The more general uncertainty principle, regarding Fourier transforms
HTML-код
- Опубликовано: 23 фев 2018
- The meaning of the uncertainty principle in the context of Fourier transforms
Help fund future projects: / 3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: 3b1b.co/uncertainty-thanks
For more on quantum mechanical wave functions, I highly recommend this video by udiprod:
• Visualization of Quant...
Minute physics on special relativity:
• Why is Relativity Hard...
Main video on the Fourier transform
• But what is the Fourie...
Louis de Broglie thesis:
aflb.ensmp.fr/LDB-oeuvres/De_B...
More on Doppler radar:
Radar basics: www.eetimes.com/document.asp?...
There's a key way in which the description I gave of the trade-off in Doppler radar differs from reality. Since the speed of light is so drastically greater than the speed of things being detected, the Fourier representation for pulse echoes of different objects would almost certainly overlap unless it was played for a very long time. In effect, this is what happens, since one does not send out a single pulse, but a whole bunch of evenly spaced pulses as some pulse repetition frequency (or PRF).
This means the Fourier representation of all those pulses together can actually be quite sharp. Assuming a large number of such pulses, it will look like several vertical lines spaced out by the PRF. As long as the pulses are far enough apart that the echoes of multiple objects on the field from different targets don't overlap, it's not a problem for position determinations that the full sequence of pulses occupies such a long duration. However, the trade-off now comes in choosing the right PRF. See the above article for more information.
Music by Vincent Rubinetti:
vincerubinetti.bandcamp.com/a...
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
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
Various social media stuffs:
Website: www.3blue1brown.com
Twitter: / 3blue1brown
Patreon: / 3blue1brown
Facebook: / 3blue1brown
Reddit: / 3blue1brown
Attentive viewers may have noticed that I broke a promise from the last video to talk about Fourier inversion. I still plan for that to come at some point, perhaps in the context of a video on Laplace transforms, or perhaps after it.
3Blue1Brown Thank you
Are you planning on making a video about Laplace Transform? Really love your videos! EDIT: never mind, just saw your answer on reddit, can't wait for the video!
Are you planning to do a multivariable calc series?
great video sir! could you please make video on z-transform and discrete/digital systems? those are most unintuitive topic of all time for me..but I believe these are most important topic of modern technology.
If you are doing transforms now, consider the Lorentz transform too. You mentioned spacetime here, so it's somewhat related. If you are interested in pursuing that, here's a Minkowski diagram of a light clock in motion, in Desmos. www.desmos.com/calculator/xc1cuqkcdp
Why is it that when I can't understand something, a RUclipsr comes out no less than a month later with a beautiful explanation of it. My FBI guy must really care. I love you man.
Your welcome,,your microphone was on.
@@Anima_Gacha More like google search etc.
That's due to quantum mechanics and uncertainties - We're all in 'a WAVE' of dark knowledge (empty head space) - however once certain thoughts are observed deeply enough, a BRIGHt one works out a great PIECE of enlightning information (-:
@@EgonSorensen BRIGHT*
*@EgonSorensen*
QM is mechanics - uncertainty as defined here often has some linkage from Event M to Event ( remote ) ~ few realize Space Lizards actually rule the non-tangible
I remember when someone first told me that the uncertainty principle was due to certain aspects of a particle being Fourier transforms of each other. Totally changed my understanding of it from "impossible to understand" to "reasonable but unexpected".
Great vid so far. Just wanted to raise the point re: quantum uncertainty principle though. It’s not only that the particle’s position/velocity cannot be known (due to length of frequency of waves etc), it’s that when you know one, it doesn’t really have the other in any sense. Ie. it’s not even ‘there’, in the conventional way, to be found.
This explanation satisfies me for a single particle. But how does it address the EPR paradox for an entangled pair?
@@tbayley6 Oh, that's easy. www.smbc-comics.com/comic/fossils-3
Pi is infact related to e" The Natural Logarithms, the Golden Ratio Taylor and Maculin series , Hyperbole, Coding theory, TRIGONOMETRY Exponents , Prime numbers the Quadratic formula,Fermat last theorem, Cantor Ordinal and Cardinal Infinitel numbers
Another one of my favorite explanations of the uncertainty principle is taking a picture of a pool table. With a fast shutter speed, you can tell exactly where all the pool balls are, but you can’t tell how fast they’re going. With a slow shutter speed, you can use the motion blur to determine how fast each pool ball is moving, but it’s much harder to say where each ball exactly is.
why not just measure both, separately?
@@broor that would be two different independent measurements, which wouldn’t actually give you any useful information about both position and velocity at the same time. When you get down to subatomic particles, it actually happens that the act of measuring a particle changes it’s behavior and you can’t have two simultaneous measurements.
@@spyguy318 good answer! But that makes me wonder; why measure at all? If it changes after you measure it anyways. Perhaps, you might answer, to see the outcome of an experiment, but then my idea of measuring the two things separately is still applicable
@@spyguy318( and also for every example in the video we can measure separately, but i realise those examples are for teaching the concept)
damn i like this analogy, thank u
I don't know if you ever read the comments, but I just want you to know that you make the world a better place with your videos. You allow people like me to gain knowledge about subjects that I have always been interested in. In a very tangible sense, the world gets better with each video that you make. I want to sincerely thank you for the effort you put into these and help you have given to so many people. Bravo!
You can say that again!
I have 24 credit hours left to get my Bachelors in Electrical engineering, and I can confidently say that I have never heard these concepts explained so clearly. Your past two 20 minute videos have given me more clarity in my field of study than every professor I have ever had combined. Absolutely incredible. #3Blue1Brown>CollegeEducation
Can say the same. Its so elegant and well thought out. No one puts this much effort anymore.
bro I swear if I knew this guy sooner I'd have passed my digital electronics paper smh
I think these videos are supplemental, not replacements. I'm sure you would be as lost if you only watched these videos.
@@ilikewaffles3689 having just watched the videos, can confirm, I'm lost in the sense that I wouldn't be able to rephrase the information in my words with any confidence in what I'm talking about. That said, as a lay person I understand the spirit of what he's explaining and would be less likely swayed by "Quantum weirdness mumbo jumbo" pseudoscience peddlers, which I think makes him an excellent science communicator for all levels of background education. I'd love to learn about these Fourier transformations in more depth someday, it's still difficult to clearly understand with just 10-20 minute videos.
I feel like 3b1b does a great job of getting you to that last huge step of truly understanding while school gets you up all the little steps of just grinding out the intuition manually
Great video as always! As a physicist, I just want to point out something that usually bothers me about some phrasings of the uncertainty principle (which you were careful to also do in the last minutes of the video). When people say "you can't know the position and momentum of a particle", you really need to bring the probabilistic interpretation of quantum mechanics to make sense of that. It certainly does not mean that you can't measure both quantities. If you have a certain localized quantum state (with low position uncertainty) and measure its momentum, you will get a definite result in your detector. It is only when you prepare the same localized state and measure its momentum again that you realize the result is now different than before (and repeating this process many many times you'll conclude indeed that the uncertainty of the momentum is large). This has to do with particles in quantum mechanics not being described by its classical state (which is characterized entirely by its position and momentum) but by its wave function. That popular phrasing of the uncertainty principle in a way extrapolates by saying that the particle "has" a position or momentum a priori, which is a little misleading (or at least debatable in the various interpretations of quantum mechanics).
As a physicist I say comments like these need more upvotes for any video talking about the uncertainty principle where this particular point isn't made very clear.
as a physics student, i am crying
Does this mean "you can measure but you can't predict"?
@@michakubisz535 You could say it yes and no. The whole thing again boils down to the argument that Quantum mechanics is not entirely deterministic. So to answer your question, you could say, you can measure it and also predict the "probability" of a particular event happening.
@@michakubisz535 You can predict but not with 100% confidence.
I love these videos. I finally understood the mathematical meaning of the uncertainty principle. And I didn’t comment those other videos, but your Linear Algebra series was excellent. I can’t tell you enough how many times in my life I was multiplying matrices without having any single idea of what it meant. Thank you!!
@@erdemmemisyazici3950 The fact of waves is more fundamental. The idea of not being able to observe electrons because that requires a photon of high energy is true. However, the fact that particles are described by wave functions rather than points in space is what makes the uncertainty principle fundamental regardless of what an observation entails. For example, the uncertainty principle also applies to measuring spin about two different axes. In this case, you don't require a photon to measure this but you can't simultaneously know the spin about two different axes regardless and that is because of the fundamental nature of waves, rather than the act of making a measurement.
@@andonimcleab994 Now that's interesting.
Pi is infact related to e" The Natural Logarithms, the Golden Ratio Taylor and Maculin series , Hyperbole, Coding theory, TRIGONOMETRY Exponents , Prime numbers the Quadratic formula,Fermat last theorem, Cantor Ordinal and Cardinal Infinitel numbers
"A particle momentum is somehow a sheet of music describing how it moves though space." How to do poetry with physics and math. Thanks for the video.
What is a sheet of music? Musical notes on a page?
@@erdemmemisyazici3950 yes, a melody written down on paper
You are a shockingly good teacher. I've never seen anything like it.
Is there a prize for science communicators? There should be a way to fund people like this, besides RUclips ads. Maybe the department of education needs to start funding people on patreon, according to some proper, formal, and transparent process of appropriate gravitas.
He has a lovely voice aswell
The graphics help a lot too
As an engineering student, even the first seconds of the video blew my mind. I got the gist of the idea (even tho I still don't understand it fully), but the connection between the mathematics and these physics phenomena have never been made for me. This video is truly amazing. I would be so happy if all my professors were only half as good as explaining stuff as you. Truly amazing.
My physics instructors have told me that we know that lumps of mass are basically a big standing wave ... this video makes the concept more tangible. My favorite on your channel so far.
Who says the sequel is never as good as the original. Great follow up to the previous video! I think 50 years from today, educators will point back to you and say- this is how we learned to effectively explain complex ideas. You have really set the bar with your style.
HOW ARE YOU SO GOOD AT EXPLAINING THINGS?!
How do you watch 19 minute videos in 2 minutes
Soufian 27 cause i watch all his videos and I already know it’s gonna be good
Soufian 27 but good catch
I thought you were going to tell us that you use a video speedup plugin to speed it up 10 times, and it somehow still makes sense to you. :-)
Extensive revision of a concept throughout the video is the key. This is what almost all school teachers have no regards about. Whatsoever.
Your videos are a blessing for engineering students
The way a relationship is established between the Fourier transform and the essence of our reality is gorgeous. Thank you for sharinng this kind of content. The way it is explained and the animations are just brilliant.
Please do more physics oriented videos. I love seeing the mathematical intuition behind it!
HOLY .... i was on a 3b1n marathon and was just wondering where Fourier part 2 was ... and thought well, 3b1b hasn't posted in a while ... that means we're gonna get something fresh soon OMGOMGOMG
"A particle's momentum is somehow the _sheet music_ describing how it moves through space" that's just a super beautiful way to put it. These videos are exceedingly good and thought provoking, I learn something new and deeper every time I come and re-watch them.
Oh my! I had the energy-time uncertainty principle as my determined question in physics state exam in university this january. The stuff I found and presented to the commission was okay but it would've been so much better with explanation in this video - all suddenly makes sense! Great job man, keep it up, such fundamental links between math and physics always gives so much food for thought.
You deserve a lot more subscribers. Your videos explain everything so well and are presented beautifully. I hope more people are interested math/physics from watching your videos!
ShockMinerX He’s getting close to one million
751K is pretty good for maths videos. It's a real shame but that's how it goes.
Also 100K views in 19 hours! Not that bad!
13:48 - Loved the subtweet to minutephysics!! Henry already said in the first video of that series that 3B1B is nagging him to get it done!
This is the most intuitive explanation of the uncertainty principle that I have ever seen. I’ve always found that analogies are one of the best tools to gain better understanding of a topic, and you’ve used them to great effect here.
I’ve been searching for an intuitive explanation to why the Heisenberg uncertainty principle works for a long time and this is the most beautiful and logically consistent explanation I’ve ever seen. I’ve never had such a high understanding of the uncertainty principle, you made it as simple as you possibly could but no simpler. I think too many of us just accept the facts of quantum mechanics without diving into why they work and the logic and intuition used to build them, why is the hardest question to answer but when it is it leads to a fundamental understanding that births new creative intuitive theories. Thank you for this video.
Great video as always. Although a minor correction regarding doppler-range tradeoff for radar: Good range resolution does not require a short-duration pulse, but on a highly localized auto-correlation function, which requires wide bandwidth due to uncertainty principle. Although time duration and bandwidth are inversely related for the wavelet signals you are using, you can use other waveforms that have both long duration (for good doppler resolution) and wide bandwidth (for good range resolution). A typical example would be a repeating set of chirps. But for a given constraint on the waveform’s time-bandwidth product, the range and doppler resolutions are fundamentally limited due to the reasons you described in the video.
Yes! Thanks for sharing. This is more or less the part I referenced “purposefully glossing over”. The original script had something closer to this, but it ended up just being too much too beside the main point the video is shooting for. My hope was to be upfront in the video about things being oversimplified and including a link to where people could learn more in the description would forgive me my sins :)
3Blue1Brown Yeah - I imagine its a constant struggle to balance technical accuracy vs accessibility and straightforwardness on all sorts of details like this. Anyway, keep up the great work!
Time to develop some more interactive format where the user converges to technical accuracy by an iterative process ;)
@@halbeard2996 Maybe 3B1B should use glossed over topics as a to-do list of videos.
@@halbeard2996 it already exists. It's called graduate school. :-)
10:38
"1917: Not a lot of physics... because war"
"1918: S'more Rutherford badassery"
LOL!
Lmao
LOL!
in the vid there was a timeline at 10:38 , on that time line in 1917 it said "Not a lot of physics... because war"
and then at 1918 it said, "S'more Rutherford badassery" which meant some more Rutherford (bad ass)-ness since he made i believe this finding about the nucleus: sites.google.com/site/atomicstructure11/history/1918-rutherford
cool ... I overlooked that one, I guess it was because "the timeline speed" was too high so I wasn't really certain about what was written there.
Rutherford was in New Zealand, and we hadn't received knowledge of the war yet.
I went from legitimately hating math after a painful undergrad degree in physics to now... I am blown away, I LOVE IT! Thank you so much for helping my visual mind see the deeper patterns underneath these phenomena. THAT is real learning and it feels so good. Reinvigorated to explore the beautiful and mysterious existence. You are an example of the future of education!
I really believe the world could be in a profoundly more advanced place if we had more teachers like you. (or more people had acces to those limited set of teachers). Think of all the people that could benefit from these learnings and deep understandings.
I studies applied physics in engineering, but your video's on algebra, linear algebra and this on on the *unsharpness* principle really bring my insight in these topics to a whole new level. I feels really wierd to realise how much I did nót grasp things in a fundamental way when I was studying this and at the same time still was able to pass these exams. Makes me wonder how many people finish with a physics degree but do not have the deep insights that you are presenting and teaching in these series of online videos.
Glad to be a patreon supporter btw, the world needs more of you.
Thank you so much.
You sir, are AMAZING! Your talent for making complex things understandable is quite remarkable. The animations, the pace, the quality of the ideas being expressed and how they are broken down is pure intellectual joy. I always thought these things were out of my reach but now I understand them much better. Thanks for all of your efforts and you're on my Patreon.
I love how 3b1b is sponsored with job openings. That's really cool :D
You ask such relevant questions about the topic of concern. And reiterate what it means. For a naturally curious person. This is gold. Thanks a lot.
Wow, I’m blown away by how clever a way it was to explain the concept of confidence growing over time by showing us how the Fourier transforms into a sharper curve, which you’d given us an indication of earlier too. Great way to make the information feel super natural!
Damn ! You got the best maths videos of the entire internet !
and that's impressive cuz the internet is BIG
Not quite as big as Graham's Number.
Updated Demo with P5js. jbracey2004.github.io/Examples/Excercise00_WindingFunction.html Still Work in progress
Well done sir! I have been experimenting with this idea as well. Here's my work ggbm.at/SbDrHq4k .
Bob Tivnan It would be interesting to see what the position vs time graph would look like with that pi creature
This would be fairly easy to do. I already parameterized the x and y coordinates of the sampled points. Why would do you think it would be interesting?
Bob Tivnan well, to see some 2d figure represented by a waveform; though, there may not actually be such a thing
+Jason Bracey Its just like the video +Bob Tivnan but if you do position vs time then it is always 2 or 3 places at once
No words to describe how beautiful it is. Thank you so much for sharing.
3B1B you are truly an excellent educator, I don't know how you do it but you take complex topics and package them in a way that is not only are accessible but inspires further thought. Your work is a fine example of teaching mastery. Long may you live and share your skills and enthusiasm. I take my hat of to you.
*_3Blue1Brown new video notification_*
Me: What a great time to be alive ! (crying with joy)
This is a particularly spectacular explanation of the HUP. Definitely puts the whole mystical aspect of it into perspective and makes it almost seem reasonable but just unexpected.
Nah that’s two minute papers notification
Is that Pauli I see?
@@sharpieman2035 I was looking for a comment like yours lol 😂
Now this video is pure gold! I'm and engineer and not a mathematician, but I've tried endlessly to describe this situation of the trade off between time and uncertainty, which applies to everything. I have tried to explain this so many times on forums, but with only limited success. Your video nails it perfectly. 🙂There is no difference between this quantum uncertainty, than the fact that a completely pure sine wave can only be one which has existed forever, which has also been measured forever too. At the limit there is a trade-off between certainty and how long it has existed and been measured - for everything in the known universe! :-)
This is beautiful. 4 years after graduating from Electrical Engineering, I have no better place to go to refresh my mind. These videos need more views.
I'm 39 and I grew up not just hating, but truly despising math because nothing was ever explained. You were given equations, told to use them and that was the end of it. I had zero intuition about many or nearly all of the formulas. If something like this had been around it may have changed my perspective and possibly my life because I loved physics, but I hated math, so I never pursued it. I hope this helps to inspire those who now have a place to learn about they "why's" of the mathematics, not just the how.
I'm telling you, physics teachers in college totally abuse the uncertainty principle - above and beyond what should be allowed.
I have always wanted to get a mathematician's explanation on this topic because those damn physicists are no good.
Thank you so much for this video, Grant!
That's a bit harsh, as every coin has two sides. Consider how many Physicist's have been abused by mathematicians fumbling on about the square roots of minus 1, the natural logarithm and division by zero before being liberated by fellow Physicists with helpful narratives of: cyclic phenomena, how to make a big number a smaller number and the role of a unit in the context of measurement. And spare a thought for the poor Chemists when they encounter semiconductors and grapple with the Fermi level and it expected probability of occupation of 0.5 even though there is no sate to occupy in the band-gap (just like no die has a face value corresponding to the expected value) despite there being a valid statistical tug of war at play. In any case it's a wonderful video. I especially love the videos on linear algebra.
@@cerioscha Yes, there's truth in that. I have always felt like I should have studied at least a few semesters of math before persuing the study of any science (Physics, Chemistry,...,). Especially as chemists, we get hung up on math really often and it personally annoys me, that I get scared just because I see a complicated looking equation.
@@astralchemistry8732 If we can "Keep what we've got by giving it away" [Ian brown] then perhaps we'll take that diagonal step across the prisoner's dilemma payoff matrix and disseminate tactic knowledge with respect and optimism and realise a "Society of minds" [Minsky] where where afford each other a "leg up" to mitigate against "A little learning is indeed a dangerous thing".
@@astralchemistry8732 I used to feel the same way, but frankly, I wasn't particularly interested in abstract algebra, group theory, analysis, etc until I spent entire classes using topics from those subjects in chemistry and physics. 18 year old me would have never guessed how enamored with mathematics I became and forcing me to take those classes beforehand probably would not have gone so well. I do wish I stayed an extra semester to pick up a math minor.
I'm Interested in the DIAGAGNOLIZATION of matrix EIGENVECTORS, and VECTOR using Taylor expansion and DETERMINANT for infinite series and PAULI MATRIX and Clifford Algebra for solving the Schoringer Equation And HEINGBER uncertainty for QUANTUM FIELD PERBUTATION
Just discovered this channel tonight...and now I want to retake every damn math and stats course I ever had, from elementary school to grad school, with a vengeance and something to prove. I have never in my life seen these concepts explained so elegantly, and with excellent choices for relating a concept usually seen in one field to an unexpectedly similar concept in another. It feels like all of the facets of math and stats that stayed disparate and unsynthesized in my mind are finally coming together. This is the kind of channel that truly exemplifies what RUclips, and other similar resources online, can be. Thank you!
Welcome to 3B1B.
My guy, you have the smoothest voice and a good enough understanding to explain this to others. Thank you!
16:35
Love your description HUP
Finally ... a “no magic” explanation!!!
In a graduate course in imaging that I taught at The University of Arizona in the 1980’s, I pointed out that the Fourier relationship between a lens diameter and the sharpness of the image is similar to the Heisenberg Uncertainty Principle (HUP) in that a larger lens results in a narrower image blur (a “sharper” image). I did express the opinion that the HUP is not so mysterious or cosmic as it is often interpreted to be.
I cannot overstate just how truly brilliant you are with these videos. The best conceptual representation of the uncertainty principle I have ever seen. Ever! Bravo.
Dude, if there were teachers like you all around, then the whole world would've been thriving even faster. Love you for your creative insights.
This is quite unrelated to the video, but could you please do more videos on topics in abstract algebra and number theory. In particular, I'd like to see your take on Galois theory, and other topics in algebraic number theory. Fantastic video by the way!
FINALLY!!! After waiting for a month. I clicked on this video so fast. I forgot to comment when I first clicked because your videos are very interesting
Intuitive Learning same I saw video that I didn't see so I insta clicked
no such thing as forgx or not, can do anyxnmw
What do you mean forgot to comment? You clearly made a comment.
shrdlu I was early and forgot to comment as soon as I clicked because of the video but later I did commented :)
Rocknrolladube lol 😂😂😂
I am really enjoying how your videos and minutephysics’ videos are touching upon each other.
Though I did a course on wavelet transform where this uncertainty principle regarding time-frequency has been taught, I learnt new things.
The presentation is simply awesome.
Appreciate your hard work.
Thank you for your videos, and I enjoyed every single one of them. Can't wait until you hit 1 million subs
I believe this video, as well as many others on your channel, are among the greatest works of our time and are incredibly important.
What makes this video so special is the depth of the concepts discussed while remaining accessible, intuitive, entertaining, and beautiful.
The car blinkers analogy is a really great one. I've seen several videos on the uncertainty principle in search of an intuitive analogy and this one perfectly satisfied that itch.
This video is beneficial beyond its entertainment value; The world would be far more enlightened and thus more satifying and beautiful if educators more often took the effort you've taken here. I believe a great majority of people are capable of understanding far more than they believe simply because the explanations provided to them were insufficient.
Another element of why this video is so great is the animations are gorgeous and meticulously created; they are such a big part of how the explanations are so easily digestible and understandable.
Such a video is inspiring to those of us who highly value education. Thank you for your effort.
After all these years, I'm finally learning the Heisenberg Uncertainty Principle formally, as well as all the physics around it and, concurrently, linear algebra. I'll be coming back to your videos many times for a broader understanding, I'm sure. So, thanks again for doing what you do.
Thank you so much! It's so hard to find good explanations of anything in quantum mechanics, but somehow you manage to do it in a creative and beautiful way.
This is easily one of the most underrated channels on youtube. I would like to thank and congratulate you for your quality content!!
Wonderful video ! Once again 3Blue1Brown you did a great job. Thanks a lot for sharing your knowledge and unique way of explaining thing making use of great graphics technology ! Today I learned several things that I hadn't realized despite being an electronics engineer and having used the Fourier transform for years. I was just about to look for a Laplace transform video on your channel. It's a fascinating topic too. So, yes, absolutely, please make one! As I've mentioned before, I wish I'd had a teacher like you and the technology we have nowadays back when I spend countless hours trying to understand principles like the ones you present. Best regards and thanks again.
I've been trying to understand this for years, watching so many explanations... and now I finally get it. You are a great explainer, Feynman would be proud.
Woah, this is probably my favourite video on this channel. The Heisenberg uncertainty principle seems like such a weird and specifically quantum concept, when in reality it applies to every day life. Amazing video 3B1B!
I just wanted to take a second and share how thankful I am and how blessed we are to have Grant. That's all
that was an elegant explanation! and visually beautiful.
I found this channel just yesterday and it's the best thing I found on internet till date.
I recently started going through a Quantum Mechanics textbook. Thanks a lot for this video, Grant. You're a brilliant teacher.
"As if a particle's momentum is somehow the sheet music describing how it moves through space". So profound 🤯
14:09 this is the first time I have understood relativity (i think). Out of phase example is great. I have not seen it anywhere else.
Another hugely insightful video. The quality of these presentations is right out of the top drawer ! Congratulations Grant !
Your graphics are always fantastic. Thanks for putting in all the work to create them.
i feel like if we could get all the students that are interested in math watch 3b1b videos instead of going to school and taking some random language class, world would be a significantly better place :>
Well, as you can see, in this case taking a German language class would have helped... it's the math/physics classes that have a problem if a 20 minutes RUclips video is able to do the job better than hours with a real teacher !
Thanks a lot for all the work you put into this!
I watch a lot of your videos on maths and they all touch me , True. I am a physics major,geek or what ever you want to call it... One video you did about physics, this...has toppled my entire understanding of physics and I see a new world after this video... filled with fourier transforms and frequencies .. It's great that I found your channel
I'm kinda proud of myself that when I saw the title of this video I was able to kinda mentally walk through the time-frequency uncertainty as I learned it before, and It managed to stick! I swear all of these concepts just fall together so well once they start to string together. And this channel is perfect to jump up a bit in math from others.
Thank you for properly explaining the difference between the uncertainty principle and the non-deterministic interpretation of it. I get really irritated by physicists that treat the two as equivalent or inseparable.
I never heard of this distinction, do you think you could explain the difference? Is this video describing the HUP or the non-deterministic interp.? The NDI just sounds like a more technical description of the HUP.
The difference comes from how you want to view the whole system. It’s a little philosophical.
In classical physics, it is often considered that to have complete deterministic knowledge of a system you must precisely know the positions and momenta of all the particles involved. From this perspective it is the HUP that gives non determinism as without the principle we could just use a really localised wave for the position and a really localised wave for momentum and retain determinism.
However you could say that a perfectly localised wave is impossible. Also you may want to measure many other quantities, energy, time, temperature, etc. All of these might have some uncertainty relation between them (infact they do). So these are all described by waves and non of the can be perfect spikes at one point. So nondeterminism can really by tracked back to the decision to use waves and define probabilities based on the wave - instead of just the HUP.
Actually it is postulated that single measurements of quantum mechanical systems yield non-deterministic outcomes. The non-deterministic interpretation of the HUP is merely a consequence of this assumption about quantum mechanics itself.
Can't relate
I'm still not following. You explain how classical mechanics and determinism is defined, I get that. Then you say that you need the HUP to dustify the unknowability in this context. This seems like, mathematically, you are simply applying some form of non-deterministic algorithm, one that slides the knowability between two quantities, say time and energy, based on a constant which will include planck's constant. That seems to define both the HUP and this "non-deterministic interpretation". I can't identify a difference!
Thank you for taking the time to try and explain this seemingly subtle distinction.
@3blue1brown this is possibly the most poetic description of a scientific observation I've heard, "a particles momentum is somehow the sheet music describing how it moves through space". You should take up poetry :)
Finally a video that clearly explains how the math round it works. Along with your Fourier transform video, it has been a very enlightening moment in my understanding of these .. thank you so much for being here!!
You have done an amazing job of demonstrating Heisenberg's Uncertainty Principal in this video. Absolutely brilliant. I feel like my understanding of it now is crystal clear compared to my grasp of it before.
I LITERALLY jumped out of excitement when I saw this video in my sub box
Nice vid. Also nice Falcon Heavy easter egg
Wow! That's the best description of the Heisenberg Uncertainty Principle on RUclips. Thank you very much! 🙏
This video along with the last video about FT are awesome! Such great work and makes so much sense.
Hats off sir🎩!
From your videos , I'm getting real meaning of maths and science.
keep it up..
Great video, man! However, regarding your pet peeve (15:50)... Keep in mind that the radar analogy (Range ambiguity resolution) isn't completely interchangeable with the Heisenberg uncertainty principle/unsharpness relation. The range ambiguity resolution is a problem with THE RADAR, not the objects being measured.
But, in the quantum realm, atomic particles like the electron adhere to the strange DUALITY PRINCIPLE, which you didn't discuss. The particle/wave duality is key to understanding the limits of range ambiguity resolution as an analogy to quantum physics because it introduces this mysterious and strange aspect of quantum mechanics. The problem in measuring the plane lies with the radar. The problem in measuring the electron is the electron itself (we could say it's inherent to nature).
P.S.: I'm a physics major, and I was thrilled that you even read De Broglie's seminal paper. Excellent work! Just highlighting something I thought was important and... flew under your radar (ba dum tss).
Your comment is very informative
@@userhandle-l thanks!
This is the best channel to understand what your lecturer does not know how to explain.
your animations make a huge difference. Congrats to whoever is making them, too!
This is my second time coming to this video, learned something new, I guess there'll be a third time after I take a complete introduction course to quantum mechanics.
3blue1brown on the Heisenberg Uncertainty principle? This is like Christmas in late February!
This is one of those videos that is worth watching a handful of times to really grasp.
I saw this before knowing what a Fourier transform is and was hella confused but intrigued. This semester I learned about what it is and can see how the math lends itself to the intuition. I can’t wait to learn about Fourier transforms and QM and come back and see this video again and see the clicks that happen. I never understand your videos but the more I learn the more I can see why you can’t just be explicit and to the point.
2:00 Perfect pitch people: "You dare underestimate me mortal?"
It should be noted that the uncertainty principle in modern formulations of quantum mechanics doesn't rely on fourier transform pairs at all. It is instead simply a consequence of non commuting observables and the postulate that single measurements only yield probabilistic outcomes that obey the probability distribution related to the quantum state. In conventional quantum mechanics all observables like position and momentum are represented by complex linear operators (i.e. matrices in most practical cases) with real eigenvalues. So if you're familiar with the linear algebra series of this channel then non-commuting observables can be thought of as pairs of matrices A, B where the product AB is not equal to BA, usually represented as the commutator [A, B] = AB - BA being different to 0. For position x and momentum p the commutator is [x, p] = ih/(2π) for example, with Planck's constant h. The fourier transform in the uncertainty principle then appears as a consequence of this commutation relation.
Also, connecting this further to the linear algebra series (albeit this particular point wasn't covered there) one important consequence of A and B not commuting is that there is no common eigenbasis of A and B. In quantum mechanics the state vector |ψ> (which is almost the wave function) of the physical system becomes the eigenvector correlated to measurement outcome of an observable, which is always an eigenvalue of the measured observable. The position observable X has eigenstates |x> with the eigenvalue equation X |x> = x |x>, where the lower case x is also the eigenvalue (just typical quantum mechanics naming conventions). Same goes for the momentum observable P with P |p> = p |p>. The position wave function ψ(x), which is shown in the video, is the scalar product ψ(x) = , so it is nothing more than a projection of the abstract state of the particle to the position space. Likewise we have ψ(p) = for the momentum wave function. So if the state is in well defined position it is one of the eigenstates of X, meaning |ψ> = |x>. But because X and P are non commuting, i.e. [X, P] = ih/(2π) is not 0, the same |ψ> is not an eigenstate of P and will thus have a range of eigenvalues p as possible measurement outcomes. This is basically the more quantum version of the uncertainty principle which can also be applied to other observables like Spin and Charge.
And btw, to anyone still reading my ramblings about the connection to quantum mechanics: If there was some addendum to the the linear alegbra series including videos about Hilbert spaces, unitary operators, change of basis by means of series expansion and the aforementioned implications of commutation relations, it would be all that is necessary for a starting point for solving actual problems for finite dimensional quantum mechanics problems. If you throw in an introduction to tensor product spaces this would enable one to tackle basic quantum information problems with qubits. After all the mathematics behind quantum mechanics is actually far easier than classical physics, since it only concerns linear algebra and some minor probability theory.
I wish so bad that I could understand you.. :'(
Halberd Rejoyceth first of all, I second this notion. Such an extension to the series would be beautiful.
What you said is absolutely true, but the uncertainty principle for Fourier transforms is simply a special instance of what you explained for dual observables, namely if you choose to represent your vector space by the Fourier basis. The commutator builds a vector field on the underlying manifold which, in this case, happens to be constant. I still think it's useful to think about this in Fourier transform terms. It makes it easier to visualize what's going on than having to think about linear algebra on complex manifolds.
Sagar13iffy Try taking a look the book “Quantum Mechanics: A Paradigms Approach” by David H. McIntyre. The book builds up to the concepts mentioned here with not much more than relatively simple linear algebra.
one of the best videos I have ever watched!! Gotta say that your animations and explanations are on another level
This video is quite an eye-opener. Never thought of or even heard of Fourier transform explained like this in my 4 years in EE
I love this series!!
OMG Heisenbergs princible boggled my Mind for so long! I had allready accepted that i'd never understand it but now there is new hope! Thanks a lot!
I love this series. I have watched this video over 10 times in the last few years. Thanks!
Awesome view and opening my eyes and new view of Unschärfe. Thank you.
Sir, you are a GOD at making hard concepts approachable!
Is there a channel like this for biology & chemistry?! ... learning intuitively is the way to go, Good job 3Blue1Brown :)
I am a second year BSc Physics student
Thank you sir for posting this videos.
It seriously helps developing intuition
I feel like even though I've learned about uncertainty principle for like a bajillion times, this is the first time I really get the gist of it. Thank tons for the awesome video.
Oh boy oh boy oh boy, new video!