Conquering my academic demon

thank you to curiositystream and nebula for sponsoring this video check out the link in the description below this is me in 2012 during my fourth year studying physics at oxford in your fourth year you chose two major options that defined your master's degree i chose atmospheric physics which is what i ended up doing for my phd and theoretical physics which was for the most part a course on quantum field theory during this year my mental health collapsed as i've talked about elsewhere and after doing really very well in my third year i did abysmally in my fourth year and the quantum field theory in particular just never really entered my brain i never really understood the subject and ever since it's been like an albatross around my neck the subject has always represented to me my failure for whatever reason in that fourth year this is the textbook that we used in the course quantum field theory in a nutshell by the cryptically named a z the oxford theoretical physics major option was basically the first section of this book but this one didn't come from a library this is my personal copy just after finishing the masters i bought myself this copy because i told myself that i would come back to it i was going to go back and beat this subject but unfortunately this textbook has just kind of sat on the shelf like this giant black monolith judging me but no more this is the month that i am going to conquer my everest i'm gonna teach myself quantum field theory again that was three months ago as you may have guessed a couple of things happened along the way before going any further i should probably briefly explain what quantum field theory is basically it's a way of describing the universe specifically how subatomic particles like electrons and photons interact with one another to produce phenomena like charges attracting or repelling each other this video isn't going to go into any great depth on how exactly that works but i'll leave some resources in the description if you're interested suffice to say qft is like an upgraded version of quantum mechanics with significantly more complicated maths now it's been nearly 10 years since i did my masters and in that time i haven't really done any quantum mechanics so i feel like jumping straight into the quantum field theory the advanced version is probably a bad idea so that's why i finally bought myself a copy of this this is paul dirac's classic textbooks principles of quantum mechanics i use this a little bit in my undergraduate but i never really appreciated it and it's such a classic text that i thought i'd buy myself a copy so what i'm going to do for the first couple of days is actually not really touch the z i'm actually going to mostly focus on the dirac and just make sure that my principles the fundamentals of quantum mechanics are up to scratch another thing i'm going to do in this experiment though is not just rely on pen and paper which is how i did things when i was at university i'm going to try and incorporate some pen and paper stuff but also mostly take notes in notion which is my preferred way of living my life at this point it's software that i always recommend students to use but i've never actually used it when trying to teach myself something so this should be an interesting experience jasmine was bitterly complaining that i had to turn off her water fountain for this so jasmine sweetheart should we do you want your water back hang on let's unplug the light you were thirsty baby yes today's the fourth of april a sunday uh it's easter sunday actually i've been going through the dirac so basically refreshing my dirac formulation of standard if you like quantum mechanics uh i'm gonna go through the first couple of chapters in total of this book not the whole thing gotta say so far i've been really enjoying doing this i honestly forgot how much i enjoyed just sitting down with a textbook taking notes and improving my understanding on a subject you don't get to do it when you're not a student very much if at all and i've really enjoyed this opportunity to just sit down and spend time quietly learning when learning any physical theory the first question you have to ask is why why do i have to learn this thing quantum mechanics came into existence because it was found that classical physics as derived by people like newton and maxwell simply did not work at small scales when you're talking about atoms and subatomic particles quantum field theory came into existence because quantum mechanics breaks down when you're looking at very small objects traveling at great energies so for example if you accelerate an electron to huge speeds that electron can spontaneously produce pairs of new particles electrons and positrons for example and that's something that simply can't be represented by a wave function in quantum mechanics you need new physics to describe that that's where qft comes in at this point in my studies i've basically got that why question i think nailed down in my initial notes from the z textbook and now there's a very small matter of how we address that need in physics to meld high energy and quantum mechanics i'm sure i'm sure this will be easy okay obviously it's not going to be easy but the time that i've spent this month so far revising quantum mechanics and also getting an appreciation for why this thing exists in the first place i think it's put me in a really good position to really get my teeth stuck into the maths of how you mathematically represent objects in a field theory in a quantum field theory in fact i'm about to do that right now on a stream just as a brief aside i now stream most days on twitch.tv for simon clark sometimes i'm playing games sometimes i'm painting warhammer a lot of the time i'm actually just working with a pomodoro timer in the corner and some chill music and you'd be very welcome to join and do some work of your own now get ready for a bit of a time jump okay so it is may 17th and this project has been batted around like a tennis ball since our last vlog for this project we have agreed to move house i've had the next round of edits back for the book and i've written a huge video about star trek which has taken up all of my time so the original plan of getting this done in a month is kind of out the window i'm now letting this stretch to the end of this month and i've got to say i actually really enjoying stretching this out because it means i get to spend more time with the subject matter and i've been really enjoying actually understanding this stuff and appreciating the mathematical beauty and appreciating it in a way that i just didn't before when i studied this as part of my masters but with that said i do happen to still have those notes from my masters and i thought it might be interesting and potentially traumatic to look through them and see how i was looking at this subject what nearly 10 years ago let's have a look so it's more organized i remember it being tip number 321 don't be a chicken just take a deep breath and jump also simon clark is super cool sc is sc i didn't write that i'm pretty sure that that was a girl that i used to study with who wrote that who i in retrospect really missed some very obvious signs right okay so at the back here is all of the um lecture notes which i didn't know i had really useful resource for this project that's actually amazingly useful but also in front i have i have notes from the main lecture notes obviously but then i also have notes from michio kaku i have notes from the z textbook which i've been taking notes about i recognize some of these diagrams and also is that julia yerman's but i was actually taking notes from multiple places which i don't remember doing i just remember like trying to um wrote learn a lot of this stuff this is bringing back some some memories of being in the dingy full you know bottom level of the library and trying to make sense of the stuff here just why and then a date 18th of the of december 2012 why i think in my head i'd actually worked this out to be like i was not working which i was i think i was working at the time and i was clearly obsessed with trying to make this as neat as possible and make it look like i knew what i was doing because at first glance these look like the notes of a man who knows what he's doing i know from the time that i wasn't i was i was really in a in a bad way i was closer than i thought to actually doing well at this i think my my brain just wasn't accepting this information yeah i don't know how i feel about this i really don't that's not what i was expecting at this point i think it's time to talk just a little more about how quantum field theory works like how it actually looks on the page and there are two very commonly used different but equivalent approaches in fact one of the main difficulties with quantum field theory is disentangling the many different approaches to the subject that you find in the literature but fortunately i knew just the guy to help me understand these two different but equivalent approaches um so i'm thomas i'm a first year detail student at the university of oxford uh specifically at baylier college and i'm working on string phenomenology which is trying to relate uh string theory to particle physics and cosmology so in quantum mechanics you have these uh commutators for people who might not have studied quantum before what does a commutator correspond to physically if you can even answer that so i think it's easy to see what it corresponds to if that is equal to zero if it turns out they don't commute uh then it turns out you can measure these two things at the same time so in the case of uh position of momentum because that commentator is equal to i you may have heard these things before about how the more you know someone's position the less you know it's momentum and that's kind of a consequence of the fact that they uh they don't commute so what you're doing quantization is you take the same kind of commutator aspect and so you take your field which you can kind of treat as being kind of like position and you take your momentum but so a momentum of the field there's field momentum so it's a weird idea and you take the commutator of both of them you impose that equal to i times some other funky stuff but this basically is a direct analogy to what we already know from quantum mechanics and that's the kind of canonical quantization approach the path integral approach is entirely different so in the pathological approach what you do is you actually just take your well-behaved and normal classical physics you exponentiate it there's something called the action as well which is related to uh to anything in kind of classical physics you see quite often and that's all classical physics everything there and then outside that you then have the path integral and the path integral then contains everything quantum so it's this nice kind of separation if you have entirely classic or entirely quantum separating each other and what this path integral does is it gives a number to each possible field configuration is what it is so if the fields it could be i don't know it could be all different shapes the field could be at any one time and you give a different number to every single possible one uh it's easy to see in in a quantum mechanics when you apply the same idea where instead of a field configuration it's then all possible paths between some initial point and some final point that a particle will take and similarly then in field theory it's given this initial starting point and some fight up some other final configuration kind of all ways you can map between these two uh these two ideas and then you weight them all in some particular way and then by summing all of those up you then have these uh you then get the full unfilled thing so it's not obvious at all these two things are related but both both work so at this point in the project this is where my head is at i've been following the path integral approach as introduced in the z textbook the quantum field theory in a nutshell and following a really useful conversation with thomas and looking at mild notes i'm starting to understand how you arrive at the same theory the same equations from those two completely different approaches but that's only part of the story because going through my old notes also showed me that my perception of how i studied this subject in my fourth year has been wrong all this time i thought that i'd failed in my fourth year because i wasn't smart enough to understand this subject it was just beyond my abilities or perhaps that i wasn't working in the right way but those notes show me doing all the right things drawing from lots of different sources questioning when i didn't understand things taking the time to sit with the subject what's apparent from learning the subject now is what i was missing then and that was what led me to my failure all right so i'm in the new house it may look very similar to the old house but that's because well i mean it's the same stuff after the house move kind of settled down and we actually got all the big stuff in place for the past week or so now i've been making a consistent effort with going through the z and i feel like actually taking a little bit of time away and letting it stew in my head has improved my understanding quite significantly because i now looking back through the textbook and the notes that i've made which is like just the condensed version of the textbook stuff is making a lot more sense mathematically i'm not as advanced as i was back then but conceptually i feel like doing the phd and studying an advanced field for as long as i have now has made it easier to make these conceptual links and i feel like that part of my brain and that part of being a student is stronger now than it ever was eventually i decided that i had to finish this project so i could make this video so went in hard on a last week or so of studying it ended up looking suspiciously like my studying as an undergraduate working after i'd finished video work past midnight just sustained by this desire to reach the next conceptual breakthrough and in the end i felt like i really had a handle on how this theory and in particular the path integral version worked and that brings us to today so i wanted to give you an example of how you practically use qft like kind of what it looks like on the page let's say that we want to describe two particles so we have uh a particle might be an electron it might be anything for a we know and another one over here and let's say that as we go up through the page that's increasing time so time let's just say we want to describe these two particles propagating up from one point in time to another point in time and we could label these if we wanted but i'm not gonna bother in order to describe this we define a field a quantum field which is phi and we specifically define an object called a partition function which is basically a way of just summarizing all the information we know about the system into one object and specifically we can write it as a path integral which i probably haven't left myself enough room for well done simon something a bit like uh this and j here specifically is describing uh like the sources and sinks of particles which we could put at minus infinity and plus infinity but it's basically like saying this is saying that something comes out the field for a bit and then also disappears back in the field for a bit the only problem with this is that this picture is really boring because we just have two particles that exist go forwards in time and then stop existing not a great story so what we can do instead is if i draw a new diagram next slide please now let's say that these particles instead of just going a straight line from their beginning to their end they actually interact in some way like they meet at what we call a vertex this would be like for example two electrons colliding i don't know something like that we could describe the strength of this interaction with a number we normally use the greek letter lambda for that now in order to represent this interaction taking place we need to add an extra term up here because this lambda letter doesn't appear anywhere up here and we typically do that because it's the simplest way of doing this by writing something like one over four factorial lambda and then the fourth power of the field now practically solving this is pretty much impossible so what you can do is define the exponent here as two different terms and separating them out like this this term here is basically the propagation term so this is the uh going from one point to another point kind of term and this term is the actual interaction the strength of the interaction that takes place here and what you can do is specify in this term because it's just an exponent and one definition of an exponent is that it's equal to an expansion like this and by expanding up to a certain number of terms your base can basically specify the number of particles that you're dealing with and so when you reach four you can we stop and that's describing this situation in fact the way that these two expansions uh combine with one another because you've got a derivative term here and it's acting on the js that are in this term here you actually only end up with certain surviving terms that then define what interactions are possible and those possible interactions are codified in a set of diagrams that you may have learned in school called feynman diagrams obviously this is a very basic example you've just got two particles existing interacting and then stopping their existence and yet this is still horrendously mathematically complicated so you might wonder well okay this is a simple example that's lots of maths but how do researchers actually use this stuff what is the practical use of this theory well i asked thomas what he researched what i end up using quantum field theory a lot for is if you look at string theory you have these vibrating strings and each one describe a different type of particle but what you can do is if you kind of zoom out enough then they start to look like particles and in particular there's an infinite number of particles in each different string theory and if you just take the massless ones you end up finding that you can find a corresponding field theory that describes the same interactions of particles uh as described by the string theorem and so this exists in ten dimensions uh and to try and relate it back down to kind of four dimensional particle physics and cosmology you have to try and hide away these additional dimensions by kind of wrapping them up in some small place but this is all done in the context of um field theory you actually kind of almost ignore the string theory part of it you kind of just say this is this is the this is the theory that comes out of my string theory and it's then yeah the string theory is a black box and you just take that ten dimensional theory and then work with that from that point onwards so after three months of on and off studying this subject what have i learned well i've definitely learned a lot about quantum field theory and i feel like i can look at expressions like these and actually understand what they're saying that doesn't intimidate me anymore i feel like in particular the path integral approach makes sense to me now and i have a way stronger conceptual grasp on it than i ever did before but in a way that stuff is the least interesting stuff that i learned during this experience i came away with a whole bunch of lessons that i wasn't expecting to learn firstly it taught me just how much of a privilege it is to be a student learning over the past couple of months has reminded me just how much i love learning how much joy there is to be taken in sitting down with a good book and a notepad and improving your own understanding slowly feeding your own brain and over the past three months i would have loved to have done that all the time but life got in the way i had to move house i had to make videos i had to earn a living and when you're a student at university so many of those distractions are removed and you are able if you want to just sit in her library and improve yourself and i feel like i appreciated it at the time but not as much as i should have done this experience taught me just how valuable your time as a student is in fact if you are a student watching this i have a couple of extra takeaways specifically for you first of all don't be afraid to use lots of different resources when pulling together your own notes your own understanding i probably used about a dozen different sources whether that's lecture notes or textbooks or online resources whatever it may be to help me understand this stuff now and that made a huge difference secondly use notion i really enjoyed using it in this experience for notes specifically it's free for students it's super easy to use hard recommend and thirdly and something you've probably already heard before don't be afraid to ask for help if you don't understand something and that doesn't have to be a teacher or a lecturer or professor which is probably where your mind initially went it can be appear if somebody one of your friends happens to understand a subject better than you perhaps they might be a little bit older than you then don't be afraid to ask them for help it can be a very casual chat like i had with thomas in this video if you can join a study group and if one doesn't exist maybe form one yourself that's something actually i tried to do in my fourth year but that uh that kind of failed to happen my experience in fourth year at oxford was the reason why i wanted to do this project and i think perhaps i came into it wanting to forgive my past self but even to show that i'd grown as an individual i was smarter now that i could do this and back then that guy couldn't but over the course of this project and in particular i think through looking at my old lecture notes i came to realize that my failure in fourth year wasn't a failure in intellectual ability or a failure in effort but it was a failure to have something that i've only very gradually acquired i think over my adult life since then and that's self-compassion when i look through this old footage and read through my old notes i see a man who is desperate to understand something desperate to prove himself equal to this incredible task and is doing all of the things that in the past had worked incredibly well to help him understand the stuff but in this circumstance they weren't working stuff wasn't going into his brain and he took this to be a failure on his part at that time something he was doing at that time must be wrong he wasn't good enough he wasn't equal to this task and that led to this negative feedback this thought spiral that eventually completely unraveled and looking back on it now i can see that there are other factors going on that man didn't understand some of the fundamental prerequisites to quantum theory theory some of the maths well enough it was like asking a person to put a brick on top of a house of cards the foundations just weren't strong enough to support this immense weight but the problem the problem that made me not understand this stuff in fourth year i think was fundamentally one of mindset when i made a mistake in fourth year i had this message in my head that i'm not good enough i can't understand this i'm not smart enough you're never gonna be able to understand this and then when you go down to problem two on the problem sheet that just gets worse and you end up in this horrible horrible spiral but when i came at this project this time i came at it with a very different mindset i came at it with this growth mindset of okay you don't understand this stuff right now and you just tried it and you got it wrong that's okay let's take a bit of time away go do something else come back to it if you still get it wrong then it's time to ask for help which could be googling or it could be asking somebody who really knows what they're doing like thomas the key to that approach though is letting your superego take a backseat and being compassionate towards yourself compassionate towards your failures and that attitude that mindset made such a difference this time i think that coming into this project i was seeking to vanquish the demon of this textbook on my shelf and in fact what i did was vanquish this demon that was still clinging onto its pages of that negative mindset and showing me the value of compassion undertaking this project was one of the most rewarding things i've ever done it taught me a lot about really interesting physics but more importantly it taught me about how important it is to have the right mindset in learning and i think it made me finally okay with what happened in my fourth year so thank you to my youtube audience for giving me the opportunity to do this for giving me the opportunity to grow the calculation i showed in this video was rather simple really a baby problem if you'd like to see a more advanced calculation getting my hands dirty in the guts of quantum field theory then i have a video showing the derivation of the electric potential between two charges and hence why like electric charges repel over on my nebula page nebula as you may have already heard is the streaming service owned and operated by a collection of educational youtubers here we upload content that might not work on youtube whether that's because it's experimental or likely to be suppressed by the algorithm as well as releasing our videos early and without any adverts at all that's right youtube but with no adverts not even in the videos themselves instead our website operates on a subscription model you can get a subscription and support all of these creators including me by signing up with our partners curiosity stream while nebula is all about small indie creators curiosity stream is about the biggest and best documentaries on the internet like for example exploring quantum history with brian greene in this series the famous physicist traces the origins of quantum theory from newtonian physics right up to field theories but that's not all they have documentaries on subjects from bioluminescence to origami to this specific bus yes really so by signing up at curiositystream.com forward slash simon clark you get the best of both worlds individual thoughtful content from creators like wendover productions and like stories of old and big budget high production value documentaries like light on earth and exploring quantum history and best of all by signing up at the link in the description you get a whopping 26 off 14.79 a year or just over 1.20 a month that's curiositystream.com simon clark linked below to get all of this and support creative ad-free educational content on the internet thanks to curiositystream for sponsoring this video and for partnering up with nebula thank you so much for watching this video all the way to the end this project was a roller coaster that i guess actually hasn't really ended like i quite like to carry on learning this stuff in my spare time in evenings when i have an hour or two maybe opening the textbook and just seeing how much more i can understand but i had to make the video at some point if you did enjoy the video then please do pop it a like and let me know what you thought down there in the comments this was more personal than the normal kinds of videos that i do so i hope you enjoyed it and if this struck a chord with you perhaps you saw some of yourself in my own journey here then let me know if you feel comfortable doing so about that down in the comments as well here's some recommended viewing next thank you again so much for watching and i will see you in the next one

Channel: Simon Clark

Views: 160,539

Keywords: drsimonclark, dr simon clark, simonoxfphys, simonoxphys, PhD, DPhil, Oxford, University of Oxford, qft, quantum, quantum field theory

Id: wDI9WTvSUwI

Length: 26min 22sec (1582 seconds)

Published: Wed Jun 30 2021