Some light quantum mechanics (with minutephysics)
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- Опубликовано: 12 сен 2017
- The math of superposition and quantum states.
Minutephysics channel: / minutephysics
Help fund future projects: / 3blue1brown
This video was sponsored by Brilliant: brilliant.org/3b1b
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: 3b1b.co/light-quantum-thanks
Huge thanks to my friend Evan Miyazono, both for encouraging me to do this project, and for helping me understand many things along the way.
This is a simple primer for how the math of quantum mechanics, specifically in the context of polarized light, relates to the math of classical waves, specifically classical electromagnetic waves.
I will say, if you do want to go off and learn the math of quantum mechanics, you just can never have too much linear algebra, so check out the series I did at • Essence of linear algebra
Mistakes: As several astute commenters have pointed out, the force arrow is pointing the wrong way at 2:18. Thanks for the catch!
*Note on conventions: Throughout this video, I use a single-headed right arrow to represent the horizontal direction. The standard in quantum mechanics is actually to use double-headed arrows for describing polarization states, while single-headed arrows are typically reserved for the context of spin.
What's the difference? Well, using a double-headed arrow to represent the horizontal direction emphasizes that in a quantum mechanical context, there's no distinction between left and right. They each have the same measurable state: horizontal (e.g. they pass through horizontally oriented filters). Once you're in QM, these kets are typically vectors in a more abstract space where vectors are not necessarily spatial directions but instead represent any kind of state.
Because of how I chose to motivate things with classical waves, where it makes sense for this arrow to represent a unit vector in the right direction, rather than the more abstract idea of a horizontal state vector, I chose to stick with the single-headed notation throughout, though this runs slightly against convention.
Music by Vincent Rubinetti:
vincerubinetti.bandcamp.com/a...
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with RUclips, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: 3b1b.co/recommended
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after a month, the Bob Ross of math is back
You have no idea how much this comparison tickles me.
"... and you just, heh... teach the devil out of it."
I have to say,your voice is smooth
"Let's represent some haaappy little numbers."
3Blue1Brown it means you have cool hair.
No lie without the animation I would be totally lost. Such a powerful tool for education
Praise manim
Exactly, makes me wonder how people learned this stuff back in the day
It would actually be amazing if you did a video series explicitly going through Maxwells equations, their meanings and derivations! More physics!
Please.
Yes please
Plaseeeeee
OH MY GOD YES an Essence of Electromagnetism would be an amazing mathematical topic for Grant to cover! :D Especially with his more recent video about divergence and curl, both of which show up in Maxwell's equations!
hella
THANK YOU both for finally making an accessible video on QM that actually dives into the mathematics instead of just saying "wow QM is weird! Look, the cat is alive AND dead! A zombie!".
You are a gift to the divulgation of science, people need to know what physics really is. Keep up the good work.
Yes interesting theories and some are correct as far as we care, but he just laid a extremely complex example and honestly if you want to learn then look at how it’s used for computation
I couldn't agree more with you!
Agreed, I found the mystification of quantum mechanics off putting as a teen because I felt it surely couldn't be right the way they explained it - as a maths graduate, it's nice to look back and watch/read stuff like this and think "ohh, that's what they meant".
Holy crap...
I finally understand (a bit) what polarization *actually* is.
Really? It's still a mystery to me. How a single photon (one wave) could be circularly polarized? It has two electric fields now? And in contrary if Spin is a measure of circular polarization, is linear polarization is a superposition of two photons? It was not clear back in 2014 ( arxiv.org/pdf/1407.2605 ) and I'm not sure it is today.
Sorry, I just copy here the abstract:
A single photon is well known to have spin S = ℏ, which would correspond to circular polarization, and all quantum transitions with photon absorption or emission correspond to ΔS = ±ℏ. However, it is also widely believed that a single photon may be linearly polarized, which would correspond to a state with S = 0. Indeed, linearly polarized single photons are central to most quantum entanglement experiments. On the contrary, it has recently been suggested (based on a realistic spinquantized wave picture of quantum states) that a linearly polarized photon state must be a superposition of a pair of circularly polarized photons, each with S = ±ℏ. This question cannot be resolved using a conventional photon detector, which generally cannot distinguish one photon from two simultaneous photons. However, it can be addressed using a superconducting microcalorimeter detector with sub-eV energy resolution and high quantum efficiency (QE). A careful experiment demonstrating this photon pairing could place in question some of the paradoxical central foundations of modern quantum theory, including quantum entanglement and nonlocality.
LazerLord10 +
Waaaaiiiit.... I thought a photon was only ever had a spin of 1. Now I'm confused lol.
Euquila, the spin is measured in ℏ. Kind of like how you measure a number of atoms in moles instead of regular numbers. So photons have a spin of either 1 ℏ or -1 ℏ in any direction you measure it in.
Golden age of online education
More like only the beginning
Unless Grant tragically dies tomorrow
@@ASLUHLUHCE way to ruin the mood
True
Most of people on earth still doesn't even have acces to internet. The internet is in fact just a pile of junk that nobody care about unless you are a fool.
Hey, i don't know if you're going to read this, but here it is. Me and my friends are graduate students in physics, we live in Brazil and we ADORE your videos. You really helped us how to understand a bunch of stuff ( the topology videos are amazing, thank you for that ).
I guess you'd like to know that your work is recognized here in Brazil. Everytime a new video is launched, we watch it with the excitement of a game of thrones episode.
So, this is it. Thank you for this incredible work, and always remember you fave a bunch of brazilian physicist fans.
Abraços!
+Protein Computer I'm touched, thanks!
14:50 - 15:38 blew my mind.
Such an eye-opening moment! Incredible what the two of you are able to explain in a 22min video!!!
This is just beautiful.
I'm in grade 5 and watching this randomly and understand a little bit of it.
-> Super-informative, serious maths and natural science content.
-> "Clicky stuffs"
Gets me every time.
:P
18:33 The smoothest transition from Classical to Quantum Mechanics I've seen in a while: "Square of amplitude of a component shows percentage of total energy vs probability of measuring the total energy."
yes that's why they are called "transition amplitudes" - check out Olivier Costa de Beauregard. " Space, Time and Probability Calculus " - lecture by Professor Olivier Costa de Beauregard, on September 1986, Colorado State University.
3blue1brown says that he might make a video on maxwells equations
Me: I NEEEEEEED IIIIIIIIIT
YEEEEEEEEEESSSSSSSS
@ ??
And again I'm left speechless. Awesome video, hoping to see this become more of a series because this is by far the best introduction to quantum mechanics video I've seen until now
Lakshay Modi eww, a squan.
For those of you who want to start learning quantum mechanics, I highly recommend the MIT course 8.04, by prof. Allan Adams. He's an amazing lecturer, and explains the topics with clarity and enthusiasm. The first few lectures are quite accessible, and they get progressively more advanced. Challenge yourself and see how far you're able to get. Link:
ruclips.net/video/lZ3bPUKo5zc/видео.html
If you want a more intermediate-level crash course, I recommend the videos by viascience, a youtuber who definitely deserves more attention: ruclips.net/user/viascienceplaylists
Pulsar77 Thanks - I'll definitely check them out!
Cecil Khokhar I think he means MIT Open Course Ware. You can find the lectures on RUclips or their website.
I second the shout out to viascience. His videos are extremely well done, and taught me loads about QM.
Thanks so much!
Wow thanks
I'm about to take quantum mechanics at the graduate level and this video cleared up so many questions I had as an undergrad in physics. Great job Henry and 3B1B!
I have come to the realization that I am actually learning things at university. Just began to understand complex numbers when I saw how they could form an equation to describe photon waves in this video. I am understanding!
So grateful we have access to resources such as this video online.
You're famous now
wow, this is a really great video. that's all i can say really. it's just so well done.
Agree!
you know what? removing the words from minutephysics will make the video even better because it will be more concise without losing any information.
@@tzhang1 I don't since both are good and the partnership is even good.
How do you do such amazing graphics? The fields blew my mind!
Composing Gloves if you check eugene physics video you will know meaninf of education and animations
I think the author uses out-of-work animators to do it by promising access to dark and terrifying powers..
github.com/3b1b/manim
He has made his own software in python. U can visit his website for more details about the software. It's free for everyone use but is not very well documented.
its because he got brilliant
This is the first time I actually understood (slightly) a video on quantum mechanics. You have earned yourself a grateful subscriber.
The Minute Physics video was interesting, and provoked a lot of interesting questions.
This video was intimidating, but ultimately managed to answer a lot of those questions in a surprisingly simple and approachable way.
Great job, guys! I learned a lot of really interesting stuff from these videos.
I love how your videos do not stray from the nitty gritty details. This is what makes your channel unique amongst most science/maths channels.
I am so thankful that you guys explained electromagnetism in the way you did, I never understood why there was a 90 degree angle to them for instance, I just thought that's the way they draw it. So eye opening.
I've been asking myself for years how introducing a third polarizing filter in between polarizing filters that cancel out each other makes them not to cancel. For me it was black magic, but it makes complete sense now.
And the fact that perceived intensity (amplitude) is the result of full amplitude turned on and off based on probability just works so well with the idea of energy being transferred in discrete steps and discrete amounts.
There's also another nice perspective on the subject. That is, because the Plank constant is so small compared to our perception of the world, the polarized filters could actually be called "temporal (quantum?) dithering filters", as what they do essentially is acting as on-off switches with a probability.
However, since the transfer speed of discrete quanta is so high, we perceive that probability as continuous intensity modulation and this is the very basis principle behind dithering.
THANK YOU FOR GOING OVER MY HEAD. Seriously. I'm not yet capable of reading the academic research papers, but I'm bored of science videos that are not challenging. Videos like this one are perfect for me. I have to go back and re-watch it several times and take notes just before it makes sense, yet I don't need to take several semesters of courses just to recognize the terminology. Time permitting, I hope to move on to the courses recommended in this video as the best follow-up. Thanks again for the challenge!
Omg, why have I not found this channel before? I had like 10 mind blown-moments, and I feel like I understand so much more now! I'm definitly subscribing
My education was a scam
Did you go to Trump University?
FAKE COURSES !
w
@@jamescollier3 If he had just put all the money he got from his Dad in a trust fund and never touched it again, he would have twice as much now. The guy is a blithering idiot.
@@Kalumbatsch Give stats in support of your comment.
I completed my degree in astrophysics a couple of years ago and i can honestly say you are able to convey the subject 100x better than the lecturers i had. If this video was available years ago it would have saved me so much more time.
Well Done!
Hello there
i never really understood before why people got excited seeing their favourite youtubers in the comment section - but now i got it. You are awesome sir. Stephen Welch - you are awesome.
Thanks
I like how he just offhandedly gives a better explanation of magnetic and electric fields than I got in all of college. Thanks for that!
omg 3b1b AND henry ?? I must be dreaming
Maybe Not?
I think this is the first video where Grant used his python lib to animate 3D stuff.
Looks absolutely gorgeous eye candy. I can't get enough of it.
Didn't he used it in the topology video ?
Usually for 3d things, I've been using Grapher (which comes built into osx).
onch onch
Honestly, guys, I have no words to describe how good your videos are..... I wish I had this stuff available when I was approaching quantum mechanics back in the days.... good job!
Few weeks after writing an exam on this and it's so nice to see what textbooks and lectures present in a somewhat cold manner, in an intuitive and visual way. Mandatory thank you for helping me pass Calculus and Linear Algebra in the previous years!
I feel like this video was better at explaining (to me) what was actually going on, which is what I really wanted from all of this. I look forward to watching more of your videos... when I'm not supposed to be working.
this is honestly one of the best physics videos on the internet. so beautiful.
The video was absolutely brilliant. I usually do not comment on videos, but the quality with which the content is made, I couldn't stop myself from actively praising it. Keep up the good work. And a ton of thanks as well!!!!
Thanks a lot for this video- I feel like I might be rewatching this a couple of times in the future, seeing that it ties so many concepts elegantly together.
I haven't even finished the video, but I gotta say . . .
Grant, you've done it again! Another amazingly eloquent dive into such a dense topic. You are awesome!
Easily the best video I've seen on the relationship between the EM wave nature of light and the probabilistic wave nature of light. Even better than my quantum teacher dude. Right on.
Let's appreciate this guy for not doing a clickbait Quantum physics video
Amazing. This video has been so helpful. Three or four times, I've done the 'Wait, what? Is that why that happens?' and then repeatedly replayed those few seconds of calmly delivered insight. And I'm only half-way through. Great job, guys. Do keep them coming.
Grant I love your videos so much. As an engineering student with a passion for learning I feel so lucky to have such brilliant educators teaching me the kinds of things I want to know, but aren't related to my work enough to be covered in lectures.
❤️ 3Blue1Brown ❤️
These 20 minutes flew in an instant!! Excellent video, please make more on Quantum Mechanics.
Amazing video. As an amateur, I've been wrestling with some quantum concepts for years. At 15:09 in this video the penny dropped. With a clang! Well done Henry and 3Blue1Brown. Truely excellent work.
Finally ! Someone explains clearly and simply the relationship between classical energy and quantum probability. This is the first time a see this explanation so clearly, this clarity and this way to go to the First Principles of things is typical of 3Blue1Brown. As I always say in my comments in this channel, I wish I'd had a teacher like this back in my college days, he would have saved me literarily hundreds of hours. Thanks a lot 3Blue1Brown !
I am currently planning out my math major. Your videos are so encouraging because I finally feel like this language I have spent my entire college career focusing on gives me the ability to understand a broad spectrum of fields. It's like spending ten years memorizing Italian in your basement then moving to Venice, fully immersing yourself in the vibrant, inspiring culture. I am truly thankful for people like you both, that dedicate countless hours to math and physics so that people can learn on a well organized and clear way. RUclips really is a wonderful platform.
Wow, I was actually blown away by the fact that superposition is just a composition of vectors in Linear Algebra. In fact, I was surprised that I had all the basic mathematic tools to understand the basics of this quantum mechanics effect, but never did (I'm an electric engineering student). I think now I finally understand the Schrodinger's cat idea, something that has become so widespread like E = mc², but not easy to explain.
All I can say to both of you is: thank you. Thank you for the amazing quality of your videos.
Oh, and awesome collab, hope you two make more videos together.
The basic postulates of quantum mechanics are extremely simple to understand if you know some elementary linear algebra! I've honestly played board games that are more complicated. The problem is that if you don't know any linear algebra, you have to rely on simplified, and sometimes downright misleading, analogies that are horribly vague and leave you feeling even more confused.
@@carloshoratio5100 That's the problem, really. Most people don't know linear algebra, and really everyone should since it comes up everywhere in pretty much every field with any kind of physical interpretation or measurement.
@@carloshoratio5100 Can someone clear my doubt,
If |a> and |b> are two basis states and the prob of both the states is 50% then we denote the total state of the e- as either 1/√2(|a> + |b>) and 1/√2(|a> - |b>). My doubt is, that the e- can also be in 1/√2( - |a> + |b>) and 1/√2(- |a> - |b>). Then why do we ignore these two states.
Ruchi You can't deduce the superposition of base states from its probability of wavefunction collapse. That is one of the most fundamental things of quantum mechanics and its part of the reason why it has some weirdness to it. To find out the actual wavefunction superposition, you need to solve the wave equations.
Actually, I disagree. I would argue that Schrödinger's cat, while popularly being weirder than E = mc^2, is easier to understand. Because as others here said: it can be very easy explained by simply talking about waves and their amplitudes, and then talking about how this translates to probabilities instead of energy. It only takes some linear algebra to understand, and you don't need to go through the entire quantum-mechanical framework to explain it.
Meanwhile, it isn't possible to talk about E = mc^2 and explore it further without going over the entirety of the theory of special relativity from scratch. I mean, yes, fundamentally, all the equation means is that a bodies energy at rest is proportional to its mass. That's very simple, but that's no deeper an understanding than the very overly simplistic misrepresentation that the mass media has given to Schrödinger's cat.
The thing about quantum mechanics is that while the math is more difficult, dissecting each concept on a qualitative level is far easier. Special relativity, on the other hand, has much simpler math, but actually dissecting the concepts qualitative is much more difficult if you can't discuss the theory in its entirety.
Incredible work on this. Thanks for creating, posting, and being great!
First time in this channel and let me say sir. I'm impressed by how clearly you explained the subject. I wish I had a teacher that explained as clearly as you. Now I'm eager to see your other videos.
This is quite brilliant. I took a year-long course my senior year of college on Quantum Mechanics. I always thought a bunch of the stuff we learned had "quantum weirdness" that couldn't be seen elsewhere. Never was it pointed out to me that you actually can see some of these effects macroscopically with waves like that polarized light experiment.
All hail to an original and very effective alternative to the historical approach to introducing this difficult subject. Huge effort no doubt, many thanks.
I can't emphasize how helpful this video was, keep up the good work guys!!
I swear, it’s addicting to watch this stuff. As a science nerd myself, I really like your content.
In the animation for the magnetic field (2:20) I think the vector Force is pointing the wrong way if the particle a positively charge, which it is.
Yeah you're right, I'm surprised they overlooked that. But they probably don't care, the point was only that the force is perpendicular, not in which direction it points exactly.
I think you're right. Up to the top!
When he tilted the magnetic field plane, the animation for it is such a clarifying visual. I love it, great work 3b1b!
Another small mistake is the angle phi_beta at 10:30, by convention they go counterclockwise like phi_alpha. (and again at 20:10)
Could be negative if the range for the argument is [-pi, pi] (which it usually is), in which case the diagram would make sense.
Actually, the force is pointing in the correct direction. The animation depicts a negative particle, so in the equation shown on screen q is negative. That means q*v (aka the electrical current I) is a vector pointing in the exact opposite direction from v itself. Take the cross product with B and your resulting vector points upwards, as shown :)
It's scary and almost frustrating, how often I tend to come back, just to see how little I understand of anything, because I'm always missing something more fundanental... non the less, great video, great collab!
Both of these videos just blew my mind! Thanks guys!
18:47, finally understood this concept. It is usually never said explicitly. Thank you!!
It's hard to describe the shear magnitude of happiness that I get from videos like this
What an epic collaboration to land. This needs to happen again
I really appreciate this. So frequently in pop science, and even in my actual physics classes in college lumped together wave mechanics and quantum mechanics, and so there was a lot of confusion about what exactly Quantum stuff is. Like the Heisenberg uncertainty principle for example, which you already did a video in this spirit on.
Thank you! This answers most of the questions I've ever had about quantum mechanics but didn't know where to ask
I remember in physics class being extremely confused about how a diagonally slanted polarizing filter could turn horizontal light into the diagonal direction. I remember seemingly everybody thought it was just "obvious" and even the teacher made it sound like it wasn't anything too special.
Honestly refreshing to know that my suspicion was 100% correct. It was especially annoying because this question was given to us on a test without the teacher ever explaining it.
@Niels Kloppenburg @Allen Finn Isn't that just projection? Like a dot product between 2 vectors: if they are perpendicular to each other, then you cannot project one onto another and the result is zero. However, if they are not, then you can do this projection. Same thing for the filters.
@@xnqmap or driving into a wall vs a gradual turn to 90 degrees? Am i in the incorrect 'obvious' camp?
How come I didn't know this channel before the minutephysics cooperation...
got yourself a new subscriber.
I'm so jealous, now you are able to watch every single video of him for the first time.
Love your work! Awesome explanation and visualization as always
This video does a great job of answering the questions brought up by the minutephysics video. For example, after watching the first video my first questio was about angles of light that wern't exactly perpendicular to the filter or whose instantaneous amplitude was zero at the point of contact with the filter.
Another excellent video! Thanks. It has triggered new ways for me to interpret some of this stuff :-)
I would love more of these QM videos! This one was so good, I was sad when it ended :(
This video is absolutely amazing! Thank you for the great content time and time again! WE WANT MORE!
Amazing video! I love how well structured it is. It really made me understand the topic in a way i never did. Thanks a lot!
Also I am so looking forward to the neural network video. In my opinion you could do a whole series on that. Its an incredibly fascinating topic and very relevant today and for the next few years.
Can I like a video multiple times? I hope you'll do more physics videos in the future!
Please make some videos on Metric space , Vector space Normed Linear space, Inner product space , banach space and Hilbert space and their co-relations . Because its tough to realize/imagine them and their physical significance.
I used to watch these knowing nothing about math. Now it hits different.
It felt like all of my confusions in EMT and QM forced the universe to make this video....This was very well put together and has so many amazing insights and unimaginable simulations. Thank you so much guys for making this :) I tried to squeeze away every bit of knowledge from this :0
Amazing video.
It's a pleasure to receive 3 blue 1 brown notification
16:30 This phenomenon has stumped me for years! Finally, someone explains it clearly!
I am studying Physics (and Maths). This semester is about waves and quanta. I gotta say your and Minutephysics collaboration has helped me alot at cementing my knowledge. Even though, there is still alot else to learn, watching your viedeos was definetly worth it. I am happily looking for more.
Greetings from Germany
how do you know EVERYTHING so well??!! being able to communicate things this clearly, you're better than Feynman...
Quantum mechanics Lite vs Quantum mechanics Pro 😁
TMR Teckk You mean "Light" and "Proton", right?
If lite is this good, I'll totally buy the pro version!
Richard Gerst Dayyyum
Pho.
Wow. Thanks again for sharing your clarity of thought! Your videos are a hugely valuable resource.
This is incredible, exactly what I was looking for to explain the deeper meaning of quantum mechanics
This was totally awesome. If you collaborate with "Looking Glass Universe" too it would be a masterpiece!
MY TWO FAVORITE CHANNELS ARE DOING A COLLAB
AM I DREAMING OR WHAT?
Not dreaming :)
minutephysics
...or he's dreaming AND not dreaming.
Ankush Menat 1/sqrt(2)|dreaming>+1/sqrt(2)|!dreaming>?
Next would be a collab with Kurzgesagt, then my life would be complete.
Minute physics answered. You're totally dreaming.
Thanks for this great video!
To be honest, I didn't really understand the arguments that were being made in the MinutePhysics video, but this explanation worked for me :)
woooow! i'm loving all these videos! :D great work @3blue1brown!!
I wish we had such videos when we were doing our degrees all those years ago..
Friday has come early!
good point. I'm interested why he posted it earlier. Is Thursday Minutephysics upload day?
HOLY CRAP YOUR CHANNEL WAS MY CHILDHOOD
I loved that video may be there are some bits that I didn't grasp very well but over all I started to get a sense of the maths behind quantum mechanics
This video explained so much about QM. THANK YOU! I'm looking forward to the day you will explain the decoherence / many worlds interpretation of this same experiment as well as you have explained the Copenhagen one in this video.
I wish henry would stop distracting grant from essence of probability
Yeah! It's *totally* Henry's fault :)
well, QM is kinda related to probability, so... prologue?
I wish more videos for essence of linear algebra
I'll make videos as quickly as I can without compromising the underlying goals of the channel. Sometimes they just take a while. These last few months I've had an unusual number of trips and other things going on, so you should see more frequency in the coming months.
xXxAwesomesockxXx Go into math; start studying immediately! Math is tough, and the earlier you start the better off you are later. Download Scripts on Analysis I and Linear Algebra I and go though the stuff to see if you have what it takes, good luck!
15:36 "Dead or Alive ... Horizontal or Vertical" ... I laughed so hard.
Wait, why is this funny?
Ok, this video is amazing! The concept of polarization and superposition is actually starting to make sense to me now, for the first time. I watched the minutephysics one first and was rather confused, because I was too focused on thinking of light as a classical particular. This video makes everything a lot clearer. It also helps that I've now had 2 semesters of linear algebra and differential equations. All these physics videos I watch make more and more sense the father along I go in math education. Seriously, if you want to understand physics, you've gotta learn the math. I've learned that the hard way.
This, and exactly when MITx 8.04.1 started on edx (same day, actually). What a treat! You guys are awesome!
I am pleased to see that you've entered the realm of Physics with this video.
Thanks to you, I can now show off to my fellow internet neckbeards that I am indeed a smart person who knows Quantum Mechanics (even though I only have a rudimentary understanding and am only pretending to be smart to woo m'lady).
Faculty of Khan thanks to you too! I love your videos
This video wasn't even on Quantum mechanics. It just discussed polarization of light.
Wow, in 40 minutes of watching RUclips I learned more about quantum mechanics than in 12 years of school.
K-12 doesn't teach quantum mechanics for obvious reasons
@@Seboobdalla high school chemistry attempts to in a really crappy way that doesn't explain any underlying phenomena and only covers electrons in an atom
3B1B, this was a stellar video. It would be cool to see more collabs with MinutePhysics!
One more time an excellent video from an excellent channel, keep up with the good work ! This video was once again mind blowing !
Can you do a collab with looking glass universe
I think that'd be a lot of fun!
I think it would be great
Ruby Gupta he's a little crazy
If you can't explain something easily, it means you don't understand it enough, 3Blue1Brown explains quantum mechanics like it's elementary algebra. I love this channel, and you are a very smart man !
Amazing video, I loved your computer graphics and minute physics sketch together
As someone who has taken years of higher math and classical physics since last visiting the ideas of relativity this was incredibly fascinating. Thank you for arming me with something more than the cat allegory I learned in high school.