Heisenberg's Uncertainty Principle EXPLAINED (for beginners)
HTML-код
- Опубликовано: 17 июн 2024
- Uncertain about what Heisenberg's Uncertainty Principle means? Worry no more - this video is here to help you :)
Let's start out this description with timestamps, because this video is super looong.
00:00 - Intro
00:42 - What is Heisenberg's Uncertainty Principle?
02:33 - Classical vs Quantum worlds, and what "uncertainty" even means
03:54 - A common description of, and misconceptions about the Uncertainty Principle
06:42 - Fourier transforms
12:22 - How Fourier transforms bring about Heisenberg's Uncertainty Principle
Most commonly, Heisenberg's Uncertainty Principle is used to describe a relationship between how much we know about two quantities: position and momentum. The principle tells us that there is a fundamental and universal limit to how much we can simultaneously know about both. In other words, the more confidently we know the position (of, let's say, a particle), the less confident we can be about its momentum. Now the word "uncertainty" just refers to the width of the probability distribution that describes a particle's position or momentum in the quantum world.
Before we find out where the Uncertainty Principle comes from, we will discuss a commonly used description that gets thrown around regarding the Principle. It's known as the Observer Effect, and it's the idea that the light we send into a particle in order to glean information about its position and momentum actually ends up changing the behaviour of the particle. High energy, small wavelength light tells us with more certainty the position of the particle, but changes its momentum by a lot so we are less certain about this. Low energy, large wavelength light doesn't give us much information about the position of the particle but does tell us more about its momentum. Annoyingly though, the observer effect is NOT the Uncertainty Principle. It's just a possible explanation for it, as suggested by Heisenberg himself.
So where can we look to find the origins of the Uncertainty Principle? Well a good place to start is to understand Fourier Transforms. Fourier transforms come about by first breaking down mathematical functions into sine wave building blocks - kind of like how we break vectors down into horizontal and vertical components. The sine wave building blocks are sine waves of different frequencies. We can then take the amplitude of each of the sine wave building blocks and plot that against the frequency of that sine wave to give us a new plot. This new plot is known as the Fourier Transform of the original function that we broke down.
The interesting thing to note is that if a function is super wide on its horizontal axis, then its Fourier transform is going to be super narrow, and vice versa. This is useful when we bring the whole thing back round to the Uncertainty Principle.
Now remember, in quantum mechanics we use "wave functions" to describe the probability distributions of position and momentum. But here's the clincher: The momentum wave function is the Fourier transform of the position wave function. This means that if we have a super wide position wave function (so it could be in a larger range of values, and thus we are more uncertain about it), then the momentum wave function is narrow (so it's in a smaller range of values and we are more certain about the momentum) and vice versa. This is where the Principle comes from - the more we know about position, the less we know about momentum, and vice versa once again.
Thank you so much for watching, if you liked the video then please subscribe!
Follow me on Instagram: @parthvlogs
I am a physics teacher, I can not make it that easy. Great job. Thank you
Sir you have not questioned anything of basic principles of physics that's reason you can't break it start questioning everything of physics theory you would know that physics what is being taught is bunch of lies and deceit hope you would not offended by my opinion 🙏🙏🙏
This is the most comment
@@nikis7742nobody in the world understands quantum mechanics in very simple everyday terms. The whole theory is a mathematical construct, we have no clue of its deep meaning. So I wouldn't say the teacher understands less compared to the guy in the video.
This was a better explanation than any other I've ever heard anywhere.
If you're from Science and like a little bit of math , you can check out '3blue1brown' .
Amazingly visualized
Yes, but he is talking about the uncertainty of a single quantity. And it's F-transform. But the uncertainty principle is about the product of two things position*momentum. Not position alone, and not momentum alone.
@@joeboxter3635 No, you are wrong. He literally said it in the video: the momentum is the Fourier transform of position. So the uncertainty principle is not talking about "two separate quantities," but rather, it is indeed talking about a quantity and its Fourier transform. In fact, this how conjugate variables are defined.
@@angelmendez-rivera351 u guys are so genius are u from 12 grade though
6:06 I've waited so long for somebody to actually say this.
My classmates still think that the Uncertainty Principle is a result of our "Technological Impotence".
This video is a good proof I can put forward......
Thanks a ton man.😊😊😊
Basically Einstein think same
i still do think that it because of human's lack of knowledge that we are unable to calculate both precisely
@@jatinthakur7887 I realize this comment is a year old but .. think of a teeter totter. You cannot push both ends down at the same time. You can't blame the people sitting on it.
Great video! In uni, when I realized how "wide in real space" gives "narrow in Fourier space" and how this physically ties to the uncertainty principle - I think that was really when quantum mechanics got REALLY cool. Excellent intuitive explanation. Feynman would be proud.
My God. You have clarified, uncertainty principle and Fourier transform in one go!!! The world needs more teachers like you. Thanks for the really simple and lucid explanation.
Explained with simplicity.
Really good.
@@ParthGChannel I just love your work, sir. I need someone to guide, please share your e-mail id.
I’ve a compute engineering degree so I’m familiar with Fourier Transforms. And I have to say you did a beautiful job describing the simple concept behind them while leaving out the intricacies communicated by the specific mathematics
You truly have an extravagant gift for explaining things. I actually just yelled out loud WOW after 3:05. Love this channel
I was hopeless at maths at secondary school. So bad, in fact, that I was relegated to arithmetic class. Now, over 55 years later, I am still hopeless at maths. Fortunately, I have an interest in astronomy and science, which is steeped in maths. A lot of the subjects you bring up are fundamental to hard science and I enjoy being able to finally grasp what I am missing out on. Keep up the very good work you are doing. Physics looks like a blast once you can figure out its tools. Where was your method of explanation when I was a lad?
Einstein wasn’t very good at math either. Almost failed in elementary school math. I understand that he had his wife or someone else go over his math for completeness and accuracy.
Dude ,
Einstein was a genius, at math
Masterd diffirential calculas by the age of 15
The only reason he was not good at maths in school was because he didn't agree with a lot of things taught at the time
You must check out 3Blue1Brown's channel here on RUclips! Trust me, his explanations are a treat!💎
I have seen heisenberg uncertainty formulas for years.
But after this explanation meaning of heisenberg uncertainty is certainty meaning in terms of what this formula is telling. 👏👏👏
More often than not I find it hard to fully comprehend subjects explained in your videos. I get the message. Most if not all the logic behind it. But due to deficiencies in my educational background and lack of any scientific experience I often fail at math or physics. Yet I find myself trying and rewinding your videos. Your explanations seem so approachable, that I always have an impression that with some extra effort (and enough replays), "I'll be there with you". Thank you for your work-is truly appreciated.
What I've always wondered, is WHY momentum is the Fourier Transform of position, and WHY position is the Fourier Transform of momentum. That part I don't understand, but I'll continue to look for an answer.
Well, maybe in some moment in your life, I don't known, in your school or college, you studied or will study a particular kind of waves, the harmonics waves. They have a perfect sinusoidal shape and are expressed by the following formula:
y(x,t)=Acos(kx-ωt)
Where A is the Amplitude, k is the wavenumber and ω is angular frequency.
But we can rewrite it using some identities:
k=2π/λ and ω=2πf, where λ is the waveleght and f is the frequency.
So
y(x,t)=Acos(2π(x/λ-ft)
If you notice, there is an special relation in this equation beetwen time (t) e frequency (f), they are being multiplied. Ideed, time and frequency are conjugate varibles when we are dealing with processing signs transported by electromagnetic waves. Is a consequence of the mathematic area of Fourier Analyze that when you are measuring the uncertanty of time and frequency, you need to respect an analagous inequality
ΔfΔt≥1/4π (The uncertainty principle is: ΔxΔp≥h/4π=ħ/2 where ħ=h/2π)
Fantastic, no?
So, you must be questioning about the uncertanty principle and why position and momentum are conjugate variables.
Well, I will not be able to demonstrate anything, but I can show that the pattern of t and f in the harmonic wave repeat for p and x. How?
Quantum mechanics is a kind of undulatory mechanics, and a free particle solution for Schrodinger`s equation can be at leat in it`s real part be represent by the same shape of harmonic waves:
Ψ(x,t)=Ψ_0cos(2π(x/λ-ft)
But particles in quantum mechanics follow the Broglie's relations, every particle behave like a wave and have a wavelengh, and his relation with momentum is given by:
p=h/λ, where h is the Planck's Constant = 6.62607004 × 10-34 m2 kg/s
So, if you want, rewriting the solucion of Schrodinger's Equation
Ψ(x,t)=Ψ_0cos(2π(px/h-ft)
p and x are simetrically together in the solution, like t and f. This is because they are profoundly related to each other.
I think this is not the final response for your doubt, but I think can confort some curiosity crise. Lol
See ya!
Gustavo de Oliveira
Thank you Gustavo, I truly appreciate your efforts and share your knowledge here. I really found this informative. Thank you, God bless.
He already explained in the start of the video that both position and velocity are conjugate variables
@@027_manishdixit7 Saying they are conjugate variables means nothing. It is like defining integration as the inverse of differentiation. Nobody cares what a variable is. Nobody cares what conjugate means. The question is clear and appropriate: Why are position and momentum the FT of each other? Actually it is more. appropriate to ask why certain "pairs" are so linked. And not the simplistic answer that momentum depends on wavelength and position depends on distance. Why aren''t wave number and angular frequency also paired?
It would help to know how the Heisenberg Principle was originally derived. Was it from the Schrodinger equation? If you've found out or ever find out, let me know.
The explanation of the link between the Fourier transforms and the Uncertainty Principle made a lot of things clear as to how this principle is in effect. Thanks, man.
Simply fantastic Partha ! Nowhere else I could find such beautiful, easy to understand, way of explaining Heisenberg uncertainty principle but also Fourier transformation. God bless you.
This is extremely helpful compared to other videos on RUclips, thank you for making it!
Very succinct, worth rewinding often and reviewing. Thanks Parth
What the hell bro seriously this is the best explanation i ever herd or veiw all about Heisenberg uncertainty principle 💯.....
Brø ¡ appreciate your work🙏 you are just awesome! ☺️
Really enjoy this series! Keep 'em coming :)
Thank you this helps clean up my very rudimentary understanding of Heisenberg's Uncertainty Principle.
Yes . Your channel is growing fast and I'm truly happy for that. Your channel is underrated . You deserve much much attention . I try to spread your channel as much as i can in my college ! Thanku your videos makes me happy . I'm a dropout physics student , you make me fall in love with physics again . (I'm currently doing engineering and your topics are in my syllabus)
No matter how long the video is , keep making such types of videos. It's really helpful to me and hopefully to other.
You are an outstanding explainer. Really well done.
Awesome man, absolutely awesome 👍
Didn't needed to rewind even once while watching at 1.5x. + more detailed than other videos on the same topic + well explained.
This is the best explanation of uncertainty principle so far! After having seeing several videos. It is understandable especially you have a STEM degree but still want to learn more about the basic physics theory.
Thanks Parth, i really enjoy listening to your podcasts.
The way you explained this topic was easy to understand for a CA student. I was stucked into this topic while reading Stephen hawking book brief history of time .
Thanks parth
The conceptual is trickier in some ways than the mathematical. Thanks for this video series that tackles concepts. You are the best, Parth!
wonderfully explained!! you gave every necessary bit of information and built it up really nicely, thank you :)
Brilliant job. Didn't connect the Fourier transform aspect at all but this makes so much more sense. Will have to watch a few more times to lock this in. Thank you so much.
I watched Up and Atom's video on the uncertainty principle where she gave the compromising the measurement of position vs compromising the measurement of velocity explanation in terms of firing a photon with more or less energy and how much that will knock off the electron and my mind was blown by finally finding an intuitive explanation. But I immediately thought that seemed more like a limitation of the technology we have to measure than a property of the electron itself.... And right after I watched your video and my mind was de-blown and re-blown all over again just like that! haha great video!!
13:05, The best moment of this video, All things started joining together, thank you soo much for this wonderful video
Found the Best way to make people love Physics... Never seen such a beautiful way of explaining "complicated" science.. ❤️
Great content! Thanks for the simple and clear explanation!! Would also like to see how the probability distribution of the position and the momentum could be mutually fourier-transformed.
Always such a pleasure to listen to your explanations! 👏👏
thank you so much! you went quite in depth! A LOT of info., i will try to review it a few more times !
Excellent job explaining what is considered a very mathematical concept in well understood but uncompromised terms
Very good! Thanks
I'll watch all your videos by now
so glad that I found this channel!!!
Love you dude..You content is amazing
I knew the uncertainty principle before, but now I understand the uncertainty principle. Thank you.
Just amazing! Today I got the feel of this concept.
Great video. You made such a difficult concept so interesting and simple 😊.
It's just mesmerizing !!! Thank you for the explanation
Very enjoyable and engaging video. In a respectable manner, I surely do envy this young guy's genius, or marginal genius. Roll on bro.
I have never seen explanation like this.awesome
Great 2 for 1 offer - Heisenberg + Fourier made simple. Great video, and love your style and energy.
I agree. 2 for one. Imagine electrical engineering or system engineering with out fourier transforms and quantum physics without uncertainty principle.
Love the way you explain Fourier.
Wish you make a video just about Fourier Transformation but with some more details.
Why ??? why no body made this link before ??? You are absolutely amazing . Thank you
Wow that's a very cool explanation about uncertainty principle never heard before like this one
Thank you so much Parth!!!
ideas you put are amazing,thanks a lot
Great teaching……and amusing as well. Keep it coming
Thanks man
You really helped me understand this
This was a great explanation
thanks man
just curious if the momentum plot in your example plots was actually correlated to be the Fourier transform of the position plot in your example plots or if you just put up a general approximation. you do an awesome job by the way and so glad your viewership is growing fast! I'm putting my friends that are wanting to learn more on to your channel. way to go!
6:06 I was waiting for this. Many a people have wrong info about the uncertainty principle. However this explanation is also stated in the " Brief history of time" by hawkings.
You have amazing tutoring skills ! Keep up the great work :-)
That was wonderful, thanks man
Superb description, thank you.
I'd love to see your explaining skills applied to gravitational waves. Specifically, how LIGO works, and what it would be like to be close to the black hole mergers that LIGO detects.
A phenomenal explanation.
Excellent, but i would not have understood it if I hadn't some clue of Fourier transformations of which I had little clue anyway but your video helped to understand them a little better. Still I'm struggling with them but it's not your fault. You're doing an amazing job. I love how you cleared up the idea of the light bouncing off the particle as not being the uncertainty principle, that was an awakening for me. I now know it is nothing to do with that but it is a fundamental law of physics. So much more beautiful a proof than the haphazard bouncing light.
Yeahhh finally after watching many videos i finally understood what that uncertainity principle thing actually is !!!! Thank youuu sooo much!!
Mate, could u come up with a video on the Fourier Transforms? U explain well, concise and clear. Guess that ll make DFT simpler explained by u.
Very nicely explained! ... I was expecting you would mention so examples other than position and momentum.
You are the best :) Thanks a lot for this video
Thanks for the video.
Great video, thank you
The way he mostly keeps things real , in depth and mathematically working than that of touching topics superficially as some non-physicist ppl do
Well done, even for me that i am a spanish speaker you explained it so well
Thank you, 10 more viewings will help. Excellent synopsis. Takes the spooky stuff out, logic in.
OK, so after watching a bunch of your brilliant videos, one thing is for certain: your videos simply are not to be watched at 1.5x speed.
A rush of information so well presented and explained. Thank you Parth! :)
I watch them at 0.75 x! It is tough to keep up else. You keep thinking as he speaks and if you watch it on higher speed then the thinking interferes with the listening!
Wow, I first ran into the videos and was amazed how much I understood but especially how much I didn't. Then when I read some of the comments I got even more confused. But still, I thought the lectures totally awesome.
Excellent explanation...
Great great explanation 😍
I really love your videos 😍
I love these videos😀😀😀😀
Very interesting and fun.
great explanation ❤
Finally some good and new explainatiin
With a 1964 Ph.D. in physics I was astonished that I did not know that conjugate variables were Fourier transforms of each other. Thanks.
best explanation...👌👌👌
Dear Parth, Could you do a video on the maths which gets applied in Physics. May be a few series. Fourier transforms, Divergence, Partial differential eqns, etc.
It would be useful.
You explanations are really great and easy to understand.
But physicists also require a little mathematics brush-up.
Thanks.
Kiran
Parth will I'm sure get round ot it. Meantime check out the math explanations given on RUclips by 3brown1blue. They're clear, visually very well illustrated, and are very helpful.
Physicists require more mathematics than a mathematician...
Wonderful. Thank you
Excellent! Please post an explanation to the two other Maxwell 's equations! Great job
Thank you soooooo much💗💗
Thanks man. You are really awesome. Can you please make a video explaining only the fourier transfer?
Good explanation 👏
Great expalination. This is first video i have seen that explain uncertinity principle in term of fourier tranform in time and frequecy domain.
Otherwise it is always expalined as act of mesurement disturbs position and momentum and light particle photon interacting with measurements. As you said all tha the mumbo jumbo.
great job .... excellent
Even speaking is a little faster for me,I do understand your explaination very well Thanks a lot.
As a lecture demonstration, I used to use a storage oscilloscope, a tuning fork, and a microphone. The tuning fork Produced a nice clean wave with well defined frequency but very poorly defined duration... I then blank the oscilloscope, and clap my hands. That produced an irregular wave form totally indeterminate in frequency but very sharply defined in time.
really nice attempt to explain uncertainty principle Parh, can we have video on what is quantum information and hawking's radiation
6:14 i was waiting for this line
Thank you very much
Sir, you are amazing.
Sir, kindly upload video on Fourier Transform.
Thanks man!
Great bhaii👍👍👍👍
Too long?
Not even 15 minutes, and I'm just getting warmed-up!
;)
Easy digestible information at one place!
Excellent.
awesome , just awesome.