I'm closing the sign ups for the live course this Tuesday! If you're interested in doing this course more intensively over 4-6 weeks with a cohort and live tutorials etc, here's some more information about that: looking-glass-universe.teachable.com/p/quantum-mechanics-fundamentals Either way though, thanks for your support! I've missed teaching a lot, and it's been very fun making this course. I've planned about 10 videos for this series, which will all be here, free on youtube.
If Physicists describe electrons as point particles with no volume, where is the mass of the particle? Can one extra spatial dimension produce a geometric explanation of the 1/2 spin of electrons? The following is an extension of the old Kaluza-Klein theory. Can a twisted 3D 4D soliton containing one extra spatial dimension help solve some of the current problems in Particle Physics? What do the Twistors of Roger Penrose and the Geometric Unity of Eric Weinstein and the exploration of one extra spatial dimension by Lisa Randall and the "Belt Trick" of Paul Dirac have in common? Is the following idea a “Quantized” model related to the “Vortex Theory” proposed by Maxwell and others during the 19th century? Has the concept of the “Aether” been resurrected from the dead and relabeled as the “Higgs Field”? In Spinors it takes two complete turns to get down the "rabbit hole" (Alpha Funnel 3D--->4D) to produce one twist cycle (1 Quantum unit). Can both Matter and Energy be described as "Quanta" of Spatial Curvature? (A string is revealed to be a twisted cord when viewed up close.) Mass= 1/Length, with each twist cycle of the 4D Hypertube proportional to Planck’s Constant. In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137. 1= Hypertubule diameter at 4D interface 137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted. The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.) If quarks have not been isolated and gluons have not been isolated, how do we know they are not parts of the same thing? The tentacles of an octopus and the body of an octopus are parts of the same creature. Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. The "Color Force" is a consequence of the XYZ orientation entanglement of the twisted tubules. The two twisted tubule entanglement of Mesons is not stable and unwinds. It takes the entanglement of three twisted tubules to produce the stable proton.
Congrats, you are my first edutainment creator to give me an "aha!" moment that utilizes the linear algebra that I took last semester in an applied way that I hadn't seen (or at least understood) previously. I'm a little behind your level 😅, but this is really clearly explained, so thank you!
Just watched the science asylum video! Excited to see your perspective on spin. Also, great background, looks like you're trapped in an emerald cave which as we all know nurtures physics
I'm about 3/4 of the way through this video and I have to say, you are amazing at explaining things. Your explanations are done in a way that I have not found anywhere else - meaning they provide the most fundamental understanding of these concepts. There are 10's of thousands of video's where the presenter is just storming through the content. But you seem to have taken the time and care to remember what it would be like to not know any of this. I am familiar with most of this, but they way you explain it fills in a bunch of holes when it comes to really understanding it at the most fundamental level which, for me, is what makes it stick. Thank you for all you do with this excellent channel.
10:50, My understanding is that the idea that electrons are point particles comes from the fact that they don't have any size when we try to measure it. We can apparently get arbitrarily close to them.
PBS spacetime just did a fantastic video on what happens as we get closer to the electron, what it "looks like," and addresses different ways to conceptualize the electron's size--and there is no actual difinitive answer about its size (or its non-size). I believe electrons are often referred to as point-like because that's how they are modeled in the math, since we don't really have a lot we can say about their size.
When I was in high school, I had to read the encyclopedia to find out that the magnetic moment had nothing to do with time. That was after consulting the physics teacher, two textbooks, and then still failing an exam. I think 90% of the confusion in physics is just down to the terrible vocabulary.
Absolutely. And not just physics, so many technical fields are laden with words and terms that are *worse* than jargon. Adopted, misappropriated, and outright pilfered words. If you're lucky, there's some esoteric etymological link like momentum/moment etc. but far from the norm.
I was thinking of the dot product as the length of one vector projected onto another, and I think that intuition matched up with the math in your examples.
20:54 I think the interesting point with this schematic is there are actually two up states: |up> where the vector pointing +y and -|up> where the vector is pointing toward -y. The same for the down states |down> and -|down> along the x axis. Another interesting point: there are actually 4 states exactly 45° in between up and down. But that means, whenever you measure up, you don't know if its +up or -up. (isnt this the spin 1/2 thing where you need a 720° rotation to come back to the initial state?)
You have my favorite educational physics channel! My field of study is pure mathematics and network engineering but I always want to know more about pjysics! Thank you!
@@LookingGlassUniverse really enjoyed this video. and for what it's worth it especially piqued my interest when you mentioned that modulus is involved in some quantum equations. I just had my own reflective epiphany about modulus, but it was with regards to cryptography. And sort of, the way I see it in my head, modulus is used there to deliberately discard information. Because if you "take only the remainder" when you divide by a big prime, there are a great many (infinite?) values that would give that remainder and you learn nothing about the slope or shape of the curve. Anyway, then you said modulus and I'm like WHAT! It's a weird thing to think about, but now I'm super curious how else modulus is being used. I only have a faint glimpse in my imagination, but wonder if the modulus is basically creating a scale. That's likely too vague a statement to truly land, but I'll try. It feels so good to watch videos like this from curious humans. Genuinely thank you so much.
If you threw a bar magnet through that machine it most definitely would change its state to be "up" or "down". Same with classical view of light, you could argue it gets twisted into the new alignment.
Except for the fact that if you threw a bar magnet perfectly aligned perpendicular to the apparatus it should experience no force up or down and pass straight through. In the case of an electron you can prepare them with a perfectly perpendicular magnetic field to the apparatus and 50% will still deflect either fully up or down. This makes it different than classical bar magnets.
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Whenever the wave function "collapses" - whenever there's a definite outcome - is when a "measurement" has occurred. It doesn't matter if we know what that outcome was.
This makes some ideas about quantum mechanics seem so clear that I wonder why there's so much confusion in explaining them! Like, the Stern Gerlach experiment simply forces the electrons to align with the magnetic field one way or another, like wooden dowels falling through a funnel with a vertical slit. I imagine that metaphor ignores the concept of superposition, but it seems like a really straightforward way to describe how measurement affects outcome, which is an explanation that so much quantum mechanics talk seems to struggle getting across.
Thank you for these videos. To summarize what I learned, light can be polarized up-down or left-right and these two polarizations are orthogonal. However, electrons are different because they can be polarized either up or down, and in the case of electrons these two polarizations are orthogonal. So I guess this has to do with electrons being spin 1/2 whereas photons are spin 1 (or so I have heard). Or am I confused?
Hi Mithuna sister..I'm also from tamilnadu, India ... thank you very much for making video on quantum spin...... Already i watched a lot of videos about this topic but I didn't understand it properly ..
Fantastic course! Thank you very much! I just have 2 questions: 1. Why it is called measurement collapse? This sounds as if there is no superposition anymore. But as I understand, after the measurement it simply is in another state or would it be better to say state of superposition? 2. In your summary the outcome of the measurement collapse is UP whereas in the video the outcome is RIGHT? Of course in the summary it does not matter but that way it would be better aligned with what you explained. Besides of that I am impressed how you explain things and even include the mathematics along the way. Cannot wait for the forthcoming videos!
The thing is, you can build models that replicate the behavior of electrons that depends on the angular momentum they carry, as little spinning balls, or as fields that hold angular momentum in a certain pattern or whatever else. There are plenty of ways to reproduce stern Gerlach that exists. Which physical picture is correct is hard to disentangle form wavefunction descriptions because wavefunctions play the part of dynamics and a sum over possible worlds as you would in classical statistical mechanics, but at the same time, so to get a clear physical picture of what is happening you have to take all the dynamics in there and hand it over to all the individual separable possible worlds so to speak. Then you can talk in this deterministic language that humans are prone to, but this amounts to a functioning hidden variables theory with no reference to the dynamics that makes use of the wavefunction directly. Think about what pilot wave theory is, it is just the simplest possible version of this, you take the wavefunction and a guiding equation, which is just servingnis dynamical laws for individual initial conditions, and you get a clear physical picture in space and time. Now do that without using a wavefunction.
5:04 I don’t recall how electrons that are “shot” into the Stern-Gerlach machine are “prepared”. Why do they expect that the electrons are “randomly” aligned? In the interpretation, how do we know that electrons with spin that’s neither up nor down are just “blocked” by the specific Stern-Gerlach device? I’m sure that some other video I’ve seen or some article online that I’ve read includes an attempted explanation, but I don’t recall it. Anyway, you then compared this scenario with polarization, and as I understand it, in the theory of polarization, lenses polarized a certain way DO block the photons that are polarized in certain directions, so that one can even make a clear glass appear opaque when the only light incident in the glass is polarized in a way that’s not permitted by the polarization preference of the material.
Thanks for the video! I always find it so interesting. I watched so many youtube videos on QM that I think I've exhausted what I can learn without picking up a text book hah. My biggest takeway from the video is how a linear combination of a basis can represent any state. I'm thinking not just orthogonal basis? Is this still true when you add complex numbers? I'm always left with many questions, but what's been on my mind lately and I wanted to understand better is measurement independence, and how would an experiment rule it out without throwing away local causality.
Yes, any basis of a vector space can be used to express any vector of that vector space, and so in particular can represent any state vector. However, orthogonal bases will be more physically relevant, because for any observable operator, the states associated with different measurement outcomes will be orthogonal. “Is the particle spin up or spin down?” and “is the particle spin left or spin right?” are each questions where there is a corresponding observable. But, “Is the particle spin up or spin left?” is not. This is because… well, the self-adjoint projections onto “the particle is spin up” and “the particle is spin left” don’t commute with each-other, and, any operator which had “spin up” and “spin left” as its two eigenstates, would not be self-adjoint? And… well, ok, I guess technically not all observables have to be self-adjoint, only “normal”? (The self-adjoint and anti-self-adjoint components have to commute) but I’m pretty sure that such an operator wouldn’t be “normal”? (I should double check this..) Well, conceptually, it shouldn’t be so surprising that “is it up or left” isn’t an observable, because like, those aren’t complementary options?
8:34 : I saw in a different video , if I’m remembering the video correctly, that when the Stern-Gerlach experiment was originally done, with silver atoms iirc, that the two experimenters *were* expecting it to split into two parts (though theirs was a minority view, which most people predicted otherwise), but that they predicted this for different reasons, thinking that the orbital angular momentum would cause it, and, that the size of the effect matched their predictions because two quantities they didn’t know about approximately canceled out? (One being the electron magnetic moment and the other being… Idr what)
And when you do the complex version, the two vectors representing the spin left preparation for an up or down measurement, is just the same complex number, just positive and negative versions. You did that just with components in a real vector space. The complex vector is equivalent, the arithmetic is just simpler. ^^
Regarding what you said about electrons being point particles in 10:29, the reason some people say that is because, in principle, one could collapse its wave function (through an observation, a measurement or whatever) with infinite precision, both in space and time: that is, localize the electron to a precise point at a given instant, so that its probability distribution in space becomes a Dirac delta. Of course, in practice, that is completely impossible. We are very far from probing very small distances, let alone a single point in space (one might say: we'll always be infinitely far from that). And that's not even considering the fact that it means pushing quantum physics to its theoretical limits: a string theorist would tell you that particles are strings, not points; someone who likes loop quantum gravity would tell you that a distance smaller than the Planck length doesn't exist; etc. I tend to believe that an electron really does spin. I don't think elementary particles are points; I think they are just much smaller than we've been able to capture so far. I also don't buy the argument that they'd need to spin faster than the speed of light to have the observed angular momentums: that argument doesn't take into account relativistic effects in the math, and simply uses the equations of classical mechanics. It's just bad physics.
13:32 If the electrons all were “spin up”, aren’t they entire NEITHER “spin up” NOR “spin down”? In that case, why aren’t they all blocked, so that the third Stern-Gerlach machine (measuring “up/down spin” only) “sees” no electrons at all?
An electron could be a "ball" spinning. The ball just isn't rigid. It does not have a fixed diameter. But it does not have to have a fixed diameter. To produce the spin of an electron you can have lots or radii. In the case of an atoms angular momentum the radius has to fixed (i.e. there's a most likely distance from the core) due to the coulomb attraction. But in an electron you don't have such an attraction and there's no mathematical prefered radius that could produce that spin, if i' not mistaken. There are just so many reasons to think that there's something spinning, that i don't find it plausible to think that nothing is spinning. Maybe we just don't understand what is spinning. Feynman had interesting information about this in his lectures, in which he looks at the electron and it's magnetic and electric field and works out that there must be an angular momentum present due to that (poynthing vector goes in a circle). But if i remember correclty this doesn't give us the correct spin either. It doesn't refute it either, i think. I think we just don't know what's is rotating since there are several things that could in principle explain the intrinsic angular momentum. I forgot precession. That's also a thing that electrons apparently do. I just find it a lot weirder to say that there's nothing spinning then to say there's something spinning.
Lets also not forget that the math (matrices) look like that of orbital angular momentum when you figure out how to deal with the Stern-Gerlach results. For example if you tried to figure out what would happen with particles with an orbital angular momentum of one, two or three, when they go through one or several Stern-Gerlach machines, then you can use the same math to figure out how spin 1/2 particles would behave. PS: I forgot to mention that spin is actual angular momentum. The Einstein-de-Hass-effect shows this.
In the last "experiment" what happens if you don't throw away half of the electrons from the "right measurment". Looking forward to an explination of that!
I dont know if it quite comes under quantum mechanics but it would be super helpful if you made a short video on the Photoelectric Effect (especially stopping potential) :)
what happens if/as we shorten the length of those stern-gerlach magnet bars ? basically if/as we shorten the interaction time between the electron and the field ?
I never understood, and I never heard explained why, the results of the Stern-Gerlach experiment would not imply that 50% of electrons (or more correctly all electrons 50% of the time) have “north” side of their spin concentrated and the “South Pole” defused, and 50 % of the them the opposite. And It intuitively seems obvious that if the electrons magnetic fields were equal defused at either pole of their axis they would always flip during their travel so the binary output would always occur but not 50:50 but simply depending on how close they were to what magnet when they first entered the apparatus.
What happens is the changing magnetic field causes the electrons to align their magnetic moments to the field. The electrons have an even distribution of all the spin angles between up and down (and left and right, as well as forward and backwards) before entering the apparatus.
@@dennisestenson7820 yes, yes we know that. This is what we have been told for multiple decades… What I cannot understand for the life of me is why that explanation (and the minor variations of it) is the only explanation that is embraced… This _model_ assumes nothing and offers nothing of the true nature of the most ubiquitous particle we experience every moment of our lives, yet because of this mathematical model we stop imagining any other possibility understandings of it’s reality. To me it is not just myopic it’s _retarded!_ ( I mean that in the most clinical definition of the word, It retards progress.) Here I hint at only one alternative possibility, encouraging those not content with simple math to imagine instead the created and natural realities of spin that this experiment could be manifesting.
The point particle thing doesn't come from anywhere. Just a position or trajectories. The trajectories of anything is like the trajectories of a pointnparticle. If you don't talk about the extent of the thing. I think the mist mature way to view electrons however is a sort of source or focus of the fields associated with it, the electrin field, photon or light field, which are basically both electromagnetic fields in a sense. And there is absolutely does have an extent. It extends to infinity in a sense. I prefer to think of the center of it as more of a focus of this big thing extended in space. That way, the spin is more so a property of a field, not a little ball bearing. Ultimately, quantum field theory doesn't have a simple and good representation of what goes on in spacetime associated with it. But it is reasonable enough to imagine the spin being held by space in a a sense bith at the location where the source if the field is in terma of the gradient and also around it, that way nothing ever has to go faster than light or any of that nonsense they used to worry about. If you think it has ti be a little charged ball, then ofc that is an issue, but that is kind of nonsense, taking the size to 0 then is just saying nothing rotates infinitely fast instead lol. But spin isn't really that either in qft it is rotating in a separate space, more akin to a field that can hold angular momentum. But this is all handwavy intuition massaging, because the physical picture we are trying to establish by saying things like this doesn't really exist in qft anyway. That doesn't mean there isn't one in potential successor theories, but itnisnwhat it is ^^
17:00 - I think I don't understand something here, is this result is surprising? The first filter "aligns" the particles to a 90-deg axis (spin-up-down/vertical), blocking them at the 0-deg filter (spin-left-right/horizontal). But if they first pass a 45-deg filter, they "realign" to 45-deg, giving them a 50/50 chance at the 0-deg filter. Why is this considered a quantum effect? Why is this at odds with classical mechanics? I know i'm misunderstanding something I just don't know what
Because in classical mechanics there isn't measurement collapse, so there wouldn't be any realignment. In classical mechanics, the fact that the light got through a filter or didn't has no effect on the light afterwards. The quantum effect is the light being "changed" by having passed through the filter, in a way that affects its ability to pass through the next one.
How to know positron or electron? Or i'ts negative or positive charged. In any observed is we think particle buts its not particle but bunch of strings or we didnot observed its rays or strings or wave. So do not confused to all as particle or elementry??? Its only vidrating strings in universaly or spining is banding or spining bunch of stirgs so we can observed. Now we observed is pattern or design of virating rays so we can percept or observed it.
There is the problem in physics defining the type of realness coherant paticles exist in. To get to this we need to understand what appearance and its relationship to what exists. The electron is charge -1. when it is detected we can only detect a unitary charge no matter how finely distributed the elements in the detector. Thus the electron is detected as an apparent point particle. A better what to say this is as an electron is undergoing decoherance it can only be detected at a single point, and so now we are in the resolution problem of quantum mechanics. But before the electron is detected its properties are distributed in spacetime (another quantum problem) its wave like properties are the result of uncertainty in its position, which theoretically is distibuted over the universe, but its observables probably follow the path of least action. Let's consider spacetime as a quantum field whose elements evolve at close to c, a wave propogating in this field cannot really exceed the dynamic evolution of the field, while it is possible, just as its possible to break the sound barrier, it requires more action. Thus actions in spacetime that exceed c are going to be very improbable. The second limit to action is momentum, momentum is conserved, so things that cause multiple changes in momentum in a path of travel require more action and are thus less probable. So in the coherant travel the electron exists in "imaginary" spacetime where many things are possible, but the actual detected state is going to be along a path that has minimized action. Getting back to the original premise, that spacetime has some level of finescale field variation due to its quantum nature, then we catch a sense of the unrealness of coherant particles, for in order for the particle to assume that path of least action it needs to be in multiple places at once, in otherwords its wavelike properties. Lets imagine it like this. A pilot takes off from an airport, he is traveling to another airport. When he takes off the weather is clear. But as he is in flight turbulance and storm cells form, so much so that he can no longer see a path to his destination. The pilot makes course changes along the path to avoid the storms and he lands at an airport close to his destination . The pilot, when he takes off, cannot know which path will result in the fewest course changes. When he reaches an acceptable airport, not his choice, his path was determined by local events which guided his choices. But in the electrons case there are no local hidden variables that are 'evident'. In order for it to take the least action its status needs to be distributed in spacetime while it remains coherant. This is the unreal nature of physics. And so now we get to the problem of the atom. if the charge on an atom was a point particle, we have the potentiallity that the electron is in the nucleus (coupled), In the case of a hydrogen atom this might cause a Neutron to form, the spin on the electron couples the electron to its orbit, but there is a slight probability the electon is in the nucleus. But if we think about the electron in its wave like properties, the density of the properties of an electron in the nucleus are exceedingly low. Another much better example is a relatively small (1mm) sheet of graphene. Because of the nature if arrangement of the P orbitals electrons are free to pair in molecular orbitals of lowest energy that cover the entire sheet. As a consequence the density of the wavelike properties of the electron are distributed on the sheet. If I put an electron on one corner, it is immediately available on the opposite corner, making very small sections of graphene superconducting at low amperage and short lengths. But where is the electron in the sheet orbital? Since many of these orbitals of lower energy can be built the electron exists in a state of flux, sometimes over the entire sheet and sometimes over a single carbon.
16:59 "this result can only be explained by measurement collapse... SO far! I am actively working on an alternative explanation that looks very promising.
Spin is actually the phenomenon of repolarization of quantum waves. When working with photons, a polarizer forces the photons to choose probabilistically between two polarization angles that are orthogonal, one that allows the photon to pass and one that blocks it. The probability that the photon passes is determined by the square of the cosine of the angle between the polarization orientation of the photon with respect to the main orientation of the polarizer. The probability that the photon is rejected is determined by the square of the sine function of the same angle. Therefore, both the cosine function and the sine function are required in the range from 0 to 2*Pi. In the case of fermions, a Stern-Gerlach device forces the fermions to choose probabilistically between two polarizations, one with the north pole up and one with the north pole down. The probability that the north pole is forced upwards is determined by the square of the sine of half the angle between the original magnetic orientation of the fermion and the orientation of the magnetic field of the Stern-Gerlach device. The probability that the north pole is forced downwards is determined by the square of the cosine of half the same angle. Therefore both the cosine and sine functions are required but only in the interval from 0 to Pi, which is mapped to the entire interval from 0 to 2*Pi, since it is calculated for half the angle. This means that Spin is the probabilistic property of repolarization, Spin 1 means that the entire interval of the probabilistic function between 0 and 2*Pi is used, while Spin 1/2 means that only half of the probabilistic function is used i.e. the interval from 0 to Pi (although mapped to the entire interval from 0 to 2*Pi). Spin 1/2 expresses the reorientation behavior of quantum magnetic dipoles under an external magnetic field, while Spin 1 expresses the reorientation behavior of a quantum alternating dipole, both in its transmission through a polarizing material (external electric-magnetic field) and in its reflection. Spin is not the source of the magnetic moment of quantum waves, but rather Spin is the result of the probabilistic interaction between the magnetic moment of quantum waves and external magnetic and/or electric fields. There is no other phenomenon that produces a magnetic dipole other than the rotation of electric charges around an axis, so it is obvious that the magnetic moment of a quantum wave is the result of its rotation, but it is not the Spin, Spin is a reorientation rotation from an original direction to a direction imposed by a device, Spin is repolarization.
If you perform the “up or down?” measurement when the particle is prepared in the “15 degrees away from up, along the axis of travel” direction, then (cos((15/2) degrees))^2 of the time, the answer will be “up”, and (sine((15/2) degrees))^2 of the time the answer will be “down”. (And similarly if you prepare it in “up” and measure “Is it 15 degrees from up or 15 degrees from down?”.) (Why are the sine and cosine applied to “(15/2) degrees” and not “15 degrees”? For the same reason that “|up>” and “|down>” are perpendicular to each-other rather than negations of each-other. There’s a kind of angle-doubling going on. It relates to how complex “rotations”(sorta) of a vector space of two complex dimensions, has a “double cover” of ordinary rotations in 3D space.)
If the electron cloud is spread out more but spins slower, shouldn't it produce exactly the same spin (magnetic field) as a smaller cloud that spins faster. Wouldn't that mean that spin still could be caused by angular momentum, but the actual angular momentum changes relative to spread. Does this make any sense to anyone, or am I taking nonsense?
- My understanding is that there is no concept of "distance" in the quantum regime. - Mass, momentum, etc. are not physical properties in quantum, unlike classical mechanics. Instead, they are hold-over nomenclature that describe the units that balance the equations, not "physical" classical mechanics properties. There is no "physical" in quantum physics. - I prefer to think of electrons as an oscillating "standing wave" that is restrained by the charge of the nucleus. - Physical phenomena, like grating slits, that interact with quantum properties, are difficult or impossible to mentally unite given these realities.
Can you please explain why can't we imagine that electrons align their "axis of rotation" with magnetic field? Like magnets but just aligning axis not "poles"? Then given that they have random orientation half of them will align up, half down. In a second machine they gona align their axis left to right and due to some imperfections in first alignment, like residual moment from first alignment or because they didn't settle yet, half of them end up right and half left. And exactly the same process in third up-down machine. For me, not a physicist, looks like there is nothing quantum in this explanation. Why it is wrong?
I can imagine something similar and mechanical for light passing thru polarisation filter, weirdly interacting with those long chain molecules and getting aligned or absorbed depending on orientation and some chaotic property like exact spot where it hits that molecule.
Finally, a video on a nice, simple subject, that anyone can understand, instead of the incomprehensible computer stuff. And it's heartbreaking how sad your electrons always are.
I asked my physics teacher in middle school, about the friend's question. Assume a spinning arm, where in the middle of its length is a c-speed. what speed will be at the end of it then
Do you think electro is 2D exist in 3D space. Cause I think as human being ofcourse we have imagination bias, which means we already give a shape to existence particle without confirming what shape it is, and in the process, we manifest natural properties and behaviors of that particles based on bias shape we have assigned to it. If that makes sense. Anyone can restate with proper English setup of my sentence if anyone understands what I am trying to say. Thank you.
"The probability of getting up is 1/sqrt(2) squared." I usually find the probability of getting up too early in the morning is considerably lower than that.
Why the emphasis on taking the absolute value before squaring? Can the coefficients have imaginary parts? Taking the absolute value is unnecessary before squaring any real number.
superposition is understood as 'an electron' being in multiple different states simultaneously (magically) and on measurement 'the electron' collapses to a single state. not true. single electron is in a single state whereas different electrons have different states and all these different states are the superposition of electron states. now on passing them through a measurement process influences their states to align to the axis of measurement
The electrons/photons end up in a direction compatible with the polarizer.. that is +-45 degrees. Only 90 degree that only allows it's own +-45 degrees don't ovlap any of the first results.... But then at that polarizer that's at 45 and does. 1/2 result against now the photon is in any of the +- 45 degrees compatible with that orientation. You make it a lot more confusing saying it's now only 'up' oriented... I bet you even confuse yourself
I'm closing the sign ups for the live course this Tuesday! If you're interested in doing this course more intensively over 4-6 weeks with a cohort and live tutorials etc, here's some more information about that: looking-glass-universe.teachable.com/p/quantum-mechanics-fundamentals
Either way though, thanks for your support! I've missed teaching a lot, and it's been very fun making this course. I've planned about 10 videos for this series, which will all be here, free on youtube.
MAKE A PLAY LIST OF THESE COURSE..❤😊
CAN U MAKE A VIDEO ABOUT ZERO POINT ENERGY THE MOST MISUNDERSTOOD CONCEPT...❤
If Physicists describe electrons as point particles with no volume, where is the mass of the particle?
Can one extra spatial dimension produce a geometric explanation of the 1/2 spin of electrons? The following is an extension of the old Kaluza-Klein theory. Can a twisted 3D 4D soliton containing one extra spatial dimension help solve some of the current problems in Particle Physics?
What do the Twistors of Roger Penrose and the Geometric Unity of Eric Weinstein and the exploration of one extra spatial dimension by Lisa Randall and the "Belt Trick" of Paul Dirac have in common? Is the following idea a “Quantized” model related to the “Vortex Theory” proposed by Maxwell and others during the 19th century? Has the concept of the “Aether” been resurrected from the dead and relabeled as the “Higgs Field”?
In Spinors it takes two complete turns to get down the "rabbit hole" (Alpha Funnel 3D--->4D) to produce one twist cycle (1 Quantum unit).
Can both Matter and Energy be described as "Quanta" of Spatial Curvature? (A string is revealed to be a twisted cord when viewed up close.) Mass= 1/Length, with each twist cycle of the 4D Hypertube proportional to Planck’s Constant.
In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
If quarks have not been isolated and gluons have not been isolated, how do we know they are not parts of the same thing? The tentacles of an octopus and the body of an octopus are parts of the same creature.
Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. The "Color Force" is a consequence of the XYZ orientation entanglement of the twisted tubules. The two twisted tubule entanglement of Mesons is not stable and unwinds. It takes the entanglement of three twisted tubules to produce the stable proton.
There is no electron!!!
Fantastic! I like the way you explain things. You are a very creative teacher and it feels like following a science thriller!
The mighty return of the quantum videos! Amazing!
As an amateur physicist, this is the best Stern-Gerlach explanation I've seen yet!! And now the maths for it feels in-reach! Thank you!!
Congrats, you are my first edutainment creator to give me an "aha!" moment that utilizes the linear algebra that I took last semester in an applied way that I hadn't seen (or at least understood) previously. I'm a little behind your level 😅, but this is really clearly explained, so thank you!
Just watched the science asylum video! Excited to see your perspective on spin. Also, great background, looks like you're trapped in an emerald cave which as we all know nurtures physics
I'm about 3/4 of the way through this video and I have to say, you are amazing at explaining things. Your explanations are done in a way that I have not found anywhere else - meaning they provide the most fundamental understanding of these concepts. There are 10's of thousands of video's where the presenter is just storming through the content. But you seem to have taken the time and care to remember what it would be like to not know any of this. I am familiar with most of this, but they way you explain it fills in a bunch of holes when it comes to really understanding it at the most fundamental level which, for me, is what makes it stick. Thank you for all you do with this excellent channel.
This is the best explanation for the Stern-Gerlach experiment I've ever heard. Thanks for the video. 😀
Thank you so much!!
10:50, My understanding is that the idea that electrons are point particles comes from the fact that they don't have any size when we try to measure it. We can apparently get arbitrarily close to them.
PBS spacetime just did a fantastic video on what happens as we get closer to the electron, what it "looks like," and addresses different ways to conceptualize the electron's size--and there is no actual difinitive answer about its size (or its non-size). I believe electrons are often referred to as point-like because that's how they are modeled in the math, since we don't really have a lot we can say about their size.
This video paired with the last one have been by far the best explanation of this I have engaged with. Very excited for more.
When I was in high school, I had to read the encyclopedia to find out that the magnetic moment had nothing to do with time. That was after consulting the physics teacher, two textbooks, and then still failing an exam. I think 90% of the confusion in physics is just down to the terrible vocabulary.
Absolutely. And not just physics, so many technical fields are laden with words and terms that are *worse* than jargon. Adopted, misappropriated, and outright pilfered words.
If you're lucky, there's some esoteric etymological link like momentum/moment etc. but far from the norm.
I was thinking of the dot product as the length of one vector projected onto another, and I think that intuition matched up with the math in your examples.
Yup, that's exactly right! In this case because the vectors have length one I don't need to worry about the lengths, only the angles
That was clear, understandable and beautifully explained. Thanks very much!
Liked and subscribed. I like finding like minded science communicators. Thank you for what you do. You're good.
20:54 I think the interesting point with this schematic is there are actually two up states: |up> where the vector pointing +y and -|up> where the vector is pointing toward -y. The same for the down states |down> and -|down> along the x axis. Another interesting point: there are actually 4 states exactly 45° in between up and down. But that means, whenever you measure up, you don't know if its +up or -up. (isnt this the spin 1/2 thing where you need a 720° rotation to come back to the initial state?)
You have my favorite educational physics channel! My field of study is pure mathematics and network engineering but I always want to know more about pjysics! Thank you!
Thank you Prof, this was super cool. Keep up the great work!
Really appreciative
Thank you so so much!!
@@LookingGlassUniverse really enjoyed this video. and for what it's worth it especially piqued my interest when you mentioned that modulus is involved in some quantum equations. I just had my own reflective epiphany about modulus, but it was with regards to cryptography. And sort of, the way I see it in my head, modulus is used there to deliberately discard information. Because if you "take only the remainder" when you divide by a big prime, there are a great many (infinite?) values that would give that remainder and you learn nothing about the slope or shape of the curve. Anyway, then you said modulus and I'm like WHAT!
It's a weird thing to think about, but now I'm super curious how else modulus is being used. I only have a faint glimpse in my imagination, but wonder if the modulus is basically creating a scale. That's likely too vague a statement to truly land, but I'll try.
It feels so good to watch videos like this from curious humans. Genuinely thank you so much.
I'm surprised that I'm totally getting this! You are doing an awesome job, thank you!
If you threw a bar magnet through that machine it most definitely would change its state to be "up" or "down". Same with classical view of light, you could argue it gets twisted into the new alignment.
Except for the fact that if you threw a bar magnet perfectly aligned perpendicular to the apparatus it should experience no force up or down and pass straight through.
In the case of an electron you can prepare them with a perfectly perpendicular magnetic field to the apparatus and 50% will still deflect either fully up or down. This makes it different than classical bar magnets.
EXTRAORDINÁRIO!!!!!!!! Muito didático, simples e objetiva.
Levei meus alunos brasileiros para competir em Goodwood no ultimo mes de outubro.
Se tivesse conhecido seu canal antes teria te convidado como Embaixadora STEM do International Finals da Greenpower Edu Trust.
CONGRATS!
TKS!!!
I’m really enjoying what you’re contributing!
Thanks!
Thank you so much ☺️
The math isn't so bad. The most mystifying part is determining what constitutes a "measurement".
Whenever the wave function "collapses" - whenever there's a definite outcome - is when a "measurement" has occurred. It doesn't matter if we know what that outcome was.
Amazing lesson! Really looking forward to the next one!
This makes some ideas about quantum mechanics seem so clear that I wonder why there's so much confusion in explaining them!
Like, the Stern Gerlach experiment simply forces the electrons to align with the magnetic field one way or another, like wooden dowels falling through a funnel with a vertical slit. I imagine that metaphor ignores the concept of superposition, but it seems like a really straightforward way to describe how measurement affects outcome, which is an explanation that so much quantum mechanics talk seems to struggle getting across.
Thank you for these videos. To summarize what I learned, light can be polarized up-down or left-right and these two polarizations are orthogonal. However, electrons are different because they can be polarized either up or down, and in the case of electrons these two polarizations are orthogonal. So I guess this has to do with electrons being spin 1/2 whereas photons are spin 1 (or so I have heard). Or am I confused?
You seem like a nice person. Thank you for your videos!
Hi Mithuna sister..I'm also from tamilnadu, India ... thank you very much for making video on quantum spin...... Already i watched a lot of videos about this topic but I didn't understand it properly ..
Fantastic course! Thank you very much! I just have 2 questions:
1. Why it is called measurement collapse? This sounds as if there is no superposition anymore. But as I understand, after the measurement it simply is in another state or would it be better to say state of superposition?
2. In your summary the outcome of the measurement collapse is UP whereas in the video the outcome is RIGHT? Of course in the summary it does not matter but that way it would be better aligned with what you explained.
Besides of that I am impressed how you explain things and even include the mathematics along the way. Cannot wait for the forthcoming videos!
You have a true talent for teaching❤
The thing is, you can build models that replicate the behavior of electrons that depends on the angular momentum they carry, as little spinning balls, or as fields that hold angular momentum in a certain pattern or whatever else. There are plenty of ways to reproduce stern Gerlach that exists. Which physical picture is correct is hard to disentangle form wavefunction descriptions because wavefunctions play the part of dynamics and a sum over possible worlds as you would in classical statistical mechanics, but at the same time, so to get a clear physical picture of what is happening you have to take all the dynamics in there and hand it over to all the individual separable possible worlds so to speak. Then you can talk in this deterministic language that humans are prone to, but this amounts to a functioning hidden variables theory with no reference to the dynamics that makes use of the wavefunction directly. Think about what pilot wave theory is, it is just the simplest possible version of this, you take the wavefunction and a guiding equation, which is just servingnis dynamical laws for individual initial conditions, and you get a clear physical picture in space and time. Now do that without using a wavefunction.
5:04
I don’t recall how electrons that are “shot” into the Stern-Gerlach machine are “prepared”. Why do they expect that the electrons are “randomly” aligned? In the interpretation, how do we know that electrons with spin that’s neither up nor down are just “blocked” by the specific Stern-Gerlach device? I’m sure that some other video I’ve seen or some article online that I’ve read includes an attempted explanation, but I don’t recall it. Anyway, you then compared this scenario with polarization, and as I understand it, in the theory of polarization, lenses polarized a certain way DO block the photons that are polarized in certain directions, so that one can even make a clear glass appear opaque when the only light incident in the glass is polarized in a way that’s not permitted by the polarization preference of the material.
Can you make a recording with an analogy explaining what parallel processing is in quantum computers?
Thanks for the video! I always find it so interesting. I watched so many youtube videos on QM that I think I've exhausted what I can learn without picking up a text book hah.
My biggest takeway from the video is how a linear combination of a basis can represent any state. I'm thinking not just orthogonal basis? Is this still true when you add complex numbers?
I'm always left with many questions, but what's been on my mind lately and I wanted to understand better is measurement independence, and how would an experiment rule it out without throwing away local causality.
Yes, any basis of a vector space can be used to express any vector of that vector space, and so in particular can represent any state vector. However, orthogonal bases will be more physically relevant, because for any observable operator, the states associated with different measurement outcomes will be orthogonal.
“Is the particle spin up or spin down?” and “is the particle spin left or spin right?” are each questions where there is a corresponding observable. But, “Is the particle spin up or spin left?” is not.
This is because…
well, the self-adjoint projections onto “the particle is spin up” and “the particle is spin left” don’t commute with each-other,
and, any operator which had “spin up” and “spin left” as its two eigenstates, would not be self-adjoint?
And…
well, ok, I guess technically not all observables have to be self-adjoint, only “normal”? (The self-adjoint and anti-self-adjoint components have to commute)
but I’m pretty sure that such an operator wouldn’t be “normal”?
(I should double check this..)
Well, conceptually, it shouldn’t be so surprising that “is it up or left” isn’t an observable, because like, those aren’t complementary options?
8:34 : I saw in a different video , if I’m remembering the video correctly, that when the Stern-Gerlach experiment was originally done, with silver atoms iirc, that the two experimenters *were* expecting it to split into two parts (though theirs was a minority view, which most people predicted otherwise), but that they predicted this for different reasons, thinking that the orbital angular momentum would cause it, and, that the size of the effect matched their predictions because two quantities they didn’t know about approximately canceled out? (One being the electron magnetic moment and the other being… Idr what)
excellent and beautiful lecture. How good and lovely you are.
Thank you, Doctor.and
With luck and more power to you.
hoping for more videos.
And when you do the complex version, the two vectors representing the spin left preparation for an up or down measurement, is just the same complex number, just positive and negative versions. You did that just with components in a real vector space. The complex vector is equivalent, the arithmetic is just simpler. ^^
Regarding what you said about electrons being point particles in 10:29, the reason some people say that is because, in principle, one could collapse its wave function (through an observation, a measurement or whatever) with infinite precision, both in space and time: that is, localize the electron to a precise point at a given instant, so that its probability distribution in space becomes a Dirac delta.
Of course, in practice, that is completely impossible. We are very far from probing very small distances, let alone a single point in space (one might say: we'll always be infinitely far from that). And that's not even considering the fact that it means pushing quantum physics to its theoretical limits: a string theorist would tell you that particles are strings, not points; someone who likes loop quantum gravity would tell you that a distance smaller than the Planck length doesn't exist; etc.
I tend to believe that an electron really does spin. I don't think elementary particles are points; I think they are just much smaller than we've been able to capture so far. I also don't buy the argument that they'd need to spin faster than the speed of light to have the observed angular momentums: that argument doesn't take into account relativistic effects in the math, and simply uses the equations of classical mechanics. It's just bad physics.
13:32
If the electrons all were “spin up”, aren’t they entire NEITHER “spin up” NOR “spin down”? In that case, why aren’t they all blocked, so that the third Stern-Gerlach machine (measuring “up/down spin” only) “sees” no electrons at all?
An electron could be a "ball" spinning. The ball just isn't rigid. It does not have a fixed diameter. But it does not have to have a fixed diameter. To produce the spin of an electron you can have lots or radii. In the case of an atoms angular momentum the radius has to fixed (i.e. there's a most likely distance from the core) due to the coulomb attraction. But in an electron you don't have such an attraction and there's no mathematical prefered radius that could produce that spin, if i' not mistaken.
There are just so many reasons to think that there's something spinning, that i don't find it plausible to think that nothing is spinning. Maybe we just don't understand what is spinning. Feynman had interesting information about this in his lectures, in which he looks at the electron and it's magnetic and electric field and works out that there must be an angular momentum present due to that (poynthing vector goes in a circle). But if i remember correclty this doesn't give us the correct spin either. It doesn't refute it either, i think. I think we just don't know what's is rotating since there are several things that could in principle explain the intrinsic angular momentum.
I forgot precession. That's also a thing that electrons apparently do. I just find it a lot weirder to say that there's nothing spinning then to say there's something spinning.
Lets also not forget that the math (matrices) look like that of orbital angular momentum when you figure out how to deal with the Stern-Gerlach results. For example if you tried to figure out what would happen with particles with an orbital angular momentum of one, two or three, when they go through one or several Stern-Gerlach machines, then you can use the same math to figure out how spin 1/2 particles would behave.
PS: I forgot to mention that spin is actual angular momentum. The Einstein-de-Hass-effect shows this.
Photons would be a kind of prime meridian spin, so the fields around the photon from the outside of the polarity.
In the last "experiment" what happens if you don't throw away half of the electrons from the "right measurment". Looking forward to an explination of that!
Not too sure about the business idea, but thanks for a good video about quantum mechanics
I dont know if it quite comes under quantum mechanics but it would be super helpful if you made a short video on the Photoelectric Effect (especially stopping potential) :)
I made a video about it- it’s in my what is a photon video :)
what happens if/as we shorten the length of those stern-gerlach magnet bars ? basically if/as we shorten the interaction time between the electron and the field ?
This should result in less correlation between the position and the spin, I think.
So, the two spots will be less separate, and may overlap.
I never understood, and I never heard explained why, the results of the Stern-Gerlach experiment would not imply that 50% of electrons (or more correctly all electrons 50% of the time) have “north” side of their spin concentrated and the “South Pole” defused, and 50 % of the them the opposite.
And It intuitively seems obvious that if the electrons magnetic fields were equal defused at either pole of their axis they would always flip during their travel so the binary output would always occur but not 50:50 but simply depending on how close they were to what magnet when they first entered the apparatus.
What happens is the changing magnetic field causes the electrons to align their magnetic moments to the field. The electrons have an even distribution of all the spin angles between up and down (and left and right, as well as forward and backwards) before entering the apparatus.
@@dennisestenson7820 yes, yes we know that. This is what we have been told for multiple decades…
What I cannot understand for the life of me is why that explanation (and the minor variations of it) is the only explanation that is embraced…
This _model_ assumes nothing and offers nothing of the true nature of the most ubiquitous particle we experience every moment of our lives, yet because of this mathematical model we stop imagining any other possibility understandings of it’s reality.
To me it is not just myopic it’s _retarded!_ ( I mean that in the most clinical definition of the word, It retards progress.)
Here I hint at only one alternative possibility, encouraging those not content with simple math to imagine instead the created and natural realities of spin that this experiment could be manifesting.
The point particle thing doesn't come from anywhere. Just a position or trajectories. The trajectories of anything is like the trajectories of a pointnparticle. If you don't talk about the extent of the thing. I think the mist mature way to view electrons however is a sort of source or focus of the fields associated with it, the electrin field, photon or light field, which are basically both electromagnetic fields in a sense. And there is absolutely does have an extent. It extends to infinity in a sense. I prefer to think of the center of it as more of a focus of this big thing extended in space. That way, the spin is more so a property of a field, not a little ball bearing. Ultimately, quantum field theory doesn't have a simple and good representation of what goes on in spacetime associated with it. But it is reasonable enough to imagine the spin being held by space in a a sense bith at the location where the source if the field is in terma of the gradient and also around it, that way nothing ever has to go faster than light or any of that nonsense they used to worry about. If you think it has ti be a little charged ball, then ofc that is an issue, but that is kind of nonsense, taking the size to 0 then is just saying nothing rotates infinitely fast instead lol. But spin isn't really that either in qft it is rotating in a separate space, more akin to a field that can hold angular momentum. But this is all handwavy intuition massaging, because the physical picture we are trying to establish by saying things like this doesn't really exist in qft anyway. That doesn't mean there isn't one in potential successor theories, but itnisnwhat it is ^^
17:00 - I think I don't understand something here, is this result is surprising?
The first filter "aligns" the particles to a 90-deg axis (spin-up-down/vertical),
blocking them at the 0-deg filter (spin-left-right/horizontal).
But if they first pass a 45-deg filter, they "realign" to 45-deg,
giving them a 50/50 chance at the 0-deg filter.
Why is this considered a quantum effect?
Why is this at odds with classical mechanics?
I know i'm misunderstanding something I just don't know what
Thinking of the "filters" and "realign-ers" is a good idea! It certainly makes this result more clear
Because in classical mechanics there isn't measurement collapse, so there wouldn't be any realignment. In classical mechanics, the fact that the light got through a filter or didn't has no effect on the light afterwards. The quantum effect is the light being "changed" by having passed through the filter, in a way that affects its ability to pass through the next one.
@@aaronherman1056, yeah it changed. Its plane of polarization rotated.
Why do people say quantum mechanics is not geometric, when we use geometry to model it? What am I missing?
MAKE A PLAYLIST...❤😊
Done :)
How to know positron or electron? Or i'ts negative or positive charged. In any observed is we think particle buts its not particle but bunch of strings or we didnot observed its rays or strings or wave. So do not confused to all as particle or elementry??? Its only vidrating strings in universaly or spining is banding or spining bunch of stirgs so we can observed. Now we observed is pattern or design of virating rays so we can percept or observed it.
There is the problem in physics defining the type of realness coherant paticles exist in.
To get to this we need to understand what appearance and its relationship to what exists.
The electron is charge -1. when it is detected we can only detect a unitary charge no matter how finely distributed the elements in the detector. Thus the electron is detected as an apparent point particle. A better what to say this is as an electron is undergoing decoherance it can only be detected at a single point, and so now we are in the resolution problem of quantum mechanics.
But before the electron is detected its properties are distributed in spacetime (another quantum problem) its wave like properties are the result of uncertainty in its position, which theoretically is distibuted over the universe, but its observables probably follow the path of least action. Let's consider spacetime as a quantum field whose elements evolve at close to c, a wave propogating in this field cannot really exceed the dynamic evolution of the field, while it is possible, just as its possible to break the sound barrier, it requires more action. Thus actions in spacetime that exceed c are going to be very improbable. The second limit to action is momentum, momentum is conserved, so things that cause multiple changes in momentum in a path of travel require more action and are thus less probable.
So in the coherant travel the electron exists in "imaginary" spacetime where many things are possible, but the actual detected state is going to be along a path that has minimized action. Getting back to the original premise, that spacetime has some level of finescale field variation due to its quantum nature, then we catch a sense of the unrealness of coherant particles, for in order for the particle to assume that path of least action it needs to be in multiple places at once, in otherwords its wavelike properties.
Lets imagine it like this. A pilot takes off from an airport, he is traveling to another airport. When he takes off the weather is clear. But as he is in flight turbulance and storm cells form, so much so that he can no longer see a path to his destination. The pilot makes course changes along the path to avoid the storms and he lands at an airport close to his destination . The pilot, when he takes off, cannot know which path will result in the fewest course changes. When he reaches an acceptable airport, not his choice, his path was determined by local events which guided his choices. But in the electrons case there are no local hidden variables that are 'evident'. In order for it to take the least action its status needs to be distributed in spacetime while it remains coherant. This is the unreal nature of physics.
And so now we get to the problem of the atom. if the charge on an atom was a point particle, we have the potentiallity that the electron is in the nucleus (coupled), In the case of a hydrogen atom this might cause a Neutron to form, the spin on the electron couples the electron to its orbit, but there is a slight probability the electon is in the nucleus. But if we think about the electron in its wave like properties, the density of the properties of an electron in the nucleus are exceedingly low.
Another much better example is a relatively small (1mm) sheet of graphene. Because of the nature if arrangement of the P orbitals electrons are free to pair in molecular orbitals of lowest energy that cover the entire sheet. As a consequence the density of the wavelike properties of the electron are distributed on the sheet. If I put an electron on one corner, it is immediately available on the opposite corner, making very small sections of graphene superconducting at low amperage and short lengths.
But where is the electron in the sheet orbital? Since many of these orbitals of lower energy can be built the electron exists in a state of flux, sometimes over the entire sheet and sometimes over a single carbon.
Such a cool explanation
16:59 "this result can only be explained by measurement collapse... SO far! I am actively working on an alternative explanation that looks very promising.
Hows your live classes thing going?
Spin is actually the phenomenon of repolarization of quantum waves. When working with photons, a polarizer forces the photons to choose probabilistically between two polarization angles that are orthogonal, one that allows the photon to pass and one that blocks it. The probability that the photon passes is determined by the square of the cosine of the angle between the polarization orientation of the photon with respect to the main orientation of the polarizer. The probability that the photon is rejected is determined by the square of the sine function of the same angle. Therefore, both the cosine function and the sine function are required in the range from 0 to 2*Pi.
In the case of fermions, a Stern-Gerlach device forces the fermions to choose probabilistically between two polarizations, one with the north pole up and one with the north pole down. The probability that the north pole is forced upwards is determined by the square of the sine of half the angle between the original magnetic orientation of the fermion and the orientation of the magnetic field of the Stern-Gerlach device. The probability that the north pole is forced downwards is determined by the square of the cosine of half the same angle. Therefore both the cosine and sine functions are required but only in the interval from 0 to Pi, which is mapped to the entire interval from 0 to 2*Pi, since it is calculated for half the angle.
This means that Spin is the probabilistic property of repolarization, Spin 1 means that the entire interval of the probabilistic function between 0 and 2*Pi is used, while Spin 1/2 means that only half of the probabilistic function is used i.e. the interval from 0 to Pi (although mapped to the entire interval from 0 to 2*Pi). Spin 1/2 expresses the reorientation behavior of quantum magnetic dipoles under an external magnetic field, while Spin 1 expresses the reorientation behavior of a quantum alternating dipole, both in its transmission through a polarizing material (external electric-magnetic field) and in its reflection.
Spin is not the source of the magnetic moment of quantum waves, but rather Spin is the result of the probabilistic interaction between the magnetic moment of quantum waves and external magnetic and/or electric fields. There is no other phenomenon that produces a magnetic dipole other than the rotation of electric charges around an axis, so it is obvious that the magnetic moment of a quantum wave is the result of its rotation, but it is not the Spin, Spin is a reorientation rotation from an original direction to a direction imposed by a device, Spin is repolarization.
Thanks for a great Video,
CAN U EXPLAIN ZERO POINT ENERGY PLEASE...🙂💖
What if the diffent measung machines were at slighter angles and not exactly perpendicular? Like if the second machine was only 15 hegrees different?
If you perform the “up or down?” measurement when the particle is prepared in the “15 degrees away from up, along the axis of travel” direction, then (cos((15/2) degrees))^2 of the time, the answer will be “up”, and (sine((15/2) degrees))^2 of the time the answer will be “down”.
(And similarly if you prepare it in “up” and measure “Is it 15 degrees from up or 15 degrees from down?”.)
(Why are the sine and cosine applied to “(15/2) degrees” and not “15 degrees”? For the same reason that “|up>” and “|down>” are perpendicular to each-other rather than negations of each-other. There’s a kind of angle-doubling going on. It relates to how complex “rotations”(sorta) of a vector space of two complex dimensions, has a “double cover” of ordinary rotations in 3D space.)
If the electron cloud is spread out more but spins slower, shouldn't it produce exactly the same spin (magnetic field) as a smaller cloud that spins faster. Wouldn't that mean that spin still could be caused by angular momentum, but the actual angular momentum changes relative to spread. Does this make any sense to anyone, or am I taking nonsense?
it's not nonsense, it's good classical thinking, but it's classical, so its:
1) wrong
2) misleading
3) useless
Stay quantum ;-)
@DrDeuteron alright just wondering why it is wrong? Trying to understand this a little bit more
Great Vid.
TWO AT ONCE?? Did Christmas come early?? Thank you! ❤
- My understanding is that there is no concept of "distance" in the quantum regime.
- Mass, momentum, etc. are not physical properties in quantum, unlike classical mechanics. Instead, they are hold-over nomenclature that describe the units that balance the equations, not "physical" classical mechanics properties. There is no "physical" in quantum physics.
- I prefer to think of electrons as an oscillating "standing wave" that is restrained by the charge of the nucleus.
- Physical phenomena, like grating slits, that interact with quantum properties, are difficult or impossible to mentally unite given these realities.
Can you please explain why can't we imagine that electrons align their "axis of rotation" with magnetic field? Like magnets but just aligning axis not "poles"? Then given that they have random orientation half of them will align up, half down. In a second machine they gona align their axis left to right and due to some imperfections in first alignment, like residual moment from first alignment or because they didn't settle yet, half of them end up right and half left. And exactly the same process in third up-down machine. For me, not a physicist, looks like there is nothing quantum in this explanation. Why it is wrong?
I can imagine something similar and mechanical for light passing thru polarisation filter, weirdly interacting with those long chain molecules and getting aligned or absorbed depending on orientation and some chaotic property like exact spot where it hits that molecule.
You must scrutinize FractalWoman's modelling of the quantum spin here: ruclips.net/video/OrlsxQHawxk/видео.html
Finally, a video on a nice, simple subject, that anyone can understand, instead of the incomprehensible computer stuff.
And it's heartbreaking how sad your electrons always are.
Thank you!!
I asked my physics teacher in middle school, about the friend's question. Assume a spinning arm, where in the middle of its length is a c-speed. what speed will be at the end of it then
Close your physical eyes 👀
Clear your mind
Do you see things???
Pray 🙏
Very good.
Do you think electro is 2D exist in 3D space. Cause I think as human being ofcourse we have imagination bias, which means we already give a shape to existence particle without confirming what shape it is, and in the process, we manifest natural properties and behaviors of that particles based on bias shape we have assigned to it. If that makes sense. Anyone can restate with proper English setup of my sentence if anyone understands what I am trying to say. Thank you.
How does Quantum Mechanic look like.?
thank you!
"The probability of getting up is 1/sqrt(2) squared." I usually find the probability of getting up too early in the morning is considerably lower than that.
Why the emphasis on taking the absolute value before squaring? Can the coefficients have imaginary parts? Taking the absolute value is unnecessary before squaring any real number.
That’s right, the coefficients can be complex. I mention it very briefly in the video- but mostly we’ll be working with real numbers
Thanks.
superposition is understood as 'an electron' being in multiple different states simultaneously (magically) and on measurement 'the electron' collapses to a single state. not true. single electron is in a single state whereas different electrons have different states and all these different states are the superposition of electron states. now on passing them through a measurement process influences their states to align to the axis of measurement
Okay, earth spins on an axis. It is angular momentum
That was has to be done in a sense to get a clear picture of what is actually going on
Hmm is that an Oz or NZ accent
To eternity end all
As someone that does PhD in mathematical physics. You really really don’t want to go deep in the rabbit whole of the mathematics of Spin 😅😅😅😅
Why not? Lie group representations is where the fun begins!
@@HilbertXVI exactly 😂
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at least now I know what I don't understand
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The electron is sad because is negative lol
The electrons/photons end up in a direction compatible with the polarizer.. that is +-45 degrees. Only 90 degree that only allows it's own +-45 degrees don't ovlap any of the first results.... But then at that polarizer that's at 45 and does. 1/2 result against now the photon is in any of the +- 45 degrees compatible with that orientation. You make it a lot more confusing saying it's now only 'up' oriented... I bet you even confuse yourself
two videos on one day... too much
I don't like the rhetoric of a blown mind in science. It's annoying.
I like the presentation though:)
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