherwise those zeros wouldn't be there they would have some value to it and um relativistic quantum field theory you can recognize the equation with this generator because every value will be filled in. Okay? And if you're dealing with classical quantum mechanics, then one of those terms along the along the way will either have a constant or or zero. Um and that's the difference between relativistic quantum field theory where everybody is really filled into the max and classical quantum field theory which makes you know is kind of a step in between Newton and uh and what we've written uh a step between relativistic quantum field theory and that Newton equation. Okay.

and um and it turned out that I used this this result uh for my Christmas card this year. Okay, so let me explain my Christmas card. That's an apple falling and it's it is gaining twice as much uh in in each kind of subsequent step as it were. And the math is uh the acceleration of gravity uh g uh which is 9.8 8 m/s squared times the square root of g a small number h a small number divided by c to the 7th a large number ends up equaling 4.42 * 10 - 51 as a number. Okay.

So it's it represents exactly the same thing. You could say this is 9.8 m/s squared acceleration or you could say it's 4.42 42 * 10 - 51. This bothered me for a full week. I'm so used to my units. Even if I had to go to 32 feet per second squared, I was more comfortable going to the English units than going completely without.

It's like you can then what is it? It's got to be describing the same thing. Okay, it's just using different units. Okay, wipe them out. Okay, but why is it so small? I liked it when it was around 10. I liked it like it was okay around 32.

Being this small bothered me until I said, "Hold it. Physics is about my relationship to the cosmos. In the cosmos, I'm sitting on a planet that is stupid joke small. It is nothing compared to the sun. The sun is nothing compared to my galaxy.

My galaxy is nothing compared to the whole collection of galaxies that make up the universe. The science has told us over and over again. You are nothing. I'm saying that message again. Okay, that's all I'm being consistent with that message.

And that's how I kind of said I I I took a step closer to saying I guess that's okay. I guess that's kind of cool. and it inspired uh some poetry and so I'll read that and I won't analyze it because analyzing poetry is probably better uh like analyzing jokes. So gravity written without units tiny beyond the tiniest tiny gives weight to mountains and butterflies even light bends to this game. Lives lived without words, alive, breathing, being and now give weight to responsibilities and laughter.

Even love bows to life. I uh sent this card, of course, through friends and family. I do send this card out every year to physicists. I'm, you know, I'm doing social experiments. You know, this is a social experiment.

I don't know how much of what I'm saying is true. Uh I hope it's a lot. I certainly can't be certain within my own shoes that it is. I do out outreach through YouTube uh through those YouTube videos. This is one of my techniques.

I send this card to uh to professors. I actually send it to uh five professors here. Alan Guth, Max Tedmark, Seth Boyd, uh Paul Jos, and Peter Fischer. These are all people I have approached personally and usually at the end of one of their talks and say, "Hi, I've got this new idea." And they were polite. They were professional and they're busy with their own world and I haven't suckered them in if you want to say it that way.

They are in their own program. They're extremely busy folks. Uh but that's at least one thing that I do to try and get So these people, they know of me. I am the weird Christmas card guy. And with this body of research, amazingly enough, every year for literally 10 years, no, maybe 15 years, I don't want to think how many years, I've come up, I generated a card based on my physics research that uh that certainly was uh somewhat unique.

I mean, it's kind of crazy that that this this mission started, I think, in uh April or May, and uh it's really been wonderful and and I really like the card for uh 2010. Don't know what'll happen next year. All right. So, let's look at the uncertainty principle. Very important.

Um the uncertainty and certainty principles of quantum mechanics um arise uh from the move to operators and the product rule of calculus. This is usually not the way it's explained. I have a hard time seeing things in the standard way. Um it's because you know the the the uh uncertainty principle that gets all the press. That's what they have books and conferences on.

That's what everybody talks about. Okay. And there are actually many schools of thought about why the uh uncertainty principle exists. Um but here the way I like to operate if I can't map it directly to an equation I'm not happy. Okay.

I need my my equation sort of thing, my math thing. Um, and it is only uh momentum in the x direction uh that is uncertain. Okay. Um, and I actually put a big x through this because it um it it it's a little bit too general or it there actually this should be a subscript but I just I know this should be a subscript. It's just it easier for you to read from back there if I put it like this.

Okay. So, so give me some slack on that. But um it really is about momentum in the x direction has this uncertainty. This is that can be zero. That can be absolutely certain.

And everybody who teaches quantum mechanics knows this. Okay? I'm not like wow this is a brand new insight. They know this. Okay? They just don't emphasize it. They just say that's that's the way it is.

I mean that's kind of obvious. There's nothing deep or mysterious about it. But the thing is for me anyway is is that whatever explanation of uncertainty you decide to settle on. Okay, make sure you can explain both the uncertainty principle with it and the certainty principle. You should not emphasize one over the other just because everybody talks about one.

You got to settle on on the other. Okay. So um well what what the way it works out is that you have these operators that act on a wave function and one of them is a derivative in this case the momentum in the x direction not a number like x and yes if you go on to graduate school you know you can actually reverse that situation and make momentum a number and position an operator but either way one is a number the other is bit of of calculus. Okay. And this is not the way it's done in standard books because they would have the h bar.

But remember my rule number two uh three uh to make this no four rule number four. Uh to make this dimensionless g I don't have to do much at all. That's nice. I don't have to remember my h bar square roots of g factors. Okay.

So um you know now we're going to look at something called a commutator which is basically writing these things in both orders and then they're going to act on this function D. And so when you do that you use the product rule and you see that you get that cancellation going on and um so basically uh this thing ends up equaling one. The commutator ends up equaling one. And if you repeat this exercise with the y momentum operator then lo and behold you get zero. So the yx commutator acting on fe equals zero.

This again is something they do teach you in a quantum mechanics course and they say well I don't know to me they're not emphasizing enough because this is purely math. It to me it's it's totally clear uh or it's pretty darn clear about what's going on and I don't have to get into philosophy. I just look at my product rule and say well in this case I'm going to end up with one. In this case I'm going to end up with zero. Um, oh, but there, um, you want your H bar in there and so I'm doing all the calculations to mention those things.

And, um, but to me, the key difference between the two is that one ends up at zero because there is no, you know, product rule kind of thing going on and, uh, and one for the other. Okay. So the next time you get into a philosophical argument about the uncertainty principle, which is easy to do, you know, people feel passionate about why the heck it is that way, uh, just ask them about the certainty principle about why if I have that position X and I come in at Y, now they might show say, well, orthogonality, which actually turns out to be the right answer. Okay, but it's kind of like it's like it's almost like they they changed the discussion a little bit. And so I like that I like my my reason for why there's uncertainty is the same reason for certainty.

See, so that to me is is being consistent in my logic. And uh so anyway, that's why I'm at peace with the uncertainty and certainty principles. All right. So we're on to uh Schroinger's equation. Um, all right.

So, Schroing's is an equation. Uh, it's a scalar second order differential operator that acts on a wave function. Um, but even though it's second order, it's actually only second order in terms of its space part and it's only first order in terms of its time derivative. And believe me, people understand this, okay? They they describe it that way in in graduate level physics books. So, we're not putting a big surprise.

We are going to rearrange the furniture in the house. Uh, that's essentially all that we do in this exercise, but again, I think the the results look prettier. Now, since prettiness is a judgment call, uh, I'm going to put that equation down at the bottom of every one of these slides, and you decide at the end whether you think it's prettier or not. Okay? All right. So, um, so there is the actual animal.

It's got these factors of i. It's got dell squ. It's got one time derivative. Okay. Um, and so the first thing I do is I drop all my factors of i.

And then I say, well, that's really a scalar operator. Um, because time derivative is scalar operator. Del is a scalar operator. Believe me, people know this. But this is again part of my let's write everything down.

Most people would say would say I've got a scalar operator. I'm not going to bother you with that zero with an arrow over it. Okay, I understand them saving some chalk, some ink, but to me I want that. I want to see it. Okay? Because it tells me that if I want to generalize this equation a little bit more than it is right now, I can I can act right there.

I mean, there's no question of where I do something. It it's it's sitting there on the page. So, again, one of my odd things is I always write my zeros. Okay. So, we're going to have a couple sidebars here.

The first one is that uh we want to make a leloian operatorian. And so all you have to do is really square one of those, but you get the curl of a curl. Okay? And um it's actually not re relevant to the Schroinger equation, but it's nice to know that anytime you see a leloian, you in the back of your mind, you should go, you know, there's a curl of a curl over here. I know you don't want to look at it because it's scary, but that's too bad. I bet nature uses that.

Um, okay. So, now we've got to get to one time derivative using uh two operators and uh by golly that should be easy. Just one times the time operator and that's it. So now we take these two observations and uh we want to take that uh that scalar derivative sorry scalar operator and write it as two operators. And so what we see is a full derivative operator.

We've got the dt time and then the the the dell thing. Okay. And then the next one, it's unity. Oh, unity. That's got to be dimensionless.

Uh and we've got this Dell thing. We can actually tell right away that that this must not longer be like fully relativistic because, you know, one is a constant. Okay. Um, and the Okay, so that's that's that's all well good. Um, so now let me see where where do we go from here? Ah, all right.

Let me just stay stay a moment long longer on this one. Um, so can we see can we see what we need to get? We can see get it the time time element out of there. apparently. Oh yeah, this I've got the scaler. The scaler thing says I'm not going to think at all about the vector part, but that means there's probably more that we could know or something.

There's there's there's more calculations that could be done if we didn't put that scalar constraint on. But since since I'm trying to get a scaler out of it, it's pretty easy to read. Okay, it's going to be the dt of v. It's going to be the second order uh you know spatial derivative of fe. It's going to have uh an h bar over 2 mc.

And that was actually fun seeing that that's a dimensionless number uh h bar over mc. So that's a momentum. And um so that's all right. Um, so I want more cowbell. I want more H bar.

Um, so you can actually wipe out my my units if you if you so choose and uh then actually go ahead and throw it uh an H bar across the way and um you'll you'll end up with exact with the right units. Okay. See, since I wrote G H bar over C5 on both sides, I mean, I can I can just wipe that out. And if I multiply through by H bar, um, yeah, it's spot on. What else? All right.

Um, All right. So, uh, I think that's it. I think that's it. That's my way of of writing uh the Schroinger uh wave equation using quitterians, using dimensionless operators. Oh, and there's there there's that line.

Nature nurtures naked numbers. It might make a bumper sticker someday. Um who does? All right. So now we're going to move on to uh relativistic uh quantum mechanics. All right.

2.6 Klein Gordon. All right. All right. So um we're going to get the Klein Gordon uh equation out of here. Um it uses both time derivatives.

Um, and we're actually going to write out the phase. Uh, even though I'm not sure if it's actually used currently in, uh, in standard physics or not. Um, this is my own issue. Uh, this is the most famous equation of all. I I wrote it so big because I mean this really reaches out into the popular culture.

You see it included in the artworks and that sort of thing. Um but I actually think it leads a a physicist a little bit of stray. Um, one of the things, uh, a little cultural element, um, Einstein's manuscript where he first didn't write this, uh, was put up for sale and it didn't meet this the the asking price, which was, I think, about $4 million because what he wrote down was E= MC^2 over the square root of 1 - B^2 over C^2. And people like, well, we don't, you know, that's that's not equally mc^². There's that part I don't understand.

Even less than e= mc². Um, and um I actually think that maybe that's the most important part of the equation. Um, but um and and so people emphasize this equivalence and certainly physicists know the the the real correct relationship. I shouldn't say the correct relationship, but the more general relationship E= MC² for only one inertial reference frame, you can come up with and it's not generally true. You know, if you're you're walking by somebody that you're going to have a different opinion about that, not very different, but different nonetheless.

Okay, so I want to equate only work with equations that are always true. Um so what I do is I square this uh for momentum and you get that E^2 minus P^2 and you get the uh that M^2 C the fourth thing and this is all I ever use. Okay. And this again makes me rather odd. Okay.

People are so at peace with E= MZ² that that you know you just choose a frame where P equals Z. It's like no, I won't do that because if I choose that reference frame, somebody else can choose another and it won't quite be true. Um, and the other thing that is just to me the the huge elephant in the room is that when I do it this way, I get this 2 e time. That's a perfectly valid thing. Okay? It's not like I've broken a math rule or something.

Uh, that should be relevant with doing these calculations. And I don't think that people use that. I mean, it doesn't even have a name as far as I know. If somebody actually knows of its name, you know, please tell me and then I'll be able to read up on it. But, um, I don't see it in the literature.

Energy times momentum. Okay. So, we got to have a couple sidebars. Again, we're going to convert numbers, the numbers E and P, uh, to operators. Okay.

So this is again another little indication that we're not quite in uh classical quantum mechanics where we had one was a number the other was an operator here they're both uh operators um okay and then sardm two has to do with four momentum um that you can rewrite uh energy and and momentum as this factor gamma gam m * gamma is energy where gamma is the square root of oh that that factor that showed up in in Einstein's original man manuscript. Um and then gamma beta is the velocity times that gamma thing. All right. And so if you square this what you end up with is you get that gamma squar* 1 - beta squ. Well hold it.

Gamma squ is also 1 - beta^ 2. So that's just unity. It's like oh that's another way reason why this is such a important relationship. We see unity unity is good. Okay.

So now we uh substitute this all in and um we we go through this this kind of process and we say okay so I get a two two time derivatives uh I get two space uh derivatives and I get a time and space derivative that's the uh the energy momentum thing um and so that's just you know kind of rewriting things and um now I divide through by m^2. And so this is my completely dimensionless expression. And here I my my phrase I I love uh nature naked numbers. You see I I I've got a real genuine one over there. Okay.

I also have gamma squar beta in the the phase. Uh but I've got this time derivative second order time derivative. Um I've got this h bar over m. Well, this time it's a h bar over mc^ squ. So that's similar to what what I saw in uh in the Schroinger equation if I recall.

And now is this uh Klein Gordon? Uh well actually it's not um because there's a sign difference because of the way that that standard physics uh writes things. They throw in factors of I the ones that I have I threw out. And so that's what it would take to to make it more like the standard equation. All right. So now you at least know a a way to derive the Klein Gordon equation which shows up in quantum mechanics.

All right. So again this you're only looking at the scalar part is the fine Gordon equation. Yes, absolutely. Vector part. Does it mean something? I think it should.

Okay. Is is have I done any calculations with it? No, I haven't. Okay. I haven't seen the consequences of it and I am not enough of a student of of real physics rel field theory to know whether they use that. It it hasn't come across in my readings.

You know, everybody's just like here's mine Gordon or I've decided to use direct and you know it's like it it doesn't come up. It's kind of like structurally it can't come up because of the the tools that they're using. So, so I'm thinking that they don't work with it. They might they well that that's where where where I stand at this point on that issue. All right.

So, I think we only have uh one more collection of slides. I am only subjecting you to half as much uh brain damage today as uh as as yesterday. All right. So, let's see. All right.

So the drack equation uh squared ends up being uh the fine coordinate equation. That's only kind of roughly true. It's not formally for all but um it's roughly what's going on. And so in in a in a handwavy way um this is uh the drack equation on top. I haven't told you what a and b are alpha side alpha and beta.

I haven't told you what those are. Um but we can see if we squared that we should get a two two factors of time derives and we square that we should get a couple of uh dell operators in there. Um but you know we get an m squ out of that thing if we divide through by h bar you know but this is all real handw weighted you know because I haven't said what alpha and beta are okay so um so I'm going to see whether I can get to uh something that looks like fine Gordon and where where things work and where where they don't. Okay. So what I'm going to do is collect spacetime terms together.

I'm going to drop all factors of i. Okay. So now I've got a time derivative and a dell operator. Okay. And uh I don't have any factors of i.

So that was step was pretty simple. Um I'm going to make this thing dimensionless by putting uh the beta on the other side. Um so I put that over there. And um oh but I'm really kind of re really rearranging things a bit. um they they usually put the the beta right next to the mass and I'm saying well if I've got an alpha this is a bit handwritten so I it's just the nature of the way I I'm operating at the time um let's I can since that's just a scaler I'll make up a new beta and and have it multiplied by time or I have to you know do something make sure alpha doesn't get too upset and and and look at it that way and then if I Now um if I just tried to think about this without those alpha betas okay this is what I would have I would have h bar over mc^2 delt okay that looks pretty easy you know if I square that thing I'm going to probably end up right right at the the Klein Gordon equation so so that's why that's good okay um so I'm going to talk a little bit about spin 1/2 uh because that's what makes this difficult is is spin 1/2 half.

Um, and what I'm going to argue is that we should embrace it and not fear spin one half. So, um, a beer uh, in the hand. Let's say I don't really have a beer. So, so why don't we just use a camera? Um, let's think about two pie symmetry. Um, so if if I've done my my D, I will come back to exactly where I started from.

And this is 2 pi uh rotation. I could do a cartwheel if I felt more energetic. I could do a back flip. Got three three different ways I could do this. Okay, that was all example of two pie symmetry.

I will same camera. I'll show you four pie symmetry cuz now I go with one twist around and I'm back to where I started. Ah, you've seen this trick before. I have to do it again. That's an example of four pie symmetry.

And what is cons? Why is this different? It's the same camera. It's the same hand. Okay. The reason is I got a shoulder here. It's connected.

Okay. And uh I think in a way it essentially constrains one degree of freedom in space. So now space is not the same. Okay. Because of my shoulder, it's saying I basically have one constraint on it that I that I don't have when I'm doing here.

My my shoulder is in a constraint there. So that uh is an example of four pie symmetry. So in if three states somehow gets split into two and one uh there's the dimension with my arm and then there's the other thing. That's when I think four pi stuff begins to happen. All right.

So um oh great thing uh and sidebar number two uh are the gamma matrices. Now this is going to be a longer sidebar. Uh because the gamma matrices are the things that make up the alpha and the beta. Okay. Uh these can be manipulated if you're in graduate school uh without really being understood.

Okay, you can look them up. You can I got one, two, three, four, five, these kinds of things. They have these types of rules. Uh, but you can't really explain it to mom. What? What? What is going on here? Yes, math is happening.

Okay, math is happening. You can apply it to this. You can solve a problem. It's great. Okay, this is what's going on.

That's a good question. Um, so it's one nice thing about owning quitterians.com is that uh people all over the planet if they do a little bit of research in in querniums they sometimes stumble over my work they communicate with me and so there's this uh an engineer in Mexico and he said you know that the 16 gamma matrices that that map uh to the 16 uh to 16 quitter triple products I was like Really? I mean that's like that at least can be summarized quickly, right? It's like a one I J K J K J K J K J K J K J K J K J K J K J K on one side, one I J K on the other, multiply them through. Oh, 1 * 1* Hey, that's going to be the same. But what happens when you start doing some of these permutations uh and um find uh the one permutation that makes sense. We've got a where you start with uh txyz and you end up with txyz.

Uh whereas in b if I just hit it on one side by a factor of i, I end up with minus x t zus y. So what this little operation does is say whatever measurement for time that you used to have, consider it now a measurement of space. And that that measurement you made of space. Now consider that going in the past in the value of the x direction. It's like that's really crazy.

Um and and don't think of that measurement of y as being no measurement of y anymore. Put put it over in the z slot as long as you take the mirror reflection of what when it happened in the y spot. And and the same for z. So z is no longer z. Z is now sitting in the y spot.

and it's just looking like it old self except that it's y. [Music] It's like you got to be insane. I mean, these are not complicated operations, are they? I mean, it's just these are triple products. These are the simplest triple products that can form, but they're whack. Uh so if you hit it on both sides by at least the same letter J and J what it does is it takes it from uh from the the the some sometime in the future to its mirror reflection in the past uh no sorry to its time in the past and the mirror reflection of Y but not the mirror reflection of X or Z.

Okay. And now if you hit it by a a K and a J, everybody ends up being negative. We get time going where space should be. We get X go where Y should be. And it's like, wow, that's that's pretty insane.

Um so um remember that sum of all possibilities, all possible histories. I think what that means in effect here is that we really are messing with time and space in every possible way. Um and so this is very very odd. It's like so so why is quantum field theory so hard? You know why this bor uh you know argument that you know it's just impossibly difficult to understand. This might be a nice concrete reason why.

I mean, I don't like my time going into space. I don't like my space going into my time. But if this is a a way to represent gamma matrices that show up in the DRA equation, which show up in quantum field theory, you know, that would be nice concrete uh reason why. So, um this is just a little sampling I'm going to provide uh of of the talk uh tomorrow. and um I need it to make this whole discussion of gamma uh matrices much more concrete.

Okay, so this is uh this is the one animation I have uh this is software that where that I wrote uh that completely uh makes sense to me and it's funny but ironic but it's about the only one that really does. Uh but the idea is that I have a pile of fraternities. When I mean I mean thousands of fraternities I sort them by time and this is a 10-second film. I specialize in 10-second film. um and depending on its time that it shows where it shows up in the in the animation and uh where it shows up in X Y and Z.

I use something called point point of view ray to to draw the 3D effect. So we have uh the animation is front and center and we have three complex planes. The reason I drew the complex planes was I found I couldn't think about the animation very precisely because our brains really are bad at thinking about video. Um, but still pictures we're much better with. So you can see it that the first complex claim is t versus y.

So you can see it goes up. The this one in the corner is time versus z. So this is going backwards into the screen into the screen. The third complex plane is um is x. So is it going left? Uh it's going from the left to the right.

Okay. Now in the upper corner is the uh basically a summation of every single possible state that that yellow ball is in. Okay. I mean I literally on a software level I merged it. Okay, the images.

Um and so to me actually that might be the wave functions which is supposed to be this has all the information in it is kind of what uh people describe the wave function as. And then um I I'm doing random sampling uh uh of that. And if I do enough random samplings of it, it would recreate exactly that same thing. I think in my 10-second video I actually there are lots of places I don't get to but that was a limitation of GIF uh software and that's what I use here. Uh okay so this is quturnian edition what I did was I started with one quitterian value and I kept on adding the same thing over and over and over and over and over and over again and I think you can agree that looks like an inertial observer.

They're traveling at a constant velocity. But what's like to me profoundly cool here is that the most basic operation of quitterians addition leads to an inertial observer which is at the base of of special relativity. Okay. Um now I think yes now we're going to try and understand what gamma matrices are. Okay.

So what did I do to make this I told you all I did was I multiplied by all 16 possibilities. Okay? I took that inertial observer that was traveling the straight line and I said I'm going to I've got let's say I've got a thousand such points. For every one of those thousand points, I'm going to multiply one side by one and the other side by one. I'll end up with the same thing. One and I one and J one and K one.

No, that's it. I one I and Jake I in you had 16. And so when you see this you go okay so what's kind of happening is I've got four clusters of four. I can actually kind of see or sense the the 16ness of of of this sort of thing. And so um now I I kind of um yeah so there are four there are four little balls coming in from four different corners and so when we when Fman says well you must do the sum over all possible histories and you hear that there's these gamma matrices and then I say well there's a way to do this with quturnians with all four permutations triple productwise it almost starts to make sense.

almost. I mean, I I don't I don't claim that I'm just totally at peace with this, but what I'm saying is I feel like I've taken a very concrete step towards appreciating kind of more of of of what the gamma matrices are actually uh actually doing. So, um, so the, uh, the trivial quote unquote trivial DRA equation, uh, is is, uh, is not a triple product. Okay. So, um, if I square that thing, then I end up with, um, and and and and squaring is okay for fraternities.

I mean, there's there's no no problem with that. You see that? Oh gee, I did end up at the Klein Gordon. When I started this exercise, I said, well, you can't really square because I haven't told you what alpha and beta are. Well, now I have told you I'm working with quitterian, so squaring is a legal thing. I haven't broken any of the math rules.

Uh there was no uh handwaving and I get to exactly the the flying work. But you say, well, you got 16 others to do work with, don't you? And it's like yes. So, so if I go ahead and do those then um well look at that. I actually get the same scaling which is good. Okay.

It's just that now the phase is different. And as I say, you know, I don't read people working with phase directly. Uh I haven't read that. Uh but it's kind of cool that now we have it's not exactly the same thing and and And maybe that's uh that's relevant. Um so uh I just want to say that that quitterians in no way uh make quantum field theory uh simple.

Um but I'm feeling like this is a a good and interesting and productive step forward. And so so so that's kind of uh one of the main things that I'm I'm doing research on on these days. So uh we'll end with a comment strict uh by ll here um says now the susi algebra closes off shell uh if we use the auxiliary fields or better known as the ugid doggies are this doggy I would like to chime in please yes susi is unnecessary um and that in fact is is one of the messages of my uh work is that um I I don't think all these super partners uh are necessary. I don't think they will be found. And I just just to understand the the nature of the t-shirt and the and the research project itself.

Uh we are going against LHC. Uh if LHC finds the Higs, you'll be able to say, "Wow, I got this weird artifact from this weird guy that said there shouldn't be a Higs Bzon." Okay. Whereas uh and if they find susie particles, the same story, my proposal collapses and I'm I'm at peace with that. Okay. But if two or three years down the line they say we still haven't found the Higs and the modification they'll say is we we haven't found the Higs and we're 99.2% confident that the Higs isn't within this range.

That's how they talk. I mean, these guys are impressively precise folks. Okay, there are already people who have said, you know, if we don't find the Higs, that's going to be exciting because it means we've got to do new physics and they don't know where they're going to do their new physics. I mean, they they know they would have to do something. Okay.

Well, then you can you can show them in your t-shirt, that sort of thing, and maybe strike up a conversation. But those are very concrete um aspects of of this uh of this work. So, uh I think that concludes day number two. And uh congratulations for all the girls in the classroom who think he's hot. He shows up wearing sandals with white socks.

He hears him giggling while he's got his back to the class. He thinks he's got an eraser mark on his ass. And all the girls from the hall show up to hear him talk. Even though most of the time he's covered in chocolate. Math prop rockar.

Math rockar. Oh yeah. Math prop rockar. He was young. Never thought he would be a math prop rockar.

[Music] And after hours outside of his office, there's a line waiting full of girls who want to ask about their quadratic equations. She leans over the desk and throws a pencil in her hair. Complains the grady game is way unfair. And all professors, they laugh about it. They wish him well.

The guys in the class are all just jealous as hell. Math profar. All right. So, what are my what are my qualifications for um being able to do a new unified field theory? Uh I must have pretty impressive credentials, right? Well, uh at MIT uh I was a 4.0 O and I think most people uh would be really impressed with that because MIT is really a difficult place except that it's on a fivepoint scale. So So you guys probably know I wasn't an A student.

I was actually straight B. Okay. Um, uh, but I think for for you kids just starting out, these are my real degrees. And I didn't have just one, I got two. So you say, well, these must be very relevant.

Okay. Uh, bachelor of science in life sciences, biology. That's not mathematical physics. Uh, and uh, this one, chemical engineering. Oops.

Didn't these things were supposed to be, you know, 7 18? No, I said eight. 8 and 18. No. Maybe I got it. Maybe I Maybe I should just erase that and it'll pen something in.

No. That would that would that that'd be wrong. That would be wrong. Okay. So, um let's see.

Is there something else that might impress you? Well, um I was out of work for like a year and a half. See, I like to deal with big abstract things, not like concrete things like making money. Uh so, I have a couple stretches of long unemployment where I was thinking about stuff and wasn't bothered by the real world. My wife was bothered by that, but anyway. Um, so I decided I would take uh the United States Postal Service exam.

And this turns out to be a very difficult exam because it's not testing your knowledge of anything. It's actually testing a bunch of little monkey tricks, mental monkey tricks. What like how fast can you spot errors in uh addresses? How fast can you memorize five addresses and then recite them over here? And um I got a study guide and I learned that in those questions they had four numbers and always the second digit was different. And even though I knew this little secret trick, it wasn't until like 3 days before the exam that I figured out a way for my brain to remember it like it was a rising collection of numbers. I'd say Elm Street, Main Street, going up and down.

And I'm one of the very few people you will meet in your life who got 100 on the United States postal service. So you say, "Well, uh, I'd like to see your postal service uniform." You can't because they have an interview process and I failed the interview. And he's like, "How could you do that?" And he was like, "Well, because you know they they said, "Well, what if you have a conflict with your boss? What if you have a conflict with a customer?" Okay, what are you going to do? And I said, well, I said the same thing. I said, I I'm going to tell them that there are laws against having concealed weapons on your person, okay? And there are people who break those laws. That's not me.

I'm not saying that. I'm just letting you know that there's some not uh I actually thought I gave rational answers to this thing. I really don't know why they they did that. I am not a postal service uh I'm the the the one postal service person who got 100 and failed exam. Okay.

So um Oh yes. So So you say am I really uh crazy or something like that? And it's like um no we we far prefer the word certified. Okay, I don't know if you're familiar with these kinds of things, but uh there are people who um who the state determines are what is it exactly? Uh gravely disabled or danger. Yeah, that's I'm gravely disa disabled. I don't know.

But this is my official certification. So, please do not call me crazy. Call me certified. I'm official. Okay.

Anyway, so that's that's my one piece that says I am uh certified enough to maybe have come up with a new idea like that. All right. Thank you very much. Oh, yeah. You didn't go post them.

Yeah, that would be a danger to others. That That's a check boxar. Oh yeah. Rockar. 3.14159265 rockar