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.
@@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.
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.
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 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.
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!
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.
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
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* .
Thank you again for your excellent explanation of extremely complex topics. It’s a skill not many people posses. I wish this knowledge was available when I went to school. I’m not good at math so it’s great to see you are sticking to explaining the principles and relationships, and leaving the detailed math in the description. This way me, a mere mortal, can focus on the essence without feeling stuck.
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.
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!"
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.
@@physics3632math 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
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.
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
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.!
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
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.
The uncertainty principle applies to position and momentum, and also to energy and time. The multiplication of these quantities should lead to something measured in mass * length² / time. Are there any other pair of physical quantities that multiply into something measured in mass * length ² / time and for which the Heisenberg uncertainty principle applies?
With energy and time while there is a similar uncertainty, it's really quite different from Heisenberg's. There is no time operator in QM, and HUP is all about pairs of operators for different observables. Anyway, in HUP we don't multiply position by time, we multiply unitless standard deviations in their probability distributions.
I’m curious, to what degree does the uncertainty get introduced by the fact that we are measuring waves with other waves. Any instrument used to measure is made up of the same wave/particle physics. How does that get factored into measurements and the cause of uncertainty? Dunno if I explained that well…
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.
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.
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.
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.
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👏👏👏🙏🙏
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.
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 ?
@@KAi-ns4zz What we call the speed of light, that speed and corresponding time is the speed and time from an observer point of view; not the speed in the reference frame of the photon. So that is not answering @markofdistinction6094 question. The photon reference frame has no time, not even distance. I am not even sure if we can call it a reference frame.
Nothing changes about that photon until it gets somewhere to interact with something, so there is no time to be had by it.! I think neutrinos (eg) do experience enough time to switch types, so they must see a kind of time, but they have mass to drive that change.. Is that the sort of thing @FermiLab? I hope this doesn't end up a definitive GPT answer!
For me too this is a mystery for which I don't find an answer: except maybe that the frequencies of photon origin when electrons jump between orbitals; But how the photon not having the concept of time/space, can have a property that has frequency is also strange to me. But then again that frequency is just something we perceive: it may not be part of the photon that is just carrying some energy (that we perceive as h.v).
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.
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.
A bit off topic but I have 2 questions: 1. Have additional time dimensions been absolutely ruled out? 2. I understand that particle charges in some way are determines by calabi-yau shaped dimensions. Has this been used to help reduce the number of such shaped that may be real to our universe.
@Fermilab we know that all atoms vibrate and at very low temperatures these vibrations are exactly what stops atoms from reaching absolute zero. Can we ever reduce an atom’s vibrations below the Planck length? What would be the consequences of doing this? Now consider neutron stars and black holes. As the pressure on individual particles increases, their vibrations must get restricted below the Planck length. Is there any relationship between restrictions on the vibrations of particles due to pressure, and the formation of neutron stars vs black holes?
Love the video, but I don't see why you couldn't have added an extra one or two minutes to explain that literally delta x and delta w are variances. This is a much clearer explanation of what these actually mean, and requires only high school probability, particularly in the context of bell curves (especially since anyone who actually knows what a bell curve is would likely be confused, as they never actually are zero and thus "width" doesn't really make sense.) Don't get me wrong, I like the intuitive "width" explanation for someone who doesn't know or remember high school probability, but it's confusing for people who do, particularly if you know what a bell curve is.
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.
Hi I have a question that I would liked to be answered in one of your next video's. What about quantization and locality of the condensated Higgs field. To make it more clear could I imagine the Higgs fields as a net the particals interact with so does exist a very very small distance a partical can travel without slowing down from the field until the next interaction.
Very nice and clear explanation. The claim at 4:47 "The two graphs have same information" is not correct. Fourier transform needs information about the amplitude *and phase*. The graph to the right has information about only the amplitudes, it has no infromation about the phase. In other words, if the different waves did not have a precise phase relationship, you won't get the square shape to the left.
The key point that I would like to better understand is whether the uncertainty is reflecting a limit on our ability to MEASURE and to know, or is reflecting an uncertainty in physical reality, itself. E.g, that a particle literally does not HAVE a definite position? My impression is that physicists lean toward the latter, but I would like to know what is the level of agreement among physicists, and what factors lead to their conclusion. Is this question merely "philosophical", or is there experimental basis?
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.
When discussing this topic, you have to address the elephant in the room (or is it??) and admit that nearly everyone will associate Heisenberg with Breaking Bad and not with where Breaking Bad got the name in the first place. Very well done!
Heisenberg was the only scientist who got famous by proving that something cannot be done. What a relief it was for all others who tried to measure the both values unsuccessfully.
@fermilab One question I had. The math assumes the relationship based on a normal distribution, but how do we know that quantum waves use such a distribution?
so it has to do with the limitations of the model used to represent probabilities in quantum mechanics which are in turn defined by fundamental truths about what it means to measure quantum phenomena?
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.
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.
Can you do this same video explaining the delta E delta t version - not dumbed down with "wiggles" please? This version of the uncertainty principle is way more unusual.
That one comes from the law of conservation of energy when you combine it with the uncertainty principle if I recall correctly. It's just expressing kinetic energy and potential energy in terms of delta x and delta p, then putting it back into the uncertainty principle formula. Which makes sense if you think about it, to measure kinetic energy is to measure momentum and to measure potential energy is to measure position, so the same principle applies. What it really uncovers though is that very energetic states can only exists for a short amount of time before breaking down, while lower energy states can last much longer and that it would take an infinite amount of time to get to a state which is purely zero. That's where the "absolute zero is impossible" thing comes from I think and why the vacuum state of particles is non-zero.
Does the new attosecond physics help to remove the quantum mechanical randomness we see? Has it all been because we’ve been observing at the wrong time scale?
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 😁
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 😅
In theory, doesn't the principal also apply to the macroscopic world? For example, if I'm spotting the location of a car in movement, the higher the precision of its location, the less accurate I can be about its speed. For example, at its most extreme, if I shoot a single photon at the car to locate it, I only have the information of that photon, which is its position..?
9:15 i think uncertainty principle says that knowledge is always limited It's not allowed by nature to know exactly position and velocity of an electron 9:15
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.
How and why are two frequencies the same? (one from Fourier transforming the PDF of x, and another being the frequency of a physical wave). The time dimension isn't even present in the first one.
In audio transistors add odd harmonics whereas valves add even harmonics. Taking this to its extreme, transistors distort to square waves and valves distort to sawtooth waves. This is why audiophiles prefer the sound of valve amplification.
I heard what sounds to me like there is a wave interpretation to how photons for example get captured by an atom. Like I mean it is somehow harmonic in size or something. Otherwise if just continues through and thus you have a transparent object?
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.
So entertaining, that ending line is gold ❤
Shout out to the editing team 👏🏼
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.
Police officer: "Did you know you were driving 100 km per hour?!" Driver: "Great, now I'm lost!"
Best physics jokes I've heard
Sorry, your delta p is enormously large, which makes your delta x very very very small. The officer knows where you are.
no uncertainty here: physicist effortlessly explains both Heisenberg and Fourier with such ease for common folks like me... thank you!
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.
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.
That was incredibly well done.
Best explanation of Fourier analysis as used in physics. Thank you.
Lmao have you even seen other videos
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'.
If TH-cam 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
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* .
Thank you again for your excellent explanation of extremely complex topics. It’s a skill not many people posses. I wish this knowledge was available when I went to school.
I’m not good at math so it’s great to see you are sticking to explaining the principles and relationships, and leaving the detailed math in the description. This way me, a mere mortal, can focus on the essence without feeling stuck.
Great explanation of the underlying relationship between position and momentum. Thanks for putting this together!
You cooked up a great episode there!
Thank you!! It feels truly amazing when all dots are connected. Physics is indeed everything.
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.
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.
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!"
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.
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…🤣
@@physics3632math 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.
Glad you're still making videos Don! Thanks for this one
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.
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.!
You got so close to saying what people actually need to know.
Uncertainty is a fundamental property of all wave mechanics.
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
Professor: What's this section of the wave called?
Me: ...a wiggle
Professor: Get out.
Another wonderful video, with Dr LIncoln again on top form. I look forward to watching more. 10/10.
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.
The uncertainty principle applies to position and momentum, and also to energy and time. The multiplication of these quantities should lead to something measured in mass * length² / time. Are there any other pair of physical quantities that multiply into something measured in mass * length ² / time and for which the Heisenberg uncertainty principle applies?
With energy and time while there is a similar uncertainty, it's really quite different from Heisenberg's. There is no time operator in QM, and HUP is all about pairs of operators for different observables.
Anyway, in HUP we don't multiply position by time, we multiply unitless standard deviations in their probability distributions.
@@thedeemon Do energy and time commute?
@@vitovittucci9801 Operators may or may not commute. Since there is no operator for time, the question doesn't make sense.
Spin ortogonal projections are also complimentary, hence HUP related
I’m curious, to what degree does the uncertainty get introduced by the fact that we are measuring waves with other waves. Any instrument used to measure is made up of the same wave/particle physics. How does that get factored into measurements and the cause of uncertainty? Dunno if I explained that well…
The uncertainty is absolutely dependent on it.
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.
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.
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.
Your videos is perfect. I'm gonna recommend it to my students along our chemistry class. Brilliant.
That physics is everything... gives me goosebumps
3:51 can we do something infinite number of times?
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!
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👏👏👏🙏🙏
When average viewer interested in mysteries of space is hit by Fourier transformation :D
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.
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.
Who else needs a demystifying video for this 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 ?
Who said you that photons don't experience time...
That's why it's said 3×10^8 m/s that second is what time... Experienced by a photon
@@KAi-ns4zz What we call the speed of light, that speed and corresponding time is the speed and time from an observer point of view; not the speed in the reference frame of the photon. So that is not answering @markofdistinction6094 question. The photon reference frame has no time, not even distance. I am not even sure if we can call it a reference frame.
Nothing changes about that photon until it gets somewhere to interact with something, so there is no time to be had by it.!
I think neutrinos (eg) do experience enough time to switch types, so they must see a kind of time, but they have mass to drive that change..
Is that the sort of thing @FermiLab? I hope this doesn't end up a definitive GPT answer!
For me too this is a mystery for which I don't find an answer: except maybe that the frequencies of photon origin when electrons jump between orbitals; But how the photon not having the concept of time/space, can have a property that has frequency is also strange to me. But then again that frequency is just something we perceive: it may not be part of the photon that is just carrying some energy (that we perceive as h.v).
Dr Don has made a video about it, title : Do photons really experience time.
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.
6 hours in and only 24 ,000 views. There is no uncertainty about your popularity. ✨
Is Plank's constant an h because p was already taken?
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.
Brilliant! Thank you Doctor Heisendon. I somewhat get it after a lifetime of not getting it.
Thanks for the free education Fermilab. Fascinating stuff!🖖🏻
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
This video connected so many topics for me, uncertainty principle, normal distributions, fourier transform 🤯
A bit off topic but I have 2 questions:
1. Have additional time dimensions been absolutely ruled out?
2. I understand that particle charges in some way are determines by calabi-yau shaped dimensions. Has this been used to help reduce the number of such shaped that may be real to our universe.
@Fermilab we know that all atoms vibrate and at very low temperatures these vibrations are exactly what stops atoms from reaching absolute zero. Can we ever reduce an atom’s vibrations below the Planck length? What would be the consequences of doing this?
Now consider neutron stars and black holes. As the pressure on individual particles increases, their vibrations must get restricted below the Planck length. Is there any relationship between restrictions on the vibrations of particles due to pressure, and the formation of neutron stars vs black holes?
I love these videos. They almost make me want to study math again.... almost.
But seriously. Thanks for making these. They're awesome.
The postlude is so cool!
9:15 Not mentioning the energy and time part is harsh. Is this giving any physics or just Fourier?
Love the video, but I don't see why you couldn't have added an extra one or two minutes to explain that literally delta x and delta w are variances. This is a much clearer explanation of what these actually mean, and requires only high school probability, particularly in the context of bell curves (especially since anyone who actually knows what a bell curve is would likely be confused, as they never actually are zero and thus "width" doesn't really make sense.)
Don't get me wrong, I like the intuitive "width" explanation for someone who doesn't know or remember high school probability, but it's confusing for people who do, particularly if you know what a bell curve is.
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.
3:30 is there a reason why you added only odd sine functions and left out the even sine functions?
Even sine functions would give you a wave with a different shape (I think a sawtooth).
Hi I have a question that I would liked to be answered in one of your next video's. What about quantization and locality of the condensated Higgs field. To make it more clear could I imagine the Higgs fields as a net the particals interact with so does exist a very very small distance a partical can travel without slowing down from the field until the next interaction.
Very nice and clear explanation. The claim at 4:47 "The two graphs have same information" is not correct. Fourier transform needs information about the amplitude *and phase*. The graph to the right has information about only the amplitudes, it has no infromation about the phase. In other words, if the different waves did not have a precise phase relationship, you won't get the square shape to the left.
The key point that I would like to better understand is whether the uncertainty is reflecting a limit on our ability to MEASURE and to know, or is reflecting an uncertainty in physical reality, itself. E.g, that a particle literally does not HAVE a definite position?
My impression is that physicists lean toward the latter, but I would like to know what is the level of agreement among physicists, and what factors lead to their conclusion. Is this question merely "philosophical", or is there experimental basis?
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.
When discussing this topic, you have to address the elephant in the room (or is it??) and admit that nearly everyone will associate Heisenberg with Breaking Bad and not with where Breaking Bad got the name in the first place. Very well done!
Thank you Dr. Lincoln (genius is when a complicated subject is expressed in a simple manner).
Heisenberg was the only scientist who got famous by proving that something cannot be done. What a relief it was for all others who tried to measure the both values unsuccessfully.
@fermilab One question I had. The math assumes the relationship based on a normal distribution, but how do we know that quantum waves use such a distribution?
They don't. That's part of the "more complicated math" that the video points to the description. This was just illustrative.
so it has to do with the limitations of the model used to represent probabilities in quantum mechanics which are in turn defined by fundamental truths about what it means to measure quantum phenomena?
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.
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
The new production on this channel is much better (with graphs, animations and stuff), makes things easier to understand.
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.
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.
Hi Dr. Lincoln, I have a question. Has the attosecond physics disapproved Heisenberg Uncertainty principle??
This is a great video. Even I was able to follow along well enough to extract info and enjoy it.
Can you do this same video explaining the delta E delta t version - not dumbed down with "wiggles" please? This version of the uncertainty principle is way more unusual.
That one comes from the law of conservation of energy when you combine it with the uncertainty principle if I recall correctly. It's just expressing kinetic energy and potential energy in terms of delta x and delta p, then putting it back into the uncertainty principle formula. Which makes sense if you think about it, to measure kinetic energy is to measure momentum and to measure potential energy is to measure position, so the same principle applies. What it really uncovers though is that very energetic states can only exists for a short amount of time before breaking down, while lower energy states can last much longer and that it would take an infinite amount of time to get to a state which is purely zero. That's where the "absolute zero is impossible" thing comes from I think and why the vacuum state of particles is non-zero.
A master piece of an episode!
Does the new attosecond physics help to remove the quantum mechanical randomness we see? Has it all been because we’ve been observing at the wrong time scale?
nope
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 😁
That was absolutely a WONDERFUL video!! Thank you
Such a elegant explanation of concepts. Thanks
Congratulations, was a real fun video.
Pls make a video on uncertainty of energy and time also. Thank you
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 😅
The Fourier transform analogy *illustrates* the HOW, but does not *explain* the WHY.
Why is a reduced Planck constant used, instead of the "full"?
In theory, doesn't the principal also apply to the macroscopic world? For example, if I'm spotting the location of a car in movement, the higher the precision of its location, the less accurate I can be about its speed. For example, at its most extreme, if I shoot a single photon at the car to locate it, I only have the information of that photon, which is its position..?
9:15 i think uncertainty principle says that knowledge is always limited
It's not allowed by nature to know exactly position and velocity of an electron 9:15
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.
Another thumbs up for the music and the whole end scene 👍
Instructions unclear, I am still uncertain about this.
How and why are two frequencies the same? (one from Fourier transforming the PDF of x, and another being the frequency of a physical wave). The time dimension isn't even present in the first one.
Simple; Math without product .
Simple physics over product..
Uncertainty every where.
Grand respect,
In audio transistors add odd harmonics whereas valves add even harmonics. Taking this to its extreme, transistors distort to square waves and valves distort to sawtooth waves. This is why audiophiles prefer the sound of valve amplification.
Nice info, thanks
Try listening to some proper hardstyle / hardcore kick drums though to hear the magic of square wave distortion
I heard what sounds to me like there is a wave interpretation to how photons for example get captured by an atom. Like I mean it is somehow harmonic in size or something. Otherwise if just continues through and thus you have a transparent object?