Quantum Mechanics Concepts: 3 Electron Spin

[@alliejoan5145]

I'm just gonna keep commenting on all your videos to let you know how helpful they are- thank you so much for uploading these!!! You're an amazing teacher!

[@funkyironman69]

Yes, and I'm going to comment so the youtube algorithms think the video is more popular.

[@urinater]

Please, get a room!

[@rath5444]

@@funkyironman69 ya that's a good idea!

[@alwaysdisputin9930]

@@rath5444 Yeah. These videos are the fastest way to understanding AFAIK so the more we comment, the more YT algorithm thinks this video is popular so the more the videos get recommended so the more people will find the videos, the greater the understanding in the world & therefore the faster the rate of scientific discovery & inventions such as robot GF literally my best chance of getting laid

[@rath5444]

@@alwaysdisputin9930 haha yes

[@pelimies1818]

Leonard Susskind should have seen these vids years ago.. They are very informative, logically constructed, and easy to follow. Thank you.

[@DrPhysicsA]

Wow. That's a formidable list of topics. Sadly, I don't think I could do justice to them. You will have noted that my channel is really about introducing the basics, firstly at A level and then introductory material for degree level. My own particular research area was nuclear physics so my more advanced videos tend to keep to that end of the market. May I wish you well in your studies.

[@kurtgodel100legit9]

Your explanation are amazing, but I promise you that one day the student will surpass the teacher...

[@dominikandrzejczuk5727]

Jesus, i learned more in the 3 hours of your videos than i ever learned in one semester @ University

[@eastofthegreenline3324]

These videos are splendid. The work is done at a measured pace and the work is crystal clear. Much appreciated.

[@roblyndon5267]

Such a good series. Sometimes the maths can be a little slow, but even that is fine -- it allows time for the ideas to sink in.

[@walidnouh1747]

Dirac himself would have been very impressed with the simplicity you presented his notation

[@DrPhysicsA]

The alpha plays the same function as the 1/ root 2 term in the eigenvector for the x direction measurement of spin. You can either include the 1/ root 2 term inside the column vector or as a multiplier outside it. It amounts to the same thing.

[@eamonnsiocain6454]

I recommend your videos to the students in my STEM classes. Thank you for your clear and robust presentation.

[@Vazhaspa]

In the beginning of the video (min 1:24), the direction of spin vector (obeying the right-hand rulr, or corkscrew rule) is drawn in wrong direction!

[@AlchemistOfNirnroot]

How? The axis or the curved arrow? I thought it was the wrong direction but then looked at it the other way and it seemed fine. 2 years too late I suppose :D

[@tejaendraengtju4788]

@@AlchemistOfNirnroot quantum effect on our eyes :P

[@bohu9128]

Yes, I thought so at first, and then realize it is a vision illusion.

[@lwskiner]

I would venture to guess that if Professor Susskind prepared his lectures as thorough as you have there would have been 70% fewer questions asked of him. Bravo.

[@DrPhysicsA]

Its preparing in the left direction (ie pass thro a magnetic field so the electron spin axis vector points left) and then measure in the up (z) direction.

[@ztac_dex]

Thank you for these videos. -From someone with an engineering degree who jumped to a graduate physics program with no actual "physics" background

[@jessicasaunders1057]

Your videos are so interesting and easy to understand! I'm incredibly glad I stumbled across them as when I had my interviews at various unis the interviewers were very much impressed! Thanks!! :)

[@david203]

The repetition at the beginning is very helpful in understanding how quantum spin measurement is different from any classical vector measurement. This is perhaps the first surprise of physics in the tiny regime, but not the last.

[@paulbaker916]

Again, brilliantly presented. I especially appreciate you keep repeating things said before, e.g. squaring really means multiplying by the complex conjugate etc. This must be tedious for you but I really think it helps to implant the applicable concepts. Thanks again for making these videos.

[@Imran52Feb]

Very impressive way of teaching. I am amazed !

[@waqassaeed674]

I feel so bad that i have not been able to see your video lectures. Which makes so sense and easy to grasp.

[@DrPhysicsA]

Its the corkscrew rule. If you turn a corkscrew clockwise (spin) then it will move into the cork (ie the direction of the axis).

[@daguaishouxd]

Thanks for the wonderful lecture Bob! Just a side note, at 1:14:52 the probability of | |^2 certainly depends on how basis vectors are defined? It could be either cos^2(theta) or cos^2(theta/2) depending on the angle between the basis vectors, just like how you explained it at 32:58.

[@gavintillman1884]

Really enjoying these. I did a 16 hour fast paced lecture course on QM in my late teens before the internet existed, and didn’t really take it in. Going back at my leisure and looking at different KZbin presentations - yours, Oxford’s Prof Binney, Geek’s Lesson and others - I feel I better understand it in my 50s than I did studying it full time. A big help to understanding is the notation and I can’t believe we weren’t taught that way. It just seems so much clearer and less pulled out of the air. Just one question. All these “two basis” problems - light polarisation and electron spin. There are no preferred axes in space. Obviously you’ve made a choice for the basis states which is fine: up and down for electron spin which is fine. Clearly, left, right, in and out have to be orthogonal and so have to be 1/root(2) time (a |u> + b |d>) where a and b are unit modulus, but it seems arbitrary exactly how you define them at around 41:17. You could make a and b 1 for any direction “along the equator” between “poles” |u> and |d> and call that |r> which obviously then fixes |l> at its antipodes, leaving a two way choice for |i> and |o>, mirror images of each other, as there are precisely two directions orthogonal to all of |u> |d> |l> and |r>. Presumably it’s just convention, and it’s easy to show that the physics is invariant with a different choice although I don’t think any of the sources I mentioned explicitly refer to this.

[@warrenchu6319]

33:52 The probability amplitude is equal to cos (theta/2). This is why the electron has a spin of 1/2. Because (theta/2) has to make two full circles (720 degrees) before cos (theta/2) goes through all its values, from 1 to 0 to -1 to 0 back to 1. Since the probability is the square of cosine, the observed states do not show the negative values of cosine. (The square of the negative probability amplitude is the same as the square of the positive amplitude). So the electron must change its original spin twice before returning to its original spin state as it go through positive and negative amplitudes.

[@aragorn0006]

This was the first time I got the concepts. :) Seen these strange state vectors and oparators before but with no understanding. Now I can 'read' them . Yesssss :) Thx.

[@alwaysdisputin9930]

Transcript of the 1st 10 min: 0:00 Hello. Today we're continuing in our series on quantum mechanics concepts, looking at the subject of electron spin. 0:07 So far we've considered polarization of photons; now we're considering the spin of an electron. 0:14 We can think of an electron spin, for these purposes, as a tennis ball spinning. 0:19 Now, a tennis ball which is spinning will spin around an axis - it can spin around any axis & it can spin at varying speeds. 0:31 So if we draw our tennis ball. [Bob Eagle, CBE writes a: ω symbol & calls it 'omega'] 0:34 We can say that it will spin on an axis - which could of course be an axis in any direction - & in spinning it will spin at a certain angular speed: ω 0:44 ω radians per second. 0:47 & it will have an axis of spin. 0:51 & that means that we can replace this whole description simply by drawing the axis. 0:58 & the arrow is an indication of spin by virtue of the corkscrew rule. 1:06 You simply say if the corkscrew is pushing in this direction then you would have to turn it clockwise - in that way, in order for the corkscrew to go in. 1:17 Therefore, the tennis ball or the electron is spinning clockwise in order for the corkscrew to move in that direction. 1:26 Therefore, the axis is shown by the line & the arrow gives you an indication of which way the spin is going. 1:34 Now, that turns out to be not a bad model for electron spin - except in 1 respect: I said that a tennis ball could rotate at varying speeds. 1:45 When it comes to an electron, there is no such notion of varying speeds of spin. 1:50 The electron just has spin. 1:53 Furthermore, it turns out that when you come to measure an electron's spin - which could of course be in any direction - you can only measure it against 1 coordinate axis. 2:07 So, we can think of a machine, rather like the 1 we used for polarization but this time it's got different electronics in it. 2:16 It has an arrow which indicates the angle or the coordinate direction that you're measuring the spin against. 2:26 It has a red light & a green light - just as we had before - which will indicate whether or not the spin is measured as up or down according to this direction. 2:38 Irrespective of this direction, it will simply measure up or down according to the direction of the equipment & that's what we're going to be looking at. 2:50 So, now I want to tell you some experimental results. 2:53 Here is my equipment, which of course I could point in any direction - I can turn this equipment around if I want to - but for the time being I'm going to keep it in the upwards direction. 3:06 The frame of reference we're going to use is that up is going to be the z frame of reference. 3:13 The, as it were, left right is going to be the x frame. 3:17 & the 'in out' is going to be called the y frame or coordinate. 3:22 So, we are measuring along the z coordinate which for our purposes we will regard as up or down. 3:30 Now, this is an experimental result. 3:33 You can prepare electrons with their spin in a certain direction. 3:38 It basically involves passing them through a magnetic field so that all the electron spins, no matter what they were previously, align such that they are aligned in any direction of your choosing - in this case, I am choosing to align them up. 3:54 They are completely up on the z axis & we're going to put them through my measuring machine which is going to measure them along the z axis. 4:04 & what that machine will tell us is whether the electrons are spin up or down according to that axis. 4:15 & you perhaps won't be surprised to know that experimentally you will determine that 100% will come out as measured up. 4:25 Because they are all up against the: z axis. 4:29 So, that's not a particularly surprising result. 4:32 If, on the other hand, I prepare my electrons such that they are all absolutely spin down along the: z axis, you perhaps won't be surprised to know that 100% of them will come out spin down. 4:48 So, let's just be sure we understand what's happening because it's crucial to ot fall what ha happens. [??? sorry no idea what he said] 4:54 We've got a machine that's got a red light & a green light. 4:59 & the whole point is that there is some electronics in this machinery here which will measure the spin of an electron against the axis of the arrow. 5:10 As I said, you can turn the equipment if you want to & it will always measure the spin of the electron in the direction of the arrow & it will give you 1 of 2 results: it will either say that the spin is up in the direction of the arrow or it is down in the direction of the arrow. 5:26 That's the only result you can get from this piece of equipment. 5:30 & what I'm saying is when you prepare the electrons such that they are all spin up against the z axis & you measure it against the z axis, every single 1 of those electrons that goes through that piece of equipment will cause the red light to come on - which indicates that they are spin up. 5:50 If you prepare your electrons spin down, every single 1 of them passing through that equipment will cause the green light to come on which means they are spin down. [Bob Eagle, CBE draws 3 arrows pointing to the top right of the screen.] 6:00 But now, suppose I prepare my electrons with their spin in this direction. 6:07 What will happen? 6:09 Well, you might argue that an electron with a spin in this direction has 2 coordinates. 6:16 It has an up coordinate because there is essentially an up direction. 6:21 & it has a right coordinate because there is essentially a coordinate that's pointing to the right. 6:27 There is no down coordinate. 6:31 Clearly, this is essentially pointing a bit up & a bit right. 6:35 & therefore, you might argue that when you put these electrons through this device which is measuring against the: z coordinate, that it should essentially simply measure that this is effectively an up direction & consequently you would expect to get 100% of those coming out as up. 6:56 But what you *actually* find is - & it depends on the angle - but you'll find sort of 80% will come out up but there will be 20% of those electrons [Bob Eagle, CBE hovers his pen above the 3 arrows that point to the top right of the screen such that his pen's pointing in the same direction.] that are at this angle [Bob Eagle, CBE hovers his pen above the red green up down machine. The pen's still pointing towards the top right of the screen.] passing through this machine [Bob Eagle, CBE points at the machine's green light] that will cause the green light to come on, indicating that they have been measured as spin *down*. [Bob Eagle, CBE draws 3 arrows pointing to the bottom right of the screen.] 7:21 Similarly, if you prepare your electrons such that they are pointing in *this* direction, again you might conclude that they are all essentially spin down & a little bit of spin right. 7:35 But you'll find, amazingly, that 80% of them will come out spin down - which is what you'd expect, but you might well get 20% of them that will be spin up. 7:50 So, the peculiarity - & this is an experimental result that even though you have *prepared* the electrons so you *know* they are pointing in this direction - when you put them through a device that is measuring whether or not they are up or down, a large proportion of them will be registered as spin up, but a small proportion of these will be registered as spin down. 8:14 Now, this is, again, the weirdness of quantum mechanics. 8:18 All of these electrons are absolutely identical - they have all been prepared with their spin in exactly the same direction, & yet *some* of them are registered as up - most of them, in fact, but some of them as spin down. 8:33 & if you prepare them such their spin is entirely along the x axis so there is no up & there is no down coordinate at all, you might expect that when you put these electrons through a measuring device in the z direction, neither the up nor the down light would come on. 8:53 But in fact, what you find is when you put these electrons 1 at a time through this piece of equipment, 50% of them will give you an up & 50% of them will give you a down. 9:07 So, even though there is, in essence, no up or down coordinates to electrons which are essentially pointing to the right along the x axis, when you put them through this equipment, you will find that ½ of them will come out as up & ½ of them down, & there is no way of predicting which 1 will be which. 9:29 So now, if we try to represent what we've just learnt in our Dirac notation, we would say that if you have an electron whose spin is prepared in this direction, then what we've learnt is that some of those electrons will give a spin up. 9:46 Don't forget our measuring device is always measuring for (at least for the time being) I'm always going to be measuring in the z direction no matter what the angle of the electron. 9:56 So the electron spin is prepared in this direction but I'm always measuring it against the: z axis & I want the result: is it going to be up or is it going to be down? [Bob Eagle, CBE points at the ⍺ & β in: |/> = ⍺|u> + β|> ✍ |¯¯¯¯¯¯| ✍ | ↑ | ✍ | | ✍ ̅ ̅o ̅ ̅o ̅ ✍ u d

[@LaureanoLuna]

Excellent trilogy. It makes one understand how it works...

[@scienceofsmile]

Really love this series. Thank you.

[@DrPhysicsA]

Yes that is right. The act of measurement changes the state.

[@wafikiri_]

The measuring device does not just measure the spin of the test particle: it measures the spin of the system composed of the electron and the measuring device (and whatever other things related).

[@pentland1942]

The fog has lifted. Thank you Dr PhysicsA

[@DrPhysicsA]

Can you let me know the time on the video where this arises. Thanks.

[@rockyshepheard6054]

What is the explanation for the exp results for 80% u and 20% d, when the spin is aligned say at 50 degrees above the pos x axis? Could it mean that the equipment is not setup to detect spin r and simply interprets it as d? Or could it be that nature somehow changes the spin to be d when on fact it is r? Or some other explanation? Excellent presentations. Is your name Chris Tindell perhaps?

[@euphoriamorninguk]

Thankyou so much for this absolutely wonderful, accessible video. beats my textbook hands down :)

[@8cccpeevostokzempf]

Love dragging Pythagorus in on a discussion of quantum electron spin!

[@amit98616]

Network graphs: matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network theorems: superposition, Thevenin and Norton's maximum power transfer, Wye-Delta

[@georgegrubbs2966]

I finally understand quantum mechanics despite Richard Feynman's statement, "If you think you understand QM, you don't." Many thanks for your lessons.

[@FelipeZucchetti]

Man, you are the best...thanks so much for these videos...

[@feralmath]

Thank you for making these videos. FYI - If you turn off your camera's auto-focus and manually focus on your writing surfaces, you won't get the occasional drifting in and out of focus, which is mildly annoying.

[@DrPhysicsA]

If you are talking about its origins, no-one knows. At some very short time after the big bang (ie less than a micro micro of a second) nature determined that there should be fundamental particles having mass (or not), spin (or not), charge (or not) etc.

[@amit98616]

Wye-Delta transformation. Steady state sinusoidal analysis using phasors. Linear constant coefficient differential equations; time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits.

[@DrPhysicsA]

As it happens I discovered how to do it just after making this video so hopefully I wont have any more going out of focus.

[@medievalmusiclover]

Your videos are more that exce5llente. Thank You for posting.

[@deepakiitd71]

Hi...just one query. At 1:11:23, after substitution of nz =1, nx =0, ny =0, you mention 0/0 equal to zero which is not true. Can you please explain that point.

[@johndennis5233]

This is an really excellent series. But it is right to say that the spin before measurement was a bit of up and a bit of down? Isn't it better to say that, before meassurement, there is some chance of it being up and some chance of it being down - and you find out which one for sure when you make the measurement?

[@Gwunderi25]

What I don't understand is why we need a third vector (in/out). The only that matters is the angle to the vertical, if than the vector points to my right/left or towards/away from me shouldn't matter, should be the same? In the video about polarization you said that the 3rd vector with the imaginary term is for circular polarized light (where the polarization changes in time). So maybe here it is something analogous, maybe a rotating magnetic field?

[@Imran52Feb]

What is meant by preparation of an electron in a certain orientation? How it is done .?

[@skypickle29]

@53:00, how do you get basis vectors for in and out? They seem to appear like magic.

[@kenchooooo]

They were derived in the previous video (part 2 of the series).

[@david203]

If electrons are prepared as spinning to the right, due to random errors, half of them (on average) will be slightly up from right, and half will be slightly down from right. The amount of this deviation can serve as the initial "particle position" (hidden variable) of the Bohm Interpretation, allowing the individual electrons to be predicted as measuring either up or down. This means, in principle, that if we can accurately measure the "upness" of a right-spinning electron (using very low energy, for accuracy), we can predict how that particular electron will be measured by the detector! So, again under BI, we can calculate, given the degree of "upness", a deterministic and fixed phase-space trajectory leading from that degree of upness to either an up or down measurement by the detector. So, once again, the BI insight removes the necessity to consider probability until an actual ensemble of particles is to be the subject of the experiment. Then the probabilities can be predicted by simply counting the ratio of "up" predictions, which should correspond with what the probabilities that are observed. I'm not sure if these experiments have been performed yet, due to the poor popularity of BI, but experiments HAVE validated the predicted deterministic trajectories of particles in double-slit experimental observations.

[@revgro]

At 30:10 you stated that once the up/down state was measured as up (or down), the electron spin is now completely in that state even though the state before the measurement was at a different angle. Does this also apply to photons passing through a polarizer? For example, a photon polarized at 45 degrees, will be completely vertical if it passes through a vertical polarizer. And, a photon polarized at 45 degrees, will be completely horizontal if it passes through a horizontal polarizer.

[@TH-ph7gg]

Brilliant, just brilliant. Thank you!

[@funkyironman69]

1:10 Is this related to Curl? (right hand rule)

[@alinarotaru9389]

±1 due to the algebraic properties of Pauli matrices where the determinant of each matrix is equal to minus 1 and the trace of each matrix is equal to zero. From above we can deduce that the eigenvalues of each σi are ±1.

[@dzFoX84]

I'm a little blurry on eigenvalues and eigenvectors. Why did we assume (at derivation of sigma-z for example) that eigenvalue for down state is -1 (not knowing what is the matrix) when eigenvector is different than up eigenvector? Why it couldn't be +1 to?

[@sergioreina6387]

But, in this way, to obtain the Pauli matrices you need to use the eigenvalues obtained by the same Pauli matrices? Is not like a snake biting its own tail? Thanks

[@Hythloday71]

33:45 Can the formula cos^2(theta / 2 ) for probability up be derived from principles ? You spoke of all that conjugation and such and then seemed to pull that out of the hat.

[@DrPhysicsA]

+Hythloday71 I derived it in an earlier section of the series. This video is part 3 of a series.

[@Hythloday71]

+DrPhysicsA - just watched the first 2 of this series again and the formula wasn't derived there. They were about photon polarization were the formula was not a half angle but straight forwardly cos^2(theta). This formula you referenced from classical lectures on light. Could you give me a pointer perhaps where you might think the derivation is located ?

[@APaleDot]

+Hythloday71 From what I can gather, the reason that θ is divided in half in the case of the electron spin, is because the angles in question are twice as large as the case of photon polarization. So, whereas in photon polarization, the "opposite" measurements were 0° and 90° (Light polarized in the 90° angle had 0 chance of going through a 0° filter), the "opposite" measurements for electron spin are always 180° from each other (electrons prepared in the up direction have 0 chance of being measured as down). As such, if we think we can apply the same mathematical model to both situations, there must be some sort of transformation between the two systems. In this case, dividing the angles in half does the trick.

[@DrPhysicsA]

+Hythloday71 Is it this one? kzbin.info/www/bejne/eKK3qmCKlM-jsKM

[@Hythloday71]

Thanks, I'm again returning to this subject. The link you provide is insightful but is a classical derivation it seems. It speaks of the intensity of light being related to cos^2(theta), which by extension must mean the individual probability of a photon is related similarly. I have derived for myself the individual quantum mechanical probabilities but from an intuitive classical spin picture of the electron. Conventional wisdom would have it that there is no such classical picture but it seems to me they have overlooked a simple conceptual adaptation. I would like to appraise for myself the derivation of the quantum sigma matrices approach to see if it is equivalent to mine. I am currently working hard on preparing a paper / presentation of my ideas and would be grateful if you were interested to examine ?

[@SpaceMilk07]

Very interesting. I really love physics, it is just a beautiful subject.

[@michaelvarney512]

Interestingly, in the derivations for the Pauli spin matrices since you assumed a given set of eigen values, then from the given form the proposed matrix has to be hermitian and thus the c value is known as soon as b is determined. This can save some computation. The question in the derivation is why did you assume the values for the eigen values to be plus or minus one?

[@mullhaldedreck6138]

They can actually be anything as long as they are in the opposite direction (+,-). Just like increasing the value x in "nx^2+ny^2+nz^2 = x" would not change the direction of n and thus not effectively changing the outcome

[@amit98616]

2-port network parameters: driving point and transfer functions. State equations for networks.

[@adamkolany1668]

Well, @t=998s, in order to find gamma you need to assume n_x and n_y are not both 0. that is n_z1 !! what if it is not the case??

[@DKonigsbach]

I absolutely love your videos. One suggestion: The denominator at 1:15:02 is somewhat problematic. If there is a way around that, perhaps add a reference to it in a text overlay?

[@maciel1055]

Olá! Seu material irá me ajudar muito, pois quero fazer mestrado e preciso me aprofundar nesse assunto para a prova. Sou professor e gostei muito do seu trabalho. Bom seria que aqui no Brasil professores fizessem um trabalho semelhante ao seu. Ainda não temos um nesse porte e quero ser um dos primeiros a fazer uma sequência de vídeos sobre Mecânica Quântica, mas isso após eu fazer o mestrado. Parabéns pela disposição!

[@laurirantaniemi6202]

Didn't you say at around 1h11min that 0/0 = 0. I might think that you just skipped something, but I'd like to know how you worked your way around that.

[@drewpass5697]

I was confused by this too. I think if instead you take the limit of nz --> 1 and set nx = 0 it will work out if you rewrite ny in terms of nz by using nx^2+ny^2+nz^2 = 1.

[@phizzhead53]

Throw caculus at it lol that what its for lol

[@akshaipadmanabhan7946]

I don't understand if the electron is detected as down , will it be down forever....?

[@davidsweeney111]

So there is there an energy or force that maintains spin? Or is spin a fundamental property? Thanks, David.

[@typhoonzeroun9394]

We tend to use the word measurement while what you are doing in quantum mechanics is an interaction with the particle. So it is of course a modification of its spin. We can't just watch, we don't use neutral particle to measure.

[@freeb1111]

If anybody can answer me, thanks ahead of time. In the early part of the video, when an electron is prepared with a spin at around a 45 degree angle, and the measuring device was straight spin up, the odds of the angle spin electron ending spin up was 80% - and spin down 20%. Later in the video, he does the same experiment it seems to me, and comes up with 50% for up and down both. +DrPhysicsA, or anyone, what did I miss, or am not seeing. Thanks

[@apivovarov2]

@1:11:16 - well, 0/0 is undefined. Not sure that we can replace it with just 0.

[@ibrahimisah8975]

Hello I love it its wonderful and easy to understand, nice work and keep up.

[@hooinkyoma8045]

Very good video. Again, a small mathematical correction: Psi = ( 1 gamma) can not be assumed without loss of generality. You will have to ensure that the first component of Psi is not zero! (For example if nz = 1, ny = nx = 0 you would find that (0 1) is an eigenvector.)

[@ryanu9772]

Divide by zero at 1:11:25? Is this allowed in the quantum world?

[@DrPhysicsA]

Mathematicians do not like divisions by zero. Physicists on the other hand regard one divided by zero as Infinity. What we usually mean it is that as the denominator tends to 0 the result will tend to infinity.

[@Algebrodadio]

DrPhysicsA As a mathematician, I know what you mean and understand the purpose of the short hand. However, you should be careful to explain to your audience the difference between x approaching 0 from above (x >0) and x approaching 0 from below (x0+ (1/x) = + \infty =\= - \infty = lim x--> 0- (1/x) = "1/0"

[@ethandrood]

At 01:11:15 there is divide by zero. Specifically 0/0, because nx-nyi =0 in the denominator. But 0/0 is undefined. This part blagged me.

[@kzterminator]

so the whole video was based on that Pamp=cos(sigma/2), is this derived from other source of just experimental result?

[@hos84688]

what do you mean by repairing in left direction and measure in the up direction?

[@david203]

When is the square of a probability amplitude not equal to the product of the p.a. and its complex conjugate? You've hinted at this, but not explained it.

[@RachidOUSALEM]

25:25 .... whats this????

[@RAZIYAKOYAPARAKKAL]

For pi-mesons S= 1 and for electron S= 1/2 what is the difference between the two (practically).

[@pellythirteen5654]

Being watching this again because DrP is such a good and patient teacher. But here is my problem , which might be a little off-topic but still worrying me : In determining the up/down state of say an electron spin , DrP makes use of an electronic device with two lamps. When the green lamp goes off , a +1 spin has been detected. When the red light goes off , a -1 spin has been detected. The spin can either be 1 or -1 , meaning either of the lamps goes off in the experiment. Is it not so then that the results are mutually exclusive ? State |1> = NOT State |-1> ? Meaning : if the red-lamp did not go off .. it implies the green light must have ! Why not use only ONE lamp then ? . H^Q = h.Q …. is only nessesary if there are 2 or more h-values (eigen) ? So , what about mutual exclusivity ? Is it a stupid question ? Does it look like entanglement (oh dear) ?

[@AndrewNicoll]

Where do the values in a hermitian operator come from?

[@byronhale9874]

Still excellent and succinct. Details of spin operators for electron (Pauli Matrices). Different verbal interpretation from Leonard Susskind's in "quantum Entanglement," though.

[@ojos33129]

Byron Hale

[@ojos33129]

Jane Zucker

[@gary.richardson]

So, if clockwise is up then left hand rule applies?

[@medfaxx]

Thanks for the nice videos. Well done and articulated in an understandable way. ? for you in the electron spin that occurs in biology where an electron can go from a singlet state to a triplet state. What allows, causes such to happen if you know?

[@jimdogma1537]

Brilliant. Great video. I understood the whole thing (pretty much). One question, at 1:05:05, you introduce alpha, and say that it is a normalization factor and not an eigenvalue. However, by the end it seems to have transformed into an eigenvalue. Is this what happened or am I missing something?

[@DrPhysicsA]

Well everything must yield to experiment. If the theory and the experiment do not agree, then the theory is (generally) wrong. Experiment gives a cos^2 outcome. And the probability amplitudes derived from the theory do the same.

[@dmartin1650]

I'm sure this is a simplistic question but it's been nagging me somewhat. It seems to be assumed that because the particle spins have been "prepared" at an angle to the detector field that they are in some implausible probabilistic state rather than a specific state. Could it not be that they are actually in a specific angular state to the detector and that it is the action of measurement which is constrained to probabilistically? Maybe it's a nonesensical distinction but it seems to me it might be significant? It seems an unwarranted assumption that because the statistical distribution of experimental measurement shows a probabilistic rather than a binary distribution of observations, that the particles actually have a probabilistic property, namely spin. COuldn't it as easily be some feature of measuring particle spin which explains the distribution?

[@AlchemistOfNirnroot]

Sounds like the Copenhagen interpretation where observation collapses the wavefunction. I too believe in a physical realism - but QM is weird.

[@samtux762]

Short answer is "no". You talk about hidden parameters. Einstein believed in those. ("God doesn't play dice"). Bell equations led to experiments, that showed that Einstein was wrong. There are no hidden variables.

[@kurtu5]

1:11:24 Why isn't (1-nz)/(nx-iny) -> (1-1)/(0-0) -> 0/0 disastrous? It is an undefined expression. Meh, nevermind. Others have also pointed it out. I suppose it's left to the 'reader' as an exercise to take the limit or do some other trickery to remove the singularity.

[@AlchemistOfNirnroot]

Jackson for president 2020 :D

[@MisterTutor2010]

If you prepared an electron that could be up, down, left, right, in, or out and I put it though device that measures say up vs. down I would be even more screwed. If the result is up then it could be any of the six directions and if the result is down then I only know it can't be up but the other five are equally likely.

[@mohammadelsayed5715]

that was really useful and insightful . thank you

[@platinumwill]

Thank you @DrPhysicsA

[@benmenanaazdine2782]

Thank you very much teacher. why you don't continue your video about nuclear physics

[@willie5069]

Add the end of the lecture you have nz = 1, nx=ny=0. You comment that (1-nz) = 0 and that (nx- I ny) = 0. But this is 0/0 which is indeterminent. Is this correct?

[@zarchy55]

There is one thing that I haven't been able to grasp. When we say that the wave function contains the probability amplitude of the electron being spin "up" and the probability amplitude of the electron being spin "down", what direction is "up" and "down"? Let's assume there is no measuring apparatus. There is just the electron and its wave function.

[@samtux762]

Practically speaking spin is measured along/against magnetic field. The direction of magnetic field dictates up or down. Without measurement apparatus the question becomes invalid.

[@roblyndon5267]

At 26:15, the maths would have been more accurate if you'd used a modulus sign instead of square brackets. I know that in this context, that's what you mean by the squared term, but changing the notation like that would give you greater accuracy, and less scope for confusion, for no extra work.

[@dirkvanderlaan31]

Great series! Very enlightening. I was wondering, the spin-measuring devices you are referring to, how do they measure the spin? Do they always use a magnetic field like in the Stern and Gerlach experiment? Or are there other methods?

[@ojos33129]

Dirk van der laan

[@ojos33129]

Jane Zucker

[@ojos33129]

Jane Zucker

[@sndik16]

Hi DrPhysicsA, if you have any suggestion on a good exercise book, it would be great, because I keep forgetting the formulas ie matrix times vetor, or vector times its complex conjugate, so I think if I practice more I might memorize better these manipulation rules. as always, thank you very much for this video.

[@ccsitaround]

Again, very nicely done, very helpful. Thank you.

[@gpcrawford8353]

Didn’t Max Born devise the probability amplitude mathematics ?

[@sicktoaster]

1:11:28 I thought dividing by zero was prohibited.

[@SenSeisetakor]

Nah, it's physics, if you've got 0/0 or any indeterminate form you're in good shape :D

[@jessstuart7495]

You have to use L'Hopital's rule to determine the limit as the vector approaches the z direction. If you think about this in spherical coordinates, you have a unit vector that is an angle θ from the z-axis. Your expression for gamma becomes (1-cos θ)/((sin θ)*((cosφ) + i*sin(φ))). Take the derivatives of the numerator and denominator with respect θ to and get (-sin θ)/((cos θ)*(cosφ) + i*sin(φ)) which is zero as θ approaches zero.

[@AlchemistOfNirnroot]

@@jessstuart7495 Cheers for that.

[@samarthsai9530]

Hello Dear Sir , I must inform you that these videos have proved to be a blessing for me. THANKS for your lessons.I had a question, In all the these videos we are using 2D matrices , but what if we want to multiply eigenvectors to 3D or any D matrix.Please do reply Sir.

[@bobbriggs4287]

near the end, when you say nz=1 and the other are zero that the gamma has a 0 in the numerator and so the result is zero, but the denominator is also zero ! 0/0 is a no-no.

[@ginaszajnbokharari470]

Observation: at 1:11:32 if nx=0 and ny=0, you have a forbidden denominator nx-iny=0

[@BarryKort]

I note that you are representing the orientation of the spin vector as some fixed value. But consider that a child's top, when spun has a nominal axis of spin that is perpendicular to the surface of the table, but actually wobbles or precesses, so that at any instant of time, it might be leaning a tad from the perfectly vertical orientation. Because of the way we measure the spin axis of an electron, we cannot distinguish between the case that there is no wobble or precession from the case that there is some time-varying wobble such that the average direction is straight up. Such a time-varying wobble would amount to a hidden variable that would introduce a small degree of independence between twin particles. The mean value of the orientations might well remain equal and opposite, but at any instant of time, the wobble amounts could be uncorrelated.

[@samtux762]

There are no hidden variables. See Bell theorem. This is a scientific fact. Einstein was wrong. God does play dice.

[@anthonypua8039]

Why when nz = 1, nx = 0 and ny = 0, 0/0 = 0?

[@saeedahmadvand2712]

DrPhysics A, humanity owes you for what you have done for science but if I'm not mistaken, it's been a long time that you haven't added anything to your video list. For example, I haven't found a video on Dirac's equation from you. I mean from the beginning where you combine special relativity and quantum mechanics and spin comes out. I would also like to see a comprehensive video on string theory. I know there are tons of videos out there but my friends and I got used to your videos and your voice and honestly, we're having a hard time to learn from other sources now. I'll be waiting for your answer, God bless you.