Understanding the Uncertainty Principle with Quantum Fourier Series | Space Time

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Sometimes intuitive, large-scale phenomena can give us incredible insights into the extremely unintuitive world of quantum mechanics. Sign up for your free trial of The Great Courses Plus at ow.ly/HAvT30beNAj
Today the humble sound wave is going to open the door to really understanding Heisenberg’s uncertainty principle, and, ultimately quantum fields and Hawking radiation.
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One of the most difficult ideas to swallow in quantum mechanics is Werner Heisenberg’s famous uncertainty principle. It expresses the fundamental limit on the knowability of our universe. We’ve discussed it in our early videos on quantum mechanics, but it’s time we looked a little deeper. See, the apparent weirdness of the uncertainty principle hints at the even weirder underlying reality that gives rise to it. The universe we experience seems to be constructed of singular particles with well-defined properties. But this intuitive, mechanical reality is emergent from underlying reality in which the particles that form matter arise from of the combination of an infinity of possible properties. And forget matter - the vacuum itself is the sum of infinite possible particles. If we fully unravel this idea we’ll be on the verge of tackling things like Hawking radiation. But as you’ll see today, in that unraveling we are led, unavoidably, to Heisenberg’s uncertainty principle.
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[@pbsspacetime]

First

[@10aDowningStreet]

Sir, I feel you have cheated.

[@hussammustafa5267]

PBS Space Time *RESPOND AND I'LL TAKE YOU TO MARS*

[@kadourimdou43]

PBS Space Time How are Quantum particles entangled. What's doing the entangling? Does this mean particles and fields need to be replaced with another deeper theory to explain it?

[@Flashfake]

I just finished the video. Take a guess when I began to watch :)

[@gregdesouza17]

PBS, Could you share that fourier picture that you used as a GIF? TY

[@ElmerBBW]

Uncertainty explained in classical terms: If I photograph a ball in flight with short exposure I would get precise position of the ball but I would not now its direction and speed (momentum). But if I photograph the ball with long exposure it will be smeared in the photo and I would not be able to tell its position but I could know its direction and speed (momentum).

[@sebastiangudino9377]

Marko Kralj Great Example!!!

[@AllTheFishAreDead]

This is a nice example but as you say purely classical. It is hard to map this to something like single slit diffraction, and is also more about the limits of measurement apparatus than the inherent uncertainty. For example, one could take two highly resolved photos a known time apart and know its position and momentum at each time (assuming it's flying in a straight line for simplicity) which is forbidden by the quantum uncertainty. Also, the simultaneity here extends beyond a single measurement

[@palcsoke]

This needs more likes! 😉

[@Rightlime7923]

this is a really good explanation

[@AaronFresh09]

Pretty good. At least a better understanding than most physicists, but a more accurate explanation is that without the principle what would the particle be made of? It's got to be made of either position or momentum uncertainty in order to be be measured or even described as a pure particle/momentum and not a wave function. This principle maintains the principle of energy conservation. We can't have one without the other (uncertainty that is).

[@zedwms]

A cop pulls over a physicist and asks, "do you know how fast you were going?" The physicist replies, "no, but i can tell you exactly where we are." The cop says, "you were going 75 miles per hour." The physicist throws his hands in the air, and cries, "oh great, now we're lost."

[@WilliamFord972]

The fallacy there is assuming that velocity can be extrapolated directly momentum via p = mv, but the uncertainty principle is between position and momentum, not position and velocity. In QM, p =/= mv necessarily.

[@captainhd9741]

He pauses for a second as he proceeds to handcuff you

[@DragonsFrogs]

Zed Williams it’s clever but it’s the top comment on pretty much every astrophysics video. Sometimes there’s the second part about the cat in the trunk too

[@justanotherguy469]

That is so funny!!

[@vanshnukala2663]

I like the one where this guy is about to kill himself, and a physicist watching cries "don't do it, you have so much potential"

[@axelandersson6314]

I’ll have to rewatch this a few times.

[@gideonjones5712]

I usually do that before I get more than maybe five minutes of the video...

[@KonradSzczygieł]

I just needed to rewind it in 3-4 moments. I had trouble with focus when xkcd comics showed up, as well as some equations ^^

[@JM-us3fr]

Yeah this video didn't have as many diagrams or animations. It was mostly just him talking

[@mellowfellow6816]

Me too, but I will have to get on the mushrooms first.

[@rocketraccoon1976]

That won't help. The more you focus on one facet of his explanation, the less you'll understand of the other facets. You can never understand all the facets. Sorry. 😐

[@PaulPaulPaulson]

Thumb up for the xkcd comics! Its original title text of the first comic is: Our phones must have great angular momentum sensors because the compasses really suck.

[@Lucroq]

No shade on xkcd. The author actually understands the subject matter of his jokes.

[@nidurnevets]

I read a statement by Feynman in which he said that Heisenberg uncertainty principle is not necessary anymore. I am wondering what he meant by that, if I have this correct

[@lorrainewilliams7896]

I used to love XKCD until the past election cycle. They weighed in and did not stay neutral. Very disappointing.

[@therach7841]

How can any thinking person stay neutral in the face of an administration that is so vehemently anti-science? Are you aware that the Trump administration has banned the Center for Disease Control from using the terms "science-based" and "evidence-based" in official documents? Measures like theses are just the tip of the iceberg. One of the jobs of science popularizers is to push back against ignoramuses that intend to drag us back to the dark ages. Neutrality in political matters is not always the de facto correct strategy.

[@jjsmith706]

Lorraine Williams "I liked him until I found out he disagreed with me politically." That's what you sound like.

[@calculon000]

This is the densest episode of PBS Spacetime I've seen, and I love it!

[@jjaj1243]

I’m sure u get this all the time but thank you for putting in the time and energy to explain this stuff so well. I couldn’t handle college just bc of all the jumping through hoops for certain grades and unnecessary classes, but with the knowledge I’ve gotten from channels like yours my craving for new information is always satiated. I wish I had the endurance to put up with college but bc of people like you my love of learning doesn’t require thousands of dollars and 10 college success or financial preparedness classes

[@foolishball9155]

Did you just make a pun of time energy and certainty?

[@marcushendriksen8415]

I've developed what amounts to a sixth sense for when he's about to unleash his final "spacetime". You can totally hear the wind-up in his voice, and his body language screams that he's about to. I find myself tensing in anticipation of it, I'm not kidding.

[@randalljones4370]

Wai... you mean your body becomes an algebraic object that has a multilinear relationship to the set of algebraic objects that predicts the appearance of Doc's last "spacetime", in vector space? Damn.... does it hurt?

[@MisakaMikotoDesu]

I thought I was starting to understand quantum physics a bit, but no.

[@yaldabaoth2]

Understanding that you do not understand quantum physics is a step towards understanding quantum physics.

[@tuele4302]

Richard Feynman once said, "I can safely say that no one understand quantum mechanics." The problem with trying to understand quantum mechanics is that people often attempt to use analogies with familiar phenomena, but the quantum world is anything but classical.

[@azmanabdula]

You cant understand it, but you can appreciate it.... Unless you are Ed witten, Then you can claim to know (Understand)

[@fusiontricycle6605]

I think I understand quantum mechanics and don't think I understand quantum mechanics at the same time! (get it?)

[@ryans9094]

It helps if you really go into the mathematics of it. Lots of linear algebra. Then when you get far enough you get back to a point where you feel you don't understand any of it again.

[@buddhapunch2486]

My physics teacher asked me where my homework was. I told him that I measured it's velocity so precisely that it could be anywhere in the universe.

[@ZelForShort]

I got pulled over and the cop ask me how fast I was going. Sadly I couldn't tell him

[@buddhapunch2486]

"I'm far too confident of my location to give you a meaningful answer, officer"

[@ZelForShort]

Buddha Punch currently sitting in jail. Needless to say my position changed and my wave function has colaspe(can't spell)

[@fcoa.1363]

Jaaaaaajaaaaajaaaa

[@zzzzzzzzzzzzzzzzzzzzzzzzz3204]

sssslllloooowwww ccccllllaaaapppp

[@astropredo]

The good about videos is that I can repeat until I get it :P

[@nachannachle2706]

+Massa C But, you will NEVER get it. It's Quantum Physics, not Classical mechanics... -_-

[@astropredo]

Nachannachle surely not fully comprehend or know why they behave this way. Im doing my physics bachelor to try to understand the best I can about nature :D

[@Earlesstag]

God I love how you always end with "Space time" seriously it's like pleasing to hear everything end on that

[@atscub]

Excelent as always. A little remark. Fourier analysis is valid for any periodic function, not just sound waves. IE: any function can be expressed as an infinite sum of weighted sinusoidal functions. In fact Fourier original work was related with heat propagation, not sound waves. I'm sure you know all this, but just for clarification. Thank you very much. I have learn a lot from this channel.

[@junkerzn7312]

First thing I learned playing with sound on little 8-bit computers in the 1980's was that a square wave wouldn't produce a pure tone. And from there everything else flowed. I eventually learned about fourier transforms. In later life, we'd use the transform to scan a wide swath of the radio frequency band simultaneously. Instead of scanning frequencies by slowly tuning the frequency of the receiver, we'd instead start at a center frequency and tap off before the IF filter and run it through a fourier transform to find which nearby frequencies had the most energy. Then jump the tuner by a considerable amount for the next sample. I loved this episode. It made Heisenberg's uncertainty principle even more clear. The fact that it happens with matter at all (not just energy, but actual particles of matter) is amazing. -Matt

[@Master_Therion]

In the early 20th century many physicists thought they were titanic, until they hit a Heisenberg.

[@the_reality_of_the_virtual3212]

I am making a meme out of this mate 😋😂

[@BC3012]

👉😎👉

[@Master_Therion]

Tech it UP Awesome! Send me a link if you can. I thought about wording it "many of the giants of physics thought..."

[@kshitizsharma386]

I'm in for the link too

[@Mernom]

Excellent one.

[@dexterrity]

Thank you PBS Space Time. As a student of physics, I truly appreciate the great animations & concise explanations in your videos. It's a great feeling when things start coming together and making sense!

[@jamespurks1694]

The study of quarks is a quite charming endeavor.

[@kconger_]

You are quite strange, James.

[@FairyRat]

nice cat james

[@kconger_]

I hope he doesn't try to Fourier transform it.

[@martijnbouman8874]

Do we think this is a top comment?

[@jamespurks1694]

FairyRat Thank you.

[@phil.s3713]

I love this channel. The fact, that they go through the fundamental maths and not only physical concepts without any appropriate mathematical descriptions like other channels do, makes it so great. It's not too hard but not too easy to understand.

[@cosmophile7663]

✓✓✓

[@phoule76]

nice Dark Matter tee-shirt, Matt.

[@alexanderf8451]

Learning the Heisenberg's Uncertainty is caused by a Fourier transform totally changed my understanding of physics. I can't express how happy I am that there is an accessible video I can point people to in the future.

[@voidisyinyangvoidisyinyang885]

Actually Fourier assumed symmetric math but it was Dirac who realized that the uncertainty principle originated from noncommutative math. He knew this from having studying Whittaker - as there is a "wattless power" that is noncommutative. But then he knew actually that the math of Whittaker was the same as the Poisson Bracket.

[@CurranEggertson]

You were getting there, but the uncertainty applied to sound frequency/time is called Gabor Uncertainty. It would have been a useful differentiation to the more popular Heisenberg principle.

[@voidisyinyangvoidisyinyang885]

I think he meant Fourier Uncertainty - as in this phys.org/news/2013-02-human-fourier-uncertainty-principle.html Human Hearing is Faster than Fourier Uncertainty. And this: “When Δν is 0.1Hz, Δt should be more than 1 /(4π *0.1) sec which is about 0.80 sec. Middle C of the equal temperament is calculated approximately as 261.6256 Hz. If you want to determine C with this precision 0.0001Hz, you need Δt of 800 sec, or 13 min 20 sec. If you want to get the exact Middle C, you need an infinite time and a continuous wave of C. In other words, theoretically we cannot get the perfect fifth tone with a frequency f ( that is ν ) from a root tone with a frequency f0 by calculating f = f0 × 3/2.” Uncertainty Principle for Temperament by Iori Fujita, www.geocities.jp/imyfujita/wtcuncertain.html

[@TheyCallMeNewb]

I repeated from De Broglie quite a number of times. Maybe spending 45 minutes with it, I think now that I take away something of a mental image that reconciles the two-sided coin of momentum and position. Positively fabulous.

[@FilingAccount]

Thank you for putting up these videos. I learn a lot, and so does the kids and parents in my neighborhood (when we try to break it down to ELI5 level). It has become a weekend gathering for an hour where parents and kids show up with some snacks and drinks and "talk science". Props and cutouts are starting to appear. One question though. If we were to "talk science" in an orderly manner, which topics should we start with and how should we progress through them? Right now we simply talk about a topic someone picked up during the week, or pick your latest video. I think it's a bit unstructured, and it may be a good idea to structure it a little bit so it's easier to connect the dots between topics. Again, thanks so much for all these videos!

[@RG-rl6hj]

This is the neighborhood I wish I lived in

[@MrHkl8324]

The kids will be the next newton.

[@kevinocta9716]

I love the comparison with sound waves! It makes things much less abstract for me personally especially!

[@idkrlyg]

Each video gets better every upload.

[@S4R1N]

Thank you so much for this, as someone with an interest in physics (but not the time/money to study properly) this channel has been an absolute godsend for me. I always struggled to get my brain past the 'Observer effect' being the main reason for the uncertainty principle, but the sound comparison made QFT make about a dozen things I knew snap together instantly, I'm kicking myself for not realising it before.

[@PrincipalAudio]

This is what I have to contend with when viewing a Fourier Transform of an audio file. _Should I choose to prioritise frequency or time?_ It all depends on how zoomed in on the waveform I am in the X-axis, as well as the depth of frequencies I'm zoomed on in the Y-axis. I can say I understand what you're describing because it's an analogy of what I deal with on a daily basis! :)

[@michaelellis4943]

I always thought the time/frequency uncertainty was circumvented by limits of sample rate. You could theoretically analyze using an arbitrarily large fft size (you might have to code it yourself), but at a point there will not be any additional information.

[@PrincipalAudio]

Ah, I see. From what I've experienced, when increasing the FFT window size it "blurs" the time axis (X) while increasing the frequency axis (Y) resolution. However, when decreasing the window size it "sharpens" the time axis while decreasing resolution in the frequency axis. I am using old software, though! :)

[@michaelellis4943]

well in terms of window size related to frequency resolution, the window "size" is the number of frequency bands the signal is represented as, so lower sizes will include more frequencies in a single band. not sure about effect on time resolution, may have to do with the math ( i only know basics of it). also most fft-based frequency analyzers i know of represent frequency on x-axis, and amplitude on y-axis. (i use voxengo's SPAN)

[@PrincipalAudio]

Ahh, I'm talking about 3D FFT. X-axis (Time), Y-axis (Frequency), "Z-axis" (Intensity displayed as colour differences). It's actually displayed as 2D but the colour/gradient could be represented as another axis in 3D like with other software that displays waterfall FFT.

[@Jacob10D]

t = 1/f. Time = 1/Frequency. If there are N samples (or a rectangular window size of N) of "intensity" (or rather, real valued pressure) within a set time, T, and we use an N-point fast Fourier transform (FFT) to transform the time-domain values into frequency-domain values we will end up with N values at N different (linearly spaced) frequencies, with a maximum frequency of F. If we reduce T then F must increase, but N remains the same. More precisely: The N different values give N/2 phase values (actually N conjugate pairs) and N/2 magnitude values. The highest positive frequency (the N/2-th frequency)(because negative frequencies are not real, physically) whose value can be unambiguously determined (Shannon-Nyquist) corresponds to two times the smallest gap between consecutive time samples. If we keep the same N-point FFT and reduce T then our time sample gap gets smaller and thus our largest frequency must get bigger. So there is higher time-resolution and lower frequency resolution.

[@michaelkreitzer1369]

That comparison with sound waves was immensely helpful. Thanks!

[@NewMessage]

Scientists. "What's the x and the p stand for?" "Position and Momentum." "Ah.. so the x is Momentum?" "Pffft.. No."

[@amisfitpuivk]

X marks the spot bro. Position. Which starts with P, but also is marked with an X or turn that 45 degrees and it's a + which may be a "t", sometimes confused for a 'j', which some people might think is a lowercase 'i' or perhaps an 'L'. IT MAKES PERFECT SENSE!

[@yaldabaoth2]

I had to think about it for half a minute to spot the joke. I'm a scientist btw.

[@gizatsby]

x as in the x-y-z axes when you describe space. p was just a symbol that wasn't being used in physics and is loosely related to the latin equivalent of "momentum"

[@BenGrem917]

@@yaldabaoth2 Someone's read his Gnostic texts, I see. Had to comment, nice name.

[@pepe6666]

Back to watching this for the second time. Making even more sense. Audio is a great way to explain the uncertainty principal. Was using it the other day

[@1ucasvb]

OMG, you guys used my animation. So happy!

[@guruyaya]

Every once in a while, you give us a lesson that blows my mind. That was one of those!

[@bilimbilin]

Hey good people all around the word. Trying to get a better understanding of the uncertainty principle but still a bit confused. So since everything is both wave and particle (de Broglie), this imposes the superposition principle - they can be in multiple places at once and their location is the sum of all the possibilities - until we measure or observe it; then the state collapses (from what I understand). So the uncertainty principle is when you limit the superposition of location lets say (or decrease the posibility of the particle being in more places - Fourier), then you increase the superposition of the momentum (when you get close to the heisenberg uncertainty limit). When it is said that the uncertainty principle is when you measure one, the other goes crazy is wrong I feel like - since the principle does not depend on an observer being there. But when you decrease the possibility of superpositions? I saw the episode that Veritasium did, and he had a light passing through a slit, and as he made the slit smaller - at one point the light that was projected on the wall started expanding - where you are limiting position, so the uncertainty in momentum has to increase. Does that sound right?

[@00ryanm00]

BilimBilin You sound like you may be on the right track but youre not quite there yet. It appears the most common misconception about the uncertainty principle is that uncertainity occurs when you make an observation, therefore collapsing the wavefunction. This is NOT true. The uncertainty principle always exists, even when you dont collapse the wave function. There are two ways to interpret this result: 1) Think of a particle as a wave (as you say from the DeBroglie relationship) . Then some intuition can show that the better defined a wavelength is, the less defined the position is. And visa versa. You can draw this on paper. Draw a pulsed wave and a standing wave. This follows from Fourier analysis. If your function is very tightly localized you need a large range of frequencies to construct this function. If the function is really spread out you dont need so many different frequencies. 2) It comes out of the math. This is the answer I perfer since QM is so hard to understand, its better to just take it as it is from the math. If you want to understand this it will take some chugging through, but look up Hermitian operators. Essentially, the first postulate of QM says, every observable corresponds to a hermitian operator. And the uncertainty principle uses the Schwarz inequality to show that if two hermitian operators dont commute, then they have an uncertainty relationship. For example, position and momentum dont commute because position has a derivative. However, in stationary states any operator will always commute with the Hamiltonian. This occurs because you can construct simulataneous eigenkets of these operators, thus when you measure their corresponding eigenvalues you measure both at the same time with no uncertainty. Id be happy to help with any questions. But basically, an uncertainty relation may or may not exists for many different observables. Observables include momentum, the hamiltonian, position, cosx, sinx, angular momentum,etc. You need to find their operators and compute their commutators. It comes out of the math and from the wave-like form of the Schrodinger equation.

[@sarabjeetsodhi3283]

Ryan M. thnx guyss ya explained better than that fella in the video

[@sarabjeetsodhi3283]

can u plzzz explain it actually i an absolute beginner:)

[@acmefixer1]

sarabjeet Sodhi If you're a beginner, you have to start at the beginning. 😟

[@KhalilEstell]

I've been watching PBS Space time since it first came out I wasn't until today and a friend saw me watching this channel when I realized that this was ultimately an educational channel. This channel is so entertaining and fun to watch. I love this channel!

[@johnregel]

As a patreon supporter, can I request an episode dedicated to guage symmetry? It's a clever math trick, but leads to testable predictions? Show us O'dowdiiWan Kenobi.

[@vampyricon7026]

The whole idea of gauge invariance is that it's a clever math trick that doesn't lead to different predictions.

[@thedeemon]

This "math trick" gives us all four fundamental forces, so it's really significant and worth studying in depth.

[@vacuumdiagrams652]

The first step to understanding gauge symmetry is to know that it's not a symmetry... :)

[@vampyricon7026]

I've heard of that saying. Why is that though?

[@vacuumdiagrams652]

Because while a symmetry does loosely refer to some transformation that leaves the system invariant, it has to be a transformation of quantities that "matter". For example, if I'm describing the electric field around a charge, I can also write a subscript that denotes my favorite pizza topping. Then I say something like E_pepperoni = k * q / r² while my friend Steve says E_cheese = k * q / r² and we have to add in a new rule that says that physics is invariant with respect to pizza toppings, so I can do a pizza transformation E_pepperoni -> E_cheese that changes nothing about experiment. Of course, this is completely absurd: my pizza preferences exist only in my head and so this pizza symmetry can't possibly have anything to do with a real symmetry of nature. Gauge invariance is a lot like this in that no gauge transformation ever changes the physical state. It changes only the mental state of the physicist. For example, while a "force" is physical (I can measure it by using it to accelerate a known mass) the potential energy is defined only up to a constant of integration. I'm free to use that constant, and my choice is completely up to me just like my favorite ice cream flavor is totally up to me. For that reason, shifting the zero of the potential energy is not usefully thought of as a symmetry.

[@JakeHarris0]

Thanks for using the Fourier example. That really helped it make sense!

[@RajuSingh-fx9lh]

“After the conversations about Indian philosophy, some of the ideas of Quantum Physics that had seemed so crazy suddenly made much more sense.” Werner Heisenberg

[@ozymandiasnullifidian5590]

He was being polite. What Indian philosophy? Hegel wrote in his History of Philosophy that there is no such thing because in India religion is still not separated from scientific, or philosophical thinking. And science and religion mix as much as oil and water.

[@felipemonteiro5877]

People always try to shoehorn their beliefs into science. It's embarrassing, really.

[@helkafen100]

@@ozymandiasnullifidian5590 There's a book on the links between buddhism metaphysics and quantum physics epistemology, cowritten by Trinh Xuan Thuan (an astrophysicist) and Mathieu Ricard (a western geneticist turned monk). I think the name of the English version is The Quantum and the Lotus. This is not much about religion itself, more about the metaphysics that was developped alongside buddhism, which you could compare to the early efforts of greek philosophers about "atoms" etc, and the interpretation of the equations discovered by science.

[@chaitanyapatel1946]

Wow. This is the best explanation I have ever heard about uncertainty principle. This will remain one of my favorite videos from this channel.

[@utsavshah5459]

My wave function just collapsed I'm localized on bed, but my brain is aching in infinite dimensions

[@d.l.918]

I always tell them: Don't measure it, it'll collapse!

[@Plafintarr]

Lmao!

[@ASLUHLUHC3]

You should've said your brain is still in superposition.

[@dmitrylopukhin8364]

That's probably the best episode so far.

[@PaulPaulPaulson]

For those who want to know more about this topic: kzbin.info/www/bejne/pmjFq3hnepqDg7s

[@michaelkreitzer1369]

Legit link, this was super helpful. Thanks!

[@Lucroq]

Video title: "Visualization of Quantum Physics"

[@RoGeorgeRoGeorge]

What a pleasant surprise, this is the best visualization found so far. Subscribed! Thanks you for that link, Paul Paulson :o)

[@justchecking905]

Well done!! It pulled a lot of things together for me and resolved some doubts I have always had about the converntional interpretation of QM properties. - Retired physicist.

[@MushroomManToad]

Just "Fourier"? I think, out of all the Foury Series, this one is the Fouriest!

[@bxdanny]

Or it might actually be Five or Sixier.

[@yandan8]

Is it me, or is it this channel? Things are getting more complicated, not less. Understanding is decreasing, not increasing. I've never had an experience where the language becomes less comprehensible the more I listen. :-)

[@ryoung1111]

When you say "The sound wave for a simple pure tone, like a middle C, is a sinusoidal wave," why is the audio guy using a piano sound? Surely he could have made a nice sine wave-at least for a while. (Granted, it couldn't be a REAL, TRUE, infinite sine wave, but hey...) Also, wouldn't it be better if the oscilloscope graph was depicting the actual waveform of the sound he did use?

[@SvenSchumacher]

As a sound engineer, this is a well-known topic. When I use an FFT display, I can choose how exactly I resolve the frequencies and get a display that is very sluggish. If I sacrifice the accuracy of frequency analysis, the temporal resolution is much better. So either I know exactly when which approximate frequency is present in an audio signal, or I know the frequency very well and lose the exact time. In practice, therefore, the compromise between the two is used: A not too precise division into frequencies with an acceptable temporal resolution.

[@voidisyinyangvoidisyinyang885]

As Alain Connes point out the truth of music is actually noncommutative time-frequency. So this got covered up eversince ARchtyas and Plato - and so quantum is also noncommutative with a dimension of zero. No one is listening - when time is zero there is nonlocal quantum consciousness, as Basil J. Hiley points out, so noncommutative time-frequency means being in two places at the same time as noncommutative phase. This is superluminal momentum force that is not conserved, as de Broglie's Law of Phase Harmony accurately modeled. Frequency is to time as momentum is to wavelength.

[@UpcycleElectronics]

I knew I should have played with digital audio instead of focusing on analogue tech ;/

[@Aziraphale686]

I would love it if you would do a (few) episode(s) about symmetry and symmetry breaking. It's fascinating that there are these fundamental symmetries built into the laws of nature, and it's not something I've seen any of the major science channels talk about.

[@voidisyinyangvoidisyinyang885]

The Higgs Field is a Mexican Hat symmetry breaking into the electroweak left-handed field that then creates the left-handed amino acids of life on Earth - with right-brain dominance. But us left-brain/right-hand dominant modern humans use symmetric math as a lie with the results being the destruction of ecology.

[@Aziraphale686]

Omg, where did you get your PHD? Teach me senpai!

[@voidisyinyangvoidisyinyang885]

"The Universal wave function is a self-organized pilot wave acting as the binary quantum switch, cohering and decohering any measured system and its sub-systems in temporal evolution." So then he states cancer cells are not random but actually adaptations of a cell's attempt to be immortal!! "Moreover, Couder et. al. (2014) corroborated that deterministic quantum fluid dynamics can experimentally validate Bohm's pilot wave theory at the millimetric scale." cyber.sci-hub.tw/MTAuMTAxNi9qLmJpb3N5c3RlbXMuMjAxNy4wMy4wMDQ=/10.1016%40j.biosystems.2017.03.004.pdf

[@sakuraslight]

WOO HOO got a mention. ^_^ I think there should be more ways to help fund SETI and other scientific research. In witch they can generate funds as well as help them with science. I don't want the Bitcoin or Gridcoin. I want them to have its so they can buy new science Equipment, staff, coffee for there late nights.

[@denravonska]

sakuraslight Within Gridcoin we've been talking about being able to automatically donate parts (0-100%) of your earnings for this exact reason. That would be an option.

[@christynpienaar]

I once had a thought that everything can and is related to sound waves.. and I am pleasantly surprised to get some validation from PBSST - Thank you.. I cant wait for my daughter to know this.

[@user-wu7ug4ly3v]

"The Born Rule" ... isn't that an up-coming movie...? Also, what if Euler hadn't given his name to e^(i*pi)=-1, Born could have given us the Identity instead...

[@allan710]

This is the best explanation ever of this subject. I had never understood up to now.

[@911gpd]

"Half a million in cash." - Heisenberg 2010

[@feynstein1004]

You're goddamn right :P

[@DavidG2P]

Pardon?

[@adarsharao]

Momentum is like frequency for position.. that's a revelation... thanks a lot 🙏

[@ゾカリクゾ]

The more I watch his supersymmetrical beard the less I understand the video. IT IS EVERYWHERE

[@pongesz2000]

oh memories... these were the best courses in the university.

[@JD-un6ul]

Great video, but I wish you would have gone into how the Energy time uncertainty is different in the sense that there is no time operator and thus time and energy can in fact be measured simultaneously to arbitrary precision. Having not yet studied QFT, I would like to know how that fits into the heuristic picture of particle antiparticle pairs borrowing energy from the vacuum.

[@i_booba]

"but I wish you would have gone into how the Energy time uncertainty is different in the sense that there is no time operator and thus time and energy can in fact be measured simultaneously to arbitrary precision." No, you still cannot measure energy and time to arbitrary precision. You are right that they don't have an operator form. But, they still satisfy the uncertainty relation \delta E \delta t >= hbar / 2.

[@ISK_VAGR]

Hi, thx very informative. I am not a physicist, but I understand your explanation as follows: exact position will be like a photograph of an object (e.g. a ball), where you can pin-point the exact position of the ball in the photograph, but not tell where it goes, means momentum is uncertain. For knowing the momentum you need contiguous photographs (or a video) of the ball, but then the object exists in each of the photograms of the video at the same time therefore it’s exact position is uncertain. Following this analogy, the duality weave-particle is just that subatomic particles like electrons when move have a defined momentum therefore they are acting as a weave (like in a video) but when they collide with an screen, which stops the electrons, then the electrons act as a particle (like in a photograph) because it’s energy stops there, therefore the electrons (or their energy signature) have an exact position? If this is correct, what we call particle is not really an object but the effect (the energy signature) of the electron(s) when are colliding with the screen. What really exists is the weave. I will be glad to know if this way of thinking is correct.

[@garethdean6382]

It's a good classical analogy, and has some strange effects. For example I can sit a ball on a table and take a photograph and say 'The ball is there and its speed is exactly zero.' But I CAN'T do this with an atom; an atom refuses to sit still, even at absolute zero. (For liquid helium this means it will NEVER freeze, its atoms move too much.) The wave just keeps on waving.

[@maidpretty]

Will you make an overview of 10-15 common interpretations of quantum mechanics?

[@vatsalyasharan4202]

Best channel for budding Physicist

[@andrewbosak8941]

I couldn't quite follow you on this one, Matt. But I think I get the gist of the idea

[@nashs.4206]

Ok so the idea is to first think of classical wave mechanics first, then apply those ideas to quantum mechanics. An important mathematical idea in classical wave mechanics is the idea of a fourier series. The fourier series allows you to approximate any general periodic waveform (i.e. something that repeats itself e.g.a sine wave) using a bunch of sines and cosines. It works the other way too -- given some random periodic waveform, you can figure out how much of sines and cosines were combined together to get that periodic waveform. It's like decomposing a dish into the ingredients-- the dish itself is the periodic waveform, and the ingredients are the sines and cosines. You can either combine the ingredients to create the dish, or you can analyze the dish and determine its ingredients. Now, it turns out that if you want to model a very sharp spike in terms of sines and cosines, you need A LOT of sines and cosines. It's pretty intuitive if you think about it -- a sharp spike is basically regular waveforms (sines and cosines) that happen to cancel each other out everywhere, except at that spike's location, where the waveforms add up to create that spike. Now, if you only have a few waveforms, then you can't make them cancel out everywhere except at some location. If you have a lot of waveforms, you can adjust them in certain ways so that they can cancel out everywhere except where you don't want them to cancel out. So the gist is that you need a lot of waves to create a singular spike. Now so far this was regular old classical wave mechanics. In quantum mechanics, the "waves" are really wavefunctions and these describe the probability of a particle being somewhere. Now, in order to make a particle appear somewhere, you have to make them disappear everywhere else, except where you want it to appear. But remember that the wavefunctions are like waves, and so they also obey the fourier series stuff I was talking about earlier. So, in order to make a particle appear somewhere, you have to have lots of different wavefunctions all added up in a fourier series.

[@jldstuff393]

Nash Shrestha great explanation! Would you mind looking at the question I posted to this video to see if you can answer it (if you can find my comment; I don't know how to link to it here).

[@pepe6666]

oh god i have been waiting for this video for ages. ever since i realized audio has its amplitude and frequency representations via fourier, i realized that quantum stuff must have similar things. havent watched the video yet. im gonna get me a chocolate bar and watch.

[@pepe6666]

damnit. i cant get enough of this show. i signed up to patreon just for pbs spacetime. after all this amazing content its just getting ridiculous. someone make this man a statue.

[@gametavt6866]

Could it be that all the stuff that makes the universe is actually in higher dimensions and we can only see a "frame" of it at a time, so infinite combinations of wavelengths packed in a perpendicular dimension to ours is what is being summed to one another to produce what we see -- a particle behaving unpredictably in a 3D "frame" of time -- but in reality it would actually be following a higher dimension wavelength "path" or... oh fuck it, I'm a graphic designer, I actually have no idea what I'm talking about...

[@MrGooglevideoviewer]

WOW, I am a layman (a science enthusiast but certainly a layman), so my opinion means little but I LOVE this idea. I don't know if it's just another way to word the multiple worlds interpretation where every "frame" gets split into another infinite set of "frames" over and over again, but the way you have worded this was really amusing... Cheers dude!

[@ChenfengBao]

What you said is quite close to the many-world interpretation of quantum mechanics, which says the universe is perfectly described by a "universal wavefunction", but we only get to experience a projection of it. Although it doesn't really have anything to do with the 3+1D space-time dimensions. Note also that the many-world interpretation does NOT say anything about the universe splitting into infinite parallel universes, despite being portrayed so in popular science.

[@garethdean6382]

This is a variation of 'hidden variables' in this case 'global' variables. In such theories 'hidden' or not immediately obvious layer of reality causes what appears to be random behavior. In theory if we knew about these hidden variables we could perfectly predict the universe. This has been proven false on a 'local' scale but your theory still holds water, if we can somehow probe this higher reality.

[@the1exnay]

The unknowability isnt a limit on our ability to measure it, but rather a result of it being a wave. What he is saying is that even with perfect knowledge of the properties of the particle there would be uncertainty. There is a similar principle for time and frequency which is perhaps easier to understand. Imagine you strum a guitar string and let that one note ring out for a while. It is very clear what the frequency is but at what time did the sound happen? Say instead you just let it play out for the smallest of moments. Now the sound wave just looks like a single spike so what is the frequency of that? But the time it happened at is very clear. This uncertainty isnt due to any hidden knowledge but rather just the nature of the sound produced

[@markseiter8208]

I'm AMAZED!!!! I'm an electrical engineer and feel a little dumb I never put this together. Doesn't the uncertainly principle look a lot like the Nyquist Criterion with the Planck constant as the sampling frequency?

[@aryamansinha9309]

I thought something made sense but then it didn’t and sadly my mind exploded.

[@peacefulpsyche]

This show helps me get to sleep every night. It always works!

[@Teboski78]

Impossible. If the geckos had infinite tensile strength that would require the electromagnetic force that binds the geckos molecules to one another to take on a value of infinity which would cause the geckos to fly apart into an expanding cloud of magnetically neutral pares of particles that would have accelerated away from each other at speeds so close to C that they would collapse into infinitely massed singularities as consequence of their excess electromagnetic potential energy being converted into mass instead of kinetic energy.

[@agiar2000]

Except that the geckos have zero mass, which means that the force required to bind them would _also_ be zero! Theoretical physics is so much more fun than engineering. We have access to *ALL* the massless ropes and frictionless pulleys! :D

[@Teboski78]

But having no mas just means they can have an infinite strength to mass ration. In order to have infinite tensile strength they would need to be able to hold together with infinite force attempting to tear them apart. Which would require the binding force to have an infinite value.

[@kconger_]

A gecko black hole. I like it.

[@Teboski78]

No a gecko black hole bomb.

[@Cythil]

Well. If there composed of Energy then they will have Mass. As the both are connected. But maybe the whole package of gecko also is composed of negative energy that has negative mass and balance out total mass to zero.

[@Adityarm.08]

Please keep uploadong more mathematically inclined content!! It's so much more awesome!!

[@slashusr]

Why did the physicist cross the road? Well, actually, he didn't quite make it. His dying words: "If only I'd known so much less about that truck's position..."

[@garethdean6382]

Should've paid more attention to the speed limit...

[@DanGrrr]

I love your channel man. You explain QM better than most people on YT. Keep up the excellent work! 👍🏼

[@amisfitpuivk]

... what?

[@alanlee1355]

What?

[@mengqiyang3523]

Your video reeeeeeeeeeeally helps me a lot to understanding the QED and even Fourier transform, thaaaaaaanks!

[@rdooski]

He goes way to deep for your above average pbs viewer....

[@maythesciencebewithyou]

That's a good thing. People usually just watch popular science shows, if any, and then convince theselves that they now know everything there is to know about the topic in all detail, somehow believeng it has turned them into experts, which allows them talk down on real experts. Here people should learn some humility and realize, how much effort and thinking you need to apply to actually. comprehend these things. And realize that there are infact people with vastly more knowledge and understanding then them, whose opinions should rather be taken into account, then that of a Trump.

[@AlbertoLopez-to9hj]

Just in time for finals. Thanks!

[@FoXsvk]

You forgot the annotation to Veritasium video: kzbin.info/www/bejne/l2mphaVoprKoqqM ;)

[@PianoMastR64]

Thanks. It wasn't showing up in the recommended section, and I was really hoping someone made this exact comment

[@macronencer]

3:55 Oh WOW, that is an OLD xkcd cartoon. I remember loving that one so much that I had it stuck to my cubicle partition at work for years :)

[@Thee_Sinner]

I bet there’s not even any meth in this video...

[@atomm4675]

Uriah Siner if you switch to gecko now you will receive 25% off on your car insurance for a year.

[@StefanReich]

lol what? (both of you)

[@mvmlego1212]

+Stefan Reich -- Uriah's comment refers to Matt's peh-kyoo-lee-ah pronunciation of some words, I think.

[@Thee_Sinner]

mvmlego1212 No, sorry. My comment is a 2 level reference from looking at the title: Uncertainty>Heisenberg>Breaking Bad

[@PuckLokin]

Hawking Radiation!!! Been waiting for that one.

[@911gpd]

"Let's cook !" - Heisenberg 2008

[@casinogiant]

This goes with a thought I just had a few moments ago. (The thought that lead me to this video). Here it is - The human life as an individual is governed by the uncertainty principle. This would explain the observer as a wave collapsing force.

[@Melomathics]

Why do I even watch these? (-_-')

[@Mernom]

Because you want to. Com'one, you know you do.

[@udaypsaroj]

This is a rare spacetime video that actually went over my head altogether haha...

[@lurts9820]

hi like one of the first :) was animating in blender and saw this notification

[@SheffieldMarkE]

Great explanation. It never occurred to me that there was a dualism to be exploited but it's really clarified this way

[@_dr_ake]

Quick physics question. By applying Heisenberg's incompleteness theorem to more intuitive wave forms should I grow my beard out? I've tried to crunch the numbers but I only have a passing knowledge of theoretical physics.

[@amisfitpuivk]

I have this same question, but at the same time, the entropy created by my right hand playing with my beard and accidentally pulling out hairs might counteract any future growth

[@davidfoster5561]

_ Drake Yes. Yes, you should.

[@therealjuan6184]

iiiiiiiiiits SPACETIME! ... Always great to see an upload.

[@kinglu6360]

This stuff is why i religion.

[@vdboor]

I liked the repeated end of the previous video, looked like it fit within the theme of the episode, so it was pretty cool IMHO :)

[@ricksanchez4798]

Wow, nice try but we all know that I am the-the only one that actually understands the suitabilities of all that ...

[@garethdean6382]

Only? You and an infinite number of alternate yous. Except for Doofus Rick of course.

[@middle_pickup]

3:10 That's how the DX7 and FM synths work! :)

[@1224chrisng]

I ship you and Kelsey Huston Edwards (former host of the PBS Infinite Series series) series series series series series series series series series series series series series series series series series series series series series series series series series series series Toyota echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo echo lol

[@hdwe1756]

Random Guy I think she's still a host, there's just another one as well.

[@drdca8263]

Please don't ship irl people that you don't know to be single? And probably best to avoid shipping irl people who you don't know in general?

[@Lucroq]

drdca, you are seriously telling me you DON'T ship the two?

[@BinaryMinecraft]

You guys should do an episode about currently unsolved problems in physics!

[@brunofagherazzi9903]

I'm loving this quantum videos, please keep going

[@eunomiac]

You, sir, have the best posture I've ever seen. (No, that's really all I came here to say: he has really excellent posture.)

[@musicalBurr]

Excellent explanation - one of the best I've seen! Thank so much.

[@UlaisisP]

This one was really hard for me, nice reality check, I don`t understand this thing. Keep doing this!

[@maryjanesyriakose8395]

Just wow!

[@CyberiusT]

Three watches so far, but... Man, that just went places I could not follow. I think I sprained my brain.

[@MakeMeThinkAgain]

I did think you were going to show SOME of what Veritasium showed. This is a good way to visualize quantum reality.

[@hsnopesium]

Can you build a playlist talking about the Heisenberg uncertainty principle and Planck length? culminating in the fundamental chunkiness of space?