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!
There's nothing particularly innovative about these explanations. It's been done thousands of times before in books and lectures and is probably taught in just about any beginner quantum mechanics university lecture, or even in high school. He just presents them very nicely.
Omg! I was just thinking about exploring this topic since my teacher couldn't explain very well, and your video came in my recommendation. Thanks!!! - Love from BD
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
Heisenberg gets pulled over by the cops, and they ask him "Do you know how fast you were going?", Heisenberg says, "No.. but I know exactly where I am".
Excellent video and I love your enthusiasm! One thing that doesn’t sit right with me anymore is talk of waves and particles. This is because of having heard David Deutsch’s ideas. Have you considered explaining things like the topic of this video in terms of multiversal quantum objects? BTW have you read The Beginning of Infinity?
hey mahesh, im a huge fan of your videos. 1)i have a doubt here, when you said “the probability of finding these locations is zero”(referring to the zero amplitude points in the wave), does it imply that the electron’s wave is a drawing wrapped around the atom that gives us a hint about the probability to find it at a certain location. im a bit confused 2) i understood how adding a new wave creates constructive or destructive interference. but what is the new wave, is it a new electron? again, many many thanks for your videos. please keep up the awesome work
Thanks, 1) Electron wave is not a thing! We just call it a wave because the math works to be similar to classical waves. But, as far as we know, it's not a physical thing at all. 2) Since these matter waves are not 'things', adding waves is just an abstract way of showing what happens when we try to confine electrons. Physically you could imagine 'adding these waves' is equivalent to putting that electron in a box.
Wow. Just wow. I got a Prof in uni, who basically just explained it the same way but with a more calm demeanour (and a longer period of time) in contrast to this energetic form. Things startet do make sense now, not sure if its the difference in presentation or the not too in depth explanation. Anyway, thank you.
When we add 2 waves, due to destructive interference, the uncertainty in position decreases. But the other wave could be another quantum particle as well, so are we decreasing the uncertainty in location for both the particles together??? And if so then adding multiple waves would decrease the uncertainty in location but as a collection of particles together, we couldn't figure it out for 1 particle/wave ALONE(while uncertainty in momentum just keeps increasing)??
I didnt really understand the last part about the explanation for the electron to not fall into the nucleus, why does the momentum go up, isn't only the uncertainty of the momentum that goes up and not the actual momentum?
but if the mean is zero (the atom is at rest), then mean absolute deviation, mad= is related to the uncertainty (std = ^{1/2}, and for the saturated HUP (gaussian), std=sqrt(pi/2)mad.
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?
Heisenberg was never a confident man. One of his characteristic personality traits was his tremendous uncertainty - hence Heisenberg's Uncertainty Principle exists.
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 🙌💛
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.
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.
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.
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)
@@Grecks75 If you understand geometric wave optics with its wave interference and superposition, you can understand quantum mechanics quite "intuitively" (intuition is a form of education and according to Albert Einstein, education is the layer of prejudices laid down upon oneself before one's reaching the age of 18).
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.
Quantum theory does not exist! We cannot travel faster than the speed of light We cannot physically travel into the past. There is no transdimensional dimension Answer this question my dear pseudo-scientist What was the temperature of the film inside the camera while filming on the Moon? Ask yourself why you can't control your mind to focus on the question and why it triggers feelings. You are in DENIAL. In reality, Everything is Energy Matter is condensed Energy Space is expanded Energy Time is Energy in movement That's it! Everything else is Mombo Jumbo nonsense
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. 😊
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.
@@foodsafari-rj3uq It's indeed possible to make quantum mechanics understood by high-schooler sophomores if we restructure education properly. Geometric Algebra with i = e1e2 and e2e1 = -i, etc. should be taught to condense a lot of mathematics.
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.
Pranav from Science is Dope sent me! Seen a bunch of your videos now, fantastic stuff, I can see why he recommended you so highly. Keep up the great work!
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.
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.
Yes. I had all sorts of confusion about Heisenberg's uncertainty till I was teaching one of my undergrad EXTC junior about Fourier and then something just clicked. Its been 13 years since but I vividly remember the moment and the insane nerd out we had after figured it out.
"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 ?
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!
I think the biggest mistake in physics is that we confuse objects (electrons, etc), with object behaviors (waves). Waves is something that all particles do, it's just a behavior, not a thing on it's own. Imagine a hill, it's a solid object, right? Now imagine that same hill collapse under a landslide, and that hill suddenly looks like it flows (like a wave, like a liquid).
Only that the quantum OBJECTS are not collapsing and turning into a wave like flowing mess. Quantum OBJECTS are like being a hill that is solid and flowing at the same time.
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!
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.
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!”
Thank you so much sir. I have loved your videos on relativity. I read about Heisenberg's Uncertainty principle a few days ago and was soo dissatisfied with the explanation in NCERT and several other books. So i turned to TH-cam. Then I got to know that the uncertainty is fundamental but i got stuck after that. Ted-ed and other creators helped me reach to that point. In my mind i was like, "Too bad, sir won't make a video on topics related to chemistry". Maybe, u heard what i said and were like "hold my art of talking with dead scientists". this is the 1st time i am asking on this channel. i want to explore the true depth of this topic. pls forgive me for my long list of questions At 12:14 i have a few questions to ask. What kind of kind value is psi ? why is |psi| there in the frame and not psi? What were the previous approximations for psi and why didn't they work? How by a fluke psi means nothing but psi squared give probability. 14:07 Where does electron exist. In some field or beside Schrodinger's cat. is this field infinite? Or is it something else. I crave to know Thanking You soo so much. Edit 1: I want even more favour. Sir could u also make vids on even more topics on quantum physics. Hope the suggestion is supported by many.
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.
12:29 Wait isnt psi² probability density and not just probability? Or i think, shouldn't the probability should be the integral of psi² times a very small volume, lets call it dv So shouldn't it be? ∫ ψ².dv Now u can take definite integral to find the probability on given 2 points
The uncertainty principle is a concept that applies to waves in general. The wider de wavelet in time, the narrower the fonction is in Fourier space. And since the position of the electron is given by the wave fonction in regard to time and the momentum is given by the wave fonction in Fourier space, the more precise you are in one dimension, the less you are in the other.
Yeah, that is the reason why an increase of a bit-rate of digital signals increases their frequency spectrum, as for higher bit-rate we have to decrease a lenght of signal impulses
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.
Lame joke 1.... Mahesh Heisenberg, Schrödinger and Ohm 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 miles per hour zone.” Heisenberg throws up his hands and shouts “Great! Now I’m lost!” The cop thinks this is suspicious and orders him to pop open the trunk. He checks it out and says “Do you know you have a dead cat back here?” “We do now, thanks to you!” shouts Schrödinger. The cop moves to arrest them. Ohm resists.
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.
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.
Your video has helped me a lot to understand the UP 👍. Still, I disagree that it be fundamental. You *can* have quantum objects with definite position and momentum, as in Bohmian Mechanics. In BM, there's both a particle and a wave, and the wave guides the particle. The UP is only due to our *ignorance* of the exact particle position; we know just it's *Bayesian* probability distribution, which is |Ψ|^2.
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.
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.
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.
NO: there are certain, equally valid, deterministic interpretations of QM which state that particles have defined positions and momenta at all times (it's just that we can't know it and/or due to non-local causality)....
That's the first time I've heard the word pronounced as proBAbility, very indian sounding, are there other words in Hindi that are pronounced like that too?
Just like people in 80s and 90s thought they have all figured out. I think we are in the same situation right now. I think after many many years, we would really discover the truth, how th universe works, and then they they will make videos on how wrong we were just like we now study how wrong people were in the 80s and 90s.
So if we extend the thought experiment to start with zero quantum objects and we start adding quantum objects an infinite number of times we get the known universe as well as a potential explanation for the big bang and SpaceTime?
It is a very good explanation.. but at the end of the video when you try to explain why electrons don't fall into the nucleus.. you have presented the electron as quantum object .. and the nucleus as a classical partical.. although it is also a quantum object
So, what happens to the Uncertainty Principle when the core of a supernova collapses because electron degeneracy pressure is overcome by gravity, forcing electrons into protons to form a Neutron star?
i understood nothing lol. why does the wave function extend everywhere to infinity? doesn't that mean the electron exists everywhere in the universe equally?
What does it mean to add more waves, is it like a measurement made , is made on several electrons or something else please explain. Btw I like watching your videos.
Why cant we just add more and more waves so that if we find its probability of Position is one While we have added so much wave that its velocity is the speed of light I know its stupid question and it came to my mind so anyways can you explain this
Just out of curiosity, what is the situation of uncertainty principle in the case of neutron stars where electrons merge with the protons due to strong gravitational pull?
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.
Why doesn't psi give the idea of probability isn't it just the amplitude?(like the peaks and valleys) where does psi square even come from? (Pls explain i think i just haven't read about it well enough to understand im kinda slow)
It comes from Kolmogorov's axioms. Individual quantum events are statistically independent. We can therefor count their frequencies and then do the law of large numbers limit, which leads us to probabilities p_1, p_2, p_3 etc. for different possible outcomes of a quantum measurements. The sum of all probabilities is one: p_1 + p_2 + p_3 +.... =1. In case of two such possible outcomes we get p_1 + p_2 = 1. In probability theory this can be satisfied with p_1 = p and p_2 = 1-p: p + (1-p)=1. This is called a partition of unity. You know another partition of unity, which comes from geometry. It's Pythagoras, which can be written with sin and cos functions: sin^2 + cos^2 = 1. This is nothing but a scalar product between two vectors = 1. In other words, the (sin, cos) vector is a two dimensional representation of our probabilities. The condition that the length of the vector is 1 is called "unitarity". If we have one such vector, then every rotated version of this vector also has length one. We can therefor introduce a unitary matrix into this scalar product and nothing changes about the total probability. That is the source of the scalar product structure of quantum mechanics and all those matrices and linear operators that seem to be falling from the sky when we explain QM. They are not falling from the sky. They are a direct consequence of the fact that we are counting event frequencies. But hey, you may ask, why does nature implement both versions, probability theory and quantum mechanics? Well, it doesn't. It does something even more tricky: it implements a mix of both. The mathematical formalism for that mix is called "the density matrix" and in general we need to use a density matrix to describe the most general possible experiments.
If the wave equation was something like \operatorname{sech}\left(x ight)\cdot\sin\left(10x ight) y = sech(x)*sin(10x), try it in desmos The wavelength of the entire function would be constant since it is sinusoidal and intersects x axis infinite times, thus having exact momentum but it is highly localised and provides an exact range for position Doesnt this violate heseinberg principal
Do a Fourier transform and see which frequencies it really contains. For each frequency there it would have a value of momentum. Also, quantum wave functions have complex values, so the basic waves are like exp(i*(kx - wt))
Lame joke 2 One day, Einstein, Newton, Pascal, and Heisenberg met up to play a game of hide and seek. While Einstein counted, Pascal ran away and hid, but Newton stood right in front of Einstein and drew a one meter by one meter square on the floor around himself. When Einstein opened his eyes, he immediately saw Newton and said “I found you Newton,” but Newton replied, “No, you found 1 Newton over a meter squared; you found Pascal!” Meanwhile, Heisenberg ran around yelling exactly how fast he was going.
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?
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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!
I really love this guy's teaching style, his knowledge, and his excitement for physics. Mahesh is unique.
Wow, wow, wow! The first 60 seconds puts it into a brilliant perspective
How do you even come up with these intuitive explanations man? I genuinely want to know.
There's nothing particularly innovative about these explanations. It's been done thousands of times before in books and lectures and is probably taught in just about any beginner quantum mechanics university lecture, or even in high school. He just presents them very nicely.
Omg! I was just thinking about exploring this topic since my teacher couldn't explain very well, and your video came in my recommendation. Thanks!!! - Love from BD
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
lucky to be early...
opened yt and this came out ✨
I've seen a few of your videos. I enjoyed them. This one earned a subscription.
Heisenberg gets pulled over by the cops, and they ask him "Do you know how fast you were going?", Heisenberg says, "No.. but I know exactly where I am".
Excellent video and I love your enthusiasm! One thing that doesn’t sit right with me anymore is talk of waves and particles. This is because of having heard David Deutsch’s ideas. Have you considered explaining things like the topic of this video in terms of multiversal quantum objects? BTW have you read The Beginning of Infinity?
Thanks for making this ❤
Thank-you! The light went on in my mind at about 15:00.
hey mahesh, im a huge fan of your videos.
1)i have a doubt here, when you said “the probability of finding these locations is zero”(referring to the zero amplitude points in the wave), does it imply that the electron’s wave is a drawing wrapped around the atom that gives us a hint about the probability to find it at a certain location. im a bit confused
2) i understood how adding a new wave creates constructive or destructive interference. but what is the new wave, is it a new electron?
again, many many thanks for your videos. please keep up the awesome work
Thanks,
1) Electron wave is not a thing! We just call it a wave because the math works to be similar to classical waves. But, as far as we know, it's not a physical thing at all.
2) Since these matter waves are not 'things', adding waves is just an abstract way of showing what happens when we try to confine electrons. Physically you could imagine 'adding these waves' is equivalent to putting that electron in a box.
Best explanation ever!! You nailed it again
Wow. Just wow. I got a Prof in uni, who basically just explained it the same way but with a more calm demeanour (and a longer period of time) in contrast to this energetic form. Things startet do make sense now, not sure if its the difference in presentation or the not too in depth explanation. Anyway, thank you.
Please make a video on Schrodinger equations😢
Thank you, i understood. For the past 40 yrs i simply heard it.
When we add 2 waves, due to destructive interference, the uncertainty in position decreases. But the other wave could be another quantum particle as well, so are we decreasing the uncertainty in location for both the particles together??? And if so then adding multiple waves would decrease the uncertainty in location but as a collection of particles together, we couldn't figure it out for 1 particle/wave ALONE(while uncertainty in momentum just keeps increasing)??
Wonderful explanation. ❤️
I didnt really understand the last part about the explanation for the electron to not fall into the nucleus, why does the momentum go up, isn't only the uncertainty of the momentum that goes up and not the actual momentum?
but if the mean is zero (the atom is at rest), then mean absolute deviation, mad= is related to the uncertainty (std = ^{1/2}, and for the saturated HUP (gaussian), std=sqrt(pi/2)mad.
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.
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.
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 🙌💛
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.
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.
I am currently studying atomic structure, which is why I came to this video
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! 😃
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)
@@Grecks75
If you understand geometric wave optics with its wave interference and superposition, you can understand quantum mechanics quite "intuitively" (intuition is a form of education and according to Albert Einstein, education is the layer of prejudices laid down upon oneself before one's reaching the age of 18).
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 ?
Quantum theory does not exist!
We cannot travel faster than the speed of light
We cannot physically travel into the past.
There is no transdimensional dimension
Answer this question my dear pseudo-scientist
What was the temperature of the film inside the camera while filming on the Moon?
Ask yourself why you can't control your mind to focus on the question and why it triggers feelings. You are in DENIAL.
In reality,
Everything is Energy
Matter is condensed Energy
Space is expanded Energy
Time is Energy in movement
That's it! Everything else is Mombo Jumbo nonsense
"...hold my cat!" Cracked me up! 😅🤣😂🙃😊
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.
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.
@@foodsafari-rj3uq
It's indeed possible to make quantum mechanics understood by high-schooler sophomores if we restructure education properly. Geometric Algebra with i = e1e2 and e2e1 = -i, etc. should be taught to condense a lot of mathematics.
@@solconcordia4315 my claim has nothing to do with high schoolers. What are you even replying to?
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.
Pranav from Science is Dope sent me! Seen a bunch of your videos now, fantastic stuff, I can see why he recommended you so highly. Keep up the great work!
Thanks a lot!! Great to hear that :) :)
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.
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.
That's becuz Heisenberg uncertainty principle is a result of a more general uncertainty that arises due to the wave nature.
Yes. I had all sorts of confusion about Heisenberg's uncertainty till I was teaching one of my undergrad EXTC junior about Fourier and then something just clicked. Its been 13 years since but I vividly remember the moment and the insane nerd out we had after figured it out.
"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 ?
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!
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.
Hi Mahesh nice explanation video , I'm Mahesh too 😂
I think the biggest mistake in physics is that we confuse objects (electrons, etc), with object behaviors (waves). Waves is something that all particles do, it's just a behavior, not a thing on it's own. Imagine a hill, it's a solid object, right? Now imagine that same hill collapse under a landslide, and that hill suddenly looks like it flows (like a wave, like a liquid).
Only that the quantum OBJECTS are not collapsing and turning into a wave like flowing mess. Quantum OBJECTS are like being a hill that is solid and flowing at the same time.
lets ask the most important question: where did you get that tshirt?
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!
Don't forget about Diracs Equation also & Maxwells Equations and the Pauli Exclusion Principle 😊
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.
Ffts for the win!
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!”
This is a terrible joke. I love it
Thanks and when is your other new video coming?
Thanks a lot!! Cleared a lot of misconceptions i had
Thanks for this Quantum Mechanics Content.
Thank you so much sir.
I have loved your videos on relativity. I read about Heisenberg's Uncertainty principle a few days ago and was soo dissatisfied with the explanation in NCERT and several other books. So i turned to TH-cam. Then I got to know that the uncertainty is fundamental but i got stuck after that. Ted-ed and other creators helped me reach to that point.
In my mind i was like, "Too bad, sir won't make a video on topics related to chemistry". Maybe, u heard what i said and were like "hold my art of talking with dead scientists".
this is the 1st time i am asking on this channel. i want to explore the true depth of this topic.
pls forgive me for my long list of questions
At 12:14 i have a few questions to ask.
What kind of kind value is psi ? why is |psi| there in the frame and not psi? What were the previous approximations for psi and why didn't they work?
How by a fluke psi means nothing but psi squared give probability.
14:07 Where does electron exist. In some field or beside Schrodinger's cat. is this field infinite? Or is it something else.
I crave to know
Thanking You soo so much.
Edit 1: I want even more favour.
Sir could u also make vids on even more topics on quantum physics. Hope the suggestion is supported by many.
Yea I too have da same doubt. Hope sir sees this comment.
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
12:29 Wait isnt psi² probability density and not just probability?
Or i think, shouldn't the probability should be the integral of psi² times a very small volume, lets call it dv
So shouldn't it be? ∫ ψ².dv
Now u can take definite integral to find the probability on given 2 points
Yes!
Literally the best science communicator I have watched. Good shit man, love this.
Who else want a video on black body radiation?
absolutely
This is the first time I've come close to understanding this topic
Great work.
The uncertainty principle is a concept that applies to waves in general. The wider de wavelet in time, the narrower the fonction is in Fourier space. And since the position of the electron is given by the wave fonction in regard to time and the momentum is given by the wave fonction in Fourier space, the more precise you are in one dimension, the less you are in the other.
Yeah, that is the reason why an increase of a bit-rate of digital signals increases their frequency spectrum, as for higher bit-rate we have to decrease a lenght of signal impulses
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.
Plot twist: Albert Einstein denied the credibility of the uncertainty principle
😮
Yes but he can't get a unifying theory before his death
Lame joke 1.... Mahesh
Heisenberg, Schrödinger and Ohm 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 miles per hour zone.” Heisenberg throws up his hands and shouts “Great! Now I’m lost!”
The cop thinks this is suspicious and orders him to pop open the trunk. He checks it out and says “Do you know you have a dead cat back here?”
“We do now, thanks to you!” shouts Schrödinger.
The cop moves to arrest them. Ohm resists.
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.
In what part of the derivation of the Uncertainty Principle does the smaller equal sign show up??
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.
Your video has helped me a lot to understand the UP 👍. Still, I disagree that it be fundamental. You *can* have quantum objects with definite position and momentum, as in Bohmian Mechanics. In BM, there's both a particle and a wave, and the wave guides the particle. The UP is only due to our *ignorance* of the exact particle position; we know just it's *Bayesian* probability distribution, which is |Ψ|^2.
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?
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.
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?
NO: there are certain, equally valid, deterministic interpretations of QM which state that particles have defined positions and momenta at all times (it's just that we can't know it and/or due to non-local causality)....
That's the first time I've heard the word pronounced as proBAbility, very indian sounding, are there other words in Hindi that are pronounced like that too?
Just like people in 80s and 90s thought they have all figured out. I think we are in the same situation right now. I think after many many years, we would really discover the truth, how th universe works, and then they they will make videos on how wrong we were just like we now study how wrong people were in the 80s and 90s.
So if we extend the thought experiment to start with zero quantum objects and we start adding quantum objects an infinite number of times we get the known universe as well as a potential explanation for the big bang and SpaceTime?
It is a very good explanation.. but at the end of the video when you try to explain why electrons don't fall into the nucleus.. you have presented the electron as quantum object .. and the nucleus as a classical partical.. although it is also a quantum object
So, what happens to the Uncertainty Principle when the core of a supernova collapses because electron degeneracy pressure is overcome by gravity, forcing electrons into protons to form a Neutron star?
Okay, now do the same for the Pauli exclusion principle
i understood nothing lol.
why does the wave function extend everywhere to infinity? doesn't that mean the electron exists everywhere in the universe equally?
Hlo sir make a video on elctronics engineering what they actually make.I know u will do the video very interesting please make it fast sir
The problem is that position and momentum don't mean anything in 4D only 4 position and 4 momentum have physical meaning.
What does it mean to add more waves, is it like a measurement made , is made on several electrons or something else please explain. Btw I like watching your videos.
Does the principle "exist"? I suggest you reconsider your use of the word.
Love this video, but the pronunciation of ‘probability’ sent me into orbit with an uncertain amount of momentum.
Why cant we just add more and more waves so that if we find its probability of Position is one
While we have added so much wave that its velocity is the speed of light
I know its stupid question and it came to my mind so anyways can you explain this
Just out of curiosity, what is the situation of uncertainty principle in the case of neutron stars where electrons merge with the protons due to strong gravitational pull?
You can have energy stored as a standing wave and if there is no losses it will be within it's limits for ever.
Such a wonderful explanation❤️
Can you explain why the energy and time uncertainty exits?
Bohr's wave is not the same as scroedinger's wave!!
I want a video on physical interpretation on wave function
Can you do a video on spin of a particle? By the way, your videos are really good!
While other you tube explainers are just plain dosa, you are the masala dosa from Saravana Bhavan!
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.
Tf, your voice is same as that one guy from khan academy
".... and that's when Schrodinger says "Hold my cat..." " ROFL!
Why doesn't psi give the idea of probability isn't it just the amplitude?(like the peaks and valleys) where does psi square even come from?
(Pls explain i think i just haven't read about it well enough to understand im kinda slow)
It comes from Kolmogorov's axioms. Individual quantum events are statistically independent. We can therefor count their frequencies and then do the law of large numbers limit, which leads us to probabilities p_1, p_2, p_3 etc. for different possible outcomes of a quantum measurements. The sum of all probabilities is one: p_1 + p_2 + p_3 +.... =1. In case of two such possible outcomes we get p_1 + p_2 = 1. In probability theory this can be satisfied with p_1 = p and p_2 = 1-p: p + (1-p)=1. This is called a partition of unity. You know another partition of unity, which comes from geometry. It's Pythagoras, which can be written with sin and cos functions: sin^2 + cos^2 = 1. This is nothing but a scalar product between two vectors = 1. In other words, the (sin, cos) vector is a two dimensional representation of our probabilities. The condition that the length of the vector is 1 is called "unitarity". If we have one such vector, then every rotated version of this vector also has length one. We can therefor introduce a unitary matrix into this scalar product and nothing changes about the total probability. That is the source of the scalar product structure of quantum mechanics and all those matrices and linear operators that seem to be falling from the sky when we explain QM. They are not falling from the sky. They are a direct consequence of the fact that we are counting event frequencies.
But hey, you may ask, why does nature implement both versions, probability theory and quantum mechanics? Well, it doesn't. It does something even more tricky: it implements a mix of both. The mathematical formalism for that mix is called "the density matrix" and in general we need to use a density matrix to describe the most general possible experiments.
I love your videos!
If the wave equation was something like
\operatorname{sech}\left(x
ight)\cdot\sin\left(10x
ight)
y = sech(x)*sin(10x), try it in desmos
The wavelength of the entire function would be constant since it is sinusoidal and intersects x axis infinite times, thus having exact momentum
but it is highly localised and provides an exact range for position
Doesnt this violate heseinberg principal
Do a Fourier transform and see which frequencies it really contains. For each frequency there it would have a value of momentum. Also, quantum wave functions have complex values, so the basic waves are like exp(i*(kx - wt))
Lame joke 2
One day, Einstein, Newton, Pascal, and Heisenberg met up to play a game of hide and seek. While Einstein counted, Pascal ran away and hid, but Newton stood right in front of Einstein and drew a one meter by one meter square on the floor around himself.
When Einstein opened his eyes, he immediately saw Newton and said “I found you Newton,” but Newton replied, “No, you found 1 Newton over a meter squared; you found Pascal!”
Meanwhile, Heisenberg ran around yelling exactly how fast he was going.
What a Bohr.
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?
Whats wrong with your mouth? Why do you make it weird to watch
From where do you read Feynman lectures?
So if an electron can't fall into a proton because of the uncertainty principle, how come matter/anti matter pairs annihilate?