Demystifying the Heisenberg Uncertainty Principle
The Heisenberg Uncertainty Principle is one of the most non-intuitive concepts in all of quantum mechanics. It says that it is impossible to precisely know both an object's location and its motion. Know one well and you must know the other poorly. The origins of this are deeply tied to the wave nature of matter and the connection between waves and momentum. In this video, Fermilab’s Dr. Don Lincoln sorts it all out.
Fourier transform square wave:
mathworld.wolfram.com/Fourier...
Fourier transform gaussian:
mathworld.wolfram.com/Fourier...
Additional Fourier transform explainer:
mriquestions.com/fourier-tran...
Wavelength, momentum, and wave number:
faculty.chas.uni.edu/~shand/Mo...
Wave Function video:
• What is quantum mechan...
Deriving Heisenberg:
math.uchicago.edu/~may/REU2021...
Fermilab physics 101:
www.fnal.gov/pub/science/part...
Fermilab home page:
fnal.gov
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.
From my perspective, the knowledge available to everyone is increasing, but the interest to learn is decreasing. At least in the US. I think we are entering a dark age.
If u understand that than tell me why light doesn't need time
@@KAi-ns4zz simple, length contraction gets infinite at the speed of light. thus space no longer exists, beginning and end of the photons journey are in the sample place. no time is needed to travel 0 space.
Chemistry is what? I detected a loss of synchronization of sound with lips at the end there..🤭.
@@richtalk34 :: He said, "Chemistry is interesting."
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.
I was lucky that when I was first getting into math and physics (I am now a PhD candidate in “pure” math, with special applications to QFT) I read P. Nahin’s book on Euler’s formula, which included a derivation of ‘the’ uncertainty principle purely via Fourier analysis; as I started my undergrad degrees I made sure to share this with all my math fellow-travelers 😆 I didn’t realize at the time that a lot of math people don’t care much about even the foundations of theoretical physics, and that I actually had particular interests. Oh, and Nahin is also an EE PhD, so I guess this is common folklore in your field! Thanks for sharing.
Time is a quantum echoing effect. If one particle is alone in the universe, it'll return to quantum information field, basically a piece of information. If another particle joins this particle, it becomes correlated and both affects each other. Both pieces of information joins the echo chamber and act as an wave. For example, the ocean is the quantum echo chamber, if you take water from the ocean, it no logers gets affected by the ocean system. Time acts equally. Information is fast than light in entanglement because its accessing the quantum information field and creates this quantum echo effect.
“The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon for proper physics. The “Doc” is seriously misinformed along with 7 billion other brains.
Are wavelets used a lot in signal processing? Are they easy to learn once you know fourier transforms? 🤔 I find them a fascinating topic; hence my question 🤓
@@jamesfrancese6091I know what you’re saying, but the time bandwidth product is not the basis of the HEP, thought it works well in most cases. The official version is from operator algebra and commutation relations.
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.
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!
Signal Processing baby, yeah :)
In theory you could replicate any sound with this method, it's just that it's so complicated in practice you are limited with what you can replicate. You can make some really gnarly EDM synths though.
It’s a Fourier transform.
Wow! It appears it's possible to explain the Heisenberg principle without a trace of mysticism and mysterious music😂 loved it!👍
The Church of the Galactic Spirit condemns your heresy! /s
You can explain everything in quantum mechanics without mysticism, but too many physicists like their mysticism and insist upon the most bizarre explanations for no discernible reason.
@@amihart9269 selling books is a discernible reason.
@@amihart9269 I’d distinguish mysticism from mystery, and there’s a profound mystery here: that the formula suggests an electron never actually has an exact position and exact momentum at the same time. Utterly bizarre and mysterious. It’s not just that our limited human minds do not yet have the tools or power to figure out exact momentum and position, it is that there’s nothing to be known! This utterly mysterious and partly why the many worlds interpretation arose.
@@RC-qf3mp That's a choice in interpretation. You say that it's not just a limitation in what we can know but you have zero proof of that, it is just something you insist on faith. Quantum mechanics only makes valid predictions over large sample sizes, it has no predictive power for a single sample, so any statements about truth values for individual systems is faith-based. We know that over large sample sizes, attempting to increase the accuracy of a measurement of one observable may decrease it for another, but whether or not that means in any given individual system that only some of the properties actually exists in reality is an assumption. Noncommuting operators are also a thing in classic probability theory, so insisting that quantum mechanics is fundamentally different is, again, an assumption, and not an assumption that the math demands you to make, but an assumption you personally choose to make for your own personal reasons, maybe just because you like the sci-fi sounding nature MWI or whatever, but there is no scientific reason to insist that is necessarily the case.
That was incredibly well done.
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!"
Best physics jokes I've heard
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'.
Everyone wants to see Dr. Don dress up as Heisenberg for Halloween now.
Great idea. On his way to the costume party, he can test whether the local sheriff has a sense of humor. "Do you know how fast you were going?" "Afraid not, officer. But I can tell you precisely where I am!"
Glad you're still making videos Don! Thanks for this one
Who else needs a demystifying video for this video.
Professor: What's this section of the wave called? Me: ...a wiggle Professor: Get out.
Thank you!! It feels truly amazing when all dots are connected. Physics is indeed everything.
If KZhead had been around, with content like this, when I did my physics degree, my life would have been so different!
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
Great explanation of the underlying relationship between position and momentum. Thanks for putting this together!
One of the best explanations of Heisenberg Uncertainty Principle. Much appreciated.
Not mentioning the energy and time part is harsh. Is this giving any physics or just Fourier?
Kudos to the editor. Great work on the ending.
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.
You cooked up a great episode there!
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.!
Best explanation of uncertainty theory yet ever. Thank you!
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.
60 symbols is also worth a look.
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
Another wonderful video, with Dr LIncoln again on top form. I look forward to watching more. 10/10.
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.
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.
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.
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.
This is a great video. Even I was able to follow along well enough to extract info and enjoy it.
ur videos are simply the best. Thank u dr lincoln 🙏🙏
The postlude is so cool!
Your videos is perfect. I'm gonna recommend it to my students along our chemistry class. Brilliant.
Brilliant! Thank you Doctor Heisendon. I somewhat get it after a lifetime of not getting it.
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.
Such a elegant explanation of concepts. Thanks
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
This video connected so many topics for me, uncertainty principle, normal distributions, fourier transform 🤯
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.
I love these videos. They almost make me want to study math again.... almost. But seriously. Thanks for making these. They're awesome.
That physics is everything... gives me goosebumps
You got so close to saying what people actually need to know. Uncertainty is a fundamental property of all wave mechanics.
That was absolutely a WONDERFUL video!! Thank you
A master piece of an episode!
Thank you Dr. Lincoln (genius is when a complicated subject is expressed in a simple manner).
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👏👏👏🙏🙏
For once, Heisenberg is about math, not meth
Nah it was a typo, in breaking bad Heisenberg cooked math, it’s common to confuse math and meth, both are very addictive
Jesse Pinkman: "Yeah, physics bitch!"
Meth Math as opposed to Meth Mouth…🤣
@@physics3240math on meth. Go on a 3 day bender and develop a grand unified theory that nobody can read because you were shaking like a damn washing machine
"For once"? Heisenberg first published in *1925.* That's a whole 83 years before Breaking Bad.
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.
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.
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.
Another thumbs up for the music and the whole end scene 👍
Wow! More than excellent explanation!!!
Absolutely brilliant. I finally get it!
The new production on this channel is much better (with graphs, animations and stuff), makes things easier to understand.
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.
There is a good video on it from Khutoryansky
Great job Don!!
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.
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 😅
Congratulations, was a real fun video.
awesome, many thanks, I now understand something so fundamental... that is great.
Thanks for the links ❤
I needed that. Thank you.
THANK YOU... PROF. DR. LINCOLN...!!!
Thanks , this is really good 💐
That was understandable even with the math. Thanks Dr!
Thank you dr Don!!
Tiank you for this! Its now clearest!!!
Another classic thank you.
Another Don Lincoln banger
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.
Your friend's father didn't understand it. The principle he described is that you can't measure a property of something unless you interact with it. For example, measuring the position of an atomic nucleus by bouncing photons off of it... to measure the nucleus' position more accurately, you would need to use photons with a shorter wavelength (such as x-rays), but photons with a shorter wavelength have more energy & more momentum, so the collisions between photons & nucleus transfer some of the photons' momentum to the nucleus, which makes its momentum less certain. Niels Bohr badgered Heisenberg into publishing a much stronger uncertainty than "measurement uncertainty." Heisenberg uncertainty is intrinsic and doesn't require measurement, because EVERY object has a wavelength with a length that's inversely proportional to the object's momentum... even when the object isn't being measured. This is why Don Lincoln mentioned DeBroglie's equation that relates any object's wavelength λ to its momentum ρ.
So it sounds like your conversation happened in the early 1950’s. Amazing to think that QM was really only about 2-3 decades old then.
Pls make a video on uncertainty of energy and time also. Thank you
Looking good Doc
Loved it!
6 hours in and only 24 ,000 views. There is no uncertainty about your popularity. ✨
Sur, you are an inspiration for me.
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.
This is a far better explanation than the Fourier Transform approach, which doesn't really explain the principle underlying the Heisenberg uncertainty principle but rather just shows how math describes it. The music note example really illustrates it in a good way. Another simple but "less correct" example would be a video of a train driving form left to right. The longer (ΔT) we can watch the video, the more certain we are about the train's kinetic energy (ΔE, calculating it using the number of cars and the velocity of the train). If we minimize ΔT, we eventually end up with a still image and can't even tell if the train is moving or not.
@@kerimgueney Thank you for your compliment!
Well that went straight over my head, but I really enjoyed the guitar outro 👌
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* .
difficult to explain simply nice work
Loving the slightly different format.
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.
Thanks Sir 👍
Very much needed video
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.
Your characterization of physics is no more accurate than saying that chemistry is pouring test tubes back and forth into one another. Good natured cross-discipline ribbing is the norm in many universities.
much appreciated - and enjoyed :) i think i even understood something for the first time on this h..berg
Great teacher
Congratulations!!!!
Heisendon haha what a great video and thankyou for leaving the tasty math in the description. One day I wish to get a degree in physics but I feel I need to study more, atleast the universe is a beauty to study one cannot complain!
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.
The Fourier Transform is an absolute treasure of mathematics
great video!!
You can tell that Dr. Lincoln had a lot of fun with this one.
LOVE YOU GUYS
Thanks again.
Using w instead of omega and the term wiggles is a nice touch!
Love this.
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.
It would indeed. But it's fairly simple: h-bar = h/2π. And as long as you're consistent (and know what you're doing) there is no right or wrong. I reckon Dirac introduced the h-bar notation as a shorthand, and then it just stuck around. Maybe people like the (slightly) less cluttered notation, maybe some were so impressed by Dirac they wanted their formulas to look like his. Or something. But this is fashion, not physics. But we could be better at making that clear. Also, I find myself increasingly opting for Planck's own old-school unbarred h, simply because I don't have an h-bar key.
I'm still looking forward to what amounts to a science history lesson. I did hear a quick summary of the difference in passing, and that what Dirac was working on was related to the geometry of excitation states - thus the 2π factor. The origin of these differences is easily enough content for a video 😁
i love your videos!!!