So entertaining, that ending line is gold ❤ Shout out to the editing team 👏🏼

I am fascinated not by the content (although I am), but the fact that physics knowledge is now made available to the masses thanks to Internet and the dedication of people like Don. We are entering a golden era.

As an Electrical Engineer with a PhD in Statistical Signal Processing it is great to finally see a video on major youtube channel addressing the connection between Fourier Analysis and the Uncertainty principle. I learned about this connection many years ago in my PhD when studying time-frequency representation, Gabor transform, etc. For those who don't know, today time-frequency representations are the common (2D-, image-like) inputs of speech recognition systems like Alexa and Siri. The minimum resolution of the spectrogram (one type of time-frequency representation) in time and frequency is controlled by what is the signal processing parallel of the uncertainty principle. Signal Processing is a wonderful field of study that is often overlooked.

the demo of sines making squares is how additive synthesizers work in a music context as well. if you add enough sine waves in the right way at the right frequencies, you can replicate all kinds of other sounds (wave shapes). this was unexpected and cool to see in this video!

Dr. Don showing his humorous side, I like it. I also like the clarity in the math even though I still have little understanding of math at this level.

That was incredibly well done.

Wow! It appears it's possible to explain the Heisenberg principle without a trace of mysticism and mysterious music😂 loved it!👍

Best explanation of Fourier analysis as used in physics. Thank you.

no uncertainty here: physicist effortlessly explains both Heisenberg and Fourier with such ease for common folks like me... thank you!

Police officer: "Did you know you were driving 100 km per hour?!" Driver: "Great, now I'm lost!"

Loving your videos, Don. Thanks very much! I was struggling to keep up a bit at steps 3 and 4, but I will watch this again until I 'get it'.

Btw the modulation of the sine wave to produce a square one is exactly the principle behind the dalek voices and many audio fx with what is called a ring modulator

For once, Heisenberg is about math, not meth

Glad you're still making videos Don! Thanks for this one

Thank you!! It feels truly amazing when all dots are connected. Physics is indeed everything.

Great explanation of the underlying relationship between position and momentum. Thanks for putting this together!

Great appreciation for you sir, and for all of your dedicated team. You have greatly contributed to doubling down on my relative perspective on the rest of the creation. Infinity is man made word, but a very real topic.

If KZfaq had been around, with content like this, when I did my physics degree, my life would have been so different!

3Blue1Brown did a video on the uncertainty principle as well if you are looking for an accessible deeper dive into the math. These two videos complement each other nicely - it's worth watching both.

You cooked up a great episode there!

The Fourier Transformation is what got me interested in delving deeper into the math. I had learned about it in the early 80's when taking electronics. This has clarified so much. Thanks

Best explanation of uncertainty theory yet ever. Thank you!

Brilliant everytime, Uncle-Don makes me happy and I learned something again! Been hooked since lockdown#1, I just need a linear-accelerator to test all this stuff out on! 🙂 Great, 10stars.!

One of the best explanations of Heisenberg Uncertainty Principle. Much appreciated.

Genuinely amazing how you can simplify all this. Its almost harder than the maths itself to be able to explain this in a digestible manner.

Kudos to the editor. Great work on the ending.

Thank you, Dr. Lincoln, for a _beautifully_ done video addressing the very heart of where the uncertainty principle comes from! Also, for folks who may find the idea of a Fourier transform a bit intimidating, think of an old-style radio station dial: Each number is a location on your dial, but it also represents a sine wave (the carrier frequency) that could be thousands of miles long. Your radio dial is a Fourier transform of carrier frequencies from all your local stations, compressed into tiny packages on the space of your dial. Particles aren't that different.

Funny that, when I started watching this channel, I was in high school wanting to study particle physics. Now I'm having Quantum Mechanics A classes in masters degree course

Another wonderful video, with Dr LIncoln again on top form. I look forward to watching more. 10/10.

Everyone wants to see Dr. Don dress up as Heisenberg for Halloween now.

Thank you again sir for a wonderful and clear intro to a difficult subject. I may watch this with my students when we investigate how metaphysics schools epistemology and epistemology schools metaphysics.

You got so close to saying what people actually need to know. Uncertainty is a fundamental property of all wave mechanics.

Thank you for this presentation of a fundamental bit of theory. I'm well versed in Fourier and LaPlace transforms but never studied the higher-up physics courses. I've enjoyed other Fermilab videos, but this one got me to press that "Subscribe" button.

Professor: What's this section of the wave called? Me: ...a wiggle Professor: Get out.

Dr. Lincoln puts out the best science videos, in my opinion. He describes the phenomena very clearly, he presents it in a more-or-less easy to understand way (how easy to understand can quantum physics EVER get??), and I always feel like I understand the world a little better after watch8ing one of his videos.

Brilliant! Thank you Doctor Heisendon. I somewhat get it after a lifetime of not getting it.

This video connected so many topics for me, uncertainty principle, normal distributions, fourier transform 🤯

Your videos is perfect. I'm gonna recommend it to my students along our chemistry class. Brilliant.

I love these videos. They almost make me want to study math again.... almost. But seriously. Thanks for making these. They're awesome.

A very good visual representation of converting a wave to a 'flat' line box or grid system, which is used all the time in electronics.

An awesome explanation for a motivation for the HUP…not to be confused with a proof but extremely illuminating….that shows how deeply the structure, strands and connections in Math determine the structure of reality and the universe as well👏👏👏🙏🙏

ur videos are simply the best. Thank u dr lincoln 🙏🙏

The postlude is so cool!

As you brought up de Broglie, I'd like to point out ðat his and Bohm's *Pilot Wave Þeory* does allow violating ðe Uncertainty Principle. In PWÞ, each particle has a definite position and speed at all times. From ðe mere starting condition, not law, ðat ðe Bayesian probability distribution of ðe particles be equal to |ψ|^2 (quantum equilibrium) follows ðat we can't *know* boþ position and momentum beyond a fixed uncertainty. Ðe Fourier stuff concerns ðe wave function and has noþing to do wið uncertainty; ðe wave is in a perfectly definite state at all times. Uncertainty comes into play only once you *interpret* ðe wave as encoding mere probabilities. Ðe non-basic nature of ðe UP is shown in PWÞ by ðe fact ðat if you have an ensemble of particles in a narrow enough non-equilibrium distribution, you can measure position and momentum to arbitrary precision, as Antony Valentini shows in *Subquantum Information and Computation* .

Luís Ferreira, walks through stargates, and your use of clip nerded me out, as he spoke the name. Some generous z axis thoughts. Deeper when higher.

Such a elegant explanation of concepts. Thanks

This is a great video. Even I was able to follow along well enough to extract info and enjoy it.

That was absolutely a WONDERFUL video!! Thank you

A master piece of an episode!

A more intuitive explanation would use the delta-E * delta-T version of the uncertainty principle. The energy of a particle (let's say a photon) is directly proportional to its frequency (and inversely to its wavelength). The "uncertainty" in time is the duration of time over which we observe the energy. NOW - think of this as playing a note, shorter and shorter and shorter. The frequency of the note is the energy. The longer the note is played, the more certain we are of the energy. But as it gets shorter and shorter, eventually the duration is too small to even begin to discern the frequency (energy). This is most easily demonstrated with sound software, as most musical instruments play notes clearly for far longer than where the "uncertainty" comes into play. If you shorten the duration of a perfect sinusoidal wave to less than half a wavelength, you don't get a note so much as a "click". That "click" is the white noise of having a sharp spike (the narrow bell curve in the video, with the "w" curve becoming very wide). There's not much more to it than that: everything at the quantum level essentially IS A WAVE, not just sorta-kinda, but IS. Because it's all waves, this "note vs duration" logic applies everywhere, and we call it "The Heisenberg Uncertainty Principle". I would rather call it the "There are only waves, no particles" principle.

Thank you Dr. Lincoln (genius is when a complicated subject is expressed in a simple manner).

Congratulations on your good taste in not having any lousy advertisements in your video. I recently had a computer problem that caused my ad block software to quit working, and consequently I've unsubscribed to channels that have too many ads in their videos.

That physics is everything... gives me goosebumps

Dig the hat and this is just mind-boggling for me. Maths are not my forte by any stretch but for some reason I am drawn to these videos and yours are some of the best. So though I will never understand this I certainly will be intrigued by them. Thanks.

It’s impressive that you explained this without summations or limits, sometimes you just want to learn without doing too much math or reading proofs.

Great job Don!!

Wow! More than excellent explanation!!!

Absolutely brilliant. I finally get it!

Oh my god, I actually understand it now! I'm an electronics guy myself, so I understand the Fourier transform I always viewed the W space as just the histogram of frequencies, I'm very familiar with this, and how it relates to shape of the sound vawes for example. Before this video I understood the delta x, every video explains this bit. But none of the videos I viewed explained that the distribution on the w space, which is fourier transform, determines the momentum. That was the missing bit. Thank you! It feels so satisfying to finally understand this 😅

Another thumbs up for the music and the whole end scene 👍

I am going back to my teenage years, over 70 years ago. My friend's father who was an engineer one day sat me down to explain the Heisenberg Uncertainty Principle, by telling me it was impossible to measure a bathtub of water as the moment a thermometer was inserted the energy would shift from the bath to the thermometer. I never understood it, but I have never forgotten it. His own two sons took off.

Thanks for the links ❤

This is SO CLEAR, thank you very much. I would appreciate very much a similar explanation on something that is very obscure and rarely explained: the Pauli Exclusion Principle. Would you? 🙂 So many thanks.

The new production on this channel is much better (with graphs, animations and stuff), makes things easier to understand.

Thank you dr Don!!

THANK YOU... PROF. DR. LINCOLN...!!!

It only checks out with GR/SP, even m-Theory/Super String or others don't have such inviolable room for both knowing p and location. Even w/ GR/SP it only checks out above quantum level, and definitely breaks down with v >= c. IF neutrinos' v == c, well it is the case that disproves Uncertainty Principle; because IF anything can move >= c, it had to be accelerated to that: even 'coming into existence' via decay processes etc, its imparted and has to check out with values for decay elements. Its really an artifact of our 'flawed' instruments: they're all based on physical observations or ultimately instruments designed around chemical processes at subluminal speeds, electrons powering the instruments v < c; fundamentally the instruments can't ever observe properly a v > c object.

As a chemist I can only remind our host that physics is the science of approximating a horse usin a sphere. I will note that since h-bar/2 is an insanely small number, we can generally determine position and momentum to a reasonable degree of precision, especially for objects of high mass. This is especially handy in that it prevents you from making the unpleasant discovery that your car is suddenly in the oncoming lane of traffic.

I needed that. Thank you.

Thanks , this is really good 💐

Looking good Doc

awesome, many thanks, I now understand something so fundamental... that is great.

Congratulations, was a real fun video.

Somethings been bugging me for a long time. On the one hand, we keep being told that photons don't experience time. A photo can cross the universe, yet it doesn't experience time. On the other hand we are taught that a photon is oscillating electric and magnetic fields. As the electric field collapses, a magnetic field grows to take its place. But hang on. Oscillating between an electric field and a magnetic field takes time. So how can a photon both be composed of an oscillating electric and magnetic fields AND not experience time ?

Another Don Lincoln banger

Another classic thank you.

Tiank you for this! Its now clearest!!!

Congratulations!!!!

Loved it!

Heisenberg's hat and beard are very becoming to you! FFT is everything. I used it intensively (Signal Acquisition, FFT-Programming, Data-Processing) for my PhD on Super - Conductors.

Thanks Sir 👍

That was understandable even with the math. Thanks Dr!

Pls make a video on uncertainty of energy and time also. Thank you

It might be a good idea to go over what both the Planck Constant and the Reduced Planck Constant were originally used for and why, as well as to take a look at where students frequently get confused about which one they should use.

Like so many things in quantum mechanics it seems simple and straightforward when you look at the math. The problem shows up as soon as one tries to explain what the math actually means in terms of what is going on.

Thanks again.

Great teacher

Simple; Math without product . Simple physics over product.. Uncertainty every where. Grand respect,

LOVE YOU GUYS

I always imagined the Heisenberg principle in relation to Energy. As the energy of a particle is inversely proportional to its wavelength, I imagined the measurement of the place of a particle as putting it in a grid of certain length, like a sieve. If it falls through the sieve, it‘s smaller than the sieve‘s openings. But if it fits through, its wavelength also has to be shorter than the sieve‘s opening, meaning that its energy gets higher and higher until it destroys the sieve instead of passing through.

great video!!

Very much needed video

I got into mathematics and number theory through the equations of quantum mechanics and relativity via the whole idea of Fourier transformations... which led me to the Riemann hypothesis, which my brain has been orbiting ever since... and not just because I could use the prize money.

Love this.

Excellent!

Sur, you are an inspiration for me.

It's like taking a picture of a fast moving car. Ether the car is blurry so you can't figure out exactly where it is, or the film is fast enough that you get a perfect image but then you can't figure out how fast it was going.

Thank you 🎇🌌

Loving the slightly different format.

Using w instead of omega and the term wiggles is a nice touch!