To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/FloatHeadPhysics . You’ll also get 20% off an annual premium subscription. Also FAQ 1) What does it mean to add two waves together? I could have been clearer here. The bottom line is since a wave packet can be mathematically constructed by adding lots of pure sine waves of different wavelengths (Fourier series), a wave packet contains multiple wavelengths. So, an electron can be thought of as a wave packet HAVING multiple wavelengths, and hence HAVING multiple momenta. 2) What's the intuition behind energy time uncertainty? If you hear a tone for a small time, you are unsure about it's frequency. (You don't know if it's a pure sine wave or not). This means you are unsure about it's energy (E = hf). But since the time interval was very small, you are pretty accurate the absolute time value when you made the measurement. On the other hand if you hear a tone for a long time, you become more sure about it's frequency. (You have much better idea about the repeating pattern). This means you are more sure about it's energy. But since the time interval was large, your accuracy about the absolute time when you made the measurement went down!
I love how every time you make a video like this you talk as if you brought the scientists back from the dead and had lunch with them to make this video.
Yeah at first I found it patronising, but then I realised it is the perfect way to explain things. The conversation is the stepping stones to understanding 👌
Haha, when you read well written books, that's exactly what it feels like. I kid you not! (Try the book, 'surely you are joking mr. Feynman'. It's so nicely written, you feel like Feynman is sitting next to you explaining his life)
@@Mahesh_Shenoy"Curiosity is the spark that ignites the flame of discovery. Embrace your curiosity, ask questions, seek answers, and never stop wondering about the world around you. For in the pursuit of knowledge, you shall find the secrets of the universe, and the universe shall reveal its secrets to you." Remember, science is a journey, not a destination. It's a mindset, a way of thinking, and a passion for understanding the world. As a scientist, you'll encounter challenges, failures, and setbacks, but also moments of triumph, wonder, and awe. So, cultivate your curiosity, stay curious, and never lose your sense of wonder. The world needs more curious minds like yours, eager to explore, discover, and push the boundaries of human knowledge. Now, go ahead, ask a question, design an experiment, collect data, analyze results, and draw conclusions. The scientific method is your tool, and the universe is your playground. Happy exploring!
Now I understand. It's been 30 years of me trying to understand the uncertainty principle. I started as a 14-year-old and a high interest in physics, but no one was ever able to just break it down and explain it to me like this. Thank you, side quest complete.
Still struggling to get my head round that! How can the probability not come from the measurement side? If The electron follows a path in the electron cloud, surely the probability of position comes down to the timing of measurement. How do we know the electron doesn't follow a specific path?
Almost 20 years ago, I first came across the uncertainty principle in Class XI Chemistry studying the atomic structure. This is the best explanation yet. Indeed intuitive. And over the years, I've realised that it's not that some subjects and some topics are tough, it is the quality of books and quality of the teachers that make a difference!! And if you're not in luck with the teacher's quality, do get good quality books!!
This is how I feel too! To have a teacher or a book that makes a subject feel easy is a blessing. And it makes you wonder if some subjects aren't intrinsically harder, but are rather just taught poorly.
Whenever I tell my students about quantum theory, I always try to highlight how necessary it is. The wave-particle duality is the entire reason we have atoms. If the electron is not a wave, but a particle, then all atomic orbitals decay in about 16 picoseconds. You can use the uncertainty principle alone to back-of-the-envelope estimate the order of magnitude an electron's energy at various distances to a proton. Within nuclear scales, it'd be enough to shoot it clean out of the proton's attractive potential. At the scale of the Bohr radius, it's on the order of a dozen or so electron volts, in agreement with the Schrödinger equation. The uncertainty principle actually implies a repulsive force between the proton and electron at sufficiently short distances, preventing orbital decay. Even though I teach this, it never fails to blow my mind every time I think about it.
@@nanotechnano7193 true but you can measure the distance the electron is from the nucleus at a given time. The probability distribution for this observable in Hydrogen's ground state peaks at the Bohr radius with a mean at about 1.5 times that distance. Whereas, the probability of measuring the electron to be within nucleon distances to the proton is so small that it's practically zero. So, the qualitative understanding we can derive from the uncertainty principle alone matches what the full theory would predict.
This is genuinely the best science education channel out there man. Have never left any of your videos without having learned something new or in a better way than I previously understood it.
Honestly, as an Indian, I never expected some Indian to be this passionate about Physics, a person really wants to understand physics for the sake of Physics, at least until now. It was my friend who first suggested your video about Quantum Spin. I thought it would be just like any other video about physics, a Lecture with a bunch of mathematical relations and claim something to be true just because math does imply so. I know and I agree that Quantum and Relativity are not intuitive in our common sense and it's true because what we say common sense, is just a genre of experiences in the macroscopic world, a classical world. Still, there is always room for improvement we can extend our domain of intuition by asking the right questions and that's what you do best. Really, I always wanted someone to share the same passion for Physics. I have seen all your videos and all I want to say is "Keep on doing"
There are Indians who are passionate about Physics, too. There are even some Nobel Prize winners among them. You as an Indian just need to dig deeper to uncover your (very ancient as well as up to modern times) civilization's cultural heritage. 😊
He explained it well. Actually, the formula actually applies to all waves. You would just use the frequency instead of the momentum for non-quantum objects.
But be careful Quantum Physics is FICTION. Like many other pseudo-sciences. Like faster than light travel, time travel to the past, and other dimensional universes. Those quack do like he did he explains something true and then switches to his pseudo-science
A sign of a smart person is being able to recognize that they do not understand something. You would be startled by the percentage of people who accept concepts that they misjudged to have understood.
Same for me. I find the quantum world very strange and confusing, even more the more I learn about it. I'm trying to get accustomed to these explanations but have still a long way to go. I always wonder how these quantum effects add up to the predictable, deterministic macroscopic world we live in!
@@Mahesh_ShenoyHi! Could you please explain the physical meaning of adding another wave to the electron wave (I mean does it mean shooting another electron to the original electron)
Got this in my recommended. Started watching and when I heard your voice, I thought that it sounded familiar. But then when you started just the voice over I immediately knew... You're MY physics teachers.I've been learning physics from your videos on Khan Academy since 8th grade!!! 5 years now, and I NEVER KNEW YOU HAD A TH-cam CHANNEL!!! Thank you so much for your videos. I owe all my grades and understanding of physics entirely to you 🙌💛
Every pop science channel ever wants you to think that such a thing is possible because it drives their views and engagement. The only intuition you can get in that subject is by a good understanding of the math or the data you see from experiments.
Time and frequency are also complementary variables. A sinewave extends to -inf to +inf. This gives us a pair of impulse functions (infinitesimally wide, but infinitely tall pulses) in the frequency domain when we take the Fourier transform. When we look at a sinewave for a non-infinite amount of time, we are always chopping off some of the sinewave (Rectangular window function). This causes the frequency spectrum to of the impulses to spread out (convolving with the fourier transform of the window function in the frequency domain). This spreading of the sinewave's spectrum gives us an uncertainty on the actual frequency of the non-chopped sinewave. If you look at the sinewave for a shorter period of time, the spectral spreading of the sinewave, and your uncertainty about the frequency of the sinewave gets worse.
Bro explained the Heisenberg Uncertainty Principle in the first 1 minute of the video better than I've EVER heard anyone explain it. Makes PERFECT INTUITIVE SENSE now. Thanks so much!! Edit: I watched the rest and yes that's the less accurate version but it ended up still working for me because I didn't assume you could determine velocity by just going to the next slide because I assumed there was no next slide, which ended up working for me. However, the next explanation he gave was even better anyways so ... win win!!
Haha. Also if you keep the ball at rest on a table, now you know both its position and momentum :D. So in Feynman’s words, I would have cheated you very badly!
A similar thing can be observed for signals in time and frequency domains. Signals which are non-zero for low time duration have their spectrum spread apart in frequency and vice versa. For instance, Fourier transform of an impulse (infinitesimally small duration signal) is constant ( i.e. spread over entire frequency spectrum) whereas Fourier transform of a sinusoidal signal (spread in time domain) consists of impulses in the frequency domain.
A fun way to get a feel for the phenomenon is to play with a sound editor like Audacity, mix in some beeps of varying lengths and pitches (arranged into chords, even), then show the track in Spectral view mode. You can adjust the vertical (frequency) resolution as much as you like, but doing so smears out the horizontal (time) resolution and vice versa. A note can only have a pure frequency when it is eternal, and a very short note is just a click, composed of all many frequencies.
"Wow, this video is truly inspiring! It's just incredible how 'INTUITIVE ' this lesson was .This is a really underrated channel, u deserve more bro. Big props to Mahesh for simplifying such a genuinely important and" hard to get ur head around " topic!"
Mahesh, again, good job on a complex topic. As a physics grad from the 80s, the thing I need better intuition is how Schrodinger arrived at his equation after saying "Hold my cat".
Is there something similar to the Hamilton-Jacobi formulation of Relativistic Mechanics which may lead to something like Dirac's equation for a relativistic electron ?
How many times have I read about this concept and only now, after years, do I come across an explanation that makes it click. Thank you once again. I think the magic of your lessons is that (a) you trust us to understand, and (b) you've remembered the questions you once had back when you didn't understand either, you remembered what made it click for you, and (c) you wanted to share that joy of discovery. Thank you so much for being you.
0:46 the problem with this analogy is that in this case we know exactly where the ball is, we have full information on it's location. though the photo of it is blurred, we do know that the ball is positioned on the edge of this blurry stain, not anywhere else.
Yes, you may know where it can be but there are clearly *TWO* different edges allowed by the direction of the momentum of the ball. When we measure the momentum of an electron, we also get a two-edged ambiguity which we call electron spin.
So far this is the best video I’ve watched about Heisenberg’s principle of uncertainty. Simple and straightforward while keeping the details. Keep up the good work! +1 follower
Excellent video! For me, the intuitive understanding of Heisenberg came as a result of developing an intuitive understanding of how Fourier transforms work. We could imagine making a normal 'amplitude over time' graph in a way like a seismograph, where the amplitude changes the vertical position of our pen on a piece of paper that is translating to the side. To do a Fourier transform, we do the same thing, only instead of drawing on an unrolling scroll of paper that translates, we put a piece of paper on a record turntable and draw on that. Normally, this will make a spirograph squiggle that is, on average, centered on the rotational axis. However, if the rotational period of our turntable record matches a frequency component of our signal, the signal will be significantly off-center compared to our usual squiggle. By the time the pen swings to the other side of the turntable, the paper has rotated around to that side as well, and most of our ink ends up on that end. If our frequency is a little wrong, the squiggle will be more spread out, but will still have an offset- it's like our squiggle has a slow precession. The Fourier transform just keeps track of this off-centeredness of the squiggle we have drawn, both in phase and amplitude. Like, imagine that the ink we are drawing with is heavy, and we find the center of mass of the squiggle. How this ties into Heisenberg is that, as we turn the dial to change the speed of our record, there is a smooth transition from being on a totally wrong frequency where our center of mass is close to the turntable's rotational axis, to a nearly right frequency where our center of mass starts to drift away from the axis, to a perfectly correct frequency where our center of mass is a maximum distance from this rotational axis. Because the center of mass makes a gradual transition, therefore there must be a fundamental resolution tradeoff between any two attributes of a system that are Fourier complements of each other. Your videos are so wonderful. It's a joy to watch them, and a joy to share them.
I was fortunate enough to have a lecturer who taught me this exact way with as much enthusiasm as you when i was in college. That guy made me love chemistry for life. His name is Murulidhar. I hope kids these days get atleast one lecturer like him in their life.
Until now I was waiting for a breakthrough that will measure an electron's position and momentum exactly. The minute I saw the "title" of this video, I knew I was wrong and that small (but persistent) itch to understand such a beautiful theory intuitively will finally be satisfied. That's my confidence level in you, and I keep recommending you to fellow physics enthusiasts.
When I was first introduced to the uncertainty principle, I understood it as a simple mathematical problem that resulted from the inaccuracy of our measurement methods. I never understood how uncertainty became some fundamental "property" , of matter . I see the NEED for uncertainty to be accounted for in every Quantum Mechanical equation ! We cannot do QM without it. But I never saw it as a fundamental property. I never understood whey some schools of Physics treated it as such. As far as I'm concerned it is just a parameter required for calculations because of our inability to measure the position or speed of a particle without changing the speed and position of the particle while measuring it.
In classical mechanics, a physical property is plotted on a real number line but in quantum mechanics, Hilbert Space is used instead, from which the probability of finding the measured physical property to be a particular real eigenvalue can be computed.
These videos can become the backbone for understanding such complex and abstract concepts for the new generation of high school students around the world. I am a software engineer who started exploring quantum computing just for fun and somehow landed up here. Been here the entire day.
I started learning uncertainty since grade 9, whenever this topic came up I tried my best to understand it but always failed, none of the explaination on books, internet fulfilled me. I wanted to learn the actual concept behind this, whether is it technological limitation or is it a universal truth. Now I’m in second year of college, finally understood the concept thanks to you,I can peacefully sleep rn
OMGGGGG VERYYY EXITED TO WATCH THIS 21 mins and 22 seconds of quantum mechanics on this channel!!! YAAAYYYYYYYYYYYY (Edit:) Nvm. I watched the video, it's a really great video, but sadly, nothing was new for me (hence didn't enjoy like I do before in this channel, Ig it's an exception for quantum physucs 😭)because I only see these types of content everywhere. His explination was what amazes me always. :) thank you sir. You're a very great teacher ❤️✨️ Keep it up!
You are almost the first person to explain quantum duality in an understandable way. It’s like bringing life to the topic, given the vague understanding and unclear media representation. Is it a wave or a particle? Your explanation honestly helped us a lot.
Where have you been all my life 😭 you’re probably the best explainer I’ve come across. Your ability to break things down to the layman(myself) without washing away at the lessons integrity is elite and absolutely unique. I’m just 1 guy so I know it’s not much but just know you have a full fledged subscriber in me. As I type this idk if you have a patreon page or anywhere that I can contribute to you so I’ll find out after I post, just know if you do I’m def contributing
Yes, his videos may have errors but he strives to give us a good feel for the subjects involved. When I asked in high school the question, "How does the electron know that it should show up not on this path, but on the other path ?" during discussion of the diffraction of electrons from a nickel crystal, exhibiting matter wave, 🤔 the teacher replied, "We *DON'T* discuss electron psychology in this class !" 🤐🤪
I am a student of Physics! I have tried but failed to understand the thing! I felt frustrated. After all these years (1993 - 2024) !! Thanks a lot! I cannot thank you more! Please take my deep respect and all the best wishes! I am at 8:22 of video still! Enjoying every frame! By the way I'm no longer related with Physics thing but still I do visit sites, podcasts, videos.....subscribed though you don't need it!
This is the best science channel on TH-cam. The way you address common misconceptions about these principles is immaculate and have really enhanced my understanding of the subject
Heisenberg was never a confident man. One of his characteristic personality traits was his tremendous uncertainty - hence Heisenberg's Uncertainty Principle exists.
I have had a semester of quantum mechanics undergrad and three semesters in graduate school. I am also very knowledgeable in Fourier Theory from a signal processing point of view. For the first time ever I "understand how it works". Buy the way, this also applies to antennas. Small aperture implies broad beam of radiation and the inverse as well. But antenna behavior is classical. Bravo to you.
This is a really good video for breaking down common misconceptions without having to invoke advanced mathematics. A tricky balance, to be sure! For those who are curious about the math details that are left out, the search term you want is "Fourier transform." It turns out there's an uncertainty principle even for classical waves. And the usual deltax deltap formula doesn't come from a vague thought experiment; there's a rigorous derivation for it. If you're careful about which sinusoidal waves you sum together, you can pack the wave amplitude pretty tightly in space, but there's a hard mathematical limit no matter how cleverly you select your sine waves.
You did give us the intuition about how it works but what about the formula and that 2pi in it? I can somewhat understand how plank's constant was there but how did 2pi show up there? It could probably be related to sine waves or the waves that define the position of electron but I need a more detailed explanation about how that formula was derived so plz make a video on that also. I think we would need a understanding of the schrodinger's wave equation (I already know about that though) so you may make a video related to that first and I will be curiously waiting for both of them.
It has to do with whether the Hertz frequency variant of Planck's constant matters, or whether the radian frequency version of Planck's constant matters. The standard formula with Planck's constant uses Hertz frequency, which is E=h*f for the energy of the photon. Planck's constant therefore has the units, Joules per Hertz, and is the energy of a hypothetical 1 Hz photon. The reduced Planck's constant, hbar, is h/(2*pi). This is what you'd get if you replace E=h*f with E=hbar*ω. The value of hbar has the units of Joules per (radian per second). It's very common in differential equations, that the radian frequency is directly determined by the coefficients of the diffEQ, rather than the Hertz frequency. You may be familiar with this, from the frequency of a mass/spring being given by ω=sqrt(k/m), while the equivalent formula for Hertz frequency will be this divided by 2*pi. This is because the calculus of trig functions is most elegant, when the trig units are radians, rather than full cycles or degrees. You end up accumulating chain rule coefficients, if you try to make it work with other angle units.
I had never understood this principle for like years . I looked for books after books, videos after videos. Now I understand it completely. Thank you so much
What do you mean add more momentum to electron ? If each electron had only one wavelength then how do we simply add different wavelengths to it to create localisation to identify its position ?
@@drdca8263 Right, I get that. But what justifies doing that? It just seems random - add a function so it proves our theory. What function? Why _that_ function? Is this another function associated with this electron? If so, what property does it represent? If not, where does it come from? There's no explanation in the video for adding a function, it's just done.
@@MichaelPiz He’s just saying that a sum of sine waves with different frequencies can result in something that is more localized than an individual frequency, which is suggestive of the fact (which can be shown more carefully, but he was aiming at intuition, not rigor) that something localized roughly in one region can be expressed as a linear combination of many different frequencies. So, a wavefunction for the quantum object being close to some location, can be seen as a linear combination of wavefunctions for a variety of different values of momentum. So, you can see it as “it is a mix of positions mostly with the ones near here” or as “it is a mix of different momenta”. It is two different overcomplete bases .
@@drdca8263 Again, I understand that. I'm trying to figure out _why_ that's the case. Or, probably more accurately, what exactly are these additional sine waves? Where do they come from? Do they represent different possible values for the electron's momentum? That would make sense, if I understand correctly, because the electron can have any of infinitely many possible values for momentum. (And the more of them we have or, better, the more we use, the more precisely we can determine the electron's position.) If not, then what? (Side note: Is this collection of sine waves a superposition?) I'm probably doing a poor job of stating what I'm asking.
How I wish such well crafted presentation was given during my school lectures. The future is so bright with folks like Mahesh, who are able to reach to so many people and potential future generations with such good videos explaining the unintuitive quantum objects, which were hiding from us since the inception of time, in simple intuitive concepts!
Heisenberg, Ohm and Schrodinger are in a car. They get pulled over. Heisenberg is driving, and the cop asks him, “Do you know how fast you were going?” “No, but I know exactly where I am,” Heisenberg replies. The cop says, “You were doing 55 in a 35.” Heisenberg throws up his hands and shouts, “Great! Now I’m lost!”
Two things I cannot understand. 1. For a single wave function if the wave stretches infinitely and we are saying ∆x = ∞, and if there is a finite amplitude, does that mean the wave has infinite energy? 2. For a standing wave of an electron, won't the position be finite?
Love this! I am seeing so many relations in the world of physics and appreciate growing in understanding. I appreciated learning to the level of being able to teach the idea, although it would also be good to learn the math behind it too. So a question I thought of worth for Gemini or ChatGPT that gave a non-definite relationship was, "And what would the relationship be thereby from the wavelength of a proton to its constituent quarks?" Then ask, "So do quarks have a wavelength?" You'll get into the de Broglie equation and quark confinement.
Uncertainty in measuring particles exists because until measured they exist in a future state. Because causality has a speed limit (c) every point in space where one observes it from will be the closest to the present moment. When one looks out into the universe they see the past which is made of particles (GR). When one tries to measure the position of a particle they are observing smaller distances and getting closer to the present moment (QM). The wave property of particles appears when we start trying to predict the future of that particle. A particle that has not had an interaction exists in a future state. It is a probability wave because the future is probabilistic. Wave function collapse is what we perceive as the present moment and is what divides the past from the future. GR is making measurements in the observed past and therefore, predictable. It can predict the future but only from information collected from the past. QM is attempting to make measurements of the unobserved future and therefore, unpredictable. Only once a particle interacts with the present moment does it become predictable. This is an observational interpretation of the mathematics we currently use based on the limited perspective we have with the experiments we choose to observe the universe with.
Excellent explanations of the uncertainty principle (indeterminacy), that is, momentum and position of quantum particles. Thank you Mahesh, you are brilliant like your sponsore
0:48 This explanation is actually not intuitive or accurate at all. We do know where the tennisball is in that second photo because it would always be exactly in the center of the blurred tennisball. Unless the shutterspeed of the camera is set so high that the ends of the blur are no longer visible (in which case it just becomes a streak) we can always know the exact location of the tennisball at every frame, we just can't make out the visual details of the tennisball.
The tennis ball example is a visual analogy. It is not a quantum object like an electron, so there is some break down in the analogy. But ask yourself what the DeBroglie wavelength of a macro object like a tennis ball would be, and you will get a feeling why the Heisenberg Uncertainty Principle is very difficult to apply to macro objects.
I feel like your reply is pedantic and I actually really like the visual explanation. Maybe postulate the very real situation where the ball is accelerating (from gravity and wind resistance+spin) in a direction unknowable from the picture. Therefore, we cannot calculate the position of the ball from our measurement device, but we could get an average velocity rather accurately. But really any useful analogy is incorrect and I think it's ok to live with it.
QUESTION: When you want to discover a particle's position(s), you add several waves of different freq's (momenta) together. But where did you get those diffrerent values of f from? Did you just make them up? Love your videos!
The example is meant to illustrate how when we already know a particle's general position, its wave function (which has few peaks) can be shown to break down into a series of many sine waves of specific wavelength (each with infinitely many peaks) added together. These numerous pure sine waves represent the many possible options for the particle's momentum, demonstrating the high degree of uncertainty in momentum that is effectively contained in the wave function of a particle whose position in known more certainly. In other words, when we are presented with a wave function that shows certainty in position, there MUST be uncertainty in momentum - due to the nature of the wave function that describes the particle, not due to issues with "measurement". So, think through the way he explained it but in reverse. It's not that we want to discover a particle's position - it's that we already have relatively certain information about its position, and we then ask, "why do we lack certainty in the particle's momentum?" It's because the wave function that contains certain (or rather, less uncertain) information about the particle's position breaks down into many pure sine waves that together represent the many momenta the particle could have, and therefore the lack of certainty in the particle's momentum. In the video, this is explained in reverse. By starting with a hypothetical particle whose momentum is known with 100% certainty (represented by an infinitely long pure sine wave), we can know nothing about its position (we are infinitely uncertain). We can then ask, "what if there were 2 options for the particle's momentum?", and add another (random) infinitely long pure sine wave to the system of information about the particle. Keep repeating this process, and the more options we introduce for the particle's momentum, the less certain it becomes, but the more certain its position becomes when we take the sum of that information and see that the amplitude of the overall wave function has been narrowed down to just a few number of peaks.
Wow, just found your channel and I already love it. Quantum mechanics is so incomprehensible in many areas, it is nice to have those small domains that we can actually wrap our heads around. I was very comfortable with the uncertainty principle before this, but now I feel a gut-level intuition about uncertainty and a better feel for wave-particle duality. Thanks!
This explaination is about how λ relates Position of a particle (as an analogy). Which it demonstrates very well. λ is defined as the wavelength of the probability wavefunction after all. Of course it will relate to position. By the very definition it will!! But De Broiglie's Hypothesis is that p (momentum) relates to λ in the physical world. Which is the crux that is hard to understand (or relate to).
Oh! let me show this video to Feynman, last time he was curious whether Mahesh is interested in Heisenberg Uncertainty Principle or not.❤ Thanks for the explanation 😊
I want to start by saying that this is the best explanation of the math and the concepts that I have ever heard. That said, how does one add wavelengths? I would assert that this explanation indicates that electrons do not exist as we understand existence. More appropritely, if momentum is conserved, every electron observed in a different location is a different electron. It is not that we find an electron in different places, it is that everywhere we look we find different electrons. And that, to me, reveals a problem with how we view energy. Are we, perhaps, looking at this wrong? It works in math but not reality?
I've never seen that analogy that your teacher used. I actually find it useful. Yet, like all analogies, there's a point where correspondence falls apart. We use analogies all the time to understand various principles and phenomena. Yet using our macroscopic world for understanding atomic and subatomic phenomena will virtually always be limited. I've never heard the "wave-particle" duality explained so succinctly. TY.
Amazing, I was studying for quantum mechanics exam and couldn't understand how uncertainty prevents electron form collapsing. This is the first place when someone actually gave a satisfactory answer. Thank you!
I *literally* said to myself out loud "WHOA ......" at your teacher's explanation of the Heisenberg Uncertainty Principle at the beginning of the video. I've never heard such an intuitive way of thinking about this phenomenon! Amazing!
This is the first time I'm seeing a video of yours, and I have to say, I'm quite impressed. You've explained it beautifully. I especially love the responsible portrayal of quantum objects as neither particles nor waves, instead of both. I've recently watched the MIT's introduction to quantum mechanics lecture 1 by Allan Adams (I recommend it to everyone, the lecture 1 has no math and is super layman-friendly), and the way he explained superposition finally made it click for me - that it's not the electron "taking both paths at the same time", but rather the electron having a very weird form of existing which does not conform to our intuitions of a solid object traveling along a path - a way of existing for which we didn't really have words or metaphors for, before discovering it in QM. Even though it's basically saying that the electron doesn't make sense in the way we're used to, him putting it this way, paradoxically, makes way more sense for me than saying "it's in two places at once". Your framing of particle-wave duality felt similar, and I really appreciate it.
Man you are amanzingly clear and practical, it’s so important to give intuitive and practical explanations of physical, avoiding to get lost in the mathematics with no understanding of the real deal. I think you are better than many university professors (maybe you are one of them, in that case good for your students). Keep going
If only everyone had the chance to learn from the great minds like Feynman & Einstein themselves. Luckily we have YT and someone as passionate as you are. Forever indebted.
Man this is awesome! I've never understood any video about the uncertainty principle, then had QM in Uni last year, understood it from a mathy view with basis', FT and so on. But this makes so clear and easy and i can see all the math you cleverly hid in the explanation. You're awesome!
Last time I dealt with deBroglie waves and Psi-squared functions was 45 years ago. I'm surprised at how much I remember, given that I've never used the information. But I had so much fun in my modern physics class, I almost delayed my graduation so I could take the second half. Thanks for the interesting presentation!
I learnt to derive Schrodinger wave equation and Heisenberg uncertainty, having a solid background in advanced electromagnetics, your explanation clarifies many untangled questions thank you.
What was that 😍😍... I just got some real feelings of joy in this 21 min video. Sir requesting please don't stop uploading this kind of mind-blowing video that give explanation of science the way it should be done.❤❤❤ Lots of love 😘
As a fresh out of highschool-going into college student this was really enlighting. Could you please make a video in Schrodingers equation and put some intuition into it. The math really overwhelms the whole idea of it.
This video is giving me wonderful insights. I love the specificity in highlighting that "wave-particle duality" doesn't mean that the object *is* a wave and a particle, which is how most people (even non-expert teachers!) will explain it. I'll definitely be taking that away from the video, if nothing else, though the thorough step-by-step in outlining the uncertainty principle is fantastic too.
I have watched dozens of videos on TH-cam to understand the Heinsenberg Uncertainty Principle and this is certainly the best video of all. It was the one I learned the most from. Your teaching is excellent. Thank you very much. But I still don't understand one thing: given that a quantum object has the property of a wave, what does it mean to add waves to locate the object? How is this done? I understood that by adding waves to "shrink" the resulting wave and decrease the uncertainty of the position, you increase the uncertainty of the momentum, since there are several simultaneous waves (with several wavelengths mixed together), but how is this done in practice? And what does it mean? Thanks!
@@geovanejag3946 hey, thanks for sharing that. I guess I could have been clearer there. It’s not that we start with an infinite wave and then keep adding more. Instead, most quantum objects are NOT like that. They are mostly localised wave packets. Now this localised wave packet can be thought of as sum of many pure sine waves, I.e. many wavelengths, i.e many momenta. So, just to the explain this above idea, I started with a pure sine wave and kept adding them.
I adore how you helped me understand how the math of the schrodinger equation leads to the uncertainty principle without having to go into in depth college math. Now that it feels more approachable tho I want to investigate the math lol
I asked my teacher why is this principle accepted? why is this true?..but she didn't give me proper answer...I'm glad i got answers for my doubts here...thank you so much sir!!!
Great video, this helped to clarify a few tings! I had a few questions: 1) You added waves to find more certainty in the position (FFT). What physical process causes the addition of the waves for the inteference? Is it measurement? 2) Imagine there is a radioactive element surround by a spherical detector. When the radioactive element decays it emits an alpha particle and the detector finds the alpha particle in one location. Could I not know both the position and momentum at the same time? I know the position because the alpha particle hit at one point on the spherical detector. I could determine the momentum because I have the mass of the alpha particle and the distance and the time could be determined. Unless is there uncertainty in the time?
i really appreciate that you separated the sponsor from the rest of the video with timestamps and that humble "i have made a video about that but you dont have to watch it, not farming views here." and definitely your enthusiasm. very nice job, you've earned a subscriber, keep it up!! and i dont usually comment but i really wanted to let you know!
5:31 “ electrons are not particles“ in a particle detector we see electrons as particles. So ultimately they must be particles. There’s something about their motion that causes them to move in a way that seems like there is an interference pattern.
We don't "see" electrons as particles, particle detectors are built with the idea that a particle and a (quantized) wave are the same thing on a quantum scale. We don't see a particle, as we fundementally lack te means of distinguishing the two at quantum scale (presumably because they are the same concept), we just see an electron. The name particle detector is arbitrary, it's called that because "wave detector" is a less clear name (since there are non-quantum waves, unlike with particles). It very well could've been called wave-particle detector or silly detector or even Frank really
Thanks for presenting physics in an intuitive way I have spent my entire 11th frustrated having not been able to feel the concepts But now that I have got a feel of it I feel the ecstasy just as you
To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/FloatHeadPhysics . You’ll also get 20% off an annual premium subscription. Also FAQ
1) What does it mean to add two waves together?
I could have been clearer here. The bottom line is since a wave packet can be mathematically constructed by adding lots of pure sine waves of different wavelengths (Fourier series), a wave packet contains multiple wavelengths. So, an electron can be thought of as a wave packet HAVING multiple wavelengths, and hence HAVING multiple momenta.
2) What's the intuition behind energy time uncertainty?
If you hear a tone for a small time, you are unsure about it's frequency. (You don't know if it's a pure sine wave or not). This means you are unsure about it's energy (E = hf). But since the time interval was very small, you are pretty accurate the absolute time value when you made the measurement.
On the other hand if you hear a tone for a long time, you become more sure about it's frequency. (You have much better idea about the repeating pattern). This means you are more sure about it's energy. But since the time interval was large, your accuracy about the absolute time when you made the measurement went down!
Shoehorn Dirac's Equation into this explanation 😊
Man you are the biggest badass physics teacher of all times.... realy a genious...
psi(relief)
I have one for you
What was the temperature of the film inside the camera while being on the Moon?
Sir
Can you please explain how time is related to motion
I love how every time you make a video like this you talk as if you brought the scientists back from the dead and had lunch with them to make this video.
Bold of you to assume he didn't.
Yeah at first I found it patronising, but then I realised it is the perfect way to explain things. The conversation is the stepping stones to understanding 👌
Haha, when you read well written books, that's exactly what it feels like. I kid you not! (Try the book, 'surely you are joking mr. Feynman'. It's so nicely written, you feel like Feynman is sitting next to you explaining his life)
You should do one about Feyman’s “why”? It is amazing!
@@Mahesh_Shenoy"Curiosity is the spark that ignites the flame of discovery. Embrace your curiosity, ask questions, seek answers, and never stop wondering about the world around you. For in the pursuit of knowledge, you shall find the secrets of the universe, and the universe shall reveal its secrets to you."
Remember, science is a journey, not a destination. It's a mindset, a way of thinking, and a passion for understanding the world. As a scientist, you'll encounter challenges, failures, and setbacks, but also moments of triumph, wonder, and awe.
So, cultivate your curiosity, stay curious, and never lose your sense of wonder. The world needs more curious minds like yours, eager to explore, discover, and push the boundaries of human knowledge.
Now, go ahead, ask a question, design an experiment, collect data, analyze results, and draw conclusions. The scientific method is your tool, and the universe is your playground. Happy exploring!
Now I understand. It's been 30 years of me trying to understand the uncertainty principle. I started as a 14-year-old and a high interest in physics, but no one was ever able to just break it down and explain it to me like this. Thank you, side quest complete.
Wow, feels incredible to hear this. Thank you for sharing :)
@@Mahesh_Shenoy
Man...
Wormhole video
@@Mahesh_Shenoy
wormhole video day 4
Still struggling to get my head round that! How can the probability not come from the measurement side? If The electron follows a path in the electron cloud, surely the probability of position comes down to the timing of measurement. How do we know the electron doesn't follow a specific path?
@@liamweavers9291 Now you're back to a double slit type experiment.
Almost 20 years ago, I first came across the uncertainty principle in Class XI Chemistry studying the atomic structure.
This is the best explanation yet. Indeed intuitive.
And over the years, I've realised that it's not that some subjects and some topics are tough, it is the quality of books and quality of the teachers that make a difference!! And if you're not in luck with the teacher's quality, do get good quality books!!
This is how I feel too! To have a teacher or a book that makes a subject feel easy is a blessing. And it makes you wonder if some subjects aren't intrinsically harder, but are rather just taught poorly.
Whenever I tell my students about quantum theory, I always try to highlight how necessary it is. The wave-particle duality is the entire reason we have atoms. If the electron is not a wave, but a particle, then all atomic orbitals decay in about 16 picoseconds.
You can use the uncertainty principle alone to back-of-the-envelope estimate the order of magnitude an electron's energy at various distances to a proton. Within nuclear scales, it'd be enough to shoot it clean out of the proton's attractive potential. At the scale of the Bohr radius, it's on the order of a dozen or so electron volts, in agreement with the Schrödinger equation. The uncertainty principle actually implies a repulsive force between the proton and electron at sufficiently short distances, preventing orbital decay.
Even though I teach this, it never fails to blow my mind every time I think about it.
Ty
no distances electrons don’t move around nucleus!!! They just waving ,and higher energy levels just means a higher electron -wave energies
@@nanotechnano7193 true but you can measure the distance the electron is from the nucleus at a given time.
The probability distribution for this observable in Hydrogen's ground state peaks at the Bohr radius with a mean at about 1.5 times that distance. Whereas, the probability of measuring the electron to be within nucleon distances to the proton is so small that it's practically zero.
So, the qualitative understanding we can derive from the uncertainty principle alone matches what the full theory would predict.
@@jmcsquared18
What's the angular momentum of a single electron in the ground state of protium ?
This is genuinely the best science education channel out there man. Have never left any of your videos without having learned something new or in a better way than I previously understood it.
ScienceClic is also one channel, it is unfortunately one of only 3 complete explaining channels I found.
Agree
@@c.jishnu378 What are the other ones?
@@alejandrocastellanos7139 This, ScienceClic and Eugene Physics, though the last one's animation is a bit old school.
Just subscribed! 😃
Honestly, as an Indian, I never expected some Indian to be this passionate about Physics, a person really wants to understand physics for the sake of Physics, at least until now. It was my friend who first suggested your video about Quantum Spin. I thought it would be just like any other video about physics, a Lecture with a bunch of mathematical relations and claim something to be true just because math does imply so. I know and I agree that Quantum and Relativity are not intuitive in our common sense and it's true because what we say common sense, is just a genre of experiences in the macroscopic world, a classical world. Still, there is always room for improvement we can extend our domain of intuition by asking the right questions and that's what you do best.
Really, I always wanted someone to share the same passion for Physics. I have seen all your videos and all I want to say is "Keep on doing"
Wow, that's truly encouraging. Thank you :)
Hey, did you sent out a message to me. Can you send me again
@@Mahesh_Shenoy hi sir ! If you love the physics this way, why didnt you become a theoretical physicist ? Or you are ?
There are Indians who are passionate about Physics, too. There are even some Nobel Prize winners among them. You as an Indian just need to dig deeper to uncover your (very ancient as well as up to modern times) civilization's cultural heritage. 😊
Bose and Chandrasekhar came to my mind. Ramanujan was a great pure mathematician, though not in physics.
The sign of a great genius is to be able to explain a complex subject to an idiot, like me, in a way I can understand! Thank you so much!
He explained it well. Actually, the formula actually applies to all waves. You would just use the frequency instead of the momentum for non-quantum objects.
But be careful Quantum Physics is FICTION. Like many other pseudo-sciences. Like faster than light travel, time travel to the past, and other dimensional universes. Those quack do like he did he explains something true and then switches to his pseudo-science
A sign of a smart person is being able to recognize that they do not understand something. You would be startled by the percentage of people who accept concepts that they misjudged to have understood.
Mahesh… that was exceptional! Thank you… my uncertainty on this is now far more certain while making my certainty more uncertain!!
I didn't expect to find you here, love your videos!
Thanks a lot :)
Same for me. I find the quantum world very strange and confusing, even more the more I learn about it. I'm trying to get accustomed to these explanations but have still a long way to go. I always wonder how these quantum effects add up to the predictable, deterministic macroscopic world we live in!
@@Mahesh_ShenoyHi! Could you please explain the physical meaning of adding another wave to the electron wave (I mean does it mean shooting another electron to the original electron)
Got this in my recommended. Started watching and when I heard your voice, I thought that it sounded familiar. But then when you started just the voice over I immediately knew...
You're MY physics teachers.I've been learning physics from your videos on Khan Academy since 8th grade!!! 5 years now, and I NEVER KNEW YOU HAD A TH-cam CHANNEL!!!
Thank you so much for your videos. I owe all my grades and understanding of physics entirely to you 🙌💛
Finally, Mahesh is heading towards the intuition of Quantum Physics!!!!!!
Every pop science channel ever wants you to think that such a thing is possible because it drives their views and engagement. The only intuition you can get in that subject is by a good understanding of the math or the data you see from experiments.
Time and frequency are also complementary variables. A sinewave extends to -inf to +inf. This gives us a pair of impulse functions (infinitesimally wide, but infinitely tall pulses) in the frequency domain when we take the Fourier transform. When we look at a sinewave for a non-infinite amount of time, we are always chopping off some of the sinewave (Rectangular window function). This causes the frequency spectrum to of the impulses to spread out (convolving with the fourier transform of the window function in the frequency domain). This spreading of the sinewave's spectrum gives us an uncertainty on the actual frequency of the non-chopped sinewave. If you look at the sinewave for a shorter period of time, the spectral spreading of the sinewave, and your uncertainty about the frequency of the sinewave gets worse.
Bro explained the Heisenberg Uncertainty Principle in the first 1 minute of the video better than I've EVER heard anyone explain it. Makes PERFECT INTUITIVE SENSE now. Thanks so much!!
Edit: I watched the rest and yes that's the less accurate version but it ended up still working for me because I didn't assume you could determine velocity by just going to the next slide because I assumed there was no next slide, which ended up working for me. However, the next explanation he gave was even better anyways so ... win win!!
and that is the LESS accurate version!
That's why we're here every time he uploads
And then he explains that this intuitive explanation does not really work. Watch the rest.
Haha. Also if you keep the ball at rest on a table, now you know both its position and momentum :D. So in Feynman’s words, I would have cheated you very badly!
"...hold my cat!" Cracked me up! 😅🤣😂🙃😊
A similar thing can be observed for signals in time and frequency domains.
Signals which are non-zero for low time duration have their spectrum spread apart in frequency and vice versa.
For instance, Fourier transform of an impulse (infinitesimally small duration signal) is constant ( i.e. spread over entire frequency spectrum) whereas Fourier transform of a sinusoidal signal (spread in time domain) consists of impulses in the frequency domain.
A fun way to get a feel for the phenomenon is to play with a sound editor like Audacity, mix in some beeps of varying lengths and pitches (arranged into chords, even), then show the track in Spectral view mode. You can adjust the vertical (frequency) resolution as much as you like, but doing so smears out the horizontal (time) resolution and vice versa. A note can only have a pure frequency when it is eternal, and a very short note is just a click, composed of all many frequencies.
I have been trying to understand the uncertainty principle for a long long time. This was, by far, the best explanation I have ever come across.
"Wow, this video is truly inspiring! It's just incredible how 'INTUITIVE ' this lesson was .This is a really underrated channel, u deserve more bro. Big props to Mahesh for simplifying such a genuinely important and" hard to get ur head around " topic!"
Mahesh, again, good job on a complex topic. As a physics grad from the 80s, the thing I need better intuition is how Schrodinger arrived at his equation after saying "Hold my cat".
from the Hamilton Jacobi Equation formulation of classical mechanics.
Is there something similar to the Hamilton-Jacobi formulation of Relativistic Mechanics which may lead to something like Dirac's equation for a relativistic electron ?
I really love this guy's teaching style, his knowledge, and his excitement for physics. Mahesh is unique.
How many times have I read about this concept and only now, after years, do I come across an explanation that makes it click. Thank you once again. I think the magic of your lessons is that (a) you trust us to understand, and (b) you've remembered the questions you once had back when you didn't understand either, you remembered what made it click for you, and (c) you wanted to share that joy of discovery. Thank you so much for being you.
0:46 the problem with this analogy is that in this case we know exactly where the ball is, we have full information on it's location. though the photo of it is blurred, we do know that the ball is positioned on the edge of this blurry stain, not anywhere else.
Yes, you may know where it can be but there are clearly *TWO* different edges allowed by the direction of the momentum of the ball. When we measure the momentum of an electron, we also get a two-edged ambiguity which we call electron spin.
@@solconcordia4315 very interesting observation, thank you
So far this is the best video I’ve watched about Heisenberg’s principle of uncertainty. Simple and straightforward while keeping the details. Keep up the good work! +1 follower
Excellent video!
For me, the intuitive understanding of Heisenberg came as a result of developing an intuitive understanding of how Fourier transforms work. We could imagine making a normal 'amplitude over time' graph in a way like a seismograph, where the amplitude changes the vertical position of our pen on a piece of paper that is translating to the side. To do a Fourier transform, we do the same thing, only instead of drawing on an unrolling scroll of paper that translates, we put a piece of paper on a record turntable and draw on that. Normally, this will make a spirograph squiggle that is, on average, centered on the rotational axis. However, if the rotational period of our turntable record matches a frequency component of our signal, the signal will be significantly off-center compared to our usual squiggle. By the time the pen swings to the other side of the turntable, the paper has rotated around to that side as well, and most of our ink ends up on that end. If our frequency is a little wrong, the squiggle will be more spread out, but will still have an offset- it's like our squiggle has a slow precession. The Fourier transform just keeps track of this off-centeredness of the squiggle we have drawn, both in phase and amplitude. Like, imagine that the ink we are drawing with is heavy, and we find the center of mass of the squiggle.
How this ties into Heisenberg is that, as we turn the dial to change the speed of our record, there is a smooth transition from being on a totally wrong frequency where our center of mass is close to the turntable's rotational axis, to a nearly right frequency where our center of mass starts to drift away from the axis, to a perfectly correct frequency where our center of mass is a maximum distance from this rotational axis. Because the center of mass makes a gradual transition, therefore there must be a fundamental resolution tradeoff between any two attributes of a system that are Fourier complements of each other.
Your videos are so wonderful. It's a joy to watch them, and a joy to share them.
I was fortunate enough to have a lecturer who taught me this exact way with as much enthusiasm as you when i was in college. That guy made me love chemistry for life. His name is Murulidhar. I hope kids these days get atleast one lecturer like him in their life.
Until now I was waiting for a breakthrough that will measure an electron's position and momentum exactly. The minute I saw the "title" of this video, I knew I was wrong and that small (but persistent) itch to understand such a beautiful theory intuitively will finally be satisfied. That's my confidence level in you, and I keep recommending you to fellow physics enthusiasts.
are you satisfied, i mean we still know nothing we are just giving theories .
When I was first introduced to the uncertainty principle, I understood it as a simple mathematical problem that resulted from the inaccuracy of our measurement methods.
I never understood how uncertainty became some fundamental "property" , of matter .
I see the NEED for uncertainty to be accounted for in every Quantum Mechanical equation ! We cannot do QM without it.
But I never saw it as a fundamental property. I never understood whey some schools of Physics treated it as such.
As far as I'm concerned it is just a parameter required for calculations because of our inability to measure the position or speed of a particle without changing the speed and position of the particle while measuring it.
In classical mechanics, a physical property is plotted on a real number line but in quantum mechanics, Hilbert Space is used instead, from which the probability of finding the measured physical property to be a particular real eigenvalue can be computed.
These videos can become the backbone for understanding such complex and abstract concepts for the new generation of high school students around the world. I am a software engineer who started exploring quantum computing just for fun and somehow landed up here. Been here the entire day.
This is the first time I've come close to understanding this topic
Great work.
I started learning uncertainty since grade 9, whenever this topic came up I tried my best to understand it but always failed, none of the explaination on books, internet fulfilled me. I wanted to learn the actual concept behind this, whether is it technological limitation or is it a universal truth. Now I’m in second year of college, finally understood the concept thanks to you,I can peacefully sleep rn
OMGGGGG VERYYY EXITED TO WATCH THIS 21 mins and 22 seconds of quantum mechanics on this channel!!! YAAAYYYYYYYYYYYY
(Edit:) Nvm. I watched the video, it's a really great video, but sadly, nothing was new for me (hence didn't enjoy like I do before in this channel, Ig it's an exception for quantum physucs 😭)because I only see these types of content everywhere. His explination was what amazes me always. :) thank you sir. You're a very great teacher ❤️✨️
Keep it up!
You are almost the first person to explain quantum duality in an understandable way. It’s like bringing life to the topic, given the vague understanding and unclear media representation. Is it a wave or a particle? Your explanation honestly helped us a lot.
Don't forget about Diracs Equation also & Maxwells Equations and the Pauli Exclusion Principle 😊
Where have you been all my life 😭 you’re probably the best explainer I’ve come across. Your ability to break things down to the layman(myself) without washing away at the lessons integrity is elite and absolutely unique. I’m just 1 guy so I know it’s not much but just know you have a full fledged subscriber in me. As I type this idk if you have a patreon page or anywhere that I can contribute to you so I’ll find out after I post, just know if you do I’m def contributing
Literally the best science communicator I have watched. Good shit man, love this.
This guy is being feynman to us. I really appreciate your content. This is true science that most teachers fail to capture.
Yes, his videos may have errors but he strives to give us a good feel for the subjects involved.
When I asked in high school the question, "How does the electron know that it should show up not on this path, but on the other path ?" during discussion of the diffraction of electrons from a nickel crystal, exhibiting matter wave, 🤔 the teacher replied, "We *DON'T* discuss electron psychology in this class !" 🤐🤪
Thanks a lot!! Cleared a lot of misconceptions i had
I am a student of Physics! I have tried but failed to understand the thing! I felt frustrated. After all these years (1993 - 2024) !! Thanks a lot! I cannot thank you more! Please take my deep respect and all the best wishes! I am at 8:22 of video still! Enjoying every frame! By the way I'm no longer related with Physics thing but still I do visit sites, podcasts, videos.....subscribed though you don't need it!
Wow, wow, wow! The first 60 seconds puts it into a brilliant perspective
This is the best science channel on TH-cam. The way you address common misconceptions about these principles is immaculate and have really enhanced my understanding of the subject
Heisenberg was never a confident man. One of his characteristic personality traits was his tremendous uncertainty - hence Heisenberg's Uncertainty Principle exists.
He was not an ignorant man. He was confident in the uncertainty.
I have had a semester of quantum mechanics undergrad and three semesters in graduate school. I am also very knowledgeable in Fourier Theory from a signal processing point of view. For the first time ever I "understand how it works". Buy the way, this also applies to antennas. Small aperture implies broad beam of radiation and the inverse as well. But antenna behavior is classical. Bravo to you.
Thanks for this Quantum Mechanics Content.
This is a really good video for breaking down common misconceptions without having to invoke advanced mathematics. A tricky balance, to be sure!
For those who are curious about the math details that are left out, the search term you want is "Fourier transform." It turns out there's an uncertainty principle even for classical waves. And the usual deltax deltap formula doesn't come from a vague thought experiment; there's a rigorous derivation for it. If you're careful about which sinusoidal waves you sum together, you can pack the wave amplitude pretty tightly in space, but there's a hard mathematical limit no matter how cleverly you select your sine waves.
You did give us the intuition about how it works but what about the formula and that 2pi in it? I can somewhat understand how plank's constant was there but how did 2pi show up there? It could probably be related to sine waves or the waves that define the position of electron but I need a more detailed explanation about how that formula was derived so plz make a video on that also. I think we would need a understanding of the schrodinger's wave equation (I already know about that though) so you may make a video related to that first and I will be curiously waiting for both of them.
Yea, I ran out of time for that. You can derive the expression using the single slit experiment actually. It's pretty cool.
It has to do with whether the Hertz frequency variant of Planck's constant matters, or whether the radian frequency version of Planck's constant matters.
The standard formula with Planck's constant uses Hertz frequency, which is E=h*f for the energy of the photon. Planck's constant therefore has the units, Joules per Hertz, and is the energy of a hypothetical 1 Hz photon.
The reduced Planck's constant, hbar, is h/(2*pi). This is what you'd get if you replace E=h*f with E=hbar*ω. The value of hbar has the units of Joules per (radian per second).
It's very common in differential equations, that the radian frequency is directly determined by the coefficients of the diffEQ, rather than the Hertz frequency. You may be familiar with this, from the frequency of a mass/spring being given by ω=sqrt(k/m), while the equivalent formula for Hertz frequency will be this divided by 2*pi. This is because the calculus of trig functions is most elegant, when the trig units are radians, rather than full cycles or degrees. You end up accumulating chain rule coefficients, if you try to make it work with other angle units.
I had never understood this principle for like years . I looked for books after books, videos after videos. Now I understand it completely. Thank you so much
What do you mean add more momentum to electron ? If each electron had only one wavelength then how do we simply add different wavelengths to it to create localisation to identify its position ?
I asked essentially the same question in my comment, though much less effectively than your version.
This isn’t describing a physical process of adding something to an object. It is describing a sum of different functions, added pointwise
@@drdca8263 Right, I get that. But what justifies doing that? It just seems random - add a function so it proves our theory. What function? Why _that_ function? Is this another function associated with this electron? If so, what property does it represent? If not, where does it come from? There's no explanation in the video for adding a function, it's just done.
@@MichaelPiz He’s just saying that a sum of sine waves with different frequencies can result in something that is more localized than an individual frequency,
which is suggestive of the fact (which can be shown more carefully, but he was aiming at intuition, not rigor) that something localized roughly in one region can be expressed as a linear combination of many different frequencies.
So, a wavefunction for the quantum object being close to some location, can be seen as a linear combination of wavefunctions for a variety of different values of momentum.
So, you can see it as “it is a mix of positions mostly with the ones near here” or as “it is a mix of different momenta”.
It is two different overcomplete bases .
@@drdca8263 Again, I understand that. I'm trying to figure out _why_ that's the case. Or, probably more accurately, what exactly are these additional sine waves? Where do they come from? Do they represent different possible values for the electron's momentum? That would make sense, if I understand correctly, because the electron can have any of infinitely many possible values for momentum. (And the more of them we have or, better, the more we use, the more precisely we can determine the electron's position.) If not, then what?
(Side note: Is this collection of sine waves a superposition?)
I'm probably doing a poor job of stating what I'm asking.
How I wish such well crafted presentation was given during my school lectures. The future is so bright with folks like Mahesh, who are able to reach to so many people and potential future generations with such good videos explaining the unintuitive quantum objects, which were hiding from us since the inception of time, in simple intuitive concepts!
Heisenberg, Ohm and Schrodinger are in a car. They get pulled over.
Heisenberg is driving, and the cop asks him, “Do you know how fast you were going?”
“No, but I know exactly where I am,” Heisenberg replies.
The cop says, “You were doing 55 in a 35.”
Heisenberg throws up his hands and shouts, “Great! Now I’m lost!”
Two things I cannot understand.
1. For a single wave function if the wave stretches infinitely and we are saying ∆x = ∞, and if there is a finite amplitude, does that mean the wave has infinite energy?
2. For a standing wave of an electron, won't the position be finite?
Are you giving jee?
@@-_-h1 Why do you ask?
lets ask the most important question: where did you get that tshirt?
This might be the most intuitive and simplistic explanation for the Heisenberg uncertainty principle I've ever came across, Thanks bro.
Love this! I am seeing so many relations in the world of physics and appreciate growing in understanding. I appreciated learning to the level of being able to teach the idea, although it would also be good to learn the math behind it too. So a question I thought of worth for Gemini or ChatGPT that gave a non-definite relationship was, "And what would the relationship be thereby from the wavelength of a proton to its constituent quarks?" Then ask, "So do quarks have a wavelength?" You'll get into the de Broglie equation and quark confinement.
don't use AI. pls. I assure chat GPT doesn't know jack about proton structure.
Uncertainty in measuring particles exists because until measured they exist in a future state. Because causality has a speed limit (c) every point in space where one observes it from will be the closest to the present moment. When one looks out into the universe they see the past which is made of particles (GR). When one tries to measure the position of a particle they are observing smaller distances and getting closer to the present moment (QM). The wave property of particles appears when we start trying to predict the future of that particle. A particle that has not had an interaction exists in a future state. It is a probability wave because the future is probabilistic. Wave function collapse is what we perceive as the present moment and is what divides the past from the future. GR is making measurements in the observed past and therefore, predictable. It can predict the future but only from information collected from the past. QM is attempting to make measurements of the unobserved future and therefore, unpredictable. Only once a particle interacts with the present moment does it become predictable. This is an observational interpretation of the mathematics we currently use based on the limited perspective we have with the experiments we choose to observe the universe with.
You couldnt have come up with a more confusing explanation if you tried lol
Just tell me you wrote this to flex
You shouldn’t state this like a fact when it is your personal speculation.
is it like a copy pasta now, I can see this comment on multiple such videos.
@@drdca8263 well you stated your comment like it’s a fact. Why do you get to but I don’t?
Listening to Mahesh pronounce “probability” is priceless. We love you Mahesh. ❤
Interesting, why is that?
Plot twist: Albert Einstein denied the credibility of the uncertainty principle
😮
Yes but he can't get a unifying theory before his death
Excellent explanations of the uncertainty principle (indeterminacy), that is, momentum and position of quantum particles.
Thank you Mahesh, you are brilliant like your sponsore
0:48 This explanation is actually not intuitive or accurate at all. We do know where the tennisball is in that second photo because it would always be exactly in the center of the blurred tennisball. Unless the shutterspeed of the camera is set so high that the ends of the blur are no longer visible (in which case it just becomes a streak) we can always know the exact location of the tennisball at every frame, we just can't make out the visual details of the tennisball.
The tennis ball example is a visual analogy. It is not a quantum object like an electron, so there is some break down in the analogy. But ask yourself what the DeBroglie wavelength of a macro object like a tennis ball would be, and you will get a feeling why the Heisenberg Uncertainty Principle is very difficult to apply to macro objects.
I feel like your reply is pedantic and I actually really like the visual explanation.
Maybe postulate the very real situation where the ball is accelerating (from gravity and wind resistance+spin) in a direction unknowable from the picture. Therefore, we cannot calculate the position of the ball from our measurement device, but we could get an average velocity rather accurately.
But really any useful analogy is incorrect and I think it's ok to live with it.
How about watching the whole video before commenting?
QUESTION: When you want to discover a particle's position(s), you add several waves of different freq's (momenta) together. But where did you get those diffrerent values of f from? Did you just make them up? Love your videos!
I had the same question
Fourier transform. Draw pretty much any shape of a function you want, do a Fourier transform and it will show you which simple waves it's a sum of.
The example is meant to illustrate how when we already know a particle's general position, its wave function (which has few peaks) can be shown to break down into a series of many sine waves of specific wavelength (each with infinitely many peaks) added together. These numerous pure sine waves represent the many possible options for the particle's momentum, demonstrating the high degree of uncertainty in momentum that is effectively contained in the wave function of a particle whose position in known more certainly.
In other words, when we are presented with a wave function that shows certainty in position, there MUST be uncertainty in momentum - due to the nature of the wave function that describes the particle, not due to issues with "measurement".
So, think through the way he explained it but in reverse. It's not that we want to discover a particle's position - it's that we already have relatively certain information about its position, and we then ask, "why do we lack certainty in the particle's momentum?" It's because the wave function that contains certain (or rather, less uncertain) information about the particle's position breaks down into many pure sine waves that together represent the many momenta the particle could have, and therefore the lack of certainty in the particle's momentum.
In the video, this is explained in reverse. By starting with a hypothetical particle whose momentum is known with 100% certainty (represented by an infinitely long pure sine wave), we can know nothing about its position (we are infinitely uncertain). We can then ask, "what if there were 2 options for the particle's momentum?", and add another (random) infinitely long pure sine wave to the system of information about the particle. Keep repeating this process, and the more options we introduce for the particle's momentum, the less certain it becomes, but the more certain its position becomes when we take the sum of that information and see that the amplitude of the overall wave function has been narrowed down to just a few number of peaks.
Excellent explanation. I always understood the 'what' of uncertainty ( x vs p), but until now, not really the 'why'. Many thanks.
Wow, just found your channel and I already love it. Quantum mechanics is so incomprehensible in many areas, it is nice to have those small domains that we can actually wrap our heads around. I was very comfortable with the uncertainty principle before this, but now I feel a gut-level intuition about uncertainty and a better feel for wave-particle duality. Thanks!
Nice! That’s the most comprehensible explanation of Heisenberg’s Uncertainty Principle that I’ve heard anywhere. Thank you.
I known the uncertainty principle, but I had never connected it to the atom stability.
It's really eyes opening.
Thank you
This explaination is about how λ relates Position of a particle (as an analogy). Which it demonstrates very well. λ is defined as the wavelength of the probability wavefunction after all. Of course it will relate to position. By the very definition it will!!
But De Broiglie's Hypothesis is that p (momentum) relates to λ in the physical world. Which is the crux that is hard to understand (or relate to).
How does lambda relate to the position?
Oh! let me show this video to Feynman, last time he was curious whether Mahesh is interested in Heisenberg Uncertainty Principle or not.❤ Thanks for the explanation
😊
I want to start by saying that this is the best explanation of the math and the concepts that I have ever heard. That said, how does one add wavelengths? I would assert that this explanation indicates that electrons do not exist as we understand existence. More appropritely, if momentum is conserved, every electron observed in a different location is a different electron. It is not that we find an electron in different places, it is that everywhere we look we find different electrons. And that, to me, reveals a problem with how we view energy. Are we, perhaps, looking at this wrong? It works in math but not reality?
I've never seen that analogy that your teacher used. I actually find it useful. Yet, like all analogies, there's a point where correspondence falls apart. We use analogies all the time to understand various principles and phenomena. Yet using our macroscopic world for understanding atomic and subatomic phenomena will virtually always be limited.
I've never heard the "wave-particle" duality explained so succinctly. TY.
Marvellous and astounding explanation I've ever seen , how do you simplify all these terrific topics ?
Amazing, I was studying for quantum mechanics exam and couldn't understand how uncertainty prevents electron form collapsing. This is the first place when someone actually gave a satisfactory answer. Thank you!
read wikipedia on Compton Wavelength of the electron, and then compare with the Bohr radius
I *literally* said to myself out loud "WHOA ......" at your teacher's explanation of the Heisenberg Uncertainty Principle at the beginning of the video. I've never heard such an intuitive way of thinking about this phenomenon! Amazing!
No - this explanation is misleading as he said!
This is the first time I'm seeing a video of yours, and I have to say, I'm quite impressed. You've explained it beautifully. I especially love the responsible portrayal of quantum objects as neither particles nor waves, instead of both. I've recently watched the MIT's introduction to quantum mechanics lecture 1 by Allan Adams (I recommend it to everyone, the lecture 1 has no math and is super layman-friendly), and the way he explained superposition finally made it click for me - that it's not the electron "taking both paths at the same time", but rather the electron having a very weird form of existing which does not conform to our intuitions of a solid object traveling along a path - a way of existing for which we didn't really have words or metaphors for, before discovering it in QM. Even though it's basically saying that the electron doesn't make sense in the way we're used to, him putting it this way, paradoxically, makes way more sense for me than saying "it's in two places at once". Your framing of particle-wave duality felt similar, and I really appreciate it.
Man you are amanzingly clear and practical, it’s so important to give intuitive and practical explanations of physical, avoiding to get lost in the mathematics with no understanding of the real deal. I think you are better than many university professors (maybe you are one of them, in that case good for your students). Keep going
This is absolutely the best video I've seen on this. You are an incredible communicator! Thank you so much!!
your enthusiasm and fascination is contagious. Wonderful!
If only everyone had the chance to learn from the great minds like Feynman & Einstein themselves.
Luckily we have YT and someone as passionate as you are.
Forever indebted.
Man this is awesome!
I've never understood any video about the uncertainty principle, then had QM in Uni last year, understood it from a mathy view with basis', FT and so on.
But this makes so clear and easy and i can see all the math you cleverly hid in the explanation. You're awesome!
this was the best explanation of the uncertainty principle i have seen , now i understand the world even better
Last time I dealt with deBroglie waves and Psi-squared functions was 45 years ago. I'm surprised at how much I remember, given that I've never used the information. But I had so much fun in my modern physics class, I almost delayed my graduation so I could take the second half. Thanks for the interesting presentation!
I learnt to derive Schrodinger wave equation and Heisenberg uncertainty, having a solid background in advanced electromagnetics, your explanation clarifies many untangled questions thank you.
I just finished day 602 on Brilliant, great courses, I am glad they are a sponsor of this brilliant video!
Nicely done! Your enthusiasm is contagious. What fun!
What was that 😍😍... I just got some real feelings of joy in this 21 min video.
Sir requesting please don't stop uploading this kind of mind-blowing video that give explanation of science the way it should be done.❤❤❤ Lots of love 😘
Wow, you’re an incredible educator. Your excitement is infectious and you have a great way of explaining things. Thank you
As a fresh out of highschool-going into college student this was really enlighting. Could you please make a video in Schrodingers equation and put some intuition into it. The math really overwhelms the whole idea of it.
Many people said they loved your explanations.
I love them too.
I will add, I love your T-Shirt too.
This video is giving me wonderful insights. I love the specificity in highlighting that "wave-particle duality" doesn't mean that the object *is* a wave and a particle, which is how most people (even non-expert teachers!) will explain it. I'll definitely be taking that away from the video, if nothing else, though the thorough step-by-step in outlining the uncertainty principle is fantastic too.
I love physics because of guys like these
I have watched dozens of videos on TH-cam to understand the Heinsenberg Uncertainty Principle and this is certainly the best video of all. It was the one I learned the most from. Your teaching is excellent. Thank you very much. But I still don't understand one thing: given that a quantum object has the property of a wave, what does it mean to add waves to locate the object? How is this done? I understood that by adding waves to "shrink" the resulting wave and decrease the uncertainty of the position, you increase the uncertainty of the momentum, since there are several simultaneous waves (with several wavelengths mixed together), but how is this done in practice? And what does it mean? Thanks!
@@geovanejag3946 hey, thanks for sharing that. I guess I could have been clearer there. It’s not that we start with an infinite wave and then keep adding more. Instead, most quantum objects are NOT like that. They are mostly localised wave packets. Now this localised wave packet can be thought of as sum of many pure sine waves, I.e. many wavelengths, i.e many momenta.
So, just to the explain this above idea, I started with a pure sine wave and kept adding them.
My favourite teacher 😢😢 !!!
Love from Tamilnadu ❤
I adore how you helped me understand how the math of the schrodinger equation leads to the uncertainty principle without having to go into in depth college math. Now that it feels more approachable tho I want to investigate the math lol
Hey!!! Thank You veery much... I understood. You explain in very practical Manner with no tons of maths. But a sense of logical explanation... ❤
I asked my teacher why is this principle accepted? why is this true?..but she didn't give me proper answer...I'm glad i got answers for my doubts here...thank you so much sir!!!
Great video, this helped to clarify a few tings! I had a few questions:
1) You added waves to find more certainty in the position (FFT). What physical process causes the addition of the waves for the inteference? Is it measurement?
2) Imagine there is a radioactive element surround by a spherical detector. When the radioactive element decays it emits an alpha particle and the detector finds the alpha particle in one location. Could I not know both the position and momentum at the same time? I know the position because the alpha particle hit at one point on the spherical detector. I could determine the momentum because I have the mass of the alpha particle and the distance and the time could be determined. Unless is there uncertainty in the time?
i really appreciate that you separated the sponsor from the rest of the video with timestamps and that humble "i have made a video about that but you dont have to watch it, not farming views here." and definitely your enthusiasm. very nice job, you've earned a subscriber, keep it up!! and i dont usually comment but i really wanted to let you know!
Thank you for this video. You offer perhaps the clearest explanation of Heisenberg's Uncertainty Principle I have yet seen.
Mahesh sir is best teacher in english and hindi as well .
He explains any topic with a very easy manner and tells evrey detail of the topic.❤
Thank you for an outstanding video. This is the best illustration of the reasoning behind the uncertainty principle I have ever watched.
Best layman explanation I’ve seen. Thank you.
5:31 “ electrons are not particles“ in a particle detector we see electrons as particles. So ultimately they must be particles. There’s something about their motion that causes them to move in a way that seems like there is an interference pattern.
We don't "see" electrons as particles, particle detectors are built with the idea that a particle and a (quantized) wave are the same thing on a quantum scale. We don't see a particle, as we fundementally lack te means of distinguishing the two at quantum scale (presumably because they are the same concept), we just see an electron. The name particle detector is arbitrary, it's called that because "wave detector" is a less clear name (since there are non-quantum waves, unlike with particles). It very well could've been called wave-particle detector or silly detector or even Frank really
Thanks for presenting physics in an intuitive way
I have spent my entire 11th frustrated having not been able to feel the concepts
But now that I have got a feel of it I feel the ecstasy just as you
You have such a charming personality. The way you explain smilingly is cherry on top! Keep up the good work.