Heisenberg's Uncertainty Principle EXPLAINED (for beginners)

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

[robblerouser]

This was a better explanation than any other I've ever heard anywhere.

[zarinawillows]

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
Thanks a ton man.😊😊😊

[MrPrimioNILOS]

I am a physics teacher, I can not make it that easy. Great job. Thank you

[KunalSharma-dxdg]

Explained with simplicity.
Really good.

[rahulsinghbaghel]

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.

[randymartin]

You truly have an extravagant gift for explaining things. I actually just yelled out loud WOW after 3:05. Love this channel

[paparoach]

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

[tasfa]

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!!

[ManojDas-oegj]

No matter how long the video is, keep making such types of videos. It's really helpful to me and hopefully to other.

[n-c]

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.

[TheFunkoDunko]

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.

[Roberto-REME]

You are an outstanding explainer. Really well done.

[douglasstrother]

Too long?
Not even 15 minutes, and I'm just getting warmed-up!
;)

[yuvrajsinghsengar]

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! ☺️

[DanyalShabirr]

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.

[ravipande]

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.

[ashishvarma]

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

[Damiii]

Yeahhh finally after watching many videos i finally understood what that uncertainity principle thing actually is !!!! Thank youuu sooo much!!

[vtbhanukiran]

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

[Forever._.curious..]

The way he mostly keeps things real, in depth and mathematically working than that of touching topics superficially as some non-physicist ppl do