I was wrong about the Heisenberg Uncertainty Principle

The 4 week live course will run from Jan 6 - 31st. More info here :) looking-glass-...
The rest of this quantum mechanics course playlist is here: • Quantum mechanics course
Here is Ozama's measurement noise - disturbance relation paper: arxiv.org/abs/...

[@inflivia]

The HUP is a general mathematical phenomenon: it states that a function and its Fourier transform cannot simultaneously be too localized. A Fourier transform of a signal over time cannot provide a very narrow frequency detection at the same time as having a very fast time resolution. We have to trade one for the other. This relationship becomes obvious when you use a STFT waterfall graph to do frequency detection of radio signals over time.

[@desudesudesu5326]

Isn't it more generally due to the non-commutativity of hermitian operators on a Hilbert space?

[@inflivia]

@desudesudesu5326 I believe that is saying the same thing using a different formalism, yes.

[@xTh3N00b]

@@inflivia Saying the same thing yes, but also more generally. The Fourier transform is just a unitary operator transforming one basis into another. Measurement in the two bases correspond to two non-commuting operators.

[@flippen-z1x]

@@xTh3N00b It's not a unitary operator, it's literally the identity since you use the completion relation with the conjugate space.

[@steffenbendel6031]

And you could say, the (complex) base is position space is complete. That tells you everything about how the particle is moving, you not not need an additional momenta, that is just a transformed base for the state space.

[@brothermine2292]

In Heisenberg's draft version of the paper in which he first described the Uncertainty Principle, he described it as the disturbance of the state caused by the measurement. But when he showed the draft version to Neils Bohr, Bohr badgered him into revising the paper to make the much bolder claim that the uncertainty relation is a fundamental property of the state regardless of whether the state was measured.

[@wernerviehhauser94]

I'd say there is no reason to assume it can't be both. The state has an uncertainty, and measuring it makes stuff worse.

[@jitteryjet7525]

Heisenberg's Microscope.

[@no-one_no1406]

Absolutely. It makes no sense at all that it would apply to "measurements". It has to be a fundamental property for it to make sense.

[@harrymills2770]

@@no-one_no1406 Ancient Chinese explained stomach pain as a dragon in the belly, which could be assuaged by a certain herb that soothed the dragon. The mechanism is fanciful, but the herb actually did cure stomach pain. Hypothesis. Experiment. Replication. Science.

[@Paulus_Brent]

@@jitteryjet7525 Is a wrong visualization for the HUP.

[@cyclonasaurusrex1525]

Either you explained that incredibly well, or I’ve recently gotten a whole lot smarter than I was.

[@jack.d7873]

She is a great physics communicator. Not many can explain really unintuitive scientific concepts like her.

[@Fisherdec]

She's actually one of the best (most underrated) physics explainers out there. Go through her older videos and notice how some of the QM explanations she has have literally never been explained better by anyone else.

[@genghisgalahad8465]

I'm uncertain about the latter!

[@cyclonasaurusrex1525]

@ Me too!

[@En_theo]

@@Fisherdec Yes, it's because she has an honest approach : if she does not get it, she will dig further. In many other videos, the authors just repeat what other papers said without really wondering if it's unclear.

[@Heulerado]

Oooh, one about my area! I've written a paper based on this stuff, and I think this is a great video, zero complaints on the accuracy of the information. If you want to dig deeper and completely exhaust the topic, I recommend Busch, Heinoen, and Lahti's 2006 paper "Heisenberg's Uncertainty Principle". It uses the operational formalism of quantum mechanics, which may be unfamiliar, but is capable of naturally and rigorously representing and disentangling all these versions of "the uncertainty principle". In the paper, they distinguish 3 versions of the principle, and they quantify the uncertainties for each of them. The measurement disturbance uncertainty relation talked about in the video is statement (C) in the paper. I do have one (1) complaint: The name is Ozawa, not Ozama.

[@LookingGlassUniverse]

That’s so cool! Thank you for the hat tip, I’ll check out that paper! What’s your paper on the topic? Sorry about messing up Ozawa’s name!

[@Heulerado]

​@@LookingGlassUniverse Our paper (I said mine, but of course I had help from a professor) is about the uncertainty principle when you consider that the observer is also a quantum system, i.e. when we have a quantum reference frame. Spoiler alert: The uncertainty bounds double! You can freely transfer uncertainty between system and observer: A sharp picture of a blurry cat is equal to a blurry picture of a sharp cat. But we also use operational QM and it's a short paper (4 pages), so you may want to read the older one first, as we don't have much space for the introduction. The paper is Riera, Loveridge 2024. It's only on arxiv so far, but it's being reviewed for publication in PRA.

[@MsSonali1980]

@@Heulerado Can you answer me a question (if you find the time and nerve) that came up for me, or it's rather an idea how to explain to myself how this makes sense. I am a lay(wo)man, physics was never my forte, compared to maths and chemistry and I only had education on classical physics and it was a very insufficient one, I learned maths and chemistry somewhere else, later in life. I am well versed in statistics and probability, though. I also hang myself up on terminology like "collapsed" since I take the wording literal (you can guess how much fun I had in the two semesters maths I studied at University, because of that, anyway). My thought: When she said, that the narrowed down location causes a wider spread in possible states, it seems only intuitive for me, when - the electron at "a" location delta x can "show" delta p states for the location delta x. But for the - whole distribution of possible x there is a possible distribution of p with different probabilities for p (min, mean, max) - what I mean is: --- i) fact: there are certain "normal" distributions for the behaviour of the electron in regard of position and state --- ii) fact: position and state are in a relation to each other (or at least delta x and delta p) --- iii) my speculation: a "collapse" towards x gives delta x, but at that location there are still different states possible (re. the relation) --- iv) my speculation: vice versa for delta p -> a certain state can be "found" at different locations x --- v) my speculation: this is a mathematical way of explaining what is observed than a realistic (whatever that is) worldview/explanation. Further thoughts: I've also thought for the longest time, that the observing device/medium causes quantum objects to "collapse" or change. But it gave me in the end further questions and I couldn't understand how anything can get reflected or go through a prism and still come out as a "wave". Science communication (and physicists) like to talk about QM like the objects show magical behaviour, and they are the only ones who can handle them. So, they tell stories about Schrödinger's Cat out of context, talk about wave collaps without explaining what it actually means, wave-particle-duality, also without explaining why and what, etc. This, not only overwhelms laypeople but also opens door to esoteric folks, using the quantum buzzword to "explain" their woo. That is one of the reasons, I try to wrap my head around QM, I won't get myself manipulated by people that try to sell their unscientific claims/products. I know a bit how measurements work (f.e. what device to use and how molecules, atoms etc react), what a FT is. One dude tried to sell me tiny stickies for my horses body, and claimed they emit "bio photons" and help with physiotherapeutic concerns (I rather guess they contained alum foil on their backside that reflects the body heat aka ir). As I asked further, he started the wave-particle-duality argumentation, I knew he was talking bs and only using the big words to quiet my questions down, but I couldn't argument back, since I didn't know enough about that topic. This is why the work of channels like this is so helpful and important, giving free education to people that never had the chance to access via classical education systems like school or higher.

[@Heulerado]

@@MsSonali1980 There is a lot of information and this is not the greatest format to discuss mathematical details, but the main message that I would like you to take home is: You are correct to be confused by collapse. Do not trust anyone telling you they have the correct explanation to collapse. Collapse, and the details around how it happens, or it seems to happen, is what differentiates all the different interpretations of QM. We know perfectly well how QM works when nothing collapses, and it's all deterministic and nice, no randomness and no sudden "jumps" in states. It's when you give a quantum system a brain and make it interact with another quantum system that noone knows what to make of the whole situation, and so multiple interpretations arise. This channel favours the Everettian interpretation. I like it but I think there's problems yet to solve, so I'm withholding judgement and adopting a temporary "minimal interpretation" until I learn more. If you have a background in (hopefully Bayesian) probability, you may enjoy QBism, or E. T. Jaynes' interpretation that preceded it. Specifically for x and p, you are right that observing x collapses the wavefunction into having narrow x distribution and wide p distribution. But you may want to think of the wavefunction as simply _the_ probability distribution of the entire quantum system, and you can choose to extract the "x" information from it, or the "p" information, or any combination of them. Some interpretations of QM interpret this collapse as being a real, physical process. Some simply take it as a mathematical description of the unknown process, and some say it never happens at all. My point is: we don't know. The maths are all basically the same, the interpretation around collapse is (nowadays) a matter of fashion. This is not to say that all interpretations are valid, just that multiple interpretations are valid, as far as we know today. You had a lot of questions, and I don't think I answered all of them, but maybe with this answer you will want to ask different questions? I'm happy to answer what I can.

[@renancenbs]

@@Heulerado Usually, I see the collapse of the wavefunction caused by the measurement of a particle's position being represented as a narrowing of a graph. Is it correct to name that graph "the wavefunction", or is it just the position part or something (given that the momentum should be more spread out)?

[@randydireen3566]

So happy you make this content. Its the best balance between real math and the exciting parts of physics ive seen. Ive been watching your stuff for years and i hope you continue for a long time. This is exactly what i think the new generation of physicsts need. Restores my faith in education.

[@dylan_curious]

Your explanation about delta x and delta p being spreads rather than uncertainties really helped me grasp the principle better.

[@robinbrowne5419]

It seems that there are many ways to look at it and to understand it. As long as they follow the basic rule dX dP > Hbar then they can be deemed to be correct.

[@AdrianBoyko]

@@dylan_curious But this video treats X and P as independent yet mysteriously linked while they are both just different ways of looking at the SAME quantum state.

[@robinbrowne5419]

@@1emiliobering You are right. Superposition is another thing to take into account.

[@TristanLaguz]

But ðey ARE uncertainties according to BM; we just *don't know* more about ðelectron's position ðan ðat its *Bayesian* probability distribution is |ψ|^2.

[@solconcordia4315]

@1emiliobering Never use the word "object" again with quantum-realm thingy's because the quantum state is centric and there's no way to objectivize any quantum state whenever we are dealing with *IDENTICAL* thingy's which may manifest their characteristic values (i.e. eigenvalues) upon being measured. There's *NO* objective measurement possible.

[@DoobooDomo]

I am having trouble finding primary sources, but the first mathematical derivation of uncertainty I saw was from my classical wave mechanics class (IIRC you can also derive the momentum of a photon without relativity or quantum). The intuition was something like: the precision to which you can identify a frequency depends on how many wavelengths you've measured. I didn't go deeper into physics, but my takeaway was that waves were strange enough even without quantum!

[@marcobiagini1878]

My name is Marco Biagini and I am a physicist; I would like to explain the “observation” problem in quantum mechanics because it is often misunderstood even by many physicists. In quantum mechanics the state of a physical system is described by the wave function and does not have defined values ​​for all the physical quantities measurable on it; on the other hand, only the probability distributions relating to the measurable values ​​for these quantities are defined. Once the measurement has been carried out, the system will have a defined value in relation to the measured quantity, and this involves a radical modification of its wave function; in fact the wave function generally describes infinite possibilities while for an event to take place, it is necessary that the wave function assigns a probability of 100% to a single possibility and 0% probability to all the others. If all other results are not eliminated by imposing the collapse "by hand" on the wave function, the predictions of subsequent measurements on the same system will be wrong. The transition between a state that describes many possibilities to a state that describes only one possibility is called “collapse of the wave function”. The time evolution of the wave function is determined by Schrödinger's equation, but this equation never determines the collapse of the wave function, which instead is imposed by the physicist "by hand"; the collapse represents a violation of the Schrödinger equation, and the cause of the collapse is therefore attributable only to an agent not described by the Schrödinger equation itself. The open problem in quantum physics is that the cause of the transition between the indeterminate state and the determined state, cannot be traced back to any physical interaction, because all known physical interactions are already included in the Schrödinger's equation; in fact, the collapse of the wave function is a violation of the Schrodinger's equation, i.e. a violation of the most fundamental laws of physics and therefore the cause of the collapse cannot be determined by the same laws of physics, in particular, it cannot be determined by the interactions already included in the Schrodinger's equation. After one century of debates, the problem of measurement in quantum mechanics is still open and still represents the crucial problem for all interpretations of quantum mechanics. In fact, on the one hand it represents a violation of the Schrodinger equation, that is, a violation of the fundamental laws of physics. On the other hand, it is necessary for the laws of quantum physics to make sense, and to be applied in the interpretation and prediction of the phenomena we observe. Indeed, since the wave function represents infinite possibilities, without the collapse there would be no event; for there to be an event, then there must be one possibility that is actualized by canceling all other possibilities. This is the inescapable contradiction against which, all attempts to reconcile quantum physics with realism, break. Quantum mechanics does not describe reality as something that exists objectively at every instant, but as a collection of events isolated in time (i.e. the phenomena we observe at the very moment in which we observe them), while among these events there are only infinite possibilities and there is no continuity between events. In fact, the properties of a physical system are determined only after the collapse of the wave function; when the properties of the system are not yet determined, the system is not real, but only an idea, a hypothesis. Only when collapse occurs do properties become real because they take on a definite value. It makes no sense to assume that the system exists but its properties are indeterminate, because properties are an intrinsic aspect of the system itself; for example, there can be no triangle with indeterminate sides and no circle with indeterminate radius. People often say that a quantum particle is in many places at the same time but this is just an absurd interpretation since it implies logical contradictions; a non-collapsed wave function describes infinite possibilities and not a particle that occupies infinite positions at the same time. If the properties are indeterminate it means that such properties do not exist which implies that the system itself does not exist; actually photons, electrons and quantum particles in general are just the name we give to some mathematical equations. The collapse represents the transition from infinite hypothetical possibilities to an actual event. Quantum mechanics is therefore incompatible with realism (that's why Einstein never accepted quantum mechanics) and all attempts to reconcile quantum mechanics with realism are flawed. Since the collapse of the wave function violates the fundamental laws of physics, it can only be associated with an agent that is not described by the Schrodinger equation, and the only event we know of that is irreducible to the Schrodinger equation is consciousness. Therefore, events can only exist when consciousness is involved in the process; contrary to what many claim, a measuring instrument cannot cause the collapse of the wave function. However, the fact that properties are created when a conscious mind observes the system in no way implies that it is the observer or his mind that creates those properties and causes the collapse; I regard this hypothesis as totally unreasonable (by the way, the universe is supposed to have existed even before the existence of humans). The point is that there must be a correlation between the existence of an event (associated to the collapse of the wave function =violation of the physical laws) and the interaction with a non-physical agent (the human mind); however, correlation does not mean causation because the concomitance of two events does not imply a causal link. No cause of collapse is necessary in an idealistic perspective, which assumes that there is no mind-independent physical reality and that physical reality exists as a concept in the mind of God that directly creates the phenomena we observe in our mind (any observed phenomenon is a mental experience) ; the collapse of the wave function is only a representation of God's act of creation in our mind of the observed phenomenon and is an element of the algorithm we have developed to make predictions and describe the phenomena we observe. This is essentially the view of the Irish philosopher George Berkeley, and in this view God is not only the Creator, but also the Sustainer of the universe. The fundamental aspect of quantum mechanics is that reality is not described as a continuum of events but as isolated events, and this is in perfect agreement with the idealistic view which presupposes that what we call "universe" is only the set of our sensory perceptions and that the idea that an external physical reality exists independently of the mind is only the product of our imagination; in other words, the universe is like a collective dream created by God in our mind. Idealism provides the only logically consistent interpretation of quantum mechanics, but most physicists do not accept idealism because it contradicts their personal beliefs, so they prefer an objectively wrong interpretation that gives them the illusion that quantum mechanics is compatible with realism.

[@mattphillips538]

Imagine a computer game in which you enter rooms in a Dungeon, fight the monsters inside, and collect what treasure you find there. You will find it is considered efficient by programmers of such games to represent these quantities by probability distributions such as 3d6 (the sum of three 6-sided dice) goblins , or 1d20 gold coints. These are resolved to fixed amounts only when the player opens a door, else the system waste resources determining the contents of rooms no one ever enters. Similarly, our Universe doesn't give the answers to questions no one has asked yet, because that is a form of waste.

[@randomthings1553]

This is a very interesting view, and one very similar to the one I’ve developed approaching the investigation of reality from philosophy. Since every time we think we found `mater` it always proves to be more empty space and even less `mater`. This implies to me the lack of actual mater/atoms (in the strict sense, something that is non-divisible). Which points toward the view that there is an active mind that sustains reality itself, a logos if you will.

[@marcobiagini1878]

@@randomthings1553 Maybe you maybe interested alsoin the following considerations that show why current physics leaves not room for the possibility that brain processes can be a sufficient condition for the existence of consciousness. The hypothesis that consciousness emerges from, or can be identified with physical, chemical or biological processes is incompatible with current physics. It is a scientifically established fact that a mental experience is associated with numerous distinct microscopic physical processes that occur at different points; there is no physical entity that connects all these distinct microscopic processes, therefore the existence of mental experience requires an element of connection that is not described by current physics. This missing element of connection can be identified with what we traditionally refer to as the soul (in my youtube channel you can find a video with more detailed explanations). Emergent properties are often thought of as arising from complex systems (like the brain). However, I argue that these properties are subjective cognitive constructs that depend on the level of abstraction we choose to analyze and describe the system. Since these descriptions are mind-dependent, consciousness, being implied by these cognitive contructs, cannot itself be an emergent property. Preliminary considerations: the concept of set refers to something that has an intrinsically conceptual and subjective nature and implies the arbitrary choice of determining which elements are to be included in the set; what can exist objectively are only the individual elements. Defining a set is like drawing an imaginary line to separate some elements from others. This line doesn't exist physically; it’s a mental construct. The same applies to sequences of processes-they are abstract concepts created by our minds. Mental experiences are necessary for the existence of subjectivity/arbitrariness and cognitive constructs; Therefore, mental experience itself cannot be just a cognitive construct. Obviously we can conceive the concept of consciousness, but the concept of consciousness is not actual consciousness; We can talk about consciousness or about pain, but merely talking about it isn’t the same as experiencing it. (With the word consciousness I do not refer to self-awareness, but to the property of being conscious= having a mental experiences such as sensations, emotions, thoughts, memories and even dreams) From the above considerations it follows that only indivisible elements may exist objectively and independently of consciousness, and consequently the only logically coherent and significant statement is that consciousness exists as a property of an indivisible element. Furthermore, this indivisible entity must interact globally with brain processes because there is a well-known correlation between brain processes and consciousness. However, this indivisible entity cannot be physical, since according to the laws of physics, there is no physical entity with such properties. The soul is the missing element that interprets globally the distinct elementary physical processes occurring at separate points in the brain as a unified mental experience. Clarifications The brain itself doesn't exist objectively as a mind-independent entity. The concept of the brain is based on separating a group of quantum particles from everything else, which is a subjective process, not dictated purely by the laws of physics. Actually there is a continuous exchange of molecules with the blood and when and how such molecules start and stop being part of the brain is decided arbitrarily. An example may clarify this point: the concept of nation. Nation is not a physical entity and does not refer to a mind-independent entity because it is just a set of arbitrarily chosen people. The same goes for the brain. Brain processes consist of many parallel sequences of ordinary elementary physical processes occurring at separate points. There is no direct connection between the separate points in the brain and such connections are just a subjective abstractions used to approximately describe sequences of many distinct physical processes. Indeed, considering consciousness as a property of an entire sequence of elementary processes implies the arbitrary definition of the entire sequence; the entire sequence as a whole (and therefore every function/property/capacity attributed to the brain) is a subjective abstraction that does not refer to any mind-independendent reality. Physicalism/naturalism is based on the belief that consciousness is an emergent property of the brain. However, an emergent property is defined as a property that is possessed by a set of elements that its individual components do not possess; my arguments prove that this definition implies that emergent properties are only subjective cognitive constructs and therefore, consciousness cannot be an emergent property. Actually, emergent properties are just simplified and approximate descriptions or subjective classifications of underlying physical processes or properties, which are described directly by the fundamental laws of physics alone, without involving any emergent properties (arbitrariness/subjectivity is involved when more than one option/description is possible). An approximate description is only an abstract idea, and no actual entity exists per se corresponding to that approximate description, simply because an actual entity is exactly what it is and not an approximation of itself. What physically exists are the underlying physical processes. Emergence is nothing more than a cognitive construct that is applied to physical phenomena, and cognition itself can only come from a mind; thus emergence can never explain mental experience as, by itself, it implies mental experience. Conclusions My approach is based on scientific knowledge of the brain's physical processes. My arguments show that physicalism is incompatible with the very foundations of scientific knowledge because current scientific understanding of molecular processes excludes the possibility that brain processes alone can account for the existence of consciousness. An indivisible non-physical element must exist as a necessary condition for the existence of consciousness because mental experiences are linked to many distinct physical processes occurring at different points; it is therefore necessary for all these distinct processes to be interpreted collectively by a mind-independent element, and a mind-independent element can only be intrinsically indivisible because it cannot depend on subjectivity. This indivisible element cannot be physical because the laws of physics do not describe any physical entity with the required properties. Marco Biagini

[@markdavis7397]

I'd rather work on a solid grasp of what is known, instead of speculating in philosophy. But I know I'm vastly in the minority on that point. It's in some sense less fun. But I just think it's a little ridiculous for a person to speculate about the big picture if s/he hasn't clearly proven her/himself to be above all the greatest minds in history (who couldn't solve this conundrum yet). And since that is not even remotely feasible for me, I'll just follow along.

[@EngRMP]

I can't get over how similar this sounds to time domain vs frequency domain in signal processing (Fourier Transforms). The finer the resolution in time (for example, approaching an impulse), the wider bandwidth in frequency domain is required to represent the finer resolution. I wonder... are we using the wrong picture to describe the quantum view of electrons (particles). Are electrons really a superposition of frequencies? And, then, trying to understand where in space the superposition of waves are all in phase (making like a breaking wave in a water analogy... the apparent instantaneous position of the electron), requires taking into account a wider bandwidth. If you only need a coarse idea of where the electron is, then less bandwidth is required. Am I way off course here???? Are the terms "position" and "momentum" really time domain and frequency domain representations of sinusoidal views of electrons (particles)????

[@LookingGlassUniverse]

Spot on! This is exactly what's going on under the hood here- if you had a state with exactly one momentum it would look like a pure frequency signal. So swapping from the position to the momentum looks like a fourier transform

[@EngRMP]

@@LookingGlassUniverse And, so, if there was a state of one momentum, is the position frequency related to the excited energy states... what determines the frequency or wavelength?

[@Fisherdec]

3Blue1Brown did a great video on exactly this. Wavelike systems all have this property. kzbin.info/www/bejne/g3PRn4uYhLJoiZYsi=-5TDepY2heIo-Vy-. Also, type into chatgpt graph a gaussian and its fourier transform on the same plot and you will see the fourtier transform of a gaussian is just a scaled gaussian where the multiplication of the standard deviations of both gaussians will always be >= 1/2

[@EngRMP]

@@Fisherdec Thanks, I hadn't seen that (from six years ago!!!). As usual, Grant did an excellent job. I thought I was going to get the answer to my follow on question when he started to assert that momentum was somehow related to the frequency domain. But... then he couldn't get the rational from the physicists. So, I can't help thinking that we're just not yet getting the right description of quantum mechanics. For example, I can make a really complicated description of the Fourier transform (orthogonal basis vectors, exponentials, etc.), but if I show an example of a few frequencies adding up to make a square wave, the Fourier Transform all of a sudden becomes very intuitive. I now understand that the Heisenberg uncertainty is not as mysterious as it has been explained for the last 20 years of my life. Hopefully, eventually we get a better description of Quantum. Or, maybe what's making it mysterious is that we're trying to shoehorn Quantum mechanics into conventional time vs frequency signal processing... maybe that's not the right mathematical language to use.

[@steffenbendel6031]

You can choose any base you want that is a complete base of the Hilbert state space. Pure position or pure momenta or energy eigenstates for bound systems or really anything you can imagine or construct. And I think maybe our choices are sometimes causing the problems. The eigenstates in location space are somehow unnatural, since that would have an infinite energy. And a pure frequency state could be realised after an infinite time (you would need an exact energy). So maybe better construct a base of normal distributed Gauss wave packets. Maybe such a base would avoid the infinities in QFT that seems more like a mathematical than a physical problem (no wonder, if the path integral calculates with states that have infinity build in)

[@andrewtaylor3152]

This is literally the best, clearest explanation of Heisenberg Uncertainty I've ever seen. Too often, the explanation is couched in attempts to dramatize the "weirdness" and counterintuitivity, really leaning into a sense that this is difficult to understand. You dispense with all that, and walk the viewer through how the reality differs from our intuition, but presenting it in a way that makes the math and the physics seem very straightforward. Well done, and thank you.

[@jack.d7873]

@@andrewtaylor3152 Well said. 100% agree. Nice to see QM explained without all the fluff

[@TristanLaguz]

It's not bad, but I'd prefer an explanation in terms of BM. If ψ didn't collapse at least apparently, ðe UP would indeed not be about uncertainty. But as ψ does collapse apparently or actually, ðe UP is about uncertainty (e.g. in Bohmian Mechanics) or undeterminedness (Objective Collapse).

[@voidisyinyangvoidisyinyang885]

@TristanLaguz Study Professor Basil J. Hiley for the update on Bohmian physics as noncommutativity. Hiley has revealed the truth as he was Bohm's collaborator. The momentum-position uncertainty originates from time-frequency uncertainty that is inherently nonlocal and noncommutative.

[@lee_at_sea]

@TristanLaguz at least a nod to the fact that Copenhagen isn't the extent of the known universe might indicate competence. Instead the OP hand waves about not knowing why while claiming it is, and declining to explain why lands outside it are not relevant and simply stating they aren't. One of the most dogmatic presentations I've ever seen right here. I'll keep following the channel, but the motivation just changed. Eye opening.

[@jack.d7873]

@TristanLaguz This presentation was better than others because she didn't introduce "interpretations". Though it does sound crazy to suggest a point particle spreads out over space. The answer to wave-particle duality is Quantum Field Theory. The "spread" is the vacuum energy state of QFT. Thinking of the double slit experiment. After a single electron is shot through two slits its energy changes from 0.511 MeV to 0 (0 isn't nothing in field theory). After a time of travel, it receives 0.511 MeV and is evident on the detection screen. QM does not explain the full Mechanics of this universe. QFT

[@philochristos]

This distinction between ontology and epistemology in quantum physics sure has lead to a lot of confusion.

[@erikziak1249]

100% agree.

[@simongross3122]

Confusion should be called Obfuscology. Not for any reason other than it rhymes better.

[@Fisherdec]

Meanwhile, Google claims quantum computers are doing calculations in parallel universes 🤦

[@lee_at_sea]

Yes. The OP is swimming in it. Eye opening video about the state of the industry.

[@Fisherdec]

@@lee_at_sea Protip: never believe anything physicists say when it comes to quantum intuition. There is a reason the expression "shut up and calculate" exists.

[@gerhardeichhorn8322]

I think that it is even more general: It is the statistic relationship of the standard deviation of two different generalized observables represented by selfadjunged operators.

[@chainbenwa2713]

Ha! It just clicked in my head earlier today listening to an audiobook today about the same time you posted this video. Tring to get everything straight confusing either way. For some reason I’ve been obsessing over quantum physics for the last 8-9 years. It’s makes so many amazing things possible!

[@robinbrowne5419]

Thanks for this. I have watched about 20 videos about the Heisenberg uncertainty principal in particular and about 50 videos about quantum mechanics in general. Each time I watch one I gain a bit more of an understanding. That is all I can say, except Thanks for posting them and Merry Christmas 🎄.

[@skhi7658]

Electrons are a quantum of ACTION. They do not exist if there is no interaction with the quantum field. A quantum is an energy transfer with a fixed value , IF AND WERE the interaction takes place. What must be disturbed (stimulated ) for this event , is the field NOT the electron. The electron is the RESULT of the disturbance that only appears when an interaction with the field takes place. A quantum has no probability of residence.There is only a probability of occurrence in the area in which the field is suitably stimulated . A quantum is not a particle and has no diachronic individual object permanents. Accordingly, it has NO individual properties. A quantum only shows the field properties as its current quantized representation during an interaction. A quantum has no place and does not follow any paths. It does not fly around on a trajectory or an orbit. Likewise, a quantum is not a wave that collapses and does not have wave properties. A wave function ( probability wave) is only a mathematical ABSTRACTION which makes possible events ( registration of stimulation through interaction ) predictable.

[@ghanshamchandel1854]

Here's how I make sense of the measurement. Every interaction of a particle (or group of particles) with the environment is a "measurement". Some interactions (colliding with a detector screen, getting deflected by magnets, ...) shrink the wavefunction in a particular base (position, momentum, angular momentum, ...) and we call it a measurement. The more the sharp shrinking, better is the measurement.

[@ExistenceUniversity]

Does this not fail to account for entanglements?

[@wheatthicks]

How do you define what is and isn’t “the environment”?

[@ExistenceUniversity]

@wheatthicks In quantum: the environment is that which is not "you"; not quantum entangled with you. Outside of Quantum: environment is that which is contained in the same regions as the cycles of life present.

[@wheatthicks]

@ Respectfully I wasn’t asking for a general answer but rather asking this particular commenter.

[@saugatbohara5404]

I rarely comment on videos. This explanation is so good you deserve to know. I never understood true quantum mechanics until I started watching your videos. Thank you

[@Richardincancale]

I recall a whole lecture on the Open University in the UK back in the 1970s explaining the uncertainty principle entirely as perturbations during to the measurement, rather than focusing on superposition. Must have set back a generation of students!

[@LookingGlassUniverse]

If you want to learn Quantum Mechanics with me, the 4 week course starts the week of January 6th! I just finished teaching this course to my first group of students, and it was a blast :) The course is designed for people of all levels of mathematical background, so everyone is welcome. But just so you know, there will be homework 📝🍎 looking-glass-universe.teachable.com/p/quantum-mechanics-fundamentals1 There’s some issue with the site (there was earlier) please email at [e-mail] and I'll sort it out!

[@nias2631]

I'll sign up, caught a typo in the landing page blurb "I'll guid you through..."

[@phasespace4700]

Unable to complete checkout for this course!

[@LookingGlassUniverse]

@@nias2631 Thank you!

[@LookingGlassUniverse]

@@phasespace4700 I'm so sorry! I've tried to find out what the bug was and couldn't figure it out. Would you mind emailing me? I think I can add you in another way. My email is looking.glass.universe@ gmail

[@LookingGlassUniverse]

The website seems to be fixed now!

[@remusgogu7545]

For me what helped me understand why this relationship exists is to actually understand that the electron wave function is actually a superposition of multiple wave functions of various fixed p (basically what you have drawn as space distribution is the result of that superposition). Any distribution like the one drawn in this video can be decomposed in a sum of fixed p by Fourier transforms. This understanding is enough because then you know that to construct a more precise distribution (low DX) you need a larger number of fixed p waves combined (therefore larger DP). A wide space distribution (wide DX) requires just a few fixed p combined (therefore lower DP). But the Ozama relationship makes total sense - although the two relationships are fundamentally different in terms of meaning.

[@2nd_foundation]

Mithuna, are you aware of the Fisher's information theory? , you could derive the uncertainty principle from the Cramer Rao lower bond. Great videos thanks!

[@peterbonucci9661]

That's what I thought. I think version 2 is about how much information you can get out of a measurement.

[@MedlifeCrisis]

If I can follow your explanation then you’ve explained it very well

[@LookingGlassUniverse]

Thanks Rohin, but you’re the real doctor, not me

[@ozachar]

In this context, a different way to think of measurement is a: state preparation. By doing the measurement, we actively created a state with confinement equal to the precision of the measurement.

[@domenicobarillari2046]

I am particle physicist, watching this content because my son asked me to check it out and comment on the presentation. I find the material interestingly done and largely quite competent, and I respect the presenter's intellectual honesty. Having said that, I would have worries about any instructor who at some point indicated to a university level class that the uncertainty principle is currently understood as a measurement precision issue. It is NOT, as she acknowledges, and I enjoyed viewing her take on the matter now, at least for a beginner's class. The dive into relating the measurement process viz-a-viz the uncertainty of a state was as good as any undergraduate author's take and presentation on the matter, of which there are perhaps a dozen. More specifically, I would like to point out that the most convenient, modern "take" on this most foundational of QM topics is this: whether in QM, or quantum field theory nowadays, simply comes from insisting that measurement operators that define the theory [ Lagrangrian, for the cogniscenti] must obey certain commutation relations - e.g., that [P,Q] = ih , or explicitly PQ - QP = ih, something that never comes up in classical mechanics [except in certain symplectic methods.] This is a founding axiom, and has no further explanation other than the primal fact that it describes the world correctly. It is also the point from which the great masters like Heisenberg left behind the "measurement interpretation" and finally moved on to matrix mechanics. It is indeed weird looking to those who have not handled matrices before, but is a refreshing sign that nature does not have to humour us with scrutable maths !! Beginners who don't mind the math may like the treatment in Cohen-Tannoudji, et al's excellent introductory 2-volume set on QM. best regards, DKB

[@Knowledge_Seeker64]

So in other words, measurement collapse of a spread creates a radically smaller spread as opposed to reducing the spread to a single value?

[@lonestarr1490]

As if the universe knows exactly how much we know and always utilizes all the wiggle room that remains.

[@erikziak1249]

@@lonestarr1490 "The universe" could not care less about us, if it had the ability to "care".

[@MsSonali1980]

@@lonestarr1490 No, it's just statistics. Those normal distributions are not "real", they are a statistical tool. And as @erikziak1249 says the Universe doesn't care. The Universe is not a mythical God that should care like one in a religious framework of believes.

[@GoogleIsNotYourFriend]

@@lonestarr1490 The universe isn't doing anything like that... this is just us, as humans, inventing a system of understanding based on probability to handle something beyond our reach (of classical physics). Why must people always try to inject some mysticism into this?

[@renancenbs]

@@GoogleIsNotYourFriend I would say the opposite -- we don't have anything to do with it, it's just the way nature works. We agree that the whole mystic stuff sucks though.

[@alyoshakaramazov8469]

When I was in the university, my professor taught the uncertainty principle using wave theory. If you know the frequency, you know the momentum, but you can’t know the frequency to a high accuracy because there would then be only one wave with no position. If you want to know position, you have to add waves of different frequencies together to get a localized particle like sum, but you can’t add frequencies together to get a highly accurate location because then you lose the frequency of the wave information from which we get the momentum. It pretty much made sense. That professor was pretty well known in high energy particle physics. By the way, we were invited to dinner with Emilio Segre one evening. It was a good school, but wasted on me, a lowly agricultural chemistry major….

[@schmetterling4477]

Yes, and as you have noticed this relationship is just as valid for classical waves. Heisenberg is therefor not a quantum mechanical phenomenon.

[@pedzsan]

To me, what I keep in mind is that particles are waves packets. There is no such thing as a “particle” as you show with the cloud with a smiley face. There are only wave packets. Thus, “things” do not have an exact position - ever. As you say, the wave packets has a distribution across some space. To me, keeping this idea front and center as you try and understand physics helps.

[@tumultuouscornucopia]

Thanks, that was a stream of words that helped reorganise the content of my head into a clearer grasp of what is going on here. I feel quite confused about the whole "nobody knows what a measurement is" thing though. As it is clear that these heisenberg-pairs are Fourier transforms of each other, isn't "a measurement" simply any interaction that is effectively applying some sort of "band pass filter" (ie your "ruler" is a comb filter on position, and half way through the vid you give it more prongs, changing the final delta-P).

[@blueckaym]

That's very good video! It's really good to clarify the "spread in position" thing, as it's very often misinterpreted (as QM usually is :D). Now I'm thinking what other ways the "spread of momentum" could be interpreted (and which is the correct one). PS. However don't forget that the Heisenberg Uncertainty Principle is based on the Fourier Transforms (admittedly one of the most powerful pieces of math we have discovered!), and the uncertainty principle comes from the math describing it, which might or might not be the nature of the subject (the electron in this case). In practical terms it's ok to consider the subject identical to our description model, though if you're interested in really understanding it and note that ALL of our models are simplifications, you should remember that even our best descriptions very rarely ARE the subject they're describing, at best they give us precise view on some aspect of the subject. I know this is rather philosophical argument, but my point is - keep your mind open, because you might discover another better way to interpret something that you thought you knew already! (it doesn't have to replace your previous understanding, but to complement it)

[@hfmichel8064]

Your position to this issue is super...

[@BlackShardStudio]

3:42 technically, we don't know this either. This is called begging the question. We can't collect information without performing a measurement, and measurement appears to affect the system, so we can't possibly know what the evolving, spreading wavefunction describing an undisturbed system actually represents: a gap in our knowledge of the system, or the physical reality of the system itself. QM is rife with UTD (underdetermination of theory by data), that's why there are so many interpretations. I appreciate that "uncertainty" implies the existence of a real location value prior to measurement, and what you're trying to remind us is that QM has, as best we can tell, left absolutely no room for local realism. But we have no way to know if we should preserve locality and dispose of realism, or preserve realism at the cost of disposing with locality, and we don't know what measurement actually is. The entire problem is that the full suite of qualities of the universe we take as utterly indisposable to our understanding of the world (space, time, causality) are incompatible at the quantum level, and we're not sure which isn't actually fundamental.

[@blueckaym]

3:42 "... in-fact the electron is spread out, so it's in all of these places" That's the way I understood it too, despite the constant repeat that the electron is a point-like particle. Yes, when you measure it, it makes a point on a screen (or a sensor), but that's the location of the measurement interaction, which doesn't have to be what the electron is.

[@blueckaym]

@@1emiliobering , scattered is your word

[@lonestarr1490]

​@@1emiliobering "what does spread mean?" Basically the variance in the probability distribution?

[@lonestarr1490]

​@@1emiliobering True, I don't understand you. I just stated what I understood spread to mean in the video. We're dealing with probability distributions and those have a variance. Seemed quite fitting to me. But maybe that's not what physicists mean when they say "spread", I don't know. Btw, is (my number of responses) × (your frequency of responding) ≥ h/2 ?

[@cademosley4886]

@@1emiliobering Welcome to quantum mechanics! 😂

[@cademosley4886]

I like another framing, instead of saying the system is spread out into all of these places, we might say that all of these places are packed into the system. This seems to be the trend of the articles you'll see these days about the emergence of space from the quantum entanglement of ground states / vacuum states.

[@MrKelaher]

To put it another way - there is no collapse of the "object" at all. The act of bucketing the "true" momentum or position seems to "distort the distribution" in a way spacetime "remembers" as it propagates in its fields while preserving its overall metric hyper-volume in relation to the Planck constant. This can be done repetitively, but the effect is always the same until the distribution is entirely erased by scattering off another propagating field "object" to create zero, one or two new "objects". Its a puzzle :)

[@MrBeiragua]

The more I think about what quantum physics is about, the more I think that it's about the "state" of the particle. Unfortunately, I don't understand what this state is supposed to be in the real world lol! Great video! Your explanations are amazing!

[@liamweavers9291]

The uncertainty principle is about timing and complexity. For example, we can be sure that things will happen but can't guarantee when. This would seem rather obvious at our level of observation, but when you scale it down to the quantum realm, it becomes a lot less certain about when things will happen...

[@flippen-z1x]

So, a huge correction is that the Heisenberg Uncertanty Principle is absolutely related with measurment and not just spread. This is a consequence of the commutator between the position and momentum operator being not 0. This is in fact how you derive the uncertanty principle in your first Quantum Mechanics course, you take the average value of the commutator (and square it), and that is porportional to the product of the variances. Since the commutator is non-zero, you cannot find a basis which is simultaneously an eigenbasis of both position and momentum and by the axiom of measurment, it implies that you cannot simultaneously measure the position and the momentum of a particle. This is absolutely what you learn in your first course in Quantum Mechanics and you are the one that's wrong.

[@joemoya9743]

Wrong? Or, simply a different way to say something similar? 🤷‍♂️

[@flippen-z1x]

@@joemoya9743 Just wrong, she literally has the words written "Heisenberg "uncertanty" isn't about measurment: its about spread". This is a wrong statement as I explained, the correct statement would be that the uncertanty is about measurment AND spread since one implies the other.

[@truejim]

When I noodle on these kinds of topics, I imagine particles as roulette wheels that spin forever, the little roulette ball that represents a property never dropping into a slot until there’s an interaction with other roulette wheels. A particle with momentum and position is represented by two roulette wheels, one for each property. An interaction that requires a ball to drop into a slot of one wheel causes the slots in the other wheel to grow narrower (so more numbers available). It’s an imperfect analogy I know, but thinking of particles as ever-spinning roulette wheels helps me not think of particles as little dots. I suppose I could have chosen the mental model of a particle as two ever-tumbling dice, where an interaction that causes one die to settle causes the other die to grow more faces. Roulette wheels makes a better image for me when I’m noodling about entanglement though. Like: two wheels for two particles set spinning simultaneously. Still a very imperfect analogy though.

[@KalterAdler]

The clearest explanation of this that I have encountered. Thank you.

[@BeardedSte]

The confusion between these interpretations of the Uncertainty Principle is due to concepts defined as useful in classical space-time physics breaking down at a quantum level. Position, momentum, energy, mass etc are to some extent meaningless where our ideas of space-time break down. By shining a proverbial light or measuring for these concepts, we inadvertently introduce a medium where the laws of space-time apply. That is how the measurement collapses the wave function and affects the event. The Uncertainty Principle defines the limits of this. This is just my take on it all.

[@attica7980]

The problem with this "definitive" explanation of the Heisenberg Uncertainty Principle is that quantum mechanics has two different sides: the mathematical side, described with Hilbert space operators by John von Neumann in his book on the Mathematical Foundations of Quantum Mechanics, and another side, interpreting the mathematical results in a somewhat mystical human language (as described by Niels Bohr or Hugh Everett). As the existence of at least two vastly different interpretations of quantum mechanics shows, there is no general agreement on the interpretation. The Heisenberg Uncertainty Principle can be explained both in the framework of the mathematical description and in the framework of each of the interpretations, and these explanations will be different.

[@MsSonali1980]

I hate the usage of the "mystical" language, it feels like they want to keep themselves up in their ivory tower. For people that must have a very clear and logical understanding of their field, it seems intentional when not self-explanatory terms are used to describe their findings to the public. It's the reason I despise the Schrödinger's cat analogy so much. It makes a funny (insider) joke, but it shouldn't be used to explain anything to people that have no background knowledge.

[@furtherback6131]

This woman has been my QP goddess for over ten years. Amazing to have been there from the start and be so privileged as to follow her in her evolutionary trajectory.

[@cesartrip]

I think the problem is thinking of electrons, or any elementary particle, as point objects. If you think from the beginning that particles are waves, or volumes in a field, the phenomenon of superposition becomes dispensable. By analogy, imagine a balloon in a dark room and that our instrument to locate it is a needle to make the balloon collapse (pop)... When you hear the pop, you will know that the needle touched the surface of a volume, but you definitely will not know where the center of that volume was. To know, you would have to pop it with 3 needles simultaneously and equidistantly, which is impossible, since the collapse will happen from only 1 of the needles.

[@schmetterling4477]

Particles are not waves. There simply are no particles. Quanta are physical system property changes. They are NOT objects, they do not have structure and, most importantly, they do not have position and path. Energy never had position and path in classical physics, either.

[@Binyamin.Tsadik]

Finally This is exactly what I've been saying for years! The reason for the measurement collapse is because of what a measurement actually is! It's the transfer of information! Information must be transferred at a location and time!

[@steffenbendel6031]

That fits my saying: There is no information in the multiverse, only in the selection of a specific branch. (That why I can predict the lottery numbers with 100% accuracy and 0% usefulness as "all of the combinations")

[@marsovac]

My understanding is that for any kind of measurement we need at least two moments in time, and since the electron is a vibration in the electron field, we will be measuring two different values every time

[@cademosley4886]

If you measure a quantum state very quickly after already measuring it a first time, then the wave function will collapse again into (almost) the same state if it's done quickly enough, and if you keep measuring it over & over very quickly, you will freeze the system into that state. It's called the Quantum Zeno Effect, and it's something they've really discovered happening.

[@reiniertl]

I like more the idea of saying that the electron is a two-dimensional distribution resulting from the interaction of two random variables (position, momentum) rather than a wave and particle at the same time. This makes much more clear that we are dealing with random variables and their resulting distributions. I never understood this too well and thus did not liked the course in my undergrad. Been an engineering student knowing this most likely will never be in my future toolbox I just focused on passing the course and so this is long forgotten beyond the utterly basic ideas. But if this concepts had been presented from the perspective of two interacting random variables instead of the contrived concept of wave-particle duality it would of clicked much better. Thanks for this explanation is very clear and concise. I also like the other comments pointing to the similarity with Fourier analysis and other more general ideas.

[@KipIngram]

The state of a particle doesn't specify things like position and momentum - the value of observables - at all. Instead, the full set of theoretically possible measurement outcomes are embodied in the OPERATOR describing your measurement INSTRUMENT. All the state contributes it the set of probabilities that you will obtain each of those possible results. See, when you choose a quantity to measure, it is tantamount to choosing a coordinate system for your Hilbert space - each of those possible results is an eigenvalue of the matrix that represents the observable operator, and the corresponding eigenvectors form a basis of the space. After the measurement, the new quantum state will BE one of those eigenvectors, meaning that the state will be perpendicular (zero probability) to all of the OTHER eigenvectors. This is just a reflection of the fact that you now know, with 100% certainty, the result of the measurement. When you make a measurement and get a result that only gives you one bit of information about the previously existing quantum state: it was not perpendicular to the eigenvector that goes with your measurement result. It might have been ALMOST perpendicular - your a priori probability of getting that particular result might have been tiny. Or it might have been 99% certain. There's absolutely no way to know any more than that one little thing about the pre-measurement state. Also, these pairs of variables, like position and momentum, are related mathematically. There exists no possible state that can be an eigenvector of both members of such pairs. An eigenvector of one corresponds to a precisely determined value for that variable, but the the other one has a uniform probability distribution across all possible values. This is just baked into the mathematics of the theory. It's important to recognize, though, that we did this ON PURPOSE. There is a step in canonical quantization where we explicitly set the commutator of the position and momentum operators to a non-zero value, and that is what puts the uncertainty principle into the theory. So it's not something derived - it's something designed in deliberately, because we observed that to be how the world works.

[@En_theo]

I don't get how momentum can potentially have a larger range of possible values ? Is not momentum a constant due to conservation of energy ? What happens if I emit a particle (and thus know its momentum) and then try to measure precisely its position : will the momentum magically change ? If I measure the momentum precisely after that, will it be different from the momentum it had at its "creation" ? I'm a little bit confused here.

[@miguelalonsoperez5609]

Nobody express Heissemberg principle as “measurement” knocks the system, and have serious doubts of a university explaining like so (possibly in a high school but not in undergraduate level). Actually there’s no consensus about the deep nature of wave collapse but Heissemberg has nothing to do with that. The correct explanation should include Born’s rule, which is the true origin of debate, Heissemberg uncertainty is just a mathematical fact of Hilbert spaces and matrix mechanics. No debate actually on that (or very little). Born’s rule states the collapse of wave function into one the eigenvectors and measurements of the corresponding eigenvalues. Suddenly the wave function becomes a one single Dirac delta or similar eigenvector of the Hilbert basis. This is the uncomfortable part of QM, because Schrödinger equations are deterministic and linear, they change randomly when OBSERVED (capital letters to differentiate the definition of observing from measurement) and this remains without any further explanation. Copenhagen interpretation states “accepted and calculate”, and a bunch of actual theories try to resolve this highly unacceptable aspect…

[@dwinsemius]

The units of the product of position and momentum are the same as the units of action. The HUP is really a statement about the minimum _action_ of an inter-"action". Likewise the other versions of the HUP are also conjugate variable with those units, for example energy and time.

[@PhilMoskowitz]

I think this is perhaps conditional probability, or quantum Bayesianism in the context of QM.

[@simongross3122]

Certainly seems like it, since the values depend on what we already know.

[@MrBrianJohnOBrien]

In order to observer something you must 'effect it. You can either know where something IS or how fast it is going, but never both at the same time. This is simply true because at lease 2 samples must be taken and this 'dt' the state has changed. I think as dt (sample time) approaches 0 you get a better value and a smaller point spread. I think that as dt approaches 0, then we can sample short wave lengths until we approach plank's length. There is also a relationship between the sampling frequency and 'Nyquist' that limits 'how short' a wavelength we can measure. P.S. I'd love to make a flip flop using your home made quantum computer. ;)

[@kevy1yt]

Makes total sense. You touched on but didn’t expand on what I think is more fundamental: that you as the observer is the “thing” that collapses the particle to an exact position when it is measured. This happens because you as the observer are also the thing that is PROJECTING the particle and the measurement in the first place. It seems like the particle and measurement of that particle are outside of you. They aren’t. They are being projected by you. This is the classic observer effect. And it also has profound implications in your life - all of our lives - as a whole. Make sense???

[@pavolgalik9764]

So it's about measurement...

[@GeoffryGifari]

Hmmm if the framework is measurement collapse and there is an uncertainty relation between measurement error and disturbance, does that mean that in reality, the value of the quantity we measure "collapses" into a range, instead of collapsing to one exact number?

[@epajarjestys9981]

I would think so. If you subscribe to the notion that the wave function is ultimately real then yes (which also seems to be the notion that Ms. LookingGlassUniverse subscribes to at least for the sake of explanation).

[@steffenbendel6031]

Yes, is has to have a range. A position distribution that goes to zero width would reach infinite energy.

[@lambdanebula8473]

Superpositions are a property of our universe because they help it remain coherent. A particle's superposition can breakdown for some of it's properties while preserving the superposition of others, and this often happens. In fact, a particle is never not in a super position. The uncertainty in it's position and momentum is necessary. Even when the superposition of a particle breaks down, it never breaks down entirely, at least not on all properties, because doing so would mean the entirety of the universe would be incoherent. You may have it's spin become defined, but it's precise path to the detector remains undefined. You get the idea. Why is this undefinition necessary? Well, I don't know, and I'm not the person who will figure it out most likely. Unfortunately, our understanding of reality remains too limited, but we'll get there eventually, I think.

[@williamverhoef4349]

Also, it is not about one experiment but about the spread of values when you repeat the experiment numerous times. You can actually get precise measurements of both position and momentum at the same time by measuring both at the same time. Or have I misunderstood something from other videos.

[@Achrononmaster]

@2:20 nope, or _"not really"._ Electrons _are_ more like "little bits" than you think. _But_ they can be entangled, i.e., can couple to ER-EPR bridges, which is the only "spreading out" they can achieve. The wavefunction is a fiction, and is nothing but an effective non-classical (non-Markov) statistical description, as you know, because Hilbert space itself is a fiction (massive gauge redundancy, and gauge is not physical... as you well know). In the Spacetime Algebra it is all much clearer what the spinor (aka. wavefunction) really is, and that is it is an instruction for dilation and rotation/boost that acts on the multivector observables. That stems from the proper algebra for QM describing a measurement theory. Hence your round-about way of going from measurement, to spread, then finding your way back ultimately to measurements and disturbance! Quite a journey. The original HUP conception (the "completely wrong" one), while not the full story, is actually not too bad. The missing piece of the naive view is why there is a limit on measurement - if you don't know why then all the subtlety is gone and it stays a merely naive not-quite-exact conception. The *_why_* is that regardless of effective superposition natural processes never violate the symmetries of spacetime. All the off-shell processes we pretend to sum over in the path integral involve non-local effects in the Minkowski frame, thus they ignore topology, but it is in the topological structure of spacetime where the conservation laws/symmetries are respected. Off-shell processes _only_ look off-shell in the Minkowski frame (the trivial topology frame).

[@ennio5763]

Once it's established the (x) * (p) must be >= limit, then it's intuitive that reducing one must increase the other one. But what is not intuitive is why is there such a limit to begin with ? That would be useful to explain. Also, the concept of superposition of speeds is much less intuitive than position spread out, yet, they are both treated as if they were the same.

[@RaubeR666]

Even if we think of an electron as a ball with a cute face on it, the virtual particles exist too. And becaue of the constant interaction with virtual particles electrons literally can't maintain a stable position or momentum. And the closer we look, the more violent it gets near the "center", hence momentum is less defined compared to the average of all/most those interactions (no outside force needed).

[@schmetterling4477]

First law of modern physics: You shall not think of system properties as little balls. ;-)

[@alexh3601]

What would happen if you were to rapidly measure the position and momentum back and forth? Would you get a random walk?

[@cademosley4886]

h-bar/2 is still very small. Think of the example of putting a cloud chamber in a magnetic field and waiting for a charged particle to fly through it. You will see a curved path created that lets you see (or measure) both the particle's position (in the chamber at a specific time) and momentum (amount of curvature at any point), and you can see it's not a random walk but a very clear curved line. It still respects Heisenberg Uncertainty because the bubble path is just fuzzy enough, if you zoomed in a lot, there's be a little uncertainty what the exact position and curvature is, but you'd still have to zoom in quite a bit to see that uncertainty fuzziness since h-bar/2 is still quite small.

[@GRosa]

You said/wrote *Ozama, but it's actually Ozawa, Masanao Ozawa.

[@LookingGlassUniverse]

Oh sorry! Thanks for the correction. And here's the paper if anyone wants- it's brilliant: arxiv.org/abs/quant-ph/0207121

[@MassimoAngotzi]

That’s because also Osama in 2003 was in a superposition of States. Emirates? Afghanistan? 😁

[@KeirRice]

I would love to see a follow up video about what a measurement is, or rather what counts as measurement.

[@emilmayev3759]

It feels like Quantum Mechanics is hopelessly stuck when explaining wave collapse, because we are making a distinction between observer and observed that nature doesn't make. Because this separation is completely artificial, the best we can do is probability waves.

[@ChannelMath]

The whole time I was just wondering what was making the electron so sad!

[@jokeyxero]

Can you do a video on all the ways we experimentally measure the position of electrons? You walked through one way in a double-slit video and it was very eye-opening to the reality of why we get the results we do.

[@LookingGlassUniverse]

Great idea! I’m going to see if I can do one of these experiments

[@roywodtke1690]

Again FYI KZbin takes control of my phone every time I try to review a new video.!

[@draoi99]

You have an intrusive R in your pronunciation of "delta X" which I could do without, but otherwise I've really been glad I watched this video and think you should do more. Thank you.

[@HoD999x]

who came up with the term superposition? isn't it much more accurate to think of particles as an "effect" that may occur with a given probability at any given point in space? like an army of randomly failing traps?

[@lonestarr1490]

But a particle really does not have a definitive location in space we just don't know beyond a certain range of probability. The notion of location itself is not well-defined beyond a probability distribution. At least that's how I understand it.

[@javiej]

Superposition is not equivalent to classical probability functions. Read about the double slit experiment, even for a single particle the wave function takes both possible paths at the same time, then interfering (both probability waves) with each other, finally collapsing into a single value when (and only if) you take a measurement. If this does not sound weird enough, think that you can now destroy the information obtained by the measurement and then the superposition (it's interference pattern) returns, like if you had never made the measurement. So no, Superposition is not just a probability function.

[@Yumy607]

Is it correct then to say as the PDF of either the momentum or position approaches a pulse (near 100% accuracy, then the other property’s PDF will approach a uniform distribution? What isn’t clear to me is where the upper/lower bounds are defined as well unless we know something about the system beforehand?

[@Heulerado]

If you want to be more quantitative, the wavefunction (whose absolute square is the PDF) of position is the Fourier transform of the wavefunction of momentum, and vice versa. If you understand what this means (3blue1brown has some amazing videos on Fourier transforms), you will see that yes, a sharp peak in a function will be reflected as an everywhere-oscillating sin + i*cos wave, which if you absolute-square is a uniform distribution. With this in mind, to answer your other questions, the bounds can be whatever you want them to be, or not be there at all, but we should know the state (i.e. the wavefunction) of the system beforehand, otherwise we are doing probability theory, not quantum mechanics. Which you have to do in the real world, but that's besides the point.

[@epajarjestys9981]

@@Heulerado > whose square is the PDF *absolute square

[@Heulerado]

@@epajarjestys9981 Yep, thanks, edited now

[@TristanLaguz]

If ψ didn't collapse, ðe UP would indeed not be about Uncertainty. But as ψ does collapse apparently or actually, ðe UP *is* about Uncertainty (e.g. in Bohmian Mechanics) or Undeterminedness (Objective Collapse).

[@matterasmachine]

Heisenberg's uncertainty principle is about discreteness of momentum

[@vickydixon7512]

Spread = Phi = the tightness of the wavelength. Shorter wavelengths are more frequent at the strongest point in a gravitational field, with longer wave lengths requiring more space so they are found more frequently away from those points of gravity. "Phi" = radial degeneracy you have 100% chance of finding Mass or energy at the center, and as you get further away as per the inverse square law of distance, that percentage drops linearly.

[@ExistenceUniversity]

For conceptual sake, it might be useful to label the misconception of the measurement problem, "an interaction problem," which is unique and different from the measurement problem

[@R_J_M]

A lot of well deserved academic praise here in the comments. But nobody has commented on the excellent shading on your electron 😂 A+ as both a science educator and illustrator! 👏

[@scene2much]

Why don't we deprecate all Quantum Mechanics that isn't a direct statement from Quantum Field Theory, and point at what we now call Quantum Mechanics as a quaint bag of analogies and 'near miss' concepts? We should challenge Physics curriculum to begin with QFT and then derive QM.

[@schmetterling4477]

You are correct. That is what we should be doing.

[@SenChandan]

Further, as I understand it, electrons in atomic orbitals are actually fuzzy clouds s, p, d, f…etc, some of which are dumbbell shaped and some are spherically symmetric… Even a free electron, say in a cathode Ray tube, is probably more like a wave packet than a particle per se. Am I correct?

[@mrfinesse]

Thanks.. Since we are taking about momentum, Are both the values of Velocity and Mass spread out. If an electron has a fixed mass, then why not use del-x times del-velocity (why momentum)? Or is this to get the units right (which does not seem correct to me)?

[@WillNordhorn]

What are position and momentum in reference to within the inequality? Are the directions in superpositions as well as the magnitude of their vectors? The examples given are one dimension of position or momentum on the X axis, but is it 3 in real life or is it one along a direction of measurement we pick?

[@bdg77]

Love your background lighting! 🎉

[@fuseteam]

the spread explanation confuses me, what is a "spread in position"? and a "spread of momentum"? is it the values of position/momentum that are in superposition? 🤔

[@jazzzAiman]

Very nice, looking forward to more content, interested in computational applications, would be nice to look at how are we using quantum effects to solve factorization.

[@b4byf4c3455451n]

who knows when we will be familiar with virtual particles if they can reveal position and momentum without disturbing. However I propose that this principle being transversal on every scale of nature, should be better called: principle of uncertainty of becoming Endrit Vuka from Bologna

[@neuralbrew2976]

The speed of an electron affects the kinetic energy of such electron. So when we say an electron is in a superposition of hi and low speeds, does this also mean the kinetic energy is in a superposition as well? Suppose we use a fixed amount of energy to accelerate an electron, then we measure the momentum to be really high, does this mean energy was magically added and we are violating conservation of energy? Or are we always uncertain about how much energy we added to the electron by accelerating it? Energy obeys Heisenberg as well I would assume?

[@Salara2130]

Can we colapse the momentum after measuring the position with an error by a second measurement and thus keep switching in states?

[@TristanLaguz]

3:45 Yep, according to BM, ðelectron *is* at one position, and ðe UP is due to our *ignorance* about precisely where it is.

[@vadim32]

Uncertainty is the most uncertain concept in physics. What is a principle, is it an axiom or theorem. In math, there are no principles, only theorems or axioms. What is a Δ, as math object? Is it an operator, is it a functional or something else? Mathematics is the language of physics. But the uncertainty relation is not expressed in the language of math. It's just an artistic pseudo-graphic that doesn't express mathematical relations, but conveys the feeling of experimental data. Try to calculate the value of Δ(sin(x)/x) and you will understand what I am talking about. Uncertainty and ambiguity are vague and incomplete mathematical concepts. They are similar to variance, but they are not variance.

[@drdca8263]

For a given operator A, the value of \Delta A in a state \omega is defined as \sqrt{\omega((A-\omega(A))^2)} .

[@NyteRazor]

9:27 Hope you update us whenever there's an explanation why there's a collapse when measuring an electron's state.

[@LookingGlassUniverse]

I was thinking about doing a video on my favourite theory: decoherence

[@sebastiandierks7919]

@@LookingGlassUniverse Decoherence only explains how to go from a superposition of base states (so-called pure state, what you've exclusively talked about so far in this series), described by a single wave function that is capable to interfere with itself, to a mixed state, i.e. a probabilitic mix of base states, where the classical probabilities quantify our ignorance (analogous to the use of probabilities in statistical mechanics). Decoherence can not explain how to then go from the mixed state to a pure base state that is observed in a measurement. pure superposition state -----decoherence----> mixed state ------measurement collapse------> pure base state (corresponding to the measurement result) How, why (and even if, according to the Many-Worlds interpretation) the wave function collapses is currently not understood, it is just a law of nature and a postulate in the standard (Copenhagen) description of quantum mechanics. If you'd find out what exactly a measurement is (amongst the set of all interactions) and how the collapses happens, you would solve one of the biggest mysteries in the foundations of physics and be guaranteed a Nobel prize. All that said, I would still love a video on decoherence (just not as a means to explain wave function collapse).

[@viinikellari]

A noob question: If the h-bar symbol would represent a much smaller number than planck's constant, wouldn't we have better results, as in, better accuracy, better resolution? Why do we have to limit ourselves like that? Is it because of the supposed "speed limit", that is the speed of light? FTL events might be true because of the entanglement.. so yeah. Speed of light is not the speed limit. It just might be the veil separating this phase of existence from the other parallel processes happening right now, here. We are in the big bang still. Nothing begins or ends. Everything is. The past is future right now (with infinite accuracy, so they kinda mix up). We just experience the passing of events like this. The only uncertainty is in our minds, methods and measurements. To say the existence itself has functions like "nothingness" or "uncertainty" requires proving an effect without a cause - or the breakdown of causality. Our methods and measurements - let alone comprehension - is not absolute, so lets not pretend our scientific extremes and limits are actually true or absolute. I'm saying this just in general. Nothing personal here! : ) We will never proceed in science if we treat it like the religious people treat the bible. More noob pondering: Quantifying is a must if we want to calculate anything at all, but is existence really quantized - as in - consisting of truly discrete objects? We should not reflect our methods and human limitations on what *the existence really is(nor should ignore if our limitations do represent the reality*) The more I read about the limitations in physics, the problems we have seem to be based on human limitations being reflected on what the reality is supposed to be. Reflecting our limitations of intuition and measurements on the existence as it is/reality - is a very unscientific approach. For example: Just because we can't observe or measure beyond a certain point, doesn't mean there is nothing beyond it. This been said, we can't say the universe begun so and so long time ago - or that space and time had a beginning. Absolute rubbish! : ) I'm serious. It is just a claim based on our inaccuracy. Almost a religious faith on measurements! That's just wrong. Anyhow! Great content you have here LGU!

[@Achrononmaster]

Wonderful exposition by the way, it invited a lot of thought.

[@ommision2850]

Nice vid! Though, I don't understand the difference between the measurement-disturbance relationship and the Heisenberg uncertainty principle. Isn't it just an interpretation of the HUP that is a little closer to the measurement? Isn't all the information you'd get out of this equation identical to the HUP? So what's new?

[@jitteryjet7525]

What I don't understand is how the Uncertainty Principle does not come into conflict with the conservation of energy? If the energy value is in a superposition and can take a range of values, how can it be conserved in an interaction?

[@LookingGlassUniverse]

It’s such a great question. I’ve been trying to understand this myself and I still don’t

[@memeoshorts]

Uncertainty Describes Measurement, Not System Evolution. The uncertainty principle applies to the simultaneous measurability of two observables. It limits what we can know about a system, not the actual values of physical quantities in the system. Conservation laws govern the actual evolution and total quantities within the system, independent of measurement. Quantum Systems Still Obey Conservation Laws, the uncertainty principle introduces probabilistic outcomes for individual measurements, the statistical averages (expectation values) of conserved quantities still obey conservation laws.

[@jitteryjet7525]

@@memeoshorts An answer copied from the Internet?

[@memeoshorts]

This is pretty basic let me reframe this. This is probably somewhere on the internet has to be. I happen to have a lot of basic knowledge on physics and this is really basic regarding specifics versus general. Just because you flip a coin 10 times and you get 8 times heads doesn't change the probabilities long-term. The uncertainty principle and the conservation laws don’t clash because they deal with totally different things. The uncertainty principle is all about what we can or can't measure precisely at the same time-like position and momentum. It says there’s a limit to how much we can know about both at once, but it doesn’t mess with the actual rules governing how stuff behaves. Conservation laws. conservation laws-are hard rules of the universe. no matter what, the total energy, momentum, or other conserved quantities in a system always add up the same before and after. We can’t perfectly measure a particle position and momentum at the same time, uncertainty principle total momentum of all the particles in the system still balances out. The system itself isn’t uncertain-just our ability to nail down every detail. If you’re juggling and someone takes a blurry video, the video might not show exactly where every ball is at every moment. But the total number of balls in the air doesn’t change just because the video’s blurry. The conservation laws are like the number of balls-it’s a big-picture rule that doesn’t care about the uncertainty in the details. uncertainty principle tells us what we can know about measurements, while conservation laws are about what actually happens. They work together because they’re looking at the situation from totally different angles.

[@hitoshiyamauchi]

I had the idea of the first type of mistake. I forget where I got there. Thanks for the video! 😀

[@ozachar]

Good distinction. I would restate your correct drawings with a bit more rigor: the eigenstates (energy states) of electrons in extended space are plane waves of infinite extension. If an electron is in any relatively localized state (say gaussian), then this state is a wave packet superposition of multiple plane waves. That state is simultaneously a corresponding wave packet superposition in momentum. The correspondence, dictated by Fourier relations, is dictated by the Heisenberg "uncertainty" relations. For the special case of Gaussian packets, it is an equality.

[@olivergroning6421]

Actually the term Heisenberg ‘uncertainty principle’ is unfortunate and ‘indeterminacy principle’ would be much better. If for example a particles position is fully determined, it is not that its momentum is unknown (or uncertain), but the particle is in a superposition state of all momenta. For those familiar with Fourier Transforms this is easy to see. An other example is spin, a particle with Spin-up in the z-direction, is in a superposition state of spin left and spin right in the x-axis. Its Sx spin is not determined it is right and left ‘at the same time’.

[@duncanmountford8426]

The Copenhagen (epistemological) interpretation does capture most of the quantum weirdness. I’d like to be able to say that the wave function is purely epistemological (so not physical) but there just has to be something ontological about it too. The Copenhagen interpretation cannot be the complete story but it’s a reasonable start.

[@duncanmountford8426]

Cont. In my thinking, the wave function is real but not physical. Is that crazy? Of course.

[@schitlipz]

I never asked this question of anybody before, but what "of" the electron is in the probability field... its mass or charge, or both. Mass seems implied by momentum, but I'm confused. Sorry, dumb question.

[@lonestarr1490]

As far as I understand it, the mass of the electron is fixed (within a given frame of reference), as its invariant mass is one of the fundamental constants of physics. Hence, the thing actually spread out is really its velocity.

[@erikziak1249]

@@lonestarr1490 I would ignore any "mass" and think only in terms of "energy". Energy and time. But I need a vector, yes...

[@cademosley4886]

Wigner came up with a representation theory of particles where a particle is a bundle or representation of quantum properties: position, spin, mass, charge, etc. Those properties are collectively called the Poincaré group, which basically come from the symmetries of movements (boosts, translations, and rotations) in special relativity spacetime. So in that framework, the package or representation of those properties is what the probability distribution is distributing. I don't know if that helps so much as level-up our confusion to a higher level, but that's still a kind of progress. XD

[@deal2live]

Have covered quantum computing? Superposition, entanglement And the multiverse?

[@scottharrison812]

I used to think I understood the Heisenberg Uncertainty Principle; now I’m uncertain.

[@colinwright5157]

The reason I chose the radius has a lot to do with quantum physics if an electron is fired toward two slits of width 2*wavelength then uncertainty is to be found into how accurate the experimentalist made the size of the slits.Since pi is involved in determining the size of the slit then the experimentalist finds that the results are in accordance with his/her expectations then what does that say about nature? To me it says that nature either knows how many significant figures he/her chose or that nature adjusts the experiment to fit the experimentalist' expectations. Which is the correct interpretation?

[@ppmealing]

Excellent exposition, and I learned something new.