phthisicy chill out dude, all he said was that he like the idea of a gradient of colours of the particles. Not everyone has a fucking brilliant 9000 IQ like you.
or else, do you want her to use the word "interpretation interpretation interpretation...... "like you!!!! i shouldn't have subscribed to your channel #asylum
German here, "Unschärfe" is a term from photography meaning *blurriness*/ "unfocusedness." I don't know whether this is where Heisenberg got the name from but maybe the idea is that you can't focus on two different objects simultaneously if they have a different distance to the camera. One of them will always be out of focus. Also, in German there are two names for the HUP, "Unschärferelation" (= blurriness relation) and "Unbestimmtheitsrelation". "Unbestimmtheit" means indefinite (or vague). I think *indefiniteness* is a much better name to describe this phenomenon than uncertainty.
@@anandsuralkar2947 anything that is based on experimentation is open to be proven wrong. Don't be overconfident, it's not going to age well. Our time period probably has just as many misconceptions about physics as they had 1000 years ago.
I love how my video is 8 mins but The Science Asylum says the same thing better in just 3. Go check it out and say I said hi: th-cam.com/video/skPI-BhohR8/w-d-xo.html
So about your question at the end f your video, it sounds simple: No, because after measuring the momentum, the uncertainty regarding the position increases so the particle can't be (for sure) at the same place, but something else left me thinking: What if you were to measure the momentum of a particle alone, stop and after a short while measure it again, would the results be the same or each time you stopped measuring it would go back to the superposition making the following result inconsistent with the previous one?
UncommonReality The evolution of a wave function is given by the Schrödinger equation. If you measure it, the wave collapses to an eigenstate. If you wait, then the wave evolves in a certain way which is determined by the Schrödinger equation. Don't ask me though what this equation does with eigenstates!
I love how your video was 8 minutes though. 5 minutes was you setting up the questions and dispelling the false answers. The only reason I knew the right answer was because you did such a good job of explaining everything in your previous videos, but it's nice having the specific myths dispelled.
Took a couple days to get to this one (Sorry!) but this really clarified the uncertainty principle for me. I went with 3 at the start, but there were definitely some mechanics I didn't really understand. Looking forward to the more technical video, although who knows if I'll understand it... On the homework, wouldn't measuring the momentum put the position back into flux, so that if you measured position afterwards it'd be in a random place again? Otherwise you'd have simultaneous exactly-accurate information for the location and momentum, and the fact that you can't do that is kind of the point of the principle in the first place. Also, I had a question on the equation: If you've just measured the location of the particle, isn't ∆x zero, at least momentarily? there's no uncertainty at all: it is where your result just said it was. And if it's zero, then no matter how large ∆p is, the product of the two is zero. Assuming I didn't just overturn almost a century's worth of quantum theory, what stops that from being the case? Does a little bit of uncertainty remain, even when measured? or do we just use an arbitrarily small non-zero number to represent no uncertainty, instead of zero?
I feel like there's something amazing about using Alice iconography to talk about quantum mechanics, a subject so keenly tied into complex numbers, when it's been theorized that Alice in Wonderland was Lewis Caroll's jab at complex numbers for being…well, as mad as the inhabitants of Wonderland. I love it and I'm loving your videos so far.
Alice and Bob are names used in cryptography to represent people or items A and B. See en.wikipedia.org/wiki/Alice_and_Bob . An alphabetic list is included in that article.
Just finished my high school studies and done a final from higher physics. As particle physics is partly in the curriculum, we covered this topic too, I remember that we specifically learned the second explanation. However, I always fellt this part too slippery, and all our theachers were very unsure when asked for another explanation. I'm not surprised that this (among a few others) came out to be false. There are a lot of cases when because of simplifying we are taught the wrong answer. Welcome back!
If you take the wave function in terms of position, you can transform it to be in terms of momentum (The wave function can hold all information possible about the particle). But in so don't, the math inevitable shows the HUP. This is where the law originated from. If you take a wave function of one position, and transform it to momentum, you find you have basically infinite uncertainty.
How so? I don't know much about probability theory, but the HUP is about _two_ distributions, not one, while the Chebyshev's inequality I see on wikipedia seems to involve only one distribution (Even the "vector" version seems to me to lead to something quite different from the HUP). I'd be interested to learn why I'm wrong. :) Maybe something can be said when the two distributions are the squared norms of two complex functions that are one the Fourier transform of the other? BTW, "quantum" probability is different from "classical" one: the lattice of "quantum events" is non-distributive (aka non-Boolean), contrary to the case of measurable subsets of a probability space. (Maybe that's more about "logic" than probability; anyways...) And the "quantumness" manifests itself for non-commuting observables, which is exactly where the HUP occurs.
This video wades back into the swamp of "interpretations of quantum mechanics", so there is bound to be disagreements. Most people would agree that description 2 is inaccurate, and glosses over the intrinsic, fundamental role the HUP (or more generally, non-commutation) plays in QM. But the question of whether or not a system has a property prior to measurement has different answers for different interpretations. The Copenhagen interpretation, for example, only concerns itself with what measurement devices report when they correlate with quantum systems. It makes no propositions about the ontology of an unmeasured quantum system, and limits itself to an epistemic understanding of experimental outcomes and their correlations. Under my favourite interpretation (Decoherent Histories), however, we can make statements about the properties a system has without the context of a measurement. We can say a particle has a position whether or not it is measured, and we can say a particle has a momentum whether or not it is measured, provided we are careful with our syntax. Unlike hidden variable theories, the Decoherent Histories interpretation uses the vanilla Hilbert spaces of QM and doesn't introduce any new mathematical structures. arxiv.org/abs/1105.3932 tl;dr Different interpretations of QM map the formalism of QM to different propositions about reality. Therefore, for better or for worse, different interpretations will map the HUP to different propositions about reality. So pinning down what the HUP means is difficult.
Damn, I picked 1. because I was picturing the equation in my head lol That σ_x.σ_p ≥ ħ/2 I interpreted 1. like "when the error on x is small, the error on p is large"
The problem with this is that error implies difference between "real" value and obtained value, which is untrue because there is no such thing as a real value. That's why we use uncertainty instead, which is related to the standard deviation of the distribution
I just watched three of these videos and I have to say I loved them. Your simplified but still somewhat technical explanations strike just the right balance for where I'm at as an amateur physics fan. Definitely subscribed!
At 4:50 Unschärfe literally means something in the range of "fuzziness", "being blurred" and "un-sharp / not sharp". The term Unschärfe is usually used in the context of optics, e.g. a blurry picture a horrible lens
Oh I didn't know TH-cam had this poll feature. It even works on mobile, neat! Unschärfe literally means unsharpness (if that's not an English word it is now), in this case like when you look through a lens and a distant object appears unfocused and fuzzy. They also sometimes use Unbestimmtheit which might have been the word translated into uncertainty and it's probably the worst translation because to me (especially for this case) it's closer to undecidedness (as in the particle hasn't decided in which particular state it is), and even in my language we say it like that.
Unless it's a reeealy small blade :D Yea I actually like indeterminacy more than undecidedness, though at this point we're just finessing the language.
I have watched video after video on TH-cam where physicists with PhDs get this wrong, and raised my voice at the video and them pointing out the flawed language they use, at Best (and wrong understanding, at Worst), to describe and explain the Uncertainty Principle. Thank you for being the ONE video on TH-cam which gets this right. Gratitude
Here's my way of interpreting the Heisenberg "Unschärfe" Principle: With light waves, there's an inverse relation between energy and wavelength. Light waves are described by Maxwell's wave equations, and doing some funky derivations with Maxwell's wave equations gives you Schrodinger's equation. In Schrodinger's equation, energy and wavelength still have an inverse correlation. But the energy of a massive particle is related to the particle's momentum (a la Newton's laws), and the wavelength is roughly related to how well we know its position (a la the Born Rule). To visualize this, just imagine the wavefunction as a slope on a mountain. The steeper the slopes around the mountain, the more localized the mountain is. But the steeper the slopes, the more the mountain moves (because the Schrodinger equation boils down to k1 * d/dx = k2 * d/dt). That's a good visualization for you in case your physics class isn't giving you a good idea of what's going on.
"The solutions to the eigenvector equations for position and momentum lead to the uncertainty principle. In other words, the wave function solution for a specific value of momentum has probabilities for the position everywhere (in the single dimension). This derivation shows that the position and momentum wave functions are Fourier transforms of each other. Thus mathematically the uncertainty principle is simply a statement about Fourier transforms." It's not a popular position yet but I definitely think Fourier Transforms are not a tool but how the universe actually functions. I think the frequency domain is not an abstraction but, real. It's something not observable so I guess that presents a conundrum.
The HUP is a statement about the statistics of a large ensemble of identically prepared systems. It says nothing about a single copy of the system; and it says nothing about the precision of individual measurements (the HUP would continue to hold even if the measurement precision was literally infinite).
Yep, that is exactly right. The momentum of a single quantum is always finite (and limited by the energy in the system), no matter how high the spatial resolution of our detector is. It does not go towards infinity just because we make an aperture smaller. Having said that, a detector with high spatial resolution won't tell us the momentum of the quantum and vice versa, a detector with good momentum resolution has to be large. That's why telescopes have to made very large to tell where the light came from. Having said that, these are perfectly classical effects. They don't require quantum mechanics. One can observe them on water waves just fine.
@@schmetterling4477: I would say they're neither quantum nor classical phenomena per se. I would say in the quantum case it's true for abstract reasons (HUP can be proven in abstract QM, given a state vector) and, in the case of the wave function of a quantum particle as state vector and X and P as observables, this theorem specializes to a relation between a function and its Fourier tansform. The latter Fourier relation (or a vector version thereof?) can also be applied to "any" function, whether it represents a classical field or a quantum wave function. I would imagine this makes particular sense when the field "is a wave" (obeys some sort of wave equation) cause then the Fourier transform tells us something about actual frequencies. Does this make sense?
@@rv706 Mathematically the uncertainty principle is a pretty trivial lemma about certain linear operators. It will show up wherever the theory has a linear vector space structure. Quantum mechanics is one example, so are all linear wave phenomena in physics and engineering. This is, unfortunately, often misunderstood.
I think the best way to translate Unschärfe is blurry or "blurryness". Image you try to see underwater, it's hard to clearly tell where exatly stuff is and the vision is blurred. In German, when Unschärfe is used, it is mostly referred to vision too. Great video, thank you :)
You said in the video that when you measure a particle you collapse the wavefunction, AND that if you measure the particle again, you will get the same result (2:18 "if you measure it again, it will certainly be in this place") because you had collapsed the wavefunction. I'm not convinced that's true. I once looked for an experiment that clearly showed what happens in sequential measurements of a single particle, and I couldn't find one. As far as I can tell, it is impossible to track and measure a single quantum particle multiple times. The act of measuring is so disruptive that the system has completely changed.
At 1:54 I started nodding to myself, saying, "Ah, she's describing what physicists call Collapsing the Wave Function. I wish she used that phrase specifically." Then at 2:30 you totally do use that phrase. Btw, this is an excellently explained video. Thanks!
The Heisenberg Uncertainty Principle follows from particle-wave duality. The momentum of a sinewave is given exactly by p=h/λ, but a sinewave is nonlocalized (extends forever in positive and negative directions). If you superimpose a continuous distribution of sinewaves with varying wavelength, the interference creates a localized wave packet. As you increase the range of wavelengths superimposed (more uncertainty about momentum), the wave packet gets more condensed (less uncertainty about position). The inverse relationship between position and momentum is a result of how the wavepacket can be thought as a superpositon of sinewaves.
why does quantum theory is more widely accepted (used) than the pilot-wave, although being very counter-intuitive itself? Is there any experiment proves that pilot-wave theory is wrong, or maybe it has some flaws? Or is it just a matter of preference? I mean like, pilot-wave theory gives a very clear image compared to quantum theory. Why most scientists out there prefer to use quantum theory, even in high-school I only got to study quantum mechanics (I didn't get pilot-wave).
No, in Bohmian mechanics a particle only has a definite position. Momentum is stored in the wavefunction. +Tadho because Bohmian mechanics is not an interpretation of quantum mechanics. It's a distinct theory with distinct predictions, and it gives incorrect ones. It also conflicts severely with special relativity, whereas quantum mechanics does not.
omg please do. i just got into bohm mech and now revising all of this quantum stuff makes the bohm interpretation so confusing. Because how do they all fit together? Doesn't bohm mech disagree with superpositions? Or does it acknowledge it stochastically?
You just shattered my entire knowledge of Quantum Mechanics. The fact that schools teach the wrong interpretation of Delta x and delta p should be a crime in itself
The video says that the uncertainty principle is not about measurement. I differ, since it´s about the linear operators that represent the observables of position and momentum. So it´s all about measurement. Any other interpretation makes assumptions about the underlying reality that are pure speculation.
Hi Mithuna! So great to have found you again on TH-cam! Will be telling my 12s to watch your channel! Where are you based at the moment and what are you up to? You can use my school email to answer. Still the same! 10 years later! Mr Carbo
I'm sooo glad I found your channel! I find your presentation to be both pleasant and informative. Every discourse is directed at some audience and I think I'm right in the audience you're aiming for. Anyway, thanks so much for this video.
This is well explained video; Great I can add here for more clarification this analogy : If you have a specific amount of money and you want to decide to buy a house ; your decision must compromise between two options : the size of the house and it's location if you choose to buy a big house you can't choose it's location ; and if you prefer to chose a luxurious location you will no longer be able to specify the size of the house ; this situation occur because you have a limited a mount of money . some one of size or location must give or at least you you can make a balance decision between both of them . You can't decide both of them in Principle because you have a limited amount of money the same here for quantum physics; Planck constant is similar to the limited amount of money in the analogy and the size and location are similar to velocity and position . By this analogy one can understand WHY it's impossible in Principle to know exactly the velocity and position at the same time . which is the most difficult thing to grasp in uncertainty principle and it was to me too . I hope this help, and thanks for this great video .
1:34 Let me just stop you right there, that's not what Quantum Mechanics says, that's what the Copenhagen interpretation says. De Broglie Bohm Theorem begs to differ.
I agree. Here I was taking QM to mean standard QM, as I personally see BM as an alternative theory. But I made a video about this recently :) th-cam.com/video/r0plv_nIzsQ/w-d-xo.html
I know its wrong, but how i generally get by on the HUP, is that within the range of super positions, we the observers are stuck looking at a more limited area than the actual range of positions. So if we were to measure X, then we get X. If we were to measure Y, then we get Y. But we aren't getting W X Y & Z, because we as not set up to measure those positions simultaneously, nor is it intuitive that a particle could occupy all of those positions. However it begins to make sense with some imagination about placement, scale and distance being products of momentum. Like I said, I know its wrong, but it helps. Now something I keep seeing making its way in with woo, is that nothing is there at all, until a measurement is made, and its the act that determines its finitude, and even its existence. Which isn't even wrong.
The bigger question in my mind is, "How doe we know that the particle exists in a super position?" I mean, if our measurements always collapse it why do we think it was ever not just in one place traveling at one speed at any given time that we can only calculate the probabilities for. I know about the double slit experiment, but to be honest all that leads me to believe is that we don't yet understand what's going on.
If that would be the case, it would mean that quantum mechanics is incomplete, because it allows you only to calculate the probability of the values that you get. That would mean that, in order to complete quantum mechanics, you'll need to find some "hidden variable" that helps you discern among the possible values that you can get. Well: it is possible to create a scenario in which this hypotetical hidden variable create a consequence in the 'non-hidden' variables that quantum mechanics gives you. So you can find out, even experimentally, if this hidden variable exists, by finding out if this consequence exists or not. Experiments have been done, and the hidden variable doesn't exist. So we must conclude that quantum mechanics is complete. If you want to find out more, look for "Bell's inequalities". To be fair, this only cancels out the possibility of a local hidden variable; that is, a hidden variable that can help you distinguish between the values of a specific quantity (for example, spin). There are some viable possibilities about global hidden variables that hasn't been falsified yet, as far as I know (I'm not sure about that).
No, it's not that obvious. In classical physics, if you know the initial position and momentum of the particle and the law of motion, you can determine without a doubt which position and momentum it will have at any given time, even without measuring. You can obviously measure it, if you wish, but you'll get, apart from experimental errors (which you can make as small as you want), exactly the number that you predict with the theory. The theory can predict the numbers that you'll get by measuring. In quantum mechanics, this is not the case. It's fundamentally different.
im having a hard time explaning to my friend why QM is not only about statistics. what is the fundemental diffrence between saying i have uncartainty and that the partical is in superpition and saying that theres for exsample 1/5 chances of finding it somwere in the system
Hmmm, if you're dealing with statistics with "classical" assumptions you wouldn't expect, for example, the probability distributions for position and momentum to be coupled the way HUP predicts. Seems to me that when you're doing statistical analysis you need to have some knowledge of how the components of the system is expected to behave, and QM is significant because it produces a different version of that knowledge than classical mechanics.
1st video on TH-cam I have seen that define the uncertainty principle correctly. All other videos , actually, define the observer effect and they use '∆' at the position of ' variance' ( small sigma). A special thanks to you
I think this is an imposition of Copenague interpretation... There are alternatives... At least 4 valid alternative interpretations made by physics... Copenague isn't only physics but philosophy... and bad philosophy... Bohr's philosophy...
The uncertainty principle is an experimentally verified fact. Its general form involves two observables A, B and an inequality with a very *specific* lower bound. And the Copenhagen interpretation is the only theory so far that could explain the lower bound correctly for arbitrarily many choices of the pair A,B which may be arbitrary functions or functionals of positions, momenta, spins, and/or fields. 1. Any realist theory that denies superpositions will predict that you should always be able to reduce the lower bound further i.e. closer to zero. The correct experiment results will always get a specific lower bound proportional to a *UNIVERSAL* constant for various forms of A and B. Therefore realist theories are falsified. 2. When you replace delta A delta B with k {A, B} you will always get k to be equal to *the Planck constant* regardless of choice of A, B, etc. With realist theories you have to tune an infinite amount of parameters for your model to get the same k for all these experiments. Why? Because your realist theory doesn't fundamentally associate the observable quantities with linear operators, good luck getting the correct lower bound for the right hand side... Even if the uncertainty is just an artifact of the apparatuses' imperfection, these apparatuses are still governed by the laws of physics and the laws of physics must have some explanation why their minimum uncertainty always seems to be what the uncertainty principle claims, right? This is an obvious yet huge task that none of the Bohmian and similar theories has even attempted to solve. I think that all of them know that only the proper apparatus of quantum mechanics (in which the observables really are linear operators, and the calculable predictions really are subjective probabilities of outcomes) can achieve this triumph. The goal of the Bohmian, many world, and similar theories is just to fake quantum mechanics: to ""embed"" quantum mechanics in some ""realist"" framework and claim that it's the better one. (and the popsci audience loves it because it "makes more sense" to them than linear operators on Hilbert space) edit. removed offensive remarks :))
@@gillbates2685 Can't agree. HUP is not part of QM or any of its interpretations. It is a law of measurement due to the inverse precision between dependent variables such as location and velocity or time and frequency.
I feel like it's more like when disproving a perpetual motion machine: for a specific machine, one can make a detailed proof as to why it's not going to work (analogous to point 2), or one can invoke the much more general and higher-level second law of thermodynamics (analogous to HUP). Do you think my feeling is correct? If not, why not?
The Heisenberg Uncertainty principle can have a very different interpretation depending on the interpretation of quantum mechanics used. According to the Copenhagen interpretation, if one of the uncertainties is completely known (ie the uncertainty =0), then the other uncertainty is not known at all, corresponding to infinite uncertainty. But According to the Pilot Wave interpretation of quantum mechanics the uncertainties have an average in the middle of the range of the uncertainty. So if one of the uncertainties is completely known, then the other uncertainty will be infinite, corresponding to an average value that is infinite. This has a very important application, so please continue reading. Experiments have now shown that nearfield light is instantaneous, and it only becomes approximately a constant in the farfield, starting about 1 wavelength from the source. This is supported by Maxwell electrodynamic theory. This has been verified by many researchers. In addition, a resent experiment showed that the front (ie information) of a nearfield electromagnetic pulse propagated instantaneously across space. This is incompatible with Relativity theory, which only based on farfield speed c light. A derivation of Relativity using instantaneous nearfield light, yields Galilean Relativity, where time is the same in all inertial frames and no Relativistic effects are observed. This can be easily seen by inserting c=infinity into the Lorentz Transform, yielding the Galilean Transform. So, Relativistic effects will observed if a moving body is observed using farfield light, but no Relativistic effects will be observed if instantaneous nearfield light is used. How can the effects of Relativity be real if they can be switched off by simply changing the frequency of the light used to observe them. The only possible conclusion is that Relativistic effects are just an optical illusion, and that Galilean Relativity is the correct theory of Relativity, where time is absolute, only the present exists, the past is gone, and the future is yet to be. Since General Relativity is based on Special Relativity, then it has the same problem. A better theory of Gravity is Gravitoelectromagnetism which assumes gravity can be mathematically described by 4 Maxwell equations, similar to to those of electromagnetic theory. It is well known that General Relativity reduces to Gravitoelectromagnetism for weak fields, which is all that we observe. Using this theory, analysis of an oscillating mass yields a wave equation set equal to a source term. Analysis of this equation shows that the phase speed, group speed, and information speed are instantaneous in the nearfield and reduce to the speed of light in the farfield. This theory then accounts for all the observed gravitational effects including instantaneous nearfield and the speed of light farfield. The main difference is that this theory is a field theory, and not a geometrical theory like General Relativity. Because it is a field theory, Gravity can be then be quantized as the Graviton. Lastly it should be mentioned that this research shows that the Pilot Wave interpretation of Quantum Mechanics can no longer be criticized for requiring instantaneous interaction of the pilot wave, thereby violating Relativity. It should also be noted that nearfield electromagnetic fields can be explained by quantum mechanics using the Pilot Wave interpretation of quantum mechanics and the Heisenberg uncertainty principle (HUP), where Δx and Δp are interpreted as averages, and not the uncertainty in the values as in other interpretations of quantum mechanics. So in HUP: Δx Δp = h, where Δp=mΔv, and m is an effective mass due to momentum, thus HUP becomes: Δx Δv = h/m. In the nearfield where the field is created, Δx=0, therefore Δv=infinity. In the farfield, HUP: Δx Δp = h, where p = h/λ. HUP then becomes: Δx h/λ = h, or Δx=λ. Also in the farfield HUP becomes: λmΔv=h, thus Δv=h/(mλ). Since p=h/λ, then Δv=p/m. Also since p=mc, then Δv=c. So in summary, in the nearfield Δv=infinity, and in the farfield Δv=c, where Δv is the average velocity of the photon according to Pilot Wave theory. Consequently the Pilot wave interpretation should become the preferred interpretation of Quantum Mechanics. It should also be noted that this argument can be applied to all fields, including the graviton. Hence all fields should exhibit instantaneous nearfield and speed c farfield behavior, and this can explain the non-local effects observed in quantum entangled particles. *TH-cam presentation of above arguments: th-cam.com/video/sePdJ7vSQvQ/w-d-xo.html *More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145 *Electromagnetic pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1 Dr. William Walker - PhD in physics from ETH Zurich, 1997
Are superpositions real ? Is anything real ? What does it mean to be real ? - I would say that to be 'real' is to have definite position at all times. Philosophically you can make a strong argument for 'reality', it's not proof, but compelling. From here, this grounding, you can resist the QM non-sense that negates reality and ask why does it appear to be so. I am not saying QM is wrong here, just that any inference that wishes to trade away 'reality' so lightly is misguided. There is only non-local hidden variable theory to my mind that does this. I'd like to add, the notion of a state 'IS' a superposition is really just a slight of hand move by the physicist to give QM some semblance of as if he's talking about reality, superposition is really a transplanted word to remove from the mathematical model used (V_SP) of a linear combination of 'states' which is an entirely abstract notion.
What philosophical principle allows you to require extremely tiny things to behave exactly like macroscopic objects? What philosophical principle allows you to force reality to conform to your expectations of what is sense and nonsense? If you ponder carefully the notion that an electron has a "definite position at all times", even when it is not observed, is the real nonsense.
Physics is a lot about interpretation and, well, metaphysics. When you have a bunch equations that let you predict the outcome of certain experiments, how do explain that? You can assign an intuition to certain mathematical objects and talk about a "superposition of eigenstates" but basically that's just a convenient story to "explain" why your equations work. You can tell a different story about the same mathematics (then called a different _interpretation_) but that doesn't change the maths. Physics often gets you in philosophical trouble.
Zardo Dhieldor Nonsense. Physics has nothing at all to do with metaphysics. It has nothing at all to do with making up stories. It is about making mathematical models of reality, and testing those models against experiment. If theory matches experiment, the only explanation is that the theory reflects reality well. Physics can't get you into philosophical trouble; if there is a conflict between physics and philosophy, philosophy loses.
Michael Sommers I know that you can do physics without the interpretation part. As a mathematician, I never understood why physicists always struggle to motivate and interpret their results. It always seemed to me like making up funny stories.
I think it's called the uncertainty principle is because Heisenberg himself initially thought it's true because the photon would disturb it.. that's why I feel it's the most famous explanation also I feel there is a ted video which also beautifully explains why delx delp MUST have a min value intuitively. Because of the associated debroglie wave and it's connection with the momentum
If we are not observing something, we can't even tell whether it exists or not. For it to exist, we need to observe it and this is simply because of our limitation to define things using reference frames. And if we can't tell whether it exists or not, there is a fundamental uncertainty in its existence. This might also imply that our description of the universe is dependent on the way we observe it and not just the way it "actually" is. The phrase "actually is" doesn't have any meaning in the physics that we have invented.
Here's a thought experiment. Let's assume that we have the most cutting edge technology at our disposal. We need an electron detection sphere, as small as possible, it must detect a single electron when it hits the surface, let diameter of it be d. Now assume that we introduce an electron in the centre, and apply a strong repulsive force on the electron from all the sides so as to stun it and after some time remove the force. Now the electron is in the centre of the sphere in resting position. But it's velocity cannot be zero due to uncertainty. So assuming that it has some velocity, it will eventually go and hit one of the walls of the sphere. NOW here comes the catch The more and more we wait without the sphere detecting the electron, the more and more certain its velocity becomes. The uncertainty in the position is ∆x = d And the uncertainty in velocity is ∆v = d/2t where t is the wait time, and m, mass of electron is a known constant so the total uncertainty is md^2/2t. So there is a threshold time, when the uncertainty melts down. All we have to do is repeat the experiment a trillion times and wait for a long long time Conclusion: Either there is something wrong in the whole logic (likely) or that uncertainty is fundamental but not elemental and absolute.
Nope. Good thought experiment, but it doesn't prove that there is something "wrong" with HUP. The statement "The more and more we wait without the sphere detecting the electron, the more and more certain its velocity becomes" is not true, I don't know where you got that from. Even if the velocity uncertainty did decrease, that would imply an increase in the position uncertainty and so the HUP would still hold. It doesn't matter how much time it takes for the electron to hit the sphere. Also, when you say "All we have to do is repeat the experiment a trillion times and wait for a long long time" you are forgetting that measuring the particle changes its wavefunction and thus your initial conclusions about velocity or position or whatever don't matter. ALSO, the electron interacting with the detector implies that the electron is not really in the correct state (i.e. center of the sphere) to do the experiment the way you describe.
as for the homework: Measuring a particle collapses it's position space wave function, which in turn flares out it's momentum space wave function, due to the uncertainty principle but is also mathematically shown when you convert from position to momentum functions. When you take a momentum measurement it collapses the momentum wave function to a specific point, which again causes the position function to flare out again, largely increasing the uncertainty in x I.e you could theoretically get the same value you just measured, however there is a wide range of values you could still measure
The particle may not be in the same spot because as we measure it's momentum, it's position will be in a superposition of one of many states again. Therefore, as we measure the particle once again, it collapses to one of the either superposition states which may not be the same position as the previous position
Describing the range in which a particle’s momentum or location can be found, and then comparing the relationship between those two as being inversely proportional is really the way to go about this. The final few minutes before the homework section were excellent - don’t disregard your penchant for explanation. If the listener understands mathematics, it makes sense to think of it as dx -> 0 (but can’t actually reach 0), dp -> infinity. Neither can be made into classical particles (excellent choice of words by you), but the closer either becomes to being classical, the greater the range of probable states the other could be in.
2:30 yes it IS doing what it was doing before BUT with a way much smaller deBroglie wavelength due to the entaglement interaction with the measurement instrument.
I've got it! Quantum mechanics is about multiple positions, multiple momentum, and multiple times future, present, and past. The photon does interact with itself because it is interacting with it's self in different times. We know that time is not constant, and that an object has an average kinetic energy. Time slows down with increase in energy. This means some of the objects time is different within different areas of the object. It is spread out in position and time.
You have to respect the madness of the people who were able to derive the fundamental nature of a reality that defies our existential experience. It's like deriving the equations for alternate universes or fairy lands -- things we don't have real world experience with.
There is a limit to the amount of information a given amount of energy can contain. If the "dot pitch" of information of the Universe was violated you could setup the ultraviolet catastrophe as a bomb by specifying arbitrarily small distances for lightweight charged particles.
Fantastic video - both very well explained but also incredibly necessary. You're right, number two is the common explanation and it makes me die a little inside when it's used. One thing which may confuse the keen viewers, however, is the idea that a position measurement pins the particle down to exactly one position in space. If this was the case, then surely the particle would suddenly have to have an infinite range of momenta? I'm not as well versed when it comes to measurement in quantum mechanics but I can only imagine that position measurements make the wave function collapse to a sort of 'dense ball' rather than a perfect Dirac delta, so that there is still a reasonably small variance in momentum. This is similar to how momentum measurements don't suddenly cause the particle's wavefunction to spread evenly over the whole universe, I guess.
Student of physics here, and I would say that QM is precisely about measurement. Just because the formalism works if we consider a particle as a superposition, does not mean the particle is actually in a superposition. To know this, we would need to somehow measure the superposition itself (not just take a weak measurement). Before measurement, our lack of knowledge of the system means that it is useful to think about the particle as a superposition of states. Better still, I like to think that it is our knowledge of the particle that is in superposition prior to measurement. So, just like we can't say that the particle has a definite position, we also can't say that it occupies an indefinite position. The question is indeterminate before measurement. Thoughts on these thoughts?
Thing about the superposition is that it is impossible, by definition, to measure directly. So instead, like many other things in physics, you make predictions based on the superposition model that ARE measureable, and then you measure those, and so far things check out. Of course, this "Copenhagen interpretation" is not the only possible interpretation of the experimental observations, but it's not obviously inferior to any other existing ones. The measurements are such that they cannot be explained by theories with any "classical" notions of properties and measurements. So yeah, you can say rightly that superposition may not be certain, to which the retort would be that all other possible competing interprtations are in a similar ballpark of weird anyway, so what's the harm in picking and explaining the most widely accepted intepretation.
Hi. If you don't measure it, you wouldn't even know there's the interference pattern. Of course it's about measuring it. Entire physics is about measuring. Heisenberg originally made a heap of measurements and arrived at the uncertainty relation empirically. It took a while to prove it theoretically, and even today there are some enhancements to it. Cheers :D
Thank you! A voice of sanity! Of course QM is all about measurement in the final analysis. That is why the Bohm interpretation makes such better sense. See my main comment.
A very very beautiful, clear, eloquent and intuitive explanation. You first gave 3 possible statements of the principle so people can compare it with their own conception. I've never seen such an approach. Also, your beautiful drawings attract people's attention because they get frustrated by all those elaborate geometrical diagrams, greek symbols etc. Now your video helps them to think more clearly about the process of quantum phenomena like Hawking Radiation, why weak force called weak, Bose-Einstein Condensate, at low energy why the vacuum is not really a vacuum? if quarks contribute only 1% of mass then from where proton gets its 99% mass? etc. From your videos, people can compose their own thought experiments more precisely like "if an electron gets caught inside the container whose walls are shrinking then after a while, would electron still be found in the container or not, as shrinking volume makes electron's position more accurate (uncertainty decreases) so by trade-off relationship, uncertainty in momentum will increase". I think helping others to understand how the universe works at the fundamental level is the greatest service to mankind. Very good job. Please, when you get free time write a book on Quantum Reality with all these Beautiful drawings. I'm sure it will be a bestseller.
The thing I like the most about HUP are its proofs - they're very mathematical. One proof in particular seems to just fall out of the linear algebra without any regard to application, it's very bizarre.
I was watching the video about the Heisenberg Uncertainty Principle and it occurred to me this may be another piece of evidence we are living in a simulation (Simulation Hypothesis). My reasoning goes like this: The assumption is that nature always finds the most efficient way to do something. Consider Photosynthesis: A Photon enters a leaf and creates a free electron in the Chlorophyll. In order for that excited electron to reach the reaction center, it has to pass through an impossible maze which normally would absorb most of the electrons before they could do any good. So at the point of creation, the electron enters a Superposition state and follows all possible paths to the reaction site where the Wave Function collapses. This results in high efficiency since few electrons are lost. This has been confirmed I believe. So if we accept the assumption that nature always finds the most efficient way to do something, and that our reality is a simulation, it would follow that if it were not for Superposition, the massive computer that runs the universe would have to calculate the exact position and exact momentum for every particle in the universe for every Planck Time (10 to the minus 43 seconds). This would require a huge amount of wasted computing energy since the precise location is not actually needed until someone requests that information by measurement or observation. So the hypothesis here is that Superposition is simply a method nature is using to avoid having to do all those detailed calculations within a super-computer for the trillions of particles in the universe, until they are actually needed. Instead, it offers an approximation based on probabilities which would require much less computing power when you consider it for every particle in the universe. At the point the Wave Function collapses, the computer switches over to a subroutine which immediately calculates the precise location of the particle based on its probability function. Anyone who has programmed computers understands the benefit of subroutines. This also explains Entanglement. When two entangled particles are unobserved, the Universe Computer (for lack of a better name) has not actually created them yet. They just exist as probabilities (i.e. approximations). But when someone looks into the box (observes) one of them, something causes the computer to jump to a subroutine which immediately creates both entangled pairs. In the real world, no computer would be fast enough to create any two things (even virtual) at the exact same time. But perhaps instantaneous creation of both particles does not happen even in Quantum Entanglement. Perhaps one particle is created first then the other, but the time between them is so short (less than Planck Time) it is not observable in our universe. I’m not sure of the precision they used to experimentally measure entangled particles. It’s hard to go into the subtleties of this hypothesis without it becoming un-manageably long, but feel free to shoot holes into it as that is what science is all about.
[The assumption is that nature always finds the most efficient way to do something.] If what you are talking about is either The principle of least action or Occam's razor than it is not an assumption. Why do you need a supercomputer when nature's field's and interactions can act on their own? In other words, why provoke an extra complication such as god or supercomputer if the simpler explanation is nature's own. You can sub god in for supercomputer in the following: Other than asking what made the supercomputer or what it runs on, how would it encode the entire universe and run it at "prime" speed"? May be interested in the series SpaceTime, perhaps the series on the holographic universe, or in particular "computing a Universe Simulation" th-cam.com/video/0GLgZvTCbaA/w-d-xo.html
[The assumption is that nature always finds the most efficient way to do something.] If what you are talking about is either The principle of least action or Occam's razor than it is not an assumption. Why do you need a supercomputer when nature's field's and interactions can act on their own? In other words, why provoke an extra complication such as god or supercomputer if the simpler explanation is nature's own. You can sub god in for supercomputer in the following: Other than asking what made the supercomputer or what it runs on, how would it encode the entire universe and run it at "prime" speed"? May be interested in the series SpaceTime, perhaps the series on the holographic universe, or in particular "computing a Universe Simulation" th-cam.com/video/0GLgZvTCbaA/w-d-xo.html
Love this video. Will be doing videos about quantum computing at any point? I was trying to explain to a friend how quantum computers don't "try every answer at the same time" and then get "the right" answer somehow, but while I know enough to know that explanation is wrong, I realized I wasn’t sure how to give a better one without committing a different but equally reprehensible sin. :P
If I had to guess why they used the word "uncertainty", I would say that it was because they were constructing quantum mechanics at the time, and the results were a bit uncomfortable to the philosophy at the time (and today). That's probably why they said the wave function was just a mathematical tool, and the all of quantum mechanics was about measurements. Well, under this old view, the first enunciation of the principle would be preferable over the third one.
I almost voted 1 (I only knew that 2 is completly wrong) because wouldn't it be kind of right in the De-Broglie-Bohm-interpretation and also in the Many-Worlds-interpretation of QM? You never mentioned that you are in fact talking about the Kopenhagen-Interpretation (which certainliy fits for Heisenberg).
You're right. Besides the vague wording of "The particle has a position and momentum", number 1 is absolutely correct. Measurement changes the wavefunction, and measuring a more precise position puts the wavefunction in a state with momentum uncertainty.
It may be a correct statement (if you modify it some), but it is not the (entire) uncertainty principle since the uncertainty principle does not rely on measurement.
Magnus Dahler Norling All of science relies on measurement. Quantum mechanics is only correct insofar as it can predict what we can measure. So saying that the Heisenberg Uncertainty Principle is defined by the fact that we can't measure position and momentum simultaneously is completely, 100% correct. The rest is just technical details.
Every time I watch this video I get that Eureka!! moment but I still don't understand it completely.. but I'm 100% sure that this video is THE best video on HUP in TH-cam .... Thank you so much for this
Wait does this mean that true randomness is not possible because particles are 'weighted' more in one position or speed than others? It is still probabilistic but not truly random, right?
I thought Heisenberg's Uncertainty Principle was about how uncertain the audience was that Walter White would make it in time to the birth of his daughter after completing a drug deal.
I picked option 3, though I wasn't happy about it because I don't think the particle actually "has" a lot of positions and momentums. It has _probabilities_ of being in a lot of different positions and momentums, but it doesn't actually have any of them until we measure, then it has just one. But I picked it because yes, if we can make statements that constrain the probabilities of position to a narrow range, then necessarily the probabilities for its momentum are spread over a wider range. Which I know because I watched your fourier video on the subject. :) But yeah. I'd have been happier about option 3 had it been phrased in terms of probabilities rather than actualities.
Uncertainty principle: Nothing to do with measurement Superposition/decoherence: Everything to do with measurement Measurement problem: No one knows No one will say that. All you can know about QM is the results of experiments and the math that works to predict results. The rest is pretense until more is known one day (maybe).
The standard translation of the German unschärf into English would be "imprecise" (my pick) or "inexact", either of which is far better than the term "uncertain."
Answer to the question at the end...NO it will not be location determined by preveous measurment...an entirely new wave function was created when you measured momentum.
Thank you for this really nice explanation. I am tempted to refer to this video any time somebody needs a non-technical explanation of HUP. But there is a flaw in it which makes me hesitating. At about 2:15 the discussion of the collapse of the superposition of the states says that once you measure the position, “if you measure it again, it will certainly be in this space”, which is completely wrong! If a particle has a position at a time, and later you surely find that particle at the same place, it means, by definition, that that particle has a velocity of zero. So, what you say means, that if somebody measures the position of a particle, it automatically sets the speed of the particle to exactly zero (and in this case both the position and the speed is known, and it contradicts the HUP).
Hey, I know what you mean, and I was hesitant about my wording here too.... Now I see I show have been more careful. I needed to say, if you measure again immediately after *then* it's in the same spot. Sorry!
2:27 a measurement does NOT collapses the state... it just entangles with the measurment instrument wave function of which the deBroglie wavelength is so small that the measured particle also looks like a point, due to its interaction with the measurement instrument ... a macroscopic object; so the particle start to behave like a macroscopic object and acts point like. !! there is a difference ! the particle becomes a part of the measurement instrument so to say due to entanglement-interaction. It gains macroscopic features due to this interaction. why ?? well the measurement instrument is so gigantic big from the particles perspective, so it is being forced to behave macroscopic ! that is point like with a very small wave length... the same magnitude as the instruments deBroglie wavelength.
Ok, I'm going to say it. Your mind is not the only thing beautiful about you. As a software engineer and backyard physics fan, I still can't get my head around Quantum Computers. Do you have any plans on doing a video on QC? What is your personal opinion of Richard Feynman's contribution to your field and his attitude in general?
Is option 3 still correct according to the Copenhagen interpretation? Because from what I read, we say that it doesn't make sense to talk about a particle's position or momentum until it is measured. Saying that it has "a lot of momenta" or "lot of positions" is wrong because we haven't measured the particle yet, we simply say that it makes no sense to talk about its position or momentum. Correct me if I'm wrong.
This is how I thought the wave function (and thus uncertainties) work, if you measure position or momentum you collapse the wave function, but after some time passes then the wave function will start to spread out again. So even if you measure position, wait a few seconds and measure it again, then you can measure a different position.
It's almost like there is an allowed ratio that had to be in equilibrium of let's set that value is 1 so your ratio of momenta to position always has to equal 1 if you have more possible positions then to equal 1 you need less momenta but if you have more momenta then to equal 1 you need less positions. It's like momentum and position are parts of the same thing that always exists in some ratio of each other that is only noticeable at the very small.
That's an interesting question. The photon is a massless particle with momentum p = h/λ. This should mean that the uncertainty would be in the photon's wavelength, and the speed of the photon is c regardless of its wavelength.
I think 3 sounds the closest to the principle to me. 2 sounds the furthest. I think 3 is the principle because it gets at the heart of transform methods behind the principle. If I take the Fourier Transform of a sine wave in position space, then it will be a delta function in momentum space because it only has one momentum and, in a sense, infinite position.
I believe that the existence of the classical "path" can be pregnantly formulated as follows: The "path" comes into existence only when we observe it. Do you think that this statement is correct?
So let's say we had scanners setup in sequence to be endlessly measuring either position or speed depending on the sensor and for them all to be active wouldn't you be able to see a particle and where it's going?
![[TH] 2024 PMSL SEA W2D5 | Fall | พลาดวันนี้ จะต้องเสียใจ](http://i.ytimg.com/vi/A5-Cuo12p6A/mqdefault.jpg)
I love how you represented likelihood in position with faded particles. Brilliant!
phthisicy chill out dude, all he said was that he like the idea of a gradient of colours of the particles. Not everyone has a fucking brilliant 9000 IQ like you.
Hey Nick
or else, do you want her to use the word "interpretation interpretation interpretation...... "like you!!!! i shouldn't have subscribed to your channel #asylum
Do you know any YT channels that explain the experiments used to prove these principles?
the two of you make videos together
German here, "Unschärfe" is a term from photography meaning *blurriness*/ "unfocusedness." I don't know whether this is where Heisenberg got the name from but maybe the idea is that you can't focus on two different objects simultaneously if they have a different distance to the camera. One of them will always be out of focus.
Also, in German there are two names for the HUP, "Unschärferelation" (= blurriness relation) and "Unbestimmtheitsrelation". "Unbestimmtheit" means indefinite (or vague). I think *indefiniteness* is a much better name to describe this phenomenon than uncertainty.
We should call it the *Fuzziness Principle*
What +Zardo said. Also the photography term "scharf" is a metaphor, literally meaning _sharp_ (e.g. referring to a knife).
The uncertainty principle is an artifact of probability theory being applied to a physical system: Chebyshev's inequality.
fuzzyness might work too.
Zardo Dhieldor Heisenberg's blurry theorem.
I used to believe in the Heisenberg Uncertainty Principle. But now I'm not so sure.
HUP is mathematics of waves and so..u have to belive it bcz its mathematically accurate and u cant prove it wrong..
@Mark Reynolds lol
hehe mark
@@anandsuralkar2947 anything that is based on experimentation is open to be proven wrong. Don't be overconfident, it's not going to age well. Our time period probably has just as many misconceptions about physics as they had 1000 years ago.
So you are uncertain, which proves the princlple
I love how my video is 8 mins but The Science Asylum says the same thing better in just 3. Go check it out and say I said hi: th-cam.com/video/skPI-BhohR8/w-d-xo.html
Ya, but. I like your voice better. And the illustrations are nice too.
Hey, don't second guess yourself! You did a great job! :)
So about your question at the end f your video, it sounds simple: No, because after measuring the momentum, the uncertainty regarding the position increases so the particle can't be (for sure) at the same place, but something else left me thinking:
What if you were to measure the momentum of a particle alone, stop and after a short while measure it again, would the results be the same or each time you stopped measuring it would go back to the superposition making the following result inconsistent with the previous one?
UncommonReality The evolution of a wave function is given by the Schrödinger equation. If you measure it, the wave collapses to an eigenstate. If you wait, then the wave evolves in a certain way which is determined by the Schrödinger equation. Don't ask me though what this equation does with eigenstates!
I love how your video was 8 minutes though. 5 minutes was you setting up the questions and dispelling the false answers. The only reason I knew the right answer was because you did such a good job of explaining everything in your previous videos, but it's nice having the specific myths dispelled.
Took a couple days to get to this one (Sorry!) but this really clarified the uncertainty principle for me. I went with 3 at the start, but there were definitely some mechanics I didn't really understand. Looking forward to the more technical video, although who knows if I'll understand it...
On the homework, wouldn't measuring the momentum put the position back into flux, so that if you measured position afterwards it'd be in a random place again? Otherwise you'd have simultaneous exactly-accurate information for the location and momentum, and the fact that you can't do that is kind of the point of the principle in the first place.
Also, I had a question on the equation: If you've just measured the location of the particle, isn't ∆x zero, at least momentarily? there's no uncertainty at all: it is where your result just said it was. And if it's zero, then no matter how large ∆p is, the product of the two is zero. Assuming I didn't just overturn almost a century's worth of quantum theory, what stops that from being the case? Does a little bit of uncertainty remain, even when measured? or do we just use an arbitrarily small non-zero number to represent no uncertainty, instead of zero?
no one ever gave an answer :(
@@damimz7026 true
@12tone I read this in your voice
That’s a great question and I’m not sure if I’m too late but actually if the delta x is zero then delta p would have to be equal to infinity
Or something like that I’m still not too sure
For me, the confusion came from Stephen Hawkin’s explanation in A Brief History of Time
I don't remember subscribing to this channel, but a big thanks to past me for doing it
same
I like calling it the "spreading" principle instead, e.g. a particle state is necessarily spread in position and/or momentum space.
I feel like there's something amazing about using Alice iconography to talk about quantum mechanics, a subject so keenly tied into complex numbers, when it's been theorized that Alice in Wonderland was Lewis Caroll's jab at complex numbers for being…well, as mad as the inhabitants of Wonderland. I love it and I'm loving your videos so far.
Alice and Bob are names used in cryptography to represent people or items A and B. See en.wikipedia.org/wiki/Alice_and_Bob . An alphabetic list is included in that article.
Just finished my high school studies and done a final from higher physics. As particle physics is partly in the curriculum, we covered this topic too, I remember that we specifically learned the second explanation.
However, I always fellt this part too slippery, and all our theachers were very unsure when asked for another explanation. I'm not surprised that this (among a few others) came out to be false. There are a lot of cases when because of simplifying we are taught the wrong answer.
Welcome back!
If you take the wave function in terms of position, you can transform it to be in terms of momentum (The wave function can hold all information possible about the particle). But in so don't, the math inevitable shows the HUP. This is where the law originated from. If you take a wave function of one position, and transform it to momentum, you find you have basically infinite uncertainty.
*doing
The uncertainty principle is an artifact of probability theory being applied to a physical system: Chebyshev's inequality.
How so? I don't know much about probability theory, but the HUP is about _two_ distributions, not one, while the Chebyshev's inequality I see on wikipedia seems to involve only one distribution (Even the "vector" version seems to me to lead to something quite different from the HUP). I'd be interested to learn why I'm wrong. :)
Maybe something can be said when the two distributions are the squared norms of two complex functions that are one the Fourier transform of the other?
BTW, "quantum" probability is different from "classical" one: the lattice of "quantum events" is non-distributive (aka non-Boolean), contrary to the case of measurable subsets of a probability space. (Maybe that's more about "logic" than probability; anyways...) And the "quantumness" manifests itself for non-commuting observables, which is exactly where the HUP occurs.
This video wades back into the swamp of "interpretations of quantum mechanics", so there is bound to be disagreements.
Most people would agree that description 2 is inaccurate, and glosses over the intrinsic, fundamental role the HUP (or more generally, non-commutation) plays in QM.
But the question of whether or not a system has a property prior to measurement has different answers for different interpretations. The Copenhagen interpretation, for example, only concerns itself with what measurement devices report when they correlate with quantum systems. It makes no propositions about the ontology of an unmeasured quantum system, and limits itself to an epistemic understanding of experimental outcomes and their correlations.
Under my favourite interpretation (Decoherent Histories), however, we can make statements about the properties a system has without the context of a measurement. We can say a particle has a position whether or not it is measured, and we can say a particle has a momentum whether or not it is measured, provided we are careful with our syntax. Unlike hidden variable theories, the Decoherent Histories interpretation uses the vanilla Hilbert spaces of QM and doesn't introduce any new mathematical structures.
arxiv.org/abs/1105.3932
tl;dr Different interpretations of QM map the formalism of QM to different propositions about reality. Therefore, for better or for worse, different interpretations will map the HUP to different propositions about reality. So pinning down what the HUP means is difficult.
Then you really don't understand Quantum Physics.
You could try to explain why you think he is wrong instead of being a dick.
@@edwardblois8646 Maybe not but who does really? Einstein would have words about a lot of assumptions in this video.
Damn, I picked 1. because I was picturing the equation in my head lol
That σ_x.σ_p ≥ ħ/2
I interpreted 1. like "when the error on x is small, the error on p is large"
The problem with this is that error implies difference between "real" value and obtained value, which is untrue because there is no such thing as a real value. That's why we use uncertainty instead, which is related to the standard deviation of the distribution
I just watched three of these videos and I have to say I loved them. Your simplified but still somewhat technical explanations strike just the right balance for where I'm at as an amateur physics fan. Definitely subscribed!
At 4:50
Unschärfe literally means something in the range of
"fuzziness", "being blurred" and "un-sharp / not sharp".
The term Unschärfe is usually used in the context of optics, e.g. a blurry picture a horrible lens
Oh I didn't know TH-cam had this poll feature. It even works on mobile, neat!
Unschärfe literally means unsharpness (if that's not an English word it is now), in this case like when you look through a lens and a distant object appears unfocused and fuzzy. They also sometimes use Unbestimmtheit which might have been the word translated into uncertainty and it's probably the worst translation because to me (especially for this case) it's closer to undecidedness (as in the particle hasn't decided in which particular state it is), and even in my language we say it like that.
unsharpness would be bluntness I think
I would suggest Unschärfe=blurriness and Unbestimmtheit=indefiniteness/indeterminacy.
+Zardo Dhieldor well blurriness would be more locigal than bluntness....
I really don't believe that this has anything to do with blades! :D
"Oh, my sword's blunt again! Damn Heisenberg!" :P
Unless it's a reeealy small blade :D
Yea I actually like indeterminacy more than undecidedness, though at this point we're just finessing the language.
Studying all this now in my second year at UQ, great vids!
UQ!? I love that place.
I have watched video after video on TH-cam where physicists with PhDs get this wrong, and raised my voice at the video and them pointing out the flawed language they use, at Best (and wrong understanding, at Worst), to describe and explain the Uncertainty Principle. Thank you for being the ONE video on TH-cam which gets this right. Gratitude
Here's my way of interpreting the Heisenberg "Unschärfe" Principle:
With light waves, there's an inverse relation between energy and wavelength.
Light waves are described by Maxwell's wave equations, and doing some funky derivations with Maxwell's wave equations gives you Schrodinger's equation.
In Schrodinger's equation, energy and wavelength still have an inverse correlation. But the energy of a massive particle is related to the particle's momentum (a la Newton's laws), and the wavelength is roughly related to how well we know its position (a la the Born Rule).
To visualize this, just imagine the wavefunction as a slope on a mountain. The steeper the slopes around the mountain, the more localized the mountain is. But the steeper the slopes, the more the mountain moves (because the Schrodinger equation boils down to k1 * d/dx = k2 * d/dt).
That's a good visualization for you in case your physics class isn't giving you a good idea of what's going on.
"The solutions to the eigenvector equations for position and momentum lead to the uncertainty principle. In other words, the wave function solution for a specific value of momentum has probabilities for the position everywhere (in the single dimension). This derivation shows that the position and momentum wave functions are Fourier transforms of each other. Thus mathematically the uncertainty principle is simply a statement about Fourier transforms."
It's not a popular position yet but I definitely think Fourier Transforms are not a tool but how the universe actually functions. I think the frequency domain is not an abstraction but, real. It's something not observable so I guess that presents a conundrum.
I don't know you, I am not sure who you are, but I like you.
The HUP is a statement about the statistics of a large ensemble of identically prepared systems. It says nothing about a single copy of the system; and it says nothing about the precision of individual measurements (the HUP would continue to hold even if the measurement precision was literally infinite).
Yep, that is exactly right. The momentum of a single quantum is always finite (and limited by the energy in the system), no matter how high the spatial resolution of our detector is. It does not go towards infinity just because we make an aperture smaller. Having said that, a detector with high spatial resolution won't tell us the momentum of the quantum and vice versa, a detector with good momentum resolution has to be large. That's why telescopes have to made very large to tell where the light came from. Having said that, these are perfectly classical effects. They don't require quantum mechanics. One can observe them on water waves just fine.
@@schmetterling4477: I would say they're neither quantum nor classical phenomena per se. I would say in the quantum case it's true for abstract reasons (HUP can be proven in abstract QM, given a state vector) and, in the case of the wave function of a quantum particle as state vector and X and P as observables, this theorem specializes to a relation between a function and its Fourier tansform.
The latter Fourier relation (or a vector version thereof?) can also be applied to "any" function, whether it represents a classical field or a quantum wave function. I would imagine this makes particular sense when the field "is a wave" (obeys some sort of wave equation) cause then the Fourier transform tells us something about actual frequencies. Does this make sense?
@@rv706 Mathematically the uncertainty principle is a pretty trivial lemma about certain linear operators. It will show up wherever the theory has a linear vector space structure. Quantum mechanics is one example, so are all linear wave phenomena in physics and engineering. This is, unfortunately, often misunderstood.
rv706
@rv706 It is also true of single measurements of single particles.
I think the best way to translate Unschärfe is blurry or "blurryness".
Image you try to see underwater, it's hard to clearly tell where exatly stuff is and the vision is blurred.
In German, when Unschärfe is used, it is mostly referred to vision too.
Great video, thank you :)
Looking Glass, you are so awesome! You deserve more subs, or a shout out from 3B1B or Minutephysics or something.
You said in the video that when you measure a particle you collapse the wavefunction, AND that if you measure the particle again, you will get the same result (2:18 "if you measure it again, it will certainly be in this place") because you had collapsed the wavefunction.
I'm not convinced that's true. I once looked for an experiment that clearly showed what happens in sequential measurements of a single particle, and I couldn't find one. As far as I can tell, it is impossible to track and measure a single quantum particle multiple times. The act of measuring is so disruptive that the system has completely changed.
so when we do measure it twice, it is in the same place right?
Yes, except when you measure the position the first time the speed is randomized so if you wait a while it will have moved.
At 1:54 I started nodding to myself, saying, "Ah, she's describing what physicists call Collapsing the Wave Function. I wish she used that phrase specifically." Then at 2:30 you totally do use that phrase. Btw, this is an excellently explained video. Thanks!
The Heisenberg Uncertainty Principle follows from particle-wave duality. The momentum of a sinewave is given exactly by p=h/λ, but a sinewave is nonlocalized (extends forever in positive and negative directions). If you superimpose a continuous distribution of sinewaves with varying wavelength, the interference creates a localized wave packet. As you increase the range of wavelengths superimposed (more uncertainty about momentum), the wave packet gets more condensed (less uncertainty about position). The inverse relationship between position and momentum is a result of how the wavepacket can be thought as a superpositon of sinewaves.
Particle/wave duality is not necessary; the rest of your explanation seems correct. See my main comment for details.
But a particle does actually have a position and a momentum in Bohmian mechanics.
yup, I should make a video about HUP in bohmian mech one day.
why does quantum theory is more widely accepted (used) than the pilot-wave, although being very counter-intuitive itself? Is there any experiment proves that pilot-wave theory is wrong, or maybe it has some flaws? Or is it just a matter of preference?
I mean like, pilot-wave theory gives a very clear image compared to quantum theory. Why most scientists out there prefer to use quantum theory, even in high-school I only got to study quantum mechanics (I didn't get pilot-wave).
No, in Bohmian mechanics a particle only has a definite position. Momentum is stored in the wavefunction.
+Tadho because Bohmian mechanics is not an interpretation of quantum mechanics. It's a distinct theory with distinct predictions, and it gives incorrect ones. It also conflicts severely with special relativity, whereas quantum mechanics does not.
omg please do. i just got into bohm mech and now revising all of this quantum stuff makes the bohm interpretation so confusing. Because how do they all fit together? Doesn't bohm mech disagree with superpositions? Or does it acknowledge it stochastically?
good point! Ok, I think Bohmian mechanics deserves a proper explanation on this channel.
I voted 2. 100% of votes are 2 now. I feel bad for making the polls so wrong :(
No that's great :P
Thanks a LOT for doing this....I loved it. I first went for Option 1 & 2 and now I'm converted!!
You just shattered my entire knowledge of Quantum Mechanics. The fact that schools teach the wrong interpretation of Delta x and delta p should be a crime in itself
Or else this video is wrong!
The video says that the uncertainty principle is not about measurement.
I differ, since it´s about the linear operators that represent the observables of position and momentum.
So it´s all about measurement.
Any other interpretation makes assumptions about the underlying reality that are pure speculation.
YES! Thank you! (Those assumptions are the mystical axioms of the Copenhagen interpretation.)
Hi Mithuna!
So great to have found you again on TH-cam!
Will be telling my 12s to watch your channel!
Where are you based at the moment and what are you up to?
You can use my school email to answer. Still the same! 10 years later!
Mr Carbo
I'm sooo glad I found your channel! I find your presentation to be both pleasant and informative. Every discourse is directed at some audience and I think I'm right in the audience you're aiming for. Anyway, thanks so much for this video.
Aw, thank you! I'm so glad I managed to get at the right level for you :) I find that very tricky- so I'm glad it worked for you.
This is well explained video; Great
I can add here for more clarification this analogy :
If you have a specific amount of money and you want to decide to buy a house ; your decision must compromise between two options :
the size of the house and it's location
if you choose to buy a big house you can't choose it's location ; and if you prefer to chose a luxurious location you will no longer be able to specify the size of the house ; this situation occur because you have a limited a mount of money .
some one of size or location must give or at least you you can make a balance decision between both of them .
You can't decide both of them in Principle because you have a limited amount of money
the same here for quantum physics; Planck constant is similar to the limited amount of money in the analogy and the size and location are similar to velocity and position .
By this analogy one can understand WHY it's impossible in Principle to know exactly the velocity and position at the same time . which is the most difficult thing to grasp in uncertainty principle and it was to me too .
I hope this help, and thanks for this great video .
1:34 Let me just stop you right there, that's not what Quantum Mechanics says, that's what the Copenhagen interpretation says. De Broglie Bohm Theorem begs to differ.
I agree. Here I was taking QM to mean standard QM, as I personally see BM as an alternative theory. But I made a video about this recently :) th-cam.com/video/r0plv_nIzsQ/w-d-xo.html
I really love ❤ your videos.
Aww, thank you! ☺️
I know its wrong, but how i generally get by on the HUP, is that within the range of super positions, we the observers are stuck looking at a more limited area than the actual range of positions. So if we were to measure X, then we get X. If we were to measure Y, then we get Y. But we aren't getting W X Y & Z, because we as not set up to measure those positions simultaneously, nor is it intuitive that a particle could occupy all of those positions. However it begins to make sense with some imagination about placement, scale and distance being products of momentum. Like I said, I know its wrong, but it helps.
Now something I keep seeing making its way in with woo, is that nothing is there at all, until a measurement is made, and its the act that determines its finitude, and even its existence. Which isn't even wrong.
The bigger question in my mind is, "How doe we know that the particle exists in a super position?" I mean, if our measurements always collapse it why do we think it was ever not just in one place traveling at one speed at any given time that we can only calculate the probabilities for. I know about the double slit experiment, but to be honest all that leads me to believe is that we don't yet understand what's going on.
If that would be the case, it would mean that quantum mechanics is incomplete, because it allows you only to calculate the probability of the values that you get. That would mean that, in order to complete quantum mechanics, you'll need to find some "hidden variable" that helps you discern among the possible values that you can get. Well: it is possible to create a scenario in which this hypotetical hidden variable create a consequence in the 'non-hidden' variables that quantum mechanics gives you. So you can find out, even experimentally, if this hidden variable exists, by finding out if this consequence exists or not.
Experiments have been done, and the hidden variable doesn't exist. So we must conclude that quantum mechanics is complete.
If you want to find out more, look for "Bell's inequalities".
To be fair, this only cancels out the possibility of a local hidden variable; that is, a hidden variable that can help you distinguish between the values of a specific quantity (for example, spin). There are some viable possibilities about global hidden variables that hasn't been falsified yet, as far as I know (I'm not sure about that).
well, OBVIOUSLY if you don't measure the particle, you won't know where it is and how fast it's going! ;)
But if you measure it YOU WONT KNOW where it is AND how fast its going, You can measure one with arbitrary precision but not the other.
No, it's not that obvious. In classical physics, if you know the initial position and momentum of the particle and the law of motion, you can determine without a doubt which position and momentum it will have at any given time, even without measuring. You can obviously measure it, if you wish, but you'll get, apart from experimental errors (which you can make as small as you want), exactly the number that you predict with the theory. The theory can predict the numbers that you'll get by measuring.
In quantum mechanics, this is not the case. It's fundamentally different.
@@TheSghetty Actually, HUP applies both to QM and classical mechanics, but in our size scale, the precision error is so small that it can't be seen.
im having a hard time explaning to my friend why QM is not only about statistics.
what is the fundemental diffrence between saying i have uncartainty and that the partical is in superpition and saying that theres for exsample 1/5 chances of finding it somwere in the system
Hmmm, if you're dealing with statistics with "classical" assumptions you wouldn't expect, for example, the probability distributions for position and momentum to be coupled the way HUP predicts. Seems to me that when you're doing statistical analysis you need to have some knowledge of how the components of the system is expected to behave, and QM is significant because it produces a different version of that knowledge than classical mechanics.
I have my quantum mechanics final in 2 hours and you absolutely saved me with these videos. Your explanations are amazing! Thank you!!!
1st video on TH-cam I have seen that define the uncertainty principle correctly.
All other videos , actually, define the observer effect and they use '∆' at the position of ' variance' ( small sigma).
A special thanks to you
I think this is an imposition of Copenague interpretation... There are alternatives... At least 4 valid alternative interpretations made by physics... Copenague isn't only physics but philosophy... and bad philosophy... Bohr's philosophy...
I feel like she doesn't understand the implications of her point two. They perfectly explain why the hup exists, including the math she showed.
Andrew church, her mere use of superposition injects Bohr into this. I don't believe in superposition at all. It's a copout. Bohm had it right.
The uncertainty principle is an experimentally verified fact. Its general form involves two observables A, B and an inequality with a very *specific* lower bound. And the Copenhagen interpretation is the only theory so far that could explain the lower bound correctly for arbitrarily many choices of the pair A,B which may be arbitrary functions or functionals of positions, momenta, spins, and/or fields.
1. Any realist theory that denies superpositions will predict that you should always be able to reduce the lower bound further i.e. closer to zero. The correct experiment results will always get a specific lower bound proportional to a *UNIVERSAL* constant for various forms of A and B. Therefore realist theories are falsified.
2. When you replace delta A delta B with k {A, B} you will always get k to be equal to *the Planck constant* regardless of choice of A, B, etc. With realist theories you have to tune an infinite amount of parameters for your model to get the same k for all these experiments.
Why? Because your realist theory doesn't fundamentally associate the observable quantities with linear operators, good luck getting the correct lower bound for the right hand side...
Even if the uncertainty is just an artifact of the apparatuses' imperfection, these apparatuses are still governed by the laws of physics and the laws of physics must have some explanation why their minimum uncertainty always seems to be what the uncertainty principle claims, right?
This is an obvious yet huge task that none of the Bohmian and similar theories has even attempted to solve. I think that all of them know that only the proper apparatus of quantum mechanics (in which the observables really are linear operators, and the calculable predictions really are subjective probabilities of outcomes) can achieve this triumph. The goal of the Bohmian, many world, and similar theories is just to fake quantum mechanics: to ""embed"" quantum mechanics in some ""realist"" framework and claim that it's the better one. (and the popsci audience loves it because it "makes more sense" to them than linear operators on Hilbert space)
edit. removed offensive remarks :))
@@arguewithmepodcast Superposition does kind of imply nondeterminism, and to that extent is incorrect in Bohm theory.
@@gillbates2685 Can't agree. HUP is not part of QM or any of its interpretations. It is a law of measurement due to the inverse precision between dependent variables such as location and velocity or time and frequency.
I still think point 2 is correct.
although it is true but it has nothing to do with Heisenberg's principle... it can even be explained using classical physics
I feel like it's more like when disproving a perpetual motion machine: for a specific machine, one can make a detailed proof as to why it's not going to work (analogous to point 2), or one can invoke the much more general and higher-level second law of thermodynamics (analogous to HUP). Do you think my feeling is correct? If not, why not?
German here. The translation for "Unschärfe" is blurryness. A blurred photo is "ein unscharfes Photo" in german.
The Heisenberg Uncertainty principle can have a very different interpretation depending on the interpretation of quantum mechanics used. According to the Copenhagen interpretation, if one of the uncertainties is completely known (ie the uncertainty =0), then the other uncertainty is not known at all, corresponding to infinite uncertainty. But According to the Pilot Wave interpretation of quantum mechanics the uncertainties have an average in the middle of the range of the uncertainty. So if one of the uncertainties is completely known, then the other uncertainty will be infinite, corresponding to an average value that is infinite. This has a very important application, so please continue reading.
Experiments have now shown that nearfield light is instantaneous, and it only becomes approximately a constant in the farfield, starting about 1 wavelength from the source. This is supported by Maxwell electrodynamic theory. This has been verified by many researchers. In addition, a resent experiment showed that the front (ie information) of a nearfield electromagnetic pulse propagated instantaneously across space. This is incompatible with Relativity theory, which only based on farfield speed c light. A derivation of Relativity using instantaneous nearfield light, yields Galilean Relativity, where time is the same in all inertial frames and no Relativistic effects are observed. This can be easily seen by inserting c=infinity into the Lorentz Transform, yielding the Galilean Transform. So, Relativistic effects will observed if a moving body is observed using farfield light, but no Relativistic effects will be observed if instantaneous nearfield light is used. How can the effects of Relativity be real if they can be switched off by simply changing the frequency of the light used to observe them. The only possible conclusion is that Relativistic effects are just an optical illusion, and that Galilean Relativity is the correct theory of Relativity, where time is absolute, only the present exists, the past is gone, and the future is yet to be.
Since General Relativity is based on Special Relativity, then it has the same problem. A better theory of Gravity is Gravitoelectromagnetism which assumes gravity can be mathematically described by 4 Maxwell equations, similar to to those of electromagnetic theory. It is well known that General Relativity reduces to Gravitoelectromagnetism for weak fields, which is all that we observe. Using this theory, analysis of an oscillating mass yields a wave equation set equal to a source term. Analysis of this equation shows that the phase speed, group speed, and information speed are instantaneous in the nearfield and reduce to the speed of light in the farfield. This theory then accounts for all the observed gravitational effects including instantaneous nearfield and the speed of light farfield. The main difference is that this theory is a field theory, and not a geometrical theory like General Relativity. Because it is a field theory, Gravity can be then be quantized as the Graviton.
Lastly it should be mentioned that this research shows that the Pilot Wave interpretation of Quantum Mechanics can no longer be criticized for requiring instantaneous interaction of the pilot wave, thereby violating Relativity. It should also be noted that nearfield electromagnetic fields can be explained by quantum mechanics using the Pilot Wave interpretation of quantum mechanics and the Heisenberg uncertainty principle (HUP), where Δx and Δp are interpreted as averages, and not the uncertainty in the values as in other interpretations of quantum mechanics. So in HUP: Δx Δp = h, where Δp=mΔv, and m is an effective mass due to momentum, thus HUP becomes: Δx Δv = h/m. In the nearfield where the field is created, Δx=0, therefore Δv=infinity. In the farfield, HUP: Δx Δp = h, where p = h/λ. HUP then becomes: Δx h/λ = h, or Δx=λ. Also in the farfield HUP becomes: λmΔv=h, thus Δv=h/(mλ). Since p=h/λ, then Δv=p/m. Also since p=mc, then Δv=c. So in summary, in the nearfield Δv=infinity, and in the farfield Δv=c, where Δv is the average velocity of the photon according to Pilot Wave theory. Consequently the Pilot wave interpretation should become the preferred interpretation of Quantum Mechanics. It should also be noted that this argument can be applied to all fields, including the graviton. Hence all fields should exhibit instantaneous nearfield and speed c farfield behavior, and this can explain the non-local effects observed in quantum entangled particles.
*TH-cam presentation of above arguments: th-cam.com/video/sePdJ7vSQvQ/w-d-xo.html
*More extensive paper for the above arguments: William D. Walker and Dag Stranneby, A New Interpretation of Relativity, 2023: vixra.org/abs/2309.0145
*Electromagnetic pulse experiment paper: www.techrxiv.org/doi/full/10.36227/techrxiv.170862178.82175798/v1
Dr. William Walker - PhD in physics from ETH Zurich, 1997
Are superpositions real ? Is anything real ? What does it mean to be real ? - I would say that to be 'real' is to have definite position at all times. Philosophically you can make a strong argument for 'reality', it's not proof, but compelling. From here, this grounding, you can resist the QM non-sense that negates reality and ask why does it appear to be so. I am not saying QM is wrong here, just that any inference that wishes to trade away 'reality' so lightly is misguided. There is only non-local hidden variable theory to my mind that does this.
I'd like to add, the notion of a state 'IS' a superposition is really just a slight of hand move by the physicist to give QM some semblance of as if he's talking about reality, superposition is really a transplanted word to remove from the mathematical model used (V_SP) of a linear combination of 'states' which is an entirely abstract notion.
That is a very strange definition of realness. You seem to have arbitrarily picked that definition to claim that it "negates reality."
What philosophical principle allows you to require extremely tiny things to behave exactly like macroscopic objects? What philosophical principle allows you to force reality to conform to your expectations of what is sense and nonsense?
If you ponder carefully the notion that an electron has a "definite position at all times", even when it is not observed, is the real nonsense.
Physics is a lot about interpretation and, well, metaphysics. When you have a bunch equations that let you predict the outcome of certain experiments, how do explain that? You can assign an intuition to certain mathematical objects and talk about a "superposition of eigenstates" but basically that's just a convenient story to "explain" why your equations work. You can tell a different story about the same mathematics (then called a different _interpretation_) but that doesn't change the maths.
Physics often gets you in philosophical trouble.
Zardo Dhieldor
Nonsense. Physics has nothing at all to do with metaphysics. It has nothing at all to do with making up stories. It is about making mathematical models of reality, and testing those models against experiment. If theory matches experiment, the only explanation is that the theory reflects reality well. Physics can't get you into philosophical trouble; if there is a conflict between physics and philosophy, philosophy loses.
Michael Sommers I know that you can do physics without the interpretation part. As a mathematician, I never understood why physicists always struggle to motivate and interpret their results. It always seemed to me like making up funny stories.
I think it's called the uncertainty principle is because Heisenberg himself initially thought it's true because the photon would disturb it.. that's why I feel it's the most famous explanation
also I feel there is a ted video which also beautifully explains why delx delp MUST have a min value intuitively. Because of the associated debroglie wave and it's connection with the momentum
If we are not observing something, we can't even tell whether it exists or not. For it to exist, we need to observe it and this is simply because of our limitation to define things using reference frames. And if we can't tell whether it exists or not, there is a fundamental uncertainty in its existence. This might also imply that our description of the universe is dependent on the way we observe it and not just the way it "actually" is. The phrase "actually is" doesn't have any meaning in the physics that we have invented.
you are awesome and the explanations were very cut and dry and easy to understand thanks :)
Came here to clear my doubt but in the end got more CONFUSED!
I think Jade is wrong. See my main comment.
Here's a thought experiment. Let's assume that we have the most cutting edge technology at our disposal.
We need an electron detection sphere, as small as possible, it must detect a single electron when it hits the surface, let diameter of it be d.
Now assume that we introduce an electron in the centre, and apply a strong repulsive force on the electron from all the sides so as to stun it and after some time remove the force.
Now the electron is in the centre of the sphere in resting position. But it's velocity cannot be zero due to uncertainty. So assuming that it has some velocity, it will eventually go and hit one of the walls of the sphere.
NOW here comes the catch
The more and more we wait without the sphere detecting the electron, the more and more certain its velocity becomes. The uncertainty in the position is ∆x = d
And the uncertainty in velocity is ∆v = d/2t where t is the wait time, and m, mass of electron is a known constant so the total uncertainty is md^2/2t.
So there is a threshold time, when the uncertainty melts down. All we have to do is repeat the experiment a trillion times and wait for a long long time
Conclusion: Either there is something wrong in the whole logic (likely) or that uncertainty is fundamental but not elemental and absolute.
Nope. Good thought experiment, but it doesn't prove that there is something "wrong" with HUP.
The statement "The more and more we wait without the sphere detecting the electron, the more and more certain its velocity becomes" is not true, I don't know where you got that from. Even if the velocity uncertainty did decrease, that would imply an increase in the position uncertainty and so the HUP would still hold. It doesn't matter how much time it takes for the electron to hit the sphere.
Also, when you say "All we have to do is repeat the experiment a trillion times and wait for a long long time" you are forgetting that measuring the particle changes its wavefunction and thus your initial conclusions about velocity or position or whatever don't matter. ALSO, the electron interacting with the detector implies that the electron is not really in the correct state (i.e. center of the sphere) to do the experiment the way you describe.
as for the homework:
Measuring a particle collapses it's position space wave function, which in turn flares out it's momentum space wave function, due to the uncertainty principle but is also mathematically shown when you convert from position to momentum functions. When you take a momentum measurement it collapses the momentum wave function to a specific point, which again causes the position function to flare out again, largely increasing the uncertainty in x
I.e you could theoretically get the same value you just measured, however there is a wide range of values you could still measure
The particle may not be in the same spot because as we measure it's momentum, it's position will be in a superposition of one of many states again. Therefore, as we measure the particle once again, it collapses to one of the either superposition states which may not be the same position as the previous position
Can you help me see if I misunderstood or a flawed concept in my understanding? Please correct me if I am wrong
or if there's* a flawed concept
You have the BEST channel about explaining this stuff in an entertaining way!
Describing the range in which a particle’s momentum or location can be found, and then comparing the relationship between those two as being inversely proportional is really the way to go about this. The final few minutes before the homework section were excellent - don’t disregard your penchant for explanation. If the listener understands mathematics, it makes sense to think of it as dx -> 0 (but can’t actually reach 0), dp -> infinity. Neither can be made into classical particles (excellent choice of words by you), but the closer either becomes to being classical, the greater the range of probable states the other could be in.
I don't think this is what Jade says. See my major comment.
2:30 yes it IS doing what it was doing before BUT with a way much smaller deBroglie wavelength due to the entaglement interaction with the measurement instrument.
I've got it! Quantum mechanics is about multiple positions, multiple
momentum, and multiple times future, present, and past. The photon does
interact with itself because it is interacting with it's self in
different times. We know that time is not constant, and that an object
has an average kinetic energy. Time slows down with increase in energy.
This means some of the objects time is different within different
areas of the object. It is spread out in position and time.
Very strange statements.
More of this in the world would be really appreciated
You have to respect the madness of the people who were able to derive the fundamental nature of a reality that defies our existential experience.
It's like deriving the equations for alternate universes or fairy lands -- things we don't have real world experience with.
There is a limit to the amount of information a given amount of energy can contain. If the "dot pitch" of information of the Universe was violated you could setup the ultraviolet catastrophe as a bomb by specifying arbitrarily small distances for lightweight charged particles.
Unschärfe usually refers to an image. You could say an image is unscharf and that would mean its not in focus, making it blurry.
Fantastic video - both very well explained but also incredibly necessary. You're right, number two is the common explanation and it makes me die a little inside when it's used.
One thing which may confuse the keen viewers, however, is the idea that a position measurement pins the particle down to exactly one position in space. If this was the case, then surely the particle would suddenly have to have an infinite range of momenta?
I'm not as well versed when it comes to measurement in quantum mechanics but I can only imagine that position measurements make the wave function collapse to a sort of 'dense ball' rather than a perfect Dirac delta, so that there is still a reasonably small variance in momentum.
This is similar to how momentum measurements don't suddenly cause the particle's wavefunction to spread evenly over the whole universe, I guess.
Your doubts are good ones.
Student of physics here, and I would say that QM is precisely about measurement.
Just because the formalism works if we consider a particle as a superposition, does not mean the particle is actually in a superposition. To know this, we would need to somehow measure the superposition itself (not just take a weak measurement).
Before measurement, our lack of knowledge of the system means that it is useful to think about the particle as a superposition of states. Better still, I like to think that it is our knowledge of the particle that is in superposition prior to measurement.
So, just like we can't say that the particle has a definite position, we also can't say that it occupies an indefinite position. The question is indeterminate before measurement.
Thoughts on these thoughts?
Thing about the superposition is that it is impossible, by definition, to measure directly. So instead, like many other things in physics, you make predictions based on the superposition model that ARE measureable, and then you measure those, and so far things check out. Of course, this "Copenhagen interpretation" is not the only possible interpretation of the experimental observations, but it's not obviously inferior to any other existing ones. The measurements are such that they cannot be explained by theories with any "classical" notions of properties and measurements.
So yeah, you can say rightly that superposition may not be certain, to which the retort would be that all other possible competing interprtations are in a similar ballpark of weird anyway, so what's the harm in picking and explaining the most widely accepted intepretation.
It's very interesting that Stephen Hawking explained Uncertainty Principle in his "The Universe in a Nutshell" with item 2! You can easily check it!
I read this book too and now i dont know who I should believe
@@meryemd2219 I think Jade is wrong in this video. See my main comment.
Hi. If you don't measure it, you wouldn't even know there's the interference pattern. Of course it's about measuring it. Entire physics is about measuring. Heisenberg originally made a heap of measurements and arrived at the uncertainty relation empirically. It took a while to prove it theoretically, and even today there are some enhancements to it. Cheers :D
Thank you! A voice of sanity! Of course QM is all about measurement in the final analysis. That is why the Bohm interpretation makes such better sense. See my main comment.
A very very beautiful, clear, eloquent and intuitive explanation. You first gave 3 possible statements of the principle so people can compare it with their own conception. I've never seen such an approach. Also, your beautiful drawings attract people's attention because they get frustrated by all those elaborate geometrical diagrams, greek symbols etc. Now your video helps them to think more clearly about the process of quantum phenomena like Hawking Radiation, why weak force called weak, Bose-Einstein Condensate, at low energy why the vacuum is not really a vacuum? if quarks contribute only 1% of mass then from where proton gets its 99% mass? etc. From your videos, people can compose their own thought experiments more precisely like "if an electron gets caught inside the container whose walls are shrinking then after a while, would electron still be found in the container or not, as shrinking volume makes electron's position more accurate (uncertainty decreases) so by trade-off relationship, uncertainty in momentum will increase". I think helping others to understand how the universe works at the fundamental level is the greatest service to mankind. Very good job. Please, when you get free time write a book on Quantum Reality with all these Beautiful drawings. I'm sure it will be a bestseller.
The thing I like the most about HUP are its proofs - they're very mathematical. One proof in particular seems to just fall out of the linear algebra without any regard to application, it's very bizarre.
I was watching the video about the Heisenberg Uncertainty Principle and it occurred to me this may be another piece of evidence we are living in a simulation (Simulation Hypothesis). My reasoning goes like this: The assumption is that nature always finds the most efficient way to do something. Consider Photosynthesis: A Photon enters a leaf and creates a free electron in the Chlorophyll. In order for that excited electron to reach the reaction center, it has to pass through an impossible maze which normally would absorb most of the electrons before they could do any good. So at the point of creation, the electron enters a Superposition state and follows all possible paths to the reaction site where the Wave Function collapses. This results in high efficiency since few electrons are lost. This has been confirmed I believe.
So if we accept the assumption that nature always finds the most efficient way to do something, and that our reality is a simulation, it would follow that if it were not for Superposition, the massive computer that runs the universe would have to calculate the exact position and exact momentum for every particle in the universe for every Planck Time (10 to the minus 43 seconds). This would require a huge amount of wasted computing energy since the precise location is not actually needed until someone requests that information by measurement or observation.
So the hypothesis here is that Superposition is simply a method nature is using to avoid having to do all those detailed calculations within a super-computer for the trillions of particles in the universe, until they are actually needed. Instead, it offers an approximation based on probabilities which would require much less computing power when you consider it for every particle in the universe. At the point the Wave Function collapses, the computer switches over to a subroutine which immediately calculates the precise location of the particle based on its probability function. Anyone who has programmed computers understands the benefit of subroutines.
This also explains Entanglement. When two entangled particles are unobserved, the Universe Computer (for lack of a better name) has not actually created them yet. They just exist as probabilities (i.e. approximations). But when someone looks into the box (observes) one of them, something causes the computer to jump to a subroutine which immediately creates both entangled pairs. In the real world, no computer would be fast enough to create any two things (even virtual) at the exact same time. But perhaps instantaneous creation of both particles does not happen even in Quantum Entanglement. Perhaps one particle is created first then the other, but the time between them is so short (less than Planck Time) it is not observable in our universe. I’m not sure of the precision they used to experimentally measure entangled particles.
It’s hard to go into the subtleties of this hypothesis without it becoming un-manageably long, but feel free to shoot holes into it as that is what science is all about.
[The assumption is that nature always finds the most efficient way to do something.]
If what you are talking about is either The principle of least action or Occam's razor than it is not an assumption.
Why do you need a supercomputer when nature's field's and interactions can act on their own? In other words, why provoke an extra complication such as god or supercomputer if the simpler explanation is nature's own.
You can sub god in for supercomputer in the following: Other than asking what made the supercomputer or what it runs on, how would it encode the entire universe and run it at "prime" speed"?
May be interested in the series SpaceTime, perhaps the series on the holographic universe, or in particular "computing a Universe Simulation" th-cam.com/video/0GLgZvTCbaA/w-d-xo.html
[The assumption is that nature always finds the most efficient way to do something.]
If what you are talking about is either The principle of least action or Occam's razor than it is not an assumption.
Why do you need a supercomputer when nature's field's and interactions can act on their own? In other words, why provoke an extra complication such as god or supercomputer if the simpler explanation is nature's own.
You can sub god in for supercomputer in the following: Other than asking what made the supercomputer or what it runs on, how would it encode the entire universe and run it at "prime" speed"?
May be interested in the series SpaceTime, perhaps the series on the holographic universe, or in particular "computing a Universe Simulation" th-cam.com/video/0GLgZvTCbaA/w-d-xo.html
Love this video. Will be doing videos about quantum computing at any point? I was trying to explain to a friend how quantum computers don't "try every answer at the same time" and then get "the right" answer somehow, but while I know enough to know that explanation is wrong, I realized I wasn’t sure how to give a better one without committing a different but equally reprehensible sin. :P
If I had to guess why they used the word "uncertainty", I would say that it was because they were constructing quantum mechanics at the time, and the results were a bit uncomfortable to the philosophy at the time (and today). That's probably why they said the wave function was just a mathematical tool, and the all of quantum mechanics was about measurements. Well, under this old view, the first enunciation of the principle would be preferable over the third one.
Yes. See my main comment.
I almost voted 1 (I only knew that 2 is completly wrong) because wouldn't it be kind of right in the De-Broglie-Bohm-interpretation and also in the Many-Worlds-interpretation of QM? You never mentioned that you are in fact talking about the Kopenhagen-Interpretation (which certainliy fits for Heisenberg).
You're right. Besides the vague wording of "The particle has a position and momentum", number 1 is absolutely correct. Measurement changes the wavefunction, and measuring a more precise position puts the wavefunction in a state with momentum uncertainty.
That's exactly why I voted 1....
It may be a correct statement (if you modify it some), but it is not the (entire) uncertainty principle since the uncertainty principle does not rely on measurement.
Magnus Dahler Norling All of science relies on measurement. Quantum mechanics is only correct insofar as it can predict what we can measure.
So saying that the Heisenberg Uncertainty Principle is defined by the fact that we can't measure position and momentum simultaneously is completely, 100% correct. The rest is just technical details.
+david21686 No, the connection to measurement is more indirect.
that gave a very clear picture of HUP.......was very helpful..................thank you so much
Every time I watch this video I get that Eureka!! moment but I still don't understand it completely.. but I'm 100% sure that this video is THE best video on HUP in TH-cam .... Thank you so much for this
As a native german and third language english speaker I would translate "Unschärfe" as some kind of "blurriness".
Wait does this mean that true randomness is not possible because particles are 'weighted' more in one position or speed than others? It is still probabilistic but not truly random, right?
HUP has nothing to do with randomness.
I thought Heisenberg's Uncertainty Principle was about how uncertain the audience was that Walter White would make it in time to the birth of his daughter after completing a drug deal.
finally someone that explains this without assuming we can't figure it out without a lot of confusing technobabble
I picked option 3, though I wasn't happy about it because I don't think the particle actually "has" a lot of positions and momentums. It has _probabilities_ of being in a lot of different positions and momentums, but it doesn't actually have any of them until we measure, then it has just one. But I picked it because yes, if we can make statements that constrain the probabilities of position to a narrow range, then necessarily the probabilities for its momentum are spread over a wider range. Which I know because I watched your fourier video on the subject. :) But yeah. I'd have been happier about option 3 had it been phrased in terms of probabilities rather than actualities.
Uncertainty principle: Nothing to do with measurement
Superposition/decoherence: Everything to do with measurement
Measurement problem: No one knows
No one will say that. All you can know about QM is the results of experiments and the math that works to predict results. The rest is pretense until more is known one day (maybe).
It took me months to find someone who saw it as I did. Well played 🎉
The standard translation of the German unschärf into English would be "imprecise" (my pick) or "inexact", either of which is far better than the term "uncertain."
Super happy that you are back. I love your videos, they are very clear.
Angelic voice and explanation that is exactly, what we call "layman's terms". Very nice, you have a new subscriber and fan!
Answer to the question at the end...NO it will not be location determined by preveous measurment...an entirely new wave function was created when you measured momentum.
Thank you for this really nice explanation. I am tempted to refer to this video any time somebody needs a non-technical explanation of HUP. But there is a flaw in it which makes me hesitating. At about 2:15 the discussion of the collapse of the superposition of the states says that once you measure the position, “if you measure it again, it will certainly be in this space”, which is completely wrong! If a particle has a position at a time, and later you surely find that particle at the same place, it means, by definition, that that particle has a velocity of zero. So, what you say means, that if somebody measures the position of a particle, it automatically sets the speed of the particle to exactly zero (and in this case both the position and the speed is known, and it contradicts the HUP).
Hey, I know what you mean, and I was hesitant about my wording here too.... Now I see I show have been more careful. I needed to say, if you measure again immediately after *then* it's in the same spot. Sorry!
2:27 a measurement does NOT collapses the state... it just entangles with the measurment instrument wave function of which the deBroglie wavelength is so small that the measured particle also looks like a point, due to its interaction with the measurement instrument ... a macroscopic object; so the particle start to behave like a macroscopic object and acts point like. !! there is a difference ! the particle becomes a part of the measurement instrument so to say due to entanglement-interaction. It gains macroscopic features due to this interaction. why ?? well the measurement instrument is so gigantic big from the particles perspective, so it is being forced to behave macroscopic ! that is point like with a very small wave length... the same magnitude as the instruments deBroglie wavelength.
Beautiful. Wave function collapse ONLY happens in the Copenhagen interpretation, and it happens when a particle ceases to exist.
Homework answer: Same spot because you've collapsed the wave function by measuring it the first time. Right or wrong?
Wrong.
@@david203 Relax spector... you obviously have a lot of pent-up stress. Maybe ditch your NSR meditation for something that actually works 😝
Out of all the books, articles, lectures I have ever seen this is the only one that says the uncertainty principle is not about measurements!
Ok, I'm going to say it. Your mind is not the only thing beautiful about you. As a software engineer and backyard physics fan, I still can't get my head around Quantum Computers. Do you have any plans on doing a video on QC? What is your personal opinion of Richard Feynman's contribution to your field and his attitude in general?
Is option 3 still correct according to the Copenhagen interpretation? Because from what I read, we say that it doesn't make sense to talk about a particle's position or momentum until it is measured. Saying that it has "a lot of momenta" or "lot of positions" is wrong because we haven't measured the particle yet, we simply say that it makes no sense to talk about its position or momentum.
Correct me if I'm wrong.
It won't pick the position randomly when you make the measurement. The position will follow a probability distribution.
Yes, but a probability distribution yields a random position.
This is how I thought the wave function (and thus uncertainties) work, if you measure position or momentum you collapse the wave function, but after some time passes then the wave function will start to spread out again. So even if you measure position, wait a few seconds and measure it again, then you can measure a different position.
It's almost like there is an allowed ratio that had to be in equilibrium of let's set that value is 1 so your ratio of momenta to position always has to equal 1 if you have more possible positions then to equal 1 you need less momenta but if you have more momenta then to equal 1 you need less positions. It's like momentum and position are parts of the same thing that always exists in some ratio of each other that is only noticeable at the very small.
So.. if we know a photon's position well, does it mean some of its speed superposition components may be above the speed of light?
That's an interesting question. The photon is a massless particle with momentum p = h/λ. This should mean that the uncertainty would be in the photon's wavelength, and the speed of the photon is c regardless of its wavelength.
No.
I think 3 sounds the closest to the principle to me. 2 sounds the furthest. I think 3 is the principle because it gets at the heart of transform methods behind the principle. If I take the Fourier Transform of a sine wave in position space, then it will be a delta function in momentum space because it only has one momentum and, in a sense, infinite position.
I believe that the existence of the classical "path" can be pregnantly formulated as follows: The "path" comes into existence only when we observe it. Do you think that this statement is correct?
So let's say we had scanners setup in sequence to be endlessly measuring either position or speed depending on the sensor and for them all to be active wouldn't you be able to see a particle and where it's going?