Shankar was the chair of our physics department when I was in grad school. He was a funny guy. For some reason, one thing that sticks in my mind is when he was introducing a seminar speaker who was going to talk about hot, compact stars, and Shankar goes, "Like Danny DeVito".
He was a legend among the undergrads as well when I was there. He taught freshman physics to the advanced students for a number of years and was much loved by his pupils.
I mean, his greatest discovery, according to Shankar, is "a small parameter that justifies most calculations performed in physics: 1/ego, where ego is the author’s ego." I want to email him a love note.
My son is ten months old and I watch your videos while chillin with him. I think he thinks you and the baby learning TH-camr "Ms Rachel" are the same person because he gets very excited and relaxed when he sees you. He has trouble keeping up with the math portions because he's a baby but he's trying
I think this is common for her audience. I’m watching this video. I’ve been served a song where cartoon anthropomorphic puppies are singing about groceries and how they should be put away. Seems to be a nexus between people who like funny physic explainers and people who are forced to watch condescending cartoons explain household chores
I'm a humanities major, but man I love listening to physicists. I nearly failed highschool physics, but something about graduate physics explained by a stress ridden semi-sarcastic women has me listening to you like a podcast. Great voice, always love your uploads
When I took undergrad physics back in the 70s we didn't have fancy CMOS spectrometers. We shine those hydrogen and neon tubes (which look just like the ones you showed) through a small slit, refracted them off a piece of diffraction grating, and measured it with a ruler. Uphill both ways
I assisted Dr Kielkopf in spectroscopy at U of Louisville in 1987, and we made good use of exactly that kind of kit augmented with a pretty fancy laser. I saw Helium ionized enough to form He2, and then watched as Dr. K. tuned the laser until the molecular bond of the He2 itself became an excimer laser (the gaussian hump on the PC turned into a razor sharp peak). I was just a Freshman but being the only undergrad physics major in the entire University but one, I was snapped up as the department's favorite pet. Working in a real life physics lab is one of the most memorable experiences I ever had, even though I didn't go all the way. Channels like these help me catch up, now that I'm in my 50s, and ready to go back and learn PDEs and tensors, etc., just for the pure intellectual enjoyment of it.
I remember sitting down for a midterm when my lab partner asks me "What's the square root of four?" I immediately pulled out my slide rule and told him, "Looks like about 1.98."
When i an astronomy undergrad 23 years ago, we also made the measurement by hand not because there weren't new digitally assisted ways to do it, but in order to teach us that it could be done by hand and the problem solving it took to figure it out. It was kind of fun since it was a one time lab and mostly we were doing the measuring.
@@joseapar Same in my astronomy undergrad we looked at the hydrogen alpha absorption line with a prism (or a slit, IDK it was 15 years ago). Just needed a good sunny day
Ångström is Swedish for "Steam rapid" ( _ånga_ = steam, _ström_ = stream/current/small river/rapid). The most common surname scheme in Sweden, after "Namesson", is "Two words from nature merged", so you usually get things like "Twig beach", "River current", "Forest land", and so on.
Wait... "steam stream" is one of the possible translations and you didn't go with that?! The size of a hydrogen atom is about half a steam stream. That's awesome! Is that true, or are you just blowing hot air?
What makes your videos amazing is the way you communicate the CULTURE of scientific research. You really humanize these famous physicists when you share their jokes, etc. I also like the tidbits you provide about how to solve problems in a physics class that's specific to a sub-discipline (like how you'd find solutions to Schrödinger's equation using approximations to a H atom.)
As a physicist, I immediately had Mann-Gell amensia and started to write a comment explaining how you were wrong, but then you added clarifications which said exactly what I was writing, so somehow you managed to raise my appreciation of you, which was already high. Well done!
As a guy learning basic physics and calculus, and enjoying the learning process, it is so interesting to watch you do the math. I love educational videos, but many times they cover up the real process with an intricate analogy. And I appreciate seeing where the math is going. The parts I understand let me know I'm on the right track. And all the stuff I don't understand I can read about, or you explain it very well. Thank you.
Swedish speaking Finn and fan here 👋I'm more inclined to think the "Ång" in "Ångström" is a form of the word "ånga" (commonly truncated when compounded) meaning "steam", so "Ångström" literally translates to "steam stream"
I really appreciate you for taking the time to do the math in front of us and not just doing prettily-illustrated metaphorical explanations so common to science communication. I dropped off of math after the first semester of calculus (wasn't in a math-heavy field and wanted to spend my electives elsewhere). your videos have made me go back to the textbooks I stopped halfway through. I love the way that you are clear about the way that the math isn't optional, but you talk about it as something that you train in, not something that you understand or don't in some binary way. the way you talk about physics makes it feel like there is a big slope to walk up to understanding, and not some impassable wall. I hope I will be reading something other than the abstracts of physics papers one of these days. :)
As a Swede: Ångström can be translated as "Steam Power". "Ånga" means steam, which in a compound word takes the form "ång". "Ström" indeed means stream, and is used like the word power is used in electrical contexts often is (e.g. "The building lost power" ). So yeah, Steam Power, Steam Current, Steam Stream, take your pick.
This is a great video! I reminds me of college when my physics major room mate would talk to my math major room mate about higher level math problems and stuff like that and then they would ask what I learned in engineering school and I would answer something like "You can bend metal so much it becomes plastic"
When I was struggling in Quantum Mechanics, my Hotel Management suitemate complained about having to write a menu. I told him I was trying to work out how many times I'd have to bang my head against the wall before I could expect it to quantum tunnel through to the other side (we were literally assigned that question for homework). The answer is... a lot more than the number of seconds in the age of the universe. It is so unlikely that events like that should be expected never to be observed no matter how much you look. But it isn't impossible...
My quantum mechanic said I was having a little problem with my wave function but he replaced it and now everything is working fine. Only cost about 900 bucks.
i did not follow the schrödinger equation part at all but honestly as someone who's started to teach themselves algreba and calculus as an adult your little speech beforehand was exactly what I needed to hear. And I had fun just listening to you do the equation while I did my nails, it was a whole vibe ❤
Don't worry y'all, I've taken all the required classes, including two years of quantum mechanics, and I didn't understand the Schrodinger equation section either.
As a Chem Student trying to get into quantum/theoretical chemistry, but feeling ever increasingly lost due to all the maths & physics knowledge that we lack and yet are presumed and expected to have by our teachers: Thank you for this, it's very reassuring!
i haven’t taken nearly as much stuff as you, but i still get lost when my professors start talking about special functions and spherical harmonics and stuff. this is probably because our mathematical methods for physicists course is given after our first quantum course (for some weird reason). being a math double major sure helps tho
I more learned how to pass my physical chem exam than to understand it intimately. I've forgotten most of it by now but I do know I had a more conceptual understanding of it back then than a mathematical one
I had the exact opposite problem! I knew how the math worked, what the answer needed to look like at the end, and a probably autistic professor who could never figure out how to verbalize a connection between the math and a conceptual framework @@johnsober
I am here for the developing character dynamics/conflict between past Angela, future Angela, and editor Angela. Oh and the science communication is also nice!
This channel is so consistently excellent I’ll watch anything she puts out, but HOLY SHIT the thumbnail and the transition images on this one are just gorgeous
Fun fact! When I took DiffEqs in college I had a classmate who said (and I quote) "Differential equations are EASY, they're just like Jeopardy with math: provide the answer in the form of a question!" and he was serious and we laughed and laughed and then I killed myself.
"Does anybody actually read these things?" yes Also I love that you pumped up that "joke" like it was the cleverest, funniest joke ever told in the context of physics and it was just the word "anyway" and what we can infer from it. Comedy is fascinating!
Currently taking PDEs as an engineering student, and hearing you mention the eigenvalue problem made the separation of variables method jump out at me, glad to see that was on the right track! We have a project in which we lecture on a topic not covered in class, and I might just make it over solving the schrodinger equation for a hydrogen atom. Thank you!
@@primenumberbuster404 Bro Lmfao ikr! All we get is an insane function that's continuous "almost everywhere" and then they ask you to integrate it! then I have to learn measure theory
after doing the exact experiment you described in physics lab class 2, I decided to do something similar at home for cheap. Was definitely possible for much cheaper, though it was some work (some of the stuff later got recycled into an optical CT though). The way to making it cheap was using - Diffraction grating instead of prism for splitting - Webcam for intensity measurement - Stepper motor + arduino to do the angle adjustment - 3D printed parts for mechanical compatibility - control everything and analyze from your computer in python Never actually calculated the hydrogen radius from it, but I checked the energy on low pressure sodium and a red diode laser and that was kinda ok. The CT is pretty much the same except you don't need the grating and the motor gets a different 3D printed attachment to hold the object. Only additional parts are collimated light source (flashlight, pinhole, random amazon lens) and a screen (white baking paper in a 3D printed mount). I love shed physics! It's such a good challenge to prove that you really understand what the experiment is about. While I was still in my masters I really wanted to go through all the typical constants (earth radius, g, e, ...) but sadly didn't find much time. So spectrometer, Jupiter G*M, CT scanner and earth radius (thanks to dan olsons video at the lake) were all I managed to do :(
I actually found the 1/137 thing really intresting, and wondered, why the hell would it be such a simple fraction. However it all gladly went away, once you told us, that it isn't exactly 1/137. It's like finishing a bag of chips: You first feel sad, that it was the last one, but then you realize that there are still some crumbs to eat.
Thanks Angela - I nearly died laughing ~32 minutes in: “[Sigh] So things here get really tedious… so I’m not gonna do the math… this is a short video so you’re just gonna have to be fine with it. Deal with it. :| Like and subscribe! :) “. Absolute comedy gold and the best physics channel on YT. 😂
I learned how small an attosecond was the other day, along with how high the temperature of a particle can be before it rips itself apart, both numbers are so far outside the realm of human comprehension and intuition it’s fascinating. Glad to be early for another banger of a video!
My favorite thing is when numbers completely beyond comprehension cancel out and leave something bizarrely comprehensible. My favorite example is the Hubble-barn. The Hubble length is the radius of the visible universe, and the barn is a unit of area used in nuclear physics that's equal to about the cross-sectional area of a uranium nucleus. If you multiply these two absurd numbers together you get the Hubble-barn, a unit of volume which is equivalent to the volume of a cylinder with a cross section the size of a uranium nucleus and a height the size of the visible universe, and you get.. about 13 liters or 3.5 gallons, a volume which sounds like you're describing the amount of gas left in your car.
I'm getting my PhD in nuclear engineering and honestly it seems a lot more like physics than engineering a lot of the time. I'm not like designing helicopter blades or reactor control systems, I'm literally doing quantum mechanics day to day. I'm not sure why physics gets such a bad rap.
High school eachers are punished by forcing them to teach math and physics resulting in the physics teachers being angry thus giving physics a bad reputation.
@@davedsilvamy high school physics teacher pointed out you can sort of tell who has primarily a math background and who doesn’t when they’re doing physics by how they do problems- if they leave variables in that could be substituted earlier on till the very end then substitute all at once they’re probably math people, and if they substitute as they go they’re probably not. I wouldn’t be surprised if when people are getting taught it can also be really hard to follow the work and keep up if the teacher just runs with the long ass equations full of variables then substitutes in when the student isn’t a math minded person. Some people prefer it that way, but for some people it gets hard to keep the equations straight and if that’s the way your taught and that’s the way you try to do it and you’re not a big math person I could see that really turning a lot of people off. Overall I’d assume it also has the same problem with Econ/finance where there just isn’t really any qualified people who actually got their education in the subject who want to teach (because there either just aren’t that many people period and they can get far better paying jobs elsewhere) so all the people teaching it are half self taught and so they’re just not as great as teachers in other subjects who formally studies the subject through undergrad and possibly grad school before going into teaching it.
I modeled the hydrogen atom in my Quantum II class on a computer over 20 years ago. It was very difficult. I ended up dropping the physics major that semester and switching to philosophy, but I stayed in the class because I wanted to study philosophy of physics. I managed to convince my professor to let me take the class pass fail and have my grade based on a philosophy of physics paper... because the homework and final were beyond my capabilities. I wrote about mereology, specifically exploring the question of whether liquid helium is 1 boson or 4 fermions. My conclusion was that it depends on why you're asking the question. Either one may be the best answer, depending on exactly what the question is and the exact nature of the question depends on it's context.
have you read sean carroll’s paper on quantum mereology? it’s been on my list to get around to but i imagine it would be a good read if you’re interested in these things!
@hattielankford4775 With my degree in philosophy... I went to law school. I do Constitutional Law now, still spending a lot of time on first principles and theories. I work with groups trying to amend the Constitution. But the stuff I study now is a little more consequential than what I studied in college. I still find metaphysics fascinating, but it isn't as important in the real world.
@@thelocalsage I hadn't heard of that. I'll look it up. Thanks. Edit: Found it. I think that's gonna be a bit over my head, just judging from the abstract: We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain localized around approximately-classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. This formalism could be relevant to the emergence of spacetime from quantum entanglement. If I had gone into philosophy of physics professionally, I'd slog through it and talk to some physicists for help with anything that tripped me up. But I study law now and I don't have time to digest something like this. You enjoy though.
@@jonbrown1654 Basically, I concluded that, if you are asking because you are interested in the behavior of liquid helium, then you are really asking a question in which "it is a boson" is the more appropriate answer. If you are asking because you are interested in the more fundamental question about how that boson-like property emerges from elementary particles, then the question you are asking is better answered by saying it is four fermions. And if you are asking about even more funamental properties than that, you need to answer about the quark interactions between within and between the particles. And you could get more funamental than that even, but then you'd be asking questions for which we don't yet know the answers. But those more funamental answers may be utterly useless if you are wondering why, for example, liquid helium has zero viscosity. All of those answers may be correct, but they are correct answers to different questions, any of which may be expressed by the words "what is liquid helium made of?" I then applied that to typical philosophical debates in mereology. Is a chair one thing or is it a collection of separate pieces of wood? Or a collection of atoms artanged "chair-wise?" The answer depends on what you really mean when you say the words "what is a chair?" And that depends on the context of the question.
just started studying mathematics for physics the last few months. self study student here for the time being, but i'm excited to learn more and understand this stuff better! :)
Usually, when I teach the hydrogen atom, I rephrase Bohr's postulate this way: Electrons are only allowed to have orbits where the length of the orbit is a multiple of the deBroglie wavelength of the electron on this orbit. This way, I skip the angular momentum, which is something the students usually have never heard before. I got this from an article where they imagined the electron not radiating energy because it is in resonance with itself, like an oscillating ring, as a way of looking at why there is not radiation from the accellerated electron.
Where are you finding students that have heard of electrons but not angular momentum. Not trying to diss anyone, it's just wild to me because I've had the ice-skater/angular momentum thing in my head for as long as I can remember. :D
@@andrewfleenor7459 curriculum. Not much to be done about that..... The students usually know about the ice skater piroutte effect, but there's not math, derivation or formula going with it.
I heard this too and the idea was even in my 13th grade textbook, but it cannot really be historically accurate, can it? DeBroglie formulated his idea of matter wave quite some time after Bohr.
@@AndDiracisHisProphet Afaik this idea came up much later, even much later than deBroglie thesis in 1924; and I do tell my students that this is not what actually happened. I like the approach, and you could have discovered and constructed it this way.
The engineering comments section was wild. It felt like half STEM-lords discounting your analysis out of hand and half "born in the wrong generation" style nostalgia for some perceived "better" historical era of theoretical physics advances. Asinine behavior either way
It's always a good day when angela posts a new video. Even though physics isnt my subject i'm always drawn to your explanations and humor, please keep making them! have a nice day!
I'm ten minutes in and I feel like the video has already covered an hour's worth of material - but I feel like I'm actually still following on; great work!
Dr. Collier, I have never cared about the radius of a hydrogen atom. I have never, until today, known that I did not know what the radius was. I have never even cared that I didn't know that I didn't know. It is a testament to your teaching skills that I'm here now, learnin' like a mofo.
As a mechanical engineer my world is decidedly Newtonian and all this atom stuff is medieval sorcery to me, but I do appreciate your not using phrases like "By inspection we see that..." or "It is intuitively obvious that........"
just wanna say this video is really good! it lines up really well with what im learning in my undergrad modern physics survey course, i appreciate the consistently great videos :)
"In this first problem, there is a car driving along a cliff, and the car just jumps off. This person has decided to end it all. Now, we want to know at what time the car hits the ground. This is the beauty of physics, because if this were a psychology class we'd want to know why the person was jumping, but we are simply concerned with how long it takes."
I learned this stuff 50 years ago. Forgot it for the most part, but you manage to bring it back to me with great clarity. You have a nice style. Works for me.
First of all anyone can watch Shankar teach intro to physics on TH-cam. I have and I highly recommend the videos. Second…these videos are such a treasure. I have taken 4 semesters of math for engineering school at the university of Pittsburgh but that was 25 years ago. I didn’t completely follow but I did enjoy going through the exercise with this wonderful young physicist. Thank you so much for this great content.
1. great video as usual 2. Holy Gates of Argonath, that's a sick painting! edit: it's good to know that people way smarter than me also hate integration by parts
Thank you for going into the math. I know an older videos you spoke about the math being important but the shift towards actually presenting it is appreciated and valued.
44:18 it is spherically symmetrical. I have a blog post on it “p orbitals are not dumbbells”. The point is these are harmonics the actual wave function is a combination of px py and pz and the combination is spherically symmetrical. This is similar to say Fourier transform but in three dimensions.
Had this video up on my phone for like two weeks before finally pressing play. Surprised to find, you're a rare person who can make such a dry and boring topic actually interesting to watch. I feel like you'd make a good teacher, as, aside from the maths, which I am not educated on, you made complicated things make sense (as much as they can with quantum physics). I was engaged throughout this hour long video, learned some cool things. Well done.
My "baby's first quantum mechanics" (not the actual title) module in my chemistry bachelors did not prepare me for this mathematical monster. That's the stuff of nightmares to me... Great video, thank you.
The correspondence principle reminds me of something my physicist brother always says. Every physical model is an approximation. Older models aren't exactly "wrong", they're just less precise approximations.
As someone who majored in Physics and works as an engineer now, this was weirdly comforting and nostalgic. Like I remember deriving this on the final exam. I may have gotten a C+ in Quantum 2, but it was still a good time, and expanded my mathematical and scientific horizons. Thanks, Dr. Collier.
Please, touching lab equipment doesn't make you an engineer. It doesn't really count as engineering until you are doing it at 5000x scale in a warehouse built in 1983 that somehow has not been cleaned since 1977 where you are one surprise EPA inspection from being a superfund site and the whole thing is operated by guys who have been in the industry for 40 years who respond to your every suggestion with "I don't know about that". All those commenters are dumb
I went to Rice Univ in 1976 with a burning desire to be a physicist. But though I won the math award in HS (400 in class), I was so lacking in math understanding that in the end I became a psychiatrist. I loved your video, reliving a long lost, beautiful dream.
Ångström has the a with the cute little circle on it, which in Swedish makes it not an a, but something pronounced half way between A and O. I checked through his Wikipedia a bit and saw he grew up in the Ångermanland province, and that that province gets Ånger from the old Norse term for "deep fjord". So his name might mean something closer to "Stream of a Deep Fjord". Though just ång in modern Swedish means steam, so it could be "Steam Stream"
I liked your point around 50:00 about people effectively gatekeeping physics and calling people engineers as if its an insult. I’m at a school with a small physics department, and people (professors included) really love trash-talking engineers. It’s upsetting, because engineering is cool! I wish this attitude wasn’t so common:/
You are right; Strom (or ström, as is the correct spelling) means stream or river, and is the origin for the English word "stream". So what then does Ang (Ång) mean? Ång comes from Ånga and means steam or mist. Hence the name comes from the river misting in the early mornings. Also many Swedish surnames are based off of nature such as Bergquist (mountain twig/outermost part of branch) or Sjöberg (lake mountain). Ångström is also one of these. The unit was named after the Swedish physicist Anders Jonas Ångström (1814-1874) But all that is boring. The true factoid you want is that if you translate it to English properly, you get: SteamStream and I think that's super cute.
Ström is _not_ the origin for the English word "stream", rather they are cognates with a shared origin. They are both derived from Proto-Germanic *strauma-, ultimately from the Proto Indo European root *sreu- "to flow."
Thanks for including information on the experiment! I've been trying to wrap my head around the entire idea of physics but I'm a social scientist who dropped physics at age 15. Seeing how things are measured and calculated gives me a lot of clarity.
32:40 - this is the best TH-cam C2A of all time. I've been a TH-cam premium/red subscriber for as long as it's been a thing because I value quality content, and this is as good as it gets
My biggest gripe with my teachers is that they made mathematics sound and feel like you need to be born with the ability to be able to do it. We should be telling kids that mathematics is also a language. No one is born with the ability to speak just any language, you learn it. And although some people can learn faster and learn more, we all have the prerequisite to learn it and speak it to a degree that will allow us to converse and make progress on some ideas. At first look (first listen), everything can sound nonsensical but once you learn the languange, it starts to make sense. But just like other languanges, we should learn to speak it to talk about things in it. This is why I have a gripe with my teachers, it is as if you can have a deeper conversation on something which does not even have the "right words" for something. It will be close to impossible to contribute without knowing the mathematics behind quantum mechanics and most of physics, in fact, it often misleads you because you have to rely on intuition alone. Unfortunately, intuition can only take you just far enough but not anywhere near the truth of things.
Your teachers sound very weird. Their job is to help people learn. If they assume some people have the capacity to learn and some don't, then they may as well not even be there. You could just hand out textbooks instead and wait for some students to learn and some to not.
@@volblaI completed a mathematics undergraduate degree in the USA. I assure you, this is not an unusual attitude. The graduate mathematics students are selected for their potential to be mathematicians.They teach math to be paid a stipend by the school and to have their tuition fees waived. Their priority is their own math classes, not teaching. Below the university level, teaching is poorly paid compared to technical jobs. This means talented people often choose more lucrative professions over teaching. The better students will receive better teachers. I was fortunate that I was placed in advanced classes in my lower grades with the better teachers. Even with this advantage, I had many bad teachers. These issues reinforce the idea that math requires a natural talent. Also, since math builds so quickly upon itself and much of the early subjects are a linear path, a student falling behind often cannot catch up. There are also issues with classroom discipline, uninvolved parents, violence in the schools which cause talented people to leave the profession. Every year I went to a public high school, I would miss school because of a teacher's strike during contract negotiations. The teacher's union made it difficult to fire incompetent teachers. This was in the 1970's. I don't think anything has improved.
I'm not taking QM (technically pchem but its quantum pchem and I'm probably gonna take QM anyway because pchem is right now my reason for wanting to go into chemistry) for another two years (chem undergrad), but I have taken a full calc series and diff eqs, so I'm watching you work on the Schrödinger equation like "every step makes sense and yet it's still nonsense to me" Edit: got to the Legendre polynomial bit and nevermind. we'll see if I understand this in 3 years
These days, pchem and QM are pretty well the same. I have a physics degree, and I'm now reading up on physical/quantum chemistry. The boundaries between materials science, solid state physics, and physical chemistry are pretty nebulous. It's really interesting to see how many people jump between departments.
I have a bachelor's degree in mathematics and only understood about 10% of this. I'd like to think that 40 years ago, when that degree was still new and shiny, that I would have understood more, but diffie-Q's and I have always had a difficult relationship. Still enjoyed the video though.
Though I learned a lot through this video, the fact that the hydrogen atom is apparently bisexual blew my mind. But seriously, hearing you gush about Shankar really warmed my heart. I have people in my own field of study that I feel that way about.
25:30 honestly, I thought it was just sloppy writing at first, but I like your upper left bracket notations to signify that you are multiplying everything on top. It doesn't change anything functionally, but makes it easier to kinda see whats going on in the equation a little bit quicker. Makes sense, im going to start doing it myself... if I go back into math... which I probably will
Another banger video. So good. If anyone is looking for another very funny and good QM text: check out How to Be a Quantum Mechanic by Charles Wohl. He taught QM at Cal for 40 years and has a really dry humor that permeates the book. 10/10
I have seen the documentary Chain Reaction and in it, it was made very clear that the Engineer was the true hero and saved the world. Also the Engineer was a no nonsense, salt of the earth working class blue collar lad and not some hoity toity university type! But somehow was working for a university. Im sure it makes sense stochastically.
@@12pentaborane Yeah, don't think any sort of explanation is given as to why a cutting edge university physic project is using external blue collar machinists to engineer their experimental prototypes.
15:24 that is eternally relatable except my version of hell would be listening to pseudohistory and pseudolinguistics forever with Great Man theories, weird tankie history, alt right history, Ural Altaic theory, Koreanic-Japanese language family, North Korea Did Nothing Wrong tankies, Park Chung Hee Apologia, Pro Japanese WW2 Apologia, Pop Roman History (lead pipes melt Roman brains), Jesus never existed /r/atheism, Library of Alexandria hysteria
@@3chl986 It's truly horrifying isn't it? add in the Heritage Foundation bros and the US Constitution Fetishists and it is truly the worst version of hell
@@jamesdakrn Sounds scary but maybe because I'm not American I can't really imagine what this is like. But as a history enthusiast your list above was... too much And the Library of Alexandria hysteria... Ugh I'm Egyptian and the amount of misinformation is annoying
Angela, i started watching you because your videos are very fun, entertaining, and have a good message. But this one in particular got my ass studying quantum again, and boy I am living. Thanks for the recommendation for Shankar. I’m having a blast, and if not for you I’d probably be still mindlessly scrolling on TH-cam wasting my life even though it’s long since been my dream to more deeply understand the Schrödinger equation etc. so thank you 😊
I want to comment about engineering hubris. I am an electrical Engineer. I worked in nuclear power in the navy before I got my Engineering degree so my physics knowledge is broad but not technically formal, Engineering is not seperate from physics. Engineering is the practical application of physics to achieve an end. My particular field is an application of the physics of Electromagnetism. A physicist with knowledge in that field can do what I do. A lot of engineers may just memorize simplifications and thumbrules to streamline the process or just copy and paste succesful designs but they dont have to,. Of course there is a lot of nuance with regulation and building code that a physicist might not appreciate, but in principle as an Engineer I see myself as the spokesman for the laws of physics. There is also Engineering Technologist which is a person that implements a design that a full engineer mathed out. They dont need physics. I think a competent engineer should be up to speed with the current physics knowledge of his field in my opinion. Engineers and physicists are the same animal. Just a different focus. One looks outward and the other inward.
I'm an Air Force pilot with an EE degree and I use physics to anticipate what control inputs are needed for landing. But so do all the pilots who don't know physics; they can land the plane perfectly as well, they just aren't aware of math describing why it works.
I found those comments truly disturbing. Engineering at its peak is something like the light bulb, the WD40, the DRAM, the cheap quartz watches. Basically bringing out top notch lab equipment from the ivory tower of science into the desolate life of everyday men. That list would not even close to Angela's list. I know great engineers, but they are not like "electrical resistance is always positive and why is it, could it be zero, could it be negative? Let's just spend the next 20 years to figure it out". If you are like that they despise you. How can they think the world is revolving around them? Anyway, hearing "engineering is important" sounded a lot like when your dog huffs at you because you were unjust and then you two are sitting down together and you say to him he is a very important part of the family and you respect his feelings.
@@richardv.2475respectfully every engineering project is a physics experiment in the laboratory of the universe. Will this structure support its own weight? Yep....pbysical laws continue to hold, what is important? I only say engineering is the application of physics. I am an engineer who considers himself a physicist albeit not licensed and any physicist could be a great engineer. And any engineer worth his degree would love to push the boundaries of what we understand about the physics. Its engineering that got us to a transistor consisting a single atom of each material in the transistor, that didnt happen without some understanding of quantum level effects. Its physics. When you can use it as a tool we call it engineering when its just academic its called Physics. But its all physics. All the time. But what is important? That is a philisophical question that you get to make up your own answer to. I'm just talking about physics.
@@TheGarmisch no doubt. I am sure thst properly trained any person could also perform physics experiments and collect data while having no grasp of the material. I am only discussing the underlying nature of the work. How it is performed is up to the performer. I would rather be in the plane with you in an extreme emergency. Your knowledge of physics IS an edge. Would you rather the guy who buolt your plane had a working knowledge of physics? Or is it ok if he just looks up what equatioms to apply and copy pastes old designs? Both people are applying physics, just because one of them doesnt know it doesnt make that false.
I like your funny words, magic woman. I don't understand a word of it, and am just listening to you because you're a super fun person. And I am procrastinating sleep.
The figure at 35:46 is why electrons are so gloriously weird: Some of those shells have multiple lobes (distinct regions of space). But the probability that a given electron, say Charlie, is in each of those lobes is nonzero. But the probability that Charlie's in between those lobes is absolute friggin' zero. So Charlie has to keep moving at infinite speed to bop back and forth between his lobes to make his time in each lobe match the probabilities. That's why a certain physicist calls these things "beables". They can't be called by a name thats already been used for something in our macroscopic world since they're simply a different kind of beable. (IMHO, that's the most beautiful word in all physics.) (Truth in advertising: I'm a computer nerd and can't do the math, but I do enjoy watching you guys busting your butts.)
It must've been nice to have fun while reading a quantum mechanics textbook. In my quantum mechanics classes, I used the Cohen-Tannoudji one (with some sprinkles from the Sakurai one), and I only ended up with tears, lots of tears. The silver lining is that this sentiment was shared by my friends who also took those classes.
btw, It is a fun exercise to do the whole calculation step-by-step; however, it quickly ceases to be enjoyable when you start working with the polynomials and normalization 😩
I love how this video serves as both a lovely informative video on the history of how we use quantum mechanics in application to the Hydrogen atom as well as a cheat sheet to the derviation worksheets (though tbf, for this particular problem there are plenty of other cheat sheets out there and a lot of the nitty gritty like converting to spherical polar coordinates from cartesian that would be in the worksheet is moved quickly through)
38:09/38:16 - I didn't even attempt to understand the math, but being around to have it left as an exercise to the reader made listening through (instead of skipping) totally worthwhile, in my book. Because yeah, I can relate to wanting to do that... and so it brought me joy that you got to. :)
Watched 40 seconds so far and the mood, the coffee, I’m here for it. It’s giving… I’ve got a headache and the world is on fire but fuck it let’s measure some atoms.
You have been able to pull a non physicist out of the fuzzy world of general science writing up to an actual sense of understanding the origins of the math behind quantum mechanics. Thanks.
"...and then she wandered over to another campfire and they were discussing whether or not the universe is a simulation. And at yet another, Tom Bombadil."
you don’t have to apologize for talking long about science to people who knowingly clicked on a video where you talk for long about science. We know and you’re awesome.
Love the video! A couple questions circling back to the problem at the beginning: 1) if you had an isolated hydrogen atom, with no other matter or light interacting with it, would the wave functions describing the electron and/or the whole atom be static, or do they change over time? 2) if the wave-function for the electron were not spherically symmetric and it was changing over time, would that produce a photon as expected of an accelerating charged particle?
Interesting questions you ask. I think I can speak to the first one: the typical definition of "isolated" may be counter-intuitive... If you have a hydrogen atom out in vast empty space, there is a continuum of quantum vacuum fluctuations which would all contribute to pushing the state of the hydrogen this way and that way. In the case that the atom is in some excited state, these fluctuations tend to promote spontaneous emission and relaxation to the ground state (the "stationary" nlm = 200 state typically lives for a few nanoseconds). If you want to suppress this effect, the trick is actually to put the atom in a tiny box. This reduces the number of electromagnetic modes which 'see' the atom, so there are fewer vacuum fluctuations that jostle the delicate excited state, and you can prolong its lifetime. Being out in vast empty space is sort of like being in a really big box, which can support a higher density of electromagnetic modes. Here's some related reading: physics.umd.edu/courses/Phys371/AnlageSpring17/Chapter_3_CCR_16_Modes_of_Oscillation.pdf (PS: putting a superconducting qubit in a small shielded box is crucial for prolonging its lifetime). As for the 2nd question, I have less experience thinking about that one, but I think you'd want to consider precisely what you mean by "not spherically symmetric". There are eigensolutions (stationary modes) of the hydrogen atom which are not spherically symmetric (i.e., look the same when you rotate them by some arbitrary angle), and they also don't radiate (if you ignore the whole spontaneous emission part discussed above). Now, one could construct a non-stationary state of the hydrogen atom which was not only 'not rotationally symmetric' in the sense I've defined, but also lacked any sort of symmetry in reflection, discrete rotation, etc. I can't say for sure as I'm not an expert on the question, but I could imagine such a situation would sort of break a wave interference condition which was otherwise prohibiting radiative effects. I'm picturing a sort of hydrogen-atom-potential version of the discussion of superposition states of "particle in a box", where sums of stationary states result in a non-stationary state. en.wikipedia.org/wiki/Particle_in_a_box ...but maybe someone closer to the subject can chime in.
Yeah absolutely Do you know any other science channels that are like that? I know a lot of math channels, and some physics. Wanted to find something for chemistry but.. can't And I mean with a scientist/ someone who's passionate about a subject Not the ones with just voice overs or even ai ugh
@3chl986 There aren't Many. On this level I have only found Sean Carroll and Futurism with Issac Authur. Up an Atom is good. But she likes to make people's brains explode with how complex the topics are. Physics girl was good, but very Bill Nye level. Hope her channel comes back though. Sabine used to be good? but she is now doing the most horrible John Stewart impression of comedy physics. She is unwatchable now.
Pretty small probably
yeah that's probably close enough for physics.
Big if true
True
Less than 2
well, fairly small. it depends on if you're looking.
Shankar was the chair of our physics department when I was in grad school. He was a funny guy. For some reason, one thing that sticks in my mind is when he was introducing a seminar speaker who was going to talk about hot, compact stars, and Shankar goes, "Like Danny DeVito".
this guy sounds like a riot, i kind of miss university
😂
What a king
He was a legend among the undergrads as well when I was there. He taught freshman physics to the advanced students for a number of years and was much loved by his pupils.
I mean, his greatest discovery, according to Shankar, is "a small parameter that justifies most calculations performed in physics: 1/ego, where ego is the author’s ego." I want to email him a love note.
My son is ten months old and I watch your videos while chillin with him. I think he thinks you and the baby learning TH-camr "Ms Rachel" are the same person because he gets very excited and relaxed when he sees you.
He has trouble keeping up with the math portions because he's a baby but he's trying
Go get him "quantum physics for babies"!
he'll get there eventually
And what's your excuse?
Thats cute as hell:)
I think this is common for her audience. I’m watching this video. I’ve been served a song where cartoon anthropomorphic puppies are singing about groceries and how they should be put away.
Seems to be a nexus between people who like funny physic explainers and people who are forced to watch condescending cartoons explain household chores
I'm a humanities major, but man I love listening to physicists. I nearly failed highschool physics, but something about graduate physics explained by a stress ridden semi-sarcastic women has me listening to you like a podcast. Great voice, always love your uploads
Same here
If you are secretly in love with Angela,
join the queue ❤❤❤
When I took undergrad physics back in the 70s we didn't have fancy CMOS spectrometers. We shine those hydrogen and neon tubes (which look just like the ones you showed) through a small slit, refracted them off a piece of diffraction grating, and measured it with a ruler.
Uphill both ways
I assisted Dr Kielkopf in spectroscopy at U of Louisville in 1987, and we made good use of exactly that kind of kit augmented with a pretty fancy laser. I saw Helium ionized enough to form He2, and then watched as Dr. K. tuned the laser until the molecular bond of the He2 itself became an excimer laser (the gaussian hump on the PC turned into a razor sharp peak). I was just a Freshman but being the only undergrad physics major in the entire University but one, I was snapped up as the department's favorite pet. Working in a real life physics lab is one of the most memorable experiences I ever had, even though I didn't go all the way. Channels like these help me catch up, now that I'm in my 50s, and ready to go back and learn PDEs and tensors, etc., just for the pure intellectual enjoyment of it.
I remember sitting down for a midterm when my lab partner asks me "What's the square root of four?" I immediately pulled out my slide rule and told him, "Looks like about 1.98."
When i an astronomy undergrad 23 years ago, we also made the measurement by hand not because there weren't new digitally assisted ways to do it, but in order to teach us that it could be done by hand and the problem solving it took to figure it out. It was kind of fun since it was a one time lab and mostly we were doing the measuring.
@@joseapar Same in my astronomy undergrad we looked at the hydrogen alpha absorption line with a prism (or a slit, IDK it was 15 years ago). Just needed a good sunny day
i skipped to 43:42, but i believe with all my heart that you did the work and proved the numbers were good numbers
We are the faithful.
Only the best numbers for our queen!
All numbers are good. Some might be negative or square or even irrational but they are all good. 🙂
@@imaginaryuniverse632specifically in atomic physics, not all numbers are good. Only time-constant eigenvalues are good quantum numbers.
@@emilyrlnwhy simping? value yourself.
you're very good at bringing humor into a dry subject, and you're a very talented and skilled science communicator. Thank you
I particularly enjoyed "a Bohr walks into a bar". Got a good chuckle out of me!
I thought she is an engineer now, I am confused
@@Skukkix23She's a theoretical physicist researching dark matter, I think.
you havent seen the video, huh?@@jss1328
engineers are practical physicists@@Skukkix23
Ångström is Swedish for "Steam rapid" ( _ånga_ = steam, _ström_ = stream/current/small river/rapid). The most common surname scheme in Sweden, after "Namesson", is "Two words from nature merged", so you usually get things like "Twig beach", "River current", "Forest land", and so on.
Wait... "steam stream" is one of the possible translations and you didn't go with that?!
The size of a hydrogen atom is about half a steam stream. That's awesome!
Is that true, or are you just blowing hot air?
I'm not fully awake so I was like "huh, what a weird coincidence that their name contains "name"" before I realized you were making an example 😅
W O R M S T R O M !!!!
@@Sam_on_TH-cam it was very tempting, I have to admit. But "rapid", as in a smaller river, is more correct. 🥲
Language is neat!
What makes your videos amazing is the way you communicate the CULTURE of scientific research. You really humanize these famous physicists when you share their jokes, etc. I also like the tidbits you provide about how to solve problems in a physics class that's specific to a sub-discipline (like how you'd find solutions to Schrödinger's equation using approximations to a H atom.)
As a physicist, I immediately had Mann-Gell amensia and started to write a comment explaining how you were wrong, but then you added clarifications which said exactly what I was writing, so somehow you managed to raise my appreciation of you, which was already high. Well done!
Hey! There was another video on that!
By someone...
wow, i'm sure this is a career defining moment for her!
I can't tell if this comment is a joke, based on the other video... but it ends well, so I appreciate it either way. :)
callback !!
I absolutely love the quote "the thing about differential equations, is.. if its possible to answer it, you just know the answer."
actually so true though
As a guy learning basic physics and calculus, and enjoying the learning process, it is so interesting to watch you do the math. I love educational videos, but many times they cover up the real process with an intricate analogy. And I appreciate seeing where the math is going. The parts I understand let me know I'm on the right track. And all the stuff I don't understand I can read about, or you explain it very well.
Thank you.
Swedish speaking Finn and fan here 👋I'm more inclined to think the "Ång" in "Ångström" is a form of the word "ånga" (commonly truncated when compounded) meaning "steam", so "Ångström" literally translates to "steam stream"
Almost word for word what I was going to write 😂
“Misty river” or “foggy river” (:
I thought it was from the word for 'meadow'.
I really appreciate you for taking the time to do the math in front of us and not just doing prettily-illustrated metaphorical explanations so common to science communication. I dropped off of math after the first semester of calculus (wasn't in a math-heavy field and wanted to spend my electives elsewhere). your videos have made me go back to the textbooks I stopped halfway through. I love the way that you are clear about the way that the math isn't optional, but you talk about it as something that you train in, not something that you understand or don't in some binary way.
the way you talk about physics makes it feel like there is a big slope to walk up to understanding, and not some impassable wall. I hope I will be reading something other than the abstracts of physics papers one of these days. :)
As a Swede: Ångström can be translated as "Steam Power". "Ånga" means steam, which in a compound word takes the form "ång". "Ström" indeed means stream, and is used like the word power is used in electrical contexts often is (e.g. "The building lost power" ). So yeah, Steam Power, Steam Current, Steam Stream, take your pick.
I mean… it IS called electronic current… stream… current. It’s the same analogy in action.
This is a great video! I reminds me of college when my physics major room mate would talk to my math major room mate about higher level math problems and stuff like that and then they would ask what I learned in engineering school and I would answer something like "You can bend metal so much it becomes plastic"
When I was struggling in Quantum Mechanics, my Hotel Management suitemate complained about having to write a menu. I told him I was trying to work out how many times I'd have to bang my head against the wall before I could expect it to quantum tunnel through to the other side (we were literally assigned that question for homework).
The answer is... a lot more than the number of seconds in the age of the universe. It is so unlikely that events like that should be expected never to be observed no matter how much you look. But it isn't impossible...
@@Sam_on_TH-cam So what you're saying, is there's a chance...
My quantum mechanic said I was having a little problem with my wave function but he replaced it and now everything is working fine. Only cost about 900 bucks.
He can tell you exactly how much it will cost to fix or exactly when it will be ready, but not both at the same time.
Replace mechanic with doctor and this conversation definitively happened. Quantum mechanic is a quack magnet, and not in the electromagnetic way
i did not follow the schrödinger equation part at all but honestly as someone who's started to teach themselves algreba and calculus as an adult your little speech beforehand was exactly what I needed to hear. And I had fun just listening to you do the equation while I did my nails, it was a whole vibe ❤
This is so wholesome
Themselves, not themselves
Don't worry y'all, I've taken all the required classes, including two years of quantum mechanics, and I didn't understand the Schrodinger equation section either.
As a Chem Student trying to get into quantum/theoretical chemistry, but feeling ever increasingly lost due to all the maths & physics knowledge that we lack and yet are presumed and expected to have by our teachers: Thank you for this, it's very reassuring!
i haven’t taken nearly as much stuff as you, but i still get lost when my professors start talking about special functions and spherical harmonics and stuff. this is probably because our mathematical methods for physicists course is given after our first quantum course (for some weird reason). being a math double major sure helps tho
I more learned how to pass my physical chem exam than to understand it intimately. I've forgotten most of it by now but I do know I had a more conceptual understanding of it back then than a mathematical one
I had the exact opposite problem! I knew how the math worked, what the answer needed to look like at the end, and a probably autistic professor who could never figure out how to verbalize a connection between the math and a conceptual framework @@johnsober
I am here for the developing character dynamics/conflict between past Angela, future Angela, and editor Angela. Oh and the science communication is also nice!
You can just sense the tension. I bet there's gonna be some backstabbing in season 2.
This channel is so consistently excellent I’ll watch anything she puts out, but HOLY SHIT the thumbnail and the transition images on this one are just gorgeous
Fun fact! When I took DiffEqs in college I had a classmate who said (and I quote) "Differential equations are EASY, they're just like Jeopardy with math: provide the answer in the form of a question!" and he was serious and we laughed and laughed and then I killed myself.
"Does anybody actually read these things?"
yes
Also I love that you pumped up that "joke" like it was the cleverest, funniest joke ever told in the context of physics and it was just the word "anyway" and what we can infer from it. Comedy is fascinating!
Currently taking PDEs as an engineering student, and hearing you mention the eigenvalue problem made the separation of variables method jump out at me, glad to see that was on the right track! We have a project in which we lecture on a topic not covered in class, and I might just make it over solving the schrodinger equation for a hydrogen atom. Thank you!
Lol if I was an engineering student I’d need to take PEDs not PDEs
As near as I can tell, any time you’re solving PDEs, it’s “let’s use separation of variables.”
@@TIO540S1it's either that or *shudder* Green's functions
As a math major I swear, Engineers be getting all the nicest looking functions to deal with. 😔
@@primenumberbuster404 Bro Lmfao ikr! All we get is an insane function that's continuous "almost everywhere" and then they ask you to integrate it! then I have to learn measure theory
after doing the exact experiment you described in physics lab class 2, I decided to do something similar at home for cheap. Was definitely possible for much cheaper, though it was some work (some of the stuff later got recycled into an optical CT though).
The way to making it cheap was using
- Diffraction grating instead of prism for splitting
- Webcam for intensity measurement
- Stepper motor + arduino to do the angle adjustment
- 3D printed parts for mechanical compatibility
- control everything and analyze from your computer in python
Never actually calculated the hydrogen radius from it, but I checked the energy on low pressure sodium and a red diode laser and that was kinda ok.
The CT is pretty much the same except you don't need the grating and the motor gets a different 3D printed attachment to hold the object. Only additional parts are collimated light source (flashlight, pinhole, random amazon lens) and a screen (white baking paper in a 3D printed mount).
I love shed physics! It's such a good challenge to prove that you really understand what the experiment is about. While I was still in my masters I really wanted to go through all the typical constants (earth radius, g, e, ...) but sadly didn't find much time. So spectrometer, Jupiter G*M, CT scanner and earth radius (thanks to dan olsons video at the lake) were all I managed to do :(
I actually found the 1/137 thing really intresting, and wondered, why the hell would it be such a simple fraction. However it all gladly went away, once you told us, that it isn't exactly 1/137.
It's like finishing a bag of chips: You first feel sad, that it was the last one, but then you realize that there are still some crumbs to eat.
Thanks Angela - I nearly died laughing ~32 minutes in:
“[Sigh] So things here get really tedious… so I’m not gonna do the math… this is a short video so you’re just gonna have to be fine with it. Deal with it. :| Like and subscribe! :) “. Absolute comedy gold and the best physics channel on YT. 😂
When I reached that point I immediately scrolled down the comments specifically to find this comment 😂
I learned how small an attosecond was the other day, along with how high the temperature of a particle can be before it rips itself apart, both numbers are so far outside the realm of human comprehension and intuition it’s fascinating.
Glad to be early for another banger of a video!
My favorite thing is when numbers completely beyond comprehension cancel out and leave something bizarrely comprehensible. My favorite example is the Hubble-barn. The Hubble length is the radius of the visible universe, and the barn is a unit of area used in nuclear physics that's equal to about the cross-sectional area of a uranium nucleus. If you multiply these two absurd numbers together you get the Hubble-barn, a unit of volume which is equivalent to the volume of a cylinder with a cross section the size of a uranium nucleus and a height the size of the visible universe, and you get.. about 13 liters or 3.5 gallons, a volume which sounds like you're describing the amount of gas left in your car.
@@oliviapgwow never heard of that, kind of hilarious 😂, just imagining a near infintely tall miniscule pole whose volume is 13 liters lol
Thats a great fun fact, thanks for sharing@@oliviapg
I'm getting my PhD in nuclear engineering and honestly it seems a lot more like physics than engineering a lot of the time. I'm not like designing helicopter blades or reactor control systems, I'm literally doing quantum mechanics day to day.
I'm not sure why physics gets such a bad rap.
High school eachers are punished by forcing them to teach math and physics resulting in the physics teachers being angry thus giving physics a bad reputation.
@@davedsilvamy high school physics teacher pointed out you can sort of tell who has primarily a math background and who doesn’t when they’re doing physics by how they do problems- if they leave variables in that could be substituted earlier on till the very end then substitute all at once they’re probably math people, and if they substitute as they go they’re probably not. I wouldn’t be surprised if when people are getting taught it can also be really hard to follow the work and keep up if the teacher just runs with the long ass equations full of variables then substitutes in when the student isn’t a math minded person. Some people prefer it that way, but for some people it gets hard to keep the equations straight and if that’s the way your taught and that’s the way you try to do it and you’re not a big math person I could see that really turning a lot of people off.
Overall I’d assume it also has the same problem with Econ/finance where there just isn’t really any qualified people who actually got their education in the subject who want to teach (because there either just aren’t that many people period and they can get far better paying jobs elsewhere) so all the people teaching it are half self taught and so they’re just not as great as teachers in other subjects who formally studies the subject through undergrad and possibly grad school before going into teaching it.
I modeled the hydrogen atom in my Quantum II class on a computer over 20 years ago. It was very difficult. I ended up dropping the physics major that semester and switching to philosophy, but I stayed in the class because I wanted to study philosophy of physics. I managed to convince my professor to let me take the class pass fail and have my grade based on a philosophy of physics paper... because the homework and final were beyond my capabilities. I wrote about mereology, specifically exploring the question of whether liquid helium is 1 boson or 4 fermions. My conclusion was that it depends on why you're asking the question. Either one may be the best answer, depending on exactly what the question is and the exact nature of the question depends on it's context.
Please post more information on this. I'm interested in knowing more.
have you read sean carroll’s paper on quantum mereology? it’s been on my list to get around to but i imagine it would be a good read if you’re interested in these things!
@hattielankford4775 With my degree in philosophy... I went to law school. I do Constitutional Law now, still spending a lot of time on first principles and theories. I work with groups trying to amend the Constitution. But the stuff I study now is a little more consequential than what I studied in college. I still find metaphysics fascinating, but it isn't as important in the real world.
@@thelocalsage I hadn't heard of that. I'll look it up. Thanks.
Edit: Found it. I think that's gonna be a bit over my head, just judging from the abstract:
We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into "system" and "environment." Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain localized around approximately-classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. This formalism could be relevant to the emergence of spacetime from quantum entanglement.
If I had gone into philosophy of physics professionally, I'd slog through it and talk to some physicists for help with anything that tripped me up. But I study law now and I don't have time to digest something like this. You enjoy though.
@@jonbrown1654 Basically, I concluded that, if you are asking because you are interested in the behavior of liquid helium, then you are really asking a question in which "it is a boson" is the more appropriate answer. If you are asking because you are interested in the more fundamental question about how that boson-like property emerges from elementary particles, then the question you are asking is better answered by saying it is four fermions. And if you are asking about even more funamental properties than that, you need to answer about the quark interactions between within and between the particles. And you could get more funamental than that even, but then you'd be asking questions for which we don't yet know the answers. But those more funamental answers may be utterly useless if you are wondering why, for example, liquid helium has zero viscosity. All of those answers may be correct, but they are correct answers to different questions, any of which may be expressed by the words "what is liquid helium made of?"
I then applied that to typical philosophical debates in mereology. Is a chair one thing or is it a collection of separate pieces of wood? Or a collection of atoms artanged "chair-wise?" The answer depends on what you really mean when you say the words "what is a chair?" And that depends on the context of the question.
just started studying mathematics for physics the last few months. self study student here for the time being, but i'm excited to learn more and understand this stuff better! :)
Usually, when I teach the hydrogen atom, I rephrase Bohr's postulate this way: Electrons are only allowed to have orbits where the length of the orbit is a multiple of the deBroglie wavelength of the electron on this orbit. This way, I skip the angular momentum, which is something the students usually have never heard before. I got this from an article where they imagined the electron not radiating energy because it is in resonance with itself, like an oscillating ring, as a way of looking at why there is not radiation from the accellerated electron.
Where are you finding students that have heard of electrons but not angular momentum. Not trying to diss anyone, it's just wild to me because I've had the ice-skater/angular momentum thing in my head for as long as I can remember. :D
Nice. Yeah, the electron orbit stuff always made me think too much... wait why doesn't it just fall in? (empty looks and whispers) he knows...
@@andrewfleenor7459 curriculum. Not much to be done about that..... The students usually know about the ice skater piroutte effect, but there's not math, derivation or formula going with it.
I heard this too and the idea was even in my 13th grade textbook, but it cannot really be historically accurate, can it? DeBroglie formulated his idea of matter wave quite some time after Bohr.
@@AndDiracisHisProphet Afaik this idea came up much later, even much later than deBroglie thesis in 1924; and I do tell my students that this is not what actually happened. I like the approach, and you could have discovered and constructed it this way.
The engineering comments section was wild. It felt like half STEM-lords discounting your analysis out of hand and half "born in the wrong generation" style nostalgia for some perceived "better" historical era of theoretical physics advances. Asinine behavior either way
It's always a good day when angela posts a new video. Even though physics isnt my subject i'm always drawn to your explanations and humor, please keep making them! have a nice day!
I'm ten minutes in and I feel like the video has already covered an hour's worth of material - but I feel like I'm actually still following on; great work!
Dr. Collier, I have never cared about the radius of a hydrogen atom. I have never, until today, known that I did not know what the radius was. I have never even cared that I didn't know that I didn't know. It is a testament to your teaching skills that I'm here now, learnin' like a mofo.
As a mechanical engineer my world is decidedly Newtonian and all this atom stuff is medieval sorcery to me, but I do appreciate your not using phrases like "By inspection we see that..." or "It is intuitively obvious that........"
Hang on, I'll grab my ruler
Matt Parker, is that you?
*proceeds to drag a man-sized steel drum full of liquid nitrogen and computer stuff across room*
just wanna say this video is really good! it lines up really well with what im learning in my undergrad modern physics survey course, i appreciate the consistently great videos :)
oh man, that one clip of dr. shankar at 3:00 makes me REALLY wanna go back and refresh myself with his lectures.
"In this first problem, there is a car driving along a cliff, and the car just jumps off. This person has decided to end it all. Now, we want to know at what time the car hits the ground. This is the beauty of physics, because if this were a psychology class we'd want to know why the person was jumping, but we are simply concerned with how long it takes."
it's a bit less than this🤏
The "squishing your head" interval
I learned this stuff 50 years ago. Forgot it for the most part, but you manage to bring it back to me with great clarity. You have a nice style. Works for me.
But don't the quantum mechanics change how they work if you read the textbook?
me when i answer true false questions on the quantum final.
to be and/or not to be? that is the uncertainty principle
Yes, but only between a finite number of possibilities. And yes, I'm fun at parties
@@alonskii You underestimate my ability to find wrong answers.
😂😂
i collapsed with laughter. you comply with humdinger's equations.
First of all anyone can watch Shankar teach intro to physics on TH-cam. I have and I highly recommend the videos. Second…these videos are such a treasure. I have taken 4 semesters of math for engineering school at the university of Pittsburgh but that was 25 years ago. I didn’t completely follow but I did enjoy going through the exercise with this wonderful young physicist. Thank you so much for this great content.
1. great video as usual
2. Holy Gates of Argonath, that's a sick painting!
edit: it's good to know that people way smarter than me also hate integration by parts
Thank you for going into the math. I know an older videos you spoke about the math being important but the shift towards actually presenting it is appreciated and valued.
I contracted engineering from a public toilet seat in the year 1991
44:18 it is spherically symmetrical. I have a blog post on it “p orbitals are not dumbbells”. The point is these are harmonics the actual wave function is a combination of px py and pz and the combination is spherically symmetrical. This is similar to say Fourier transform but in three dimensions.
The analogy about the getting the joke is absolutely spot on
Bruh- I went on the channel binge last week - officially up to date 😮
This is quickly becoming one of my go-to channels for background listening during housework.
Had this video up on my phone for like two weeks before finally pressing play. Surprised to find, you're a rare person who can make such a dry and boring topic actually interesting to watch. I feel like you'd make a good teacher, as, aside from the maths, which I am not educated on, you made complicated things make sense (as much as they can with quantum physics). I was engaged throughout this hour long video, learned some cool things. Well done.
'Does anybody actually read these things? '
Yes 🙂
Very nice video Dr. C, more please!
My "baby's first quantum mechanics" (not the actual title) module in my chemistry bachelors did not prepare me for this mathematical monster. That's the stuff of nightmares to me...
Great video, thank you.
The correspondence principle reminds me of something my physicist brother always says. Every physical model is an approximation. Older models aren't exactly "wrong", they're just less precise approximations.
As someone who majored in Physics and works as an engineer now, this was weirdly comforting and nostalgic. Like I remember deriving this on the final exam. I may have gotten a C+ in Quantum 2, but it was still a good time, and expanded my mathematical and scientific horizons. Thanks, Dr. Collier.
Please, touching lab equipment doesn't make you an engineer. It doesn't really count as engineering until you are doing it at 5000x scale in a warehouse built in 1983 that somehow has not been cleaned since 1977 where you are one surprise EPA inspection from being a superfund site and the whole thing is operated by guys who have been in the industry for 40 years who respond to your every suggestion with "I don't know about that". All those commenters are dumb
I went to Rice Univ in 1976 with a burning desire to be a physicist. But though I won the math award in HS (400 in class), I was so lacking in math understanding that in the end I became a psychiatrist. I loved your video, reliving a long lost, beautiful dream.
I teach differential equations and I'd love to hear your take on how its usually taught.
Yes, I read those things! I always appreciate videos with links/citations in the description.
i remember trying to Google this during my 1st year of undergrad and being so confused at all the seemingly conflicting information
War flashbacks
As someone who only got through three semesters of calculus, watching you do advanced math was weirdly awesome.
Ångström has the a with the cute little circle on it, which in Swedish makes it not an a, but something pronounced half way between A and O. I checked through his Wikipedia a bit and saw he grew up in the Ångermanland province, and that that province gets Ånger from the old Norse term for "deep fjord". So his name might mean something closer to "Stream of a Deep Fjord".
Though just ång in modern Swedish means steam, so it could be "Steam Stream"
Fun tangential fact: "ånger" also translates to "regret".
I liked your point around 50:00 about people effectively gatekeeping physics and calling people engineers as if its an insult.
I’m at a school with a small physics department, and people (professors included) really love trash-talking engineers. It’s upsetting, because engineering is cool! I wish this attitude wasn’t so common:/
You are right; Strom (or ström, as is the correct spelling) means stream or river, and is the origin for the English word "stream".
So what then does Ang (Ång) mean?
Ång comes from Ånga and means steam or mist. Hence the name comes from the river misting in the early mornings. Also many Swedish surnames are based off of nature such as Bergquist (mountain twig/outermost part of branch) or Sjöberg (lake mountain). Ångström is also one of these. The unit was named after the Swedish physicist Anders Jonas Ångström (1814-1874)
But all that is boring. The true factoid you want is that if you translate it to English properly, you get:
SteamStream
and I think that's super cute.
Ström is _not_ the origin for the English word "stream", rather they are cognates with a shared origin. They are both derived from Proto-Germanic *strauma-, ultimately from the Proto Indo European root *sreu- "to flow."
@@verditelabs6550couldn't have said it better myself!
Thanks for including information on the experiment! I've been trying to wrap my head around the entire idea of physics but I'm a social scientist who dropped physics at age 15. Seeing how things are measured and calculated gives me a lot of clarity.
I have (what is probably a dumb) question: why use 0.014 x 10⁻¹³ rather than 1.4 x 10⁻¹⁵? Is it to indicate the precision/significant digits?
32:40 - this is the best TH-cam C2A of all time. I've been a TH-cam premium/red subscriber for as long as it's been a thing because I value quality content, and this is as good as it gets
My biggest gripe with my teachers is that they made mathematics sound and feel like you need to be born with the ability to be able to do it. We should be telling kids that mathematics is also a language. No one is born with the ability to speak just any language, you learn it. And although some people can learn faster and learn more, we all have the prerequisite to learn it and speak it to a degree that will allow us to converse and make progress on some ideas. At first look (first listen), everything can sound nonsensical but once you learn the languange, it starts to make sense. But just like other languanges, we should learn to speak it to talk about things in it. This is why I have a gripe with my teachers, it is as if you can have a deeper conversation on something which does not even have the "right words" for something. It will be close to impossible to contribute without knowing the mathematics behind quantum mechanics and most of physics, in fact, it often misleads you because you have to rely on intuition alone. Unfortunately, intuition can only take you just far enough but not anywhere near the truth of things.
Your teachers sound very weird. Their job is to help people learn. If they assume some people have the capacity to learn and some don't, then they may as well not even be there. You could just hand out textbooks instead and wait for some students to learn and some to not.
@@volblaI completed a mathematics undergraduate degree in the USA. I assure you, this is not an unusual attitude. The graduate mathematics students are selected for their potential to be mathematicians.They teach math to be paid a stipend by the school and to have their tuition fees waived. Their priority is their own math classes, not teaching.
Below the university level, teaching is poorly paid compared to technical jobs. This means talented people often choose more lucrative professions over teaching. The better students will receive better teachers. I was fortunate that I was placed in advanced classes in my lower grades with the better teachers. Even with this advantage, I had many bad teachers.
These issues reinforce the idea that math requires a natural talent.
Also, since math builds so quickly upon itself and much of the early subjects are a linear path, a student falling behind often cannot catch up.
There are also issues with classroom discipline, uninvolved parents, violence in the schools which cause talented people to leave the profession. Every year I went to a public high school, I would miss school because of a teacher's strike during contract negotiations. The teacher's union made it difficult to fire incompetent teachers. This was in the 1970's. I don't think anything has improved.
Thanks for the new video Angela. I was fiending and you're going to make the rest of my work day great.
I'm not taking QM (technically pchem but its quantum pchem and I'm probably gonna take QM anyway because pchem is right now my reason for wanting to go into chemistry) for another two years (chem undergrad), but I have taken a full calc series and diff eqs, so I'm watching you work on the Schrödinger equation like "every step makes sense and yet it's still nonsense to me"
Edit: got to the Legendre polynomial bit and nevermind. we'll see if I understand this in 3 years
These days, pchem and QM are pretty well the same. I have a physics degree, and I'm now reading up on physical/quantum chemistry. The boundaries between materials science, solid state physics, and physical chemistry are pretty nebulous. It's really interesting to see how many people jump between departments.
I'm not at risk of becoming a physicist OR engineer, but it's so good of those people to care like that ❤
I have a bachelor's degree in mathematics and only understood about 10% of this. I'd like to think that 40 years ago, when that degree was still new and shiny, that I would have understood more, but diffie-Q's and I have always had a difficult relationship. Still enjoyed the video though.
I'm glad other folks also enjoyed the comedy of Shankar's red QM book. Easily my favorite physics text from undergrad.
Ångström is actually ång and ström. Which means steam/vapor and river/creek. So it's steamyriver. :D
"My psis are starting to look like phis, but it should be clear from context" sounding more and more like a physics prof
Though I learned a lot through this video, the fact that the hydrogen atom is apparently bisexual blew my mind.
But seriously, hearing you gush about Shankar really warmed my heart. I have people in my own field of study that I feel that way about.
25:30 honestly, I thought it was just sloppy writing at first, but I like your upper left bracket notations to signify that you are multiplying everything on top. It doesn't change anything functionally, but makes it easier to kinda see whats going on in the equation a little bit quicker. Makes sense, im going to start doing it myself... if I go back into math... which I probably will
Another banger video. So good. If anyone is looking for another very funny and good QM text: check out How to Be a Quantum Mechanic by Charles Wohl. He taught QM at Cal for 40 years and has a really dry humor that permeates the book. 10/10
I love that your channel is blowing up
I have seen the documentary Chain Reaction and in it, it was made very clear that the Engineer was the true hero and saved the world. Also the Engineer was a no nonsense, salt of the earth working class blue collar lad and not some hoity toity university type! But somehow was working for a university. Im sure it makes sense stochastically.
Jokes aside that's the one with Morgan Freeman and Keanu Reeves right?
@@12pentaborane Yeah, don't think any sort of explanation is given as to why a cutting edge university physic project is using external blue collar machinists to engineer their experimental prototypes.
A good lab tech is almost as good as a glass blower.
Over an hour of physics from my favorite youtube physicist, nice!
15:24 that is eternally relatable except my version of hell would be listening to pseudohistory and pseudolinguistics forever with Great Man theories, weird tankie history, alt right history, Ural Altaic theory, Koreanic-Japanese language family, North Korea Did Nothing Wrong tankies, Park Chung Hee Apologia, Pro Japanese WW2 Apologia, Pop Roman History (lead pipes melt Roman brains), Jesus never existed /r/atheism, Library of Alexandria hysteria
That seems like too much even for hell...
You could have stopped at the 3rd sentence and it's still horrifying
@@3chl986 It's truly horrifying isn't it? add in the Heritage Foundation bros and the US Constitution Fetishists and it is truly the worst version of hell
@@jamesdakrn Sounds scary but maybe because I'm not American I can't really imagine what this is like.
But as a history enthusiast your list above was... too much
And the Library of Alexandria hysteria... Ugh
I'm Egyptian and the amount of misinformation is annoying
@@3chl986 if you’re egyptian
black Cleopatra is up there huh
😆😆
@@jamesdakrn oh no... I almost forgot about that 💔
Angela, i started watching you because your videos are very fun, entertaining, and have a good message. But this one in particular got my ass studying quantum again, and boy I am living. Thanks for the recommendation for Shankar.
I’m having a blast, and if not for you I’d probably be still mindlessly scrolling on TH-cam wasting my life even though it’s long since been my dream to more deeply understand the Schrödinger equation etc. so thank you 😊
I want to comment about engineering hubris. I am an electrical Engineer. I worked in nuclear power in the navy before I got my Engineering degree so my physics knowledge is broad but not technically formal,
Engineering is not seperate from physics. Engineering is the practical application of physics to achieve an end. My particular field is an application of the physics of Electromagnetism. A physicist with knowledge in that field can do what I do. A lot of engineers may just memorize simplifications and thumbrules to streamline the process or just copy and paste succesful designs but they dont have to,. Of course there is a lot of nuance with regulation and building code that a physicist might not appreciate, but in principle as an Engineer I see myself as the spokesman for the laws of physics.
There is also Engineering Technologist which is a person that implements a design that a full engineer mathed out. They dont need physics.
I think a competent engineer should be up to speed with the current physics knowledge of his field in my opinion. Engineers and physicists are the same animal. Just a different focus. One looks outward and the other inward.
I'm an Air Force pilot with an EE degree and I use physics to anticipate what control inputs are needed for landing. But so do all the pilots who don't know physics; they can land the plane perfectly as well, they just aren't aware of math describing why it works.
I found those comments truly disturbing. Engineering at its peak is something like the light bulb, the WD40, the DRAM, the cheap quartz watches. Basically bringing out top notch lab equipment from the ivory tower of science into the desolate life of everyday men. That list would not even close to Angela's list. I know great engineers, but they are not like "electrical resistance is always positive and why is it, could it be zero, could it be negative? Let's just spend the next 20 years to figure it out". If you are like that they despise you. How can they think the world is revolving around them?
Anyway, hearing "engineering is important" sounded a lot like when your dog huffs at you because you were unjust and then you two are sitting down together and you say to him he is a very important part of the family and you respect his feelings.
@@richardv.2475respectfully every engineering project is a physics experiment in the laboratory of the universe. Will this structure support its own weight? Yep....pbysical laws continue to hold, what is important? I only say engineering is the application of physics. I am an engineer who considers himself a physicist albeit not licensed and any physicist could be a great engineer. And any engineer worth his degree would love to push the boundaries of what we understand about the physics. Its engineering that got us to a transistor consisting a single atom of each material in the transistor, that didnt happen without some understanding of quantum level effects. Its physics. When you can use it as a tool we call it engineering when its just academic its called Physics. But its all physics. All the time. But what is important? That is a philisophical question that you get to make up your own answer to. I'm just talking about physics.
@@TheGarmisch no doubt. I am sure thst properly trained any person could also perform physics experiments and collect data while having no grasp of the material. I am only discussing the underlying nature of the work. How it is performed is up to the performer. I would rather be in the plane with you in an extreme emergency. Your knowledge of physics IS an edge. Would you rather the guy who buolt your plane had a working knowledge of physics? Or is it ok if he just looks up what equatioms to apply and copy pastes old designs? Both people are applying physics, just because one of them doesnt know it doesnt make that false.
@@TheJDanley that's a good point, I think you changed my mind on that a bit
I like your funny words, magic woman.
I don't understand a word of it, and am just listening to you because you're a super fun person. And I am procrastinating sleep.
The figure at 35:46 is why electrons are so gloriously weird: Some of those shells have multiple lobes (distinct regions of space). But the probability that a given electron, say Charlie, is in each of those lobes is nonzero. But the probability that Charlie's in between those lobes is absolute friggin' zero. So Charlie has to keep moving at infinite speed to bop back and forth between his lobes to make his time in each lobe match the probabilities. That's why a certain physicist calls these things "beables". They can't be called by a name thats already been used for something in our macroscopic world since they're simply a different kind of beable. (IMHO, that's the most beautiful word in all physics.)
(Truth in advertising: I'm a computer nerd and can't do the math, but I do enjoy watching you guys busting your butts.)
Hey, love your content! I think a video about the vacuum/zero-point energy problem could be really interesting!
It must've been nice to have fun while reading a quantum mechanics textbook. In my quantum mechanics classes, I used the Cohen-Tannoudji one (with some sprinkles from the Sakurai one), and I only ended up with tears, lots of tears. The silver lining is that this sentiment was shared by my friends who also took those classes.
btw, It is a fun exercise to do the whole calculation step-by-step; however, it quickly ceases to be enjoyable when you start working with the polynomials and normalization 😩
your videos are very relaxing and enjoyable, love the funny tidbits! thanks
I love how this video serves as both a lovely informative video on the history of how we use quantum mechanics in application to the Hydrogen atom as well as a cheat sheet to the derviation worksheets (though tbf, for this particular problem there are plenty of other cheat sheets out there and a lot of the nitty gritty like converting to spherical polar coordinates from cartesian that would be in the worksheet is moved quickly through)
38:09/38:16 - I didn't even attempt to understand the math, but being around to have it left as an exercise to the reader made listening through (instead of skipping) totally worthwhile, in my book. Because yeah, I can relate to wanting to do that... and so it brought me joy that you got to. :)
Watched 40 seconds so far and the mood, the coffee, I’m here for it. It’s giving… I’ve got a headache and the world is on fire but fuck it let’s measure some atoms.
I love how you address the meaning of physics behinde the math. I learned how to do the calculations, but never got an explanation about the meaning.
I'm learning the Hydrogen atom right now in undergrad QM1 so this is such a fun video to watch
You have been able to pull a non physicist out of the fuzzy world of general science writing up to an actual sense of understanding the origins of the math behind quantum mechanics. Thanks.
"...and then she wandered over to another campfire and they were discussing whether or not the universe is a simulation. And at yet another, Tom Bombadil."
you don’t have to apologize for talking long about science to people who knowingly clicked on a video where you talk for long about science. We know and you’re awesome.
Love the video! A couple questions circling back to the problem at the beginning:
1) if you had an isolated hydrogen atom, with no other matter or light interacting with it, would the wave functions describing the electron and/or the whole atom be static, or do they change over time?
2) if the wave-function for the electron were not spherically symmetric and it was changing over time, would that produce a photon as expected of an accelerating charged particle?
Interesting questions you ask. I think I can speak to the first one: the typical definition of "isolated" may be counter-intuitive...
If you have a hydrogen atom out in vast empty space, there is a continuum of quantum vacuum fluctuations which would all contribute to pushing the state of the hydrogen this way and that way. In the case that the atom is in some excited state, these fluctuations tend to promote spontaneous emission and relaxation to the ground state (the "stationary" nlm = 200 state typically lives for a few nanoseconds).
If you want to suppress this effect, the trick is actually to put the atom in a tiny box. This reduces the number of electromagnetic modes which 'see' the atom, so there are fewer vacuum fluctuations that jostle the delicate excited state, and you can prolong its lifetime.
Being out in vast empty space is sort of like being in a really big box, which can support a higher density of electromagnetic modes.
Here's some related reading:
physics.umd.edu/courses/Phys371/AnlageSpring17/Chapter_3_CCR_16_Modes_of_Oscillation.pdf
(PS: putting a superconducting qubit in a small shielded box is crucial for prolonging its lifetime).
As for the 2nd question, I have less experience thinking about that one, but I think you'd want to consider precisely what you mean by "not spherically symmetric". There are eigensolutions (stationary modes) of the hydrogen atom which are not spherically symmetric (i.e., look the same when you rotate them by some arbitrary angle), and they also don't radiate (if you ignore the whole spontaneous emission part discussed above).
Now, one could construct a non-stationary state of the hydrogen atom which was not only 'not rotationally symmetric' in the sense I've defined, but also lacked any sort of symmetry in reflection, discrete rotation, etc. I can't say for sure as I'm not an expert on the question, but I could imagine such a situation would sort of break a wave interference condition which was otherwise prohibiting radiative effects.
I'm picturing a sort of hydrogen-atom-potential version of the discussion of superposition states of "particle in a box", where sums of stationary states result in a non-stationary state.
en.wikipedia.org/wiki/Particle_in_a_box
...but maybe someone closer to the subject can chime in.
You have one of the coolest science channels.
I have never watched a whole math lecture before. Even in business school. Omg calculus trauma is real
Yeah absolutely
Do you know any other science channels that are like that?
I know a lot of math channels, and some physics. Wanted to find something for chemistry but.. can't
And I mean with a scientist/ someone who's passionate about a subject
Not the ones with just voice overs or even ai ugh
@3chl986 There aren't Many. On this level I have only found Sean Carroll and Futurism with Issac Authur.
Up an Atom is good. But she likes to make people's brains explode with how complex the topics are.
Physics girl was good, but very Bill Nye level. Hope her channel comes back though.
Sabine used to be good? but she is now doing the most horrible John Stewart impression of comedy physics. She is unwatchable now.
I forgot Kathy her channel is good.youtube.com/@KathyLovesPhysics?si=qDyfTv9x-92jR4Cv