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
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".
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.
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.
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!
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!
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.
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.
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!
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
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.
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.
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: ua-cam.com/video/lZ3bPUKo5zc/v-deo.html If you want a more intermediate-level crash course, I recommend the videos by viascience, a youtuber who definitely deserves more attention: ua-cam.com/users/viascienceplaylists
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!
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 :)
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.
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.
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
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 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.
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!
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. UA-cam really is a wonderful platform.
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.
Thank you so much for this amazing video.... the stuff u teach is genuinely mind blowing to me. Im so glad that i stumbled upon this legendary channel. The best one of this platform fr
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.
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 ❤️
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 !
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!
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.
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.
All hail to an original and very effective alternative to the historical approach to introducing this difficult subject. Huge effort no doubt, many thanks.
@@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.
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.
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.
Along with the minutephysics's video, this is the best intuitive explanation on the Bell's theorem I've seen. For me the aha moment comes at 16:19. Mind-blowing! Thank you!
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!!!!
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!
I wanted to take the time to thank you Grant for all your educational videos that inspire me so much to understand problems I'd never understood before. You've been such a help in the understanding of many mathematical concepts, and I just wanted to say I'm grateful for you and all the other educators on UA-cam. I hope you have great day :)
The explanation of the Venn Diagram Paradox presented so beautifully in your other video is actually clearer for me in the brief description given here, starting around 16:10 (and based on understanding the couple of minutes shown just before). Anyone whose head is still aching after watching the Venn Diagram video should definitely watch this one. The realization that ALL of the photon's quantized energy must change its polarization to the diagonal state after interacting with filter B - and will therefore have a different interaction with filter C than we would predict from a purely classical perspective, is the key. I wish you would add this conclusion just as succinctly to the other video. That said, these video are fantastic and I'm yet another deeply appreciative admirer.
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 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).
I studied quantum mechanics in both a physics class (half a quarter) and when I took physical chemistry (a full quarter.) You have been able to explain the concepts far better than any professor or grad student I've ever had. The Internet is very lucky that this is how you have chosen to spend your time, and I hope you are proud of the work you are doing. You are the Carl Sagan of mathematics.
@@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
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'm recommending this video to all quantum mechanics students. I wasn't taught the connection between the math and the actual physical phenomenon but this vid makes it so easy like I thought it was supposed to be.
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
Brilliant is excited to continue supporting 3blue1brown's explanatory videos, and supplement them with our problem solving courses. Help us support him - brilliant.org/3blue1brown/.
Calvin Lin ,,can u please make some videos on vector calculas?E.g.Grad,, Divergence,,Curl specially,,this is only place in youtube where I can understand all the fundamentals,,probably because of your high quality graphics of the videos,,whatever it may be,i am your big fan,so please make some videos on vector calculas
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
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 !
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!
@3blue1brown I (personally) am very grateful to your for posting such wonderful animated math videos, and this collaboration from @minutephysics was much required for amatuers (like me, who just learnt some vector algebra and calculus) to realize how exactly the math behind quantum physics works.
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.
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.
Around 17:45 I realized that cosine is just sine with a co tacked onto it. It's so simple and obvius that I never noticed it before! It totally blew my mind!
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.
Sadly, formal Maxwell's equations nowadays are introduced by Heaviside, who is a true genius invented vector calculus and simplified lots of content in electromagnetic theory..... The original Maxwell's equations are horrible. and almost no one know him
Maxwell used Hamilton's Quaternions (a generalization of complex numbers in three dimensions) in his formulation of electromagnetic theory (organizing the experimental results of Faraday, Oersted, and many others), because there were no other approppiated mathematical entities for the task at the time. Several decades later, Gibbs simplified quaternion theory into vector calculus, without considering it a theory on its own right (he just wrote a thin pamphlet not intended to be published, but used by his pupils only!) By the same time Heaviside reformulate Electromagnetic Theory with the new vector tools. So, is rather unfair to say that Heaviside or Gibbs invented vector calculus by their own... But you (and Jeff Ahn) are definitely right when you say that both men and their contributions to physics (and mathematics!) are severely underknown. Sorry for my English, it's not my native language.
Wow this is incredible! I know about this guy from his work in mathematics, but I had totally forgot he was the one that made the jump to vector operators in Maxwell's equations! Am so glad you shared this, this is the kind of work I hope to be able to accomplish in my career. Edit: Just read a bit about him. I think this man might be my spirit animal. :^)
You're right, my apologies. I guess writing "(a generalization of the complex numbers in order to model 3d space movements using 4 parameters)" would've been more accurate? This is not a trick question, I'm genuinely interested.
Holy shit years late but im a polarimetrist and this has to be the best intro for physics students to that concept and how it relates to quantum I've seen. Going to point students here.
No, not really. Wave mechanics was a different thing altogether from which quantum mechanics originated. And one of the earlier interpretations of quantum mechanics pre-QFT was pilot wave theory, but this is a very different thing.
@@angelmendez-rivera351 de Broglie considered his greatest discovery to be the "Law of Phase Harmony" - a good article on this is "Light is Heavy" by Nobel physicist Gerard 't Hooft.
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.
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
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.
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.
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.
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!
Perfeito job
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
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.
Golden age of online education
More like only the beginning
Unless Grant tragically dies tomorrow
@@ASLUHLUHC3 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.
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!
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.
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.
-> Super-informative, serious maths and natural science content.
-> "Clicky stuffs"
Gets me every time.
:P
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
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:
ua-cam.com/video/lZ3bPUKo5zc/v-deo.html
If you want a more intermediate-level crash course, I recommend the videos by viascience, a youtuber who definitely deserves more attention: ua-cam.com/users/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 UA-cam 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
This is the first time I actually understood (slightly) a video on quantum mechanics. You have earned yourself a grateful subscriber.
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 :)
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.
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.
3blue1brown says that he might make a video on maxwells equations
Me: I NEEEEEEED IIIIIIIIIT
YEEEEEEEEEESSSSSSSS
@ ??
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'm in grade 5 and watching this randomly and understand a little bit of it.
Hi bro you too smart
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
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 like how he just offhandedly gives a better explanation of magnetic and electric fields than I got in all of college. Thanks for that!
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.
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.
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!
this is honestly one of the best physics videos on the internet. so beautiful.
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. UA-cam really is a wonderful platform.
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.
Thank you so much for this amazing video.... the stuff u teach is genuinely mind blowing to me. Im so glad that i stumbled upon this legendary channel. The best one of this platform fr
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
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 ❤️
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 !
These 20 minutes flew in an instant!! Excellent video, please make more on Quantum Mechanics.
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!
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.
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.
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
I used to watch these knowing nothing about math. Now it hits different.
I swear, it’s addicting to watch this stuff. As a science nerd myself, I really like your content.
All hail to an original and very effective alternative to the historical approach to introducing this difficult subject. Huge effort no doubt, many thanks.
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.
after a month, the Bob Ross of math is back. Holy crap...I finally understand (a bit) what polarization actually is..
It's hard to describe the shear magnitude of happiness that I get from videos like this
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 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?
Along with the minutephysics's video, this is the best intuitive explanation on the Bell's theorem I've seen. For me the aha moment comes at 16:19. Mind-blowing! Thank you!
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.
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!!!!
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.
18:47, finally understood this concept. It is usually never said explicitly. Thank you!!
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!
I wanted to take the time to thank you Grant for all your educational videos that inspire me so much to understand problems I'd never understood before. You've been such a help in the understanding of many mathematical concepts, and I just wanted to say I'm grateful for you and all the other educators on UA-cam. I hope you have great day :)
I’m taking wave mechanics this semester and I think I learn more in this video then my hole semester😅
The explanation of the Venn Diagram Paradox presented so beautifully in your other video is actually clearer for me in the brief description given here, starting around 16:10 (and based on understanding the couple of minutes shown just before). Anyone whose head is still aching after watching the Venn Diagram video should definitely watch this one. The realization that ALL of the photon's quantized energy must change its polarization to the diagonal state after interacting with filter B - and will therefore have a different interaction with filter C than we would predict from a purely classical perspective, is the key. I wish you would add this conclusion just as succinctly to the other video. That said, these video are fantastic and I'm yet another deeply appreciative admirer.
Can I like a video multiple times? I hope you'll do more physics videos in the future!
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 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.
Let's appreciate this guy for not doing a clickbait Quantum physics video
It's a pleasure to receive 3 blue 1 brown notification
I studied quantum mechanics in both a physics class (half a quarter) and when I took physical chemistry (a full quarter.) You have been able to explain the concepts far better than any professor or grad student I've ever had. The Internet is very lucky that this is how you have chosen to spend your time, and I hope you are proud of the work you are doing. You are the Carl Sagan of mathematics.
Wow, in 40 minutes of watching UA-cam 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
9:32 I love that the 3b1b music subtlety incorporates some parts of the minute physics music
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.
16:30 This phenomenon has stumped me for years! Finally, someone explains it clearly!
MY TWO FAVORITE CHANNELS ARE DOING A COLLAB
AM I DREAMING OR WHAT?
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.
I guess you're in a superposition of being in a dream, and not being in a dream
I'm recommending this video to all quantum mechanics students. I wasn't taught the connection between the math and the actual physical phenomenon but this vid makes it so easy like I thought it was supposed to be.
Another excellent video! Thanks. It has triggered new ways for me to interpret some of this stuff :-)
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
Liking video before fully watching
Customary practice when watching 3b1b
85% probability of a like
Tbh. I learned more from this channel than from my college level math classes.
Brilliant is excited to continue supporting 3blue1brown's explanatory videos, and supplement them with our problem solving courses.
Help us support him - brilliant.org/3blue1brown/.
Calvin Lin hey sir! you are on brilliant .i am your fan.
>paying for education in 2017
Brilliant became shit when you ended weekly competitions (back in 2013).
only a matter of time before i patreon Grant here; already did so for BBB
Calvin Lin ,,can u please make some videos on vector calculas?E.g.Grad,, Divergence,,Curl specially,,this is only place in youtube where I can understand all the fundamentals,,probably because of your high quality graphics of the videos,,whatever it may be,i am your big fan,so please make some videos on vector calculas
Bedankt
I would love more of these QM videos! This one was so good, I was sad when it ended :(
I think I finally understand a little bit how the math I was doing in Pchem actually relates to the physical reality of the quantum world, thank you!
how do you know EVERYTHING so well??!! being able to communicate things this clearly, you're better than Feynman...
This channel is one of those extremely valuable and rare gems of UA-cam
Point after 20:20 very interesting. Harmonic Mechanics would have been a much better term.
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
I wish we had such videos when we were doing our degrees all those years ago..
This is so well explained and so clear that I don't understand any more that there is a paradox. Thank you.
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 !
A great video to watch on 2/22/22, given that it's 22:22 long.
Lol
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!
@3blue1brown I (personally) am very grateful to your for posting such wonderful animated math videos, and this collaboration from @minutephysics was much required for amatuers (like me, who just learnt some vector algebra and calculus) to realize how exactly the math behind quantum physics works.
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
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.
This was totally awesome. If you collaborate with "Looking Glass Universe" too it would be a masterpiece!
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.
15:36 "Dead or Alive ... Horizontal or Vertical" ... I laughed so hard.
Wait, why is this funny?
Around 17:45 I realized that cosine is just sine with a co tacked onto it. It's so simple and obvius that I never noticed it before! It totally blew my mind!
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
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.
Sadly, formal Maxwell's equations nowadays are introduced by Heaviside, who is a true genius invented vector calculus and simplified lots of content in electromagnetic theory..... The original Maxwell's equations are horrible. and almost no one know him
黃俊軒 Don't forget Willard Gibbs who also independently invented vector.
Maxwell used Hamilton's Quaternions (a generalization of complex numbers in three dimensions) in his formulation of electromagnetic theory (organizing the experimental results of Faraday, Oersted, and many others), because there were no other approppiated mathematical entities for the task at the time. Several decades later, Gibbs simplified quaternion theory into vector calculus, without considering it a theory on its own right (he just wrote a thin pamphlet not intended to be published, but used by his pupils only!) By the same time Heaviside reformulate Electromagnetic Theory with the new vector tools. So, is rather unfair to say that Heaviside or Gibbs invented vector calculus by their own...
But you (and Jeff Ahn) are definitely right when you say that both men and their contributions to physics (and mathematics!) are severely underknown.
Sorry for my English, it's not my native language.
Wow this is incredible! I know about this guy from his work in mathematics, but I had totally forgot he was the one that made the jump to vector operators in Maxwell's equations! Am so glad you shared this, this is the kind of work I hope to be able to accomplish in my career.
Edit: Just read a bit about him. I think this man might be my spirit animal. :^)
Quaternions are 4d, not 3d, hence the name, it's just they can be used to model 3d space by ignoring the real component.
You're right, my apologies. I guess writing "(a generalization of the complex numbers in order to model 3d space movements using 4 parameters)" would've been more accurate? This is not a trick question, I'm genuinely interested.
Holy shit years late but im a polarimetrist and this has to be the best intro for physics students to that concept and how it relates to quantum I've seen. Going to point students here.
Ahhh more please. More polarization math
20:40 Well, at the start quantum mechanics was known as "Wave Mechanics".
No, not really. Wave mechanics was a different thing altogether from which quantum mechanics originated. And one of the earlier interpretations of quantum mechanics pre-QFT was pilot wave theory, but this is a very different thing.
@@angelmendez-rivera351 de Broglie considered his greatest discovery to be the "Law of Phase Harmony" - a good article on this is "Light is Heavy" by Nobel physicist Gerard 't Hooft.
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.