Lecture 3 | Quantum Entanglements, Part 1 (Stanford)
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- Опубликовано: 26 сен 2024
- Lecture 3 of Leonard Susskind's course concentrating on Quantum Entanglements (Part 1, Fall 2006). Recorded October 9, 2006 at Stanford University.
This Stanford Continuing Studies course is the first of a three-quarter sequence of classes exploring the "quantum entanglements" in modern theoretical physics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.
Complete playlist for the course:
www.youtube.com...
Stanford Continuing Studies: continuingstudi...
About Leonard Susskind: www.stanford.ed....
Stanford University channel on RUclips:
/ stanford
As a student who is first exposed to quantum mechanics, without a doubt this is an excellent series of lectures.
Learn the math so you can focus on the science is my best advice,
Reality is ok but imagination is more nice,
I don't know why I decided to rhyme
Abstraction is devine
The physicist, shocked and amazed
By the century old mathematical face
This is not very good poetry
I'm a mathematician, don't blame me
@@gaussianvector2093 pp0000e00pm
Eigenvectors and eigenvalues 40:00; Pauli Matrices 50:00; Eigenvectors of different eigenvalues are orthogonal 59:00; Electron spin 1:10:00; Probabilistic interpretation 1:20:00; Pointer in 3D 1:32:30;
Lies again? Duck Rice
Brilliant presentation of the power of complex analysis,particularly the power of imaginary numbers (!!!). Leonardo is God (!!!)
leonardo even his confusion is instructive
All the different comments made by this virtual audience are in themselves quite phenomenal
Does anyone else find Leonard Susskind hilarious?! It's so funny when he rubs out |a> and |b> and then immediately forgets which one was which! Don't get me wrong I love these lectures all the more for it! He's obviously so clever he's thinking about stuff other than a's and b's but the humanity of it makes me laugh, as with "Chocolate Chip"!
ChOcOlAtE ChIp
Great, now I know how to get (without learning it by heart) sin (a+b) and cos (a+b), thanks to the e^ia notation. Beautiful.
perfect video material to get a headache.
When waves from the universe enfolds down the spiral vortex of an atom, it will recoil, expanding into three-dimensional spacetime
Magnetic fields are always enfolding+/-unfolding spacetime at right-angle's
Symmetry is broken forming a Fibonacci spiral where the two wave's meet, creating the wobbly particle effect, as these like charged wave-center's repel becoming equally spaced around the expanding spiral vortex, polarized wave-centers share the same expanding moments of time until acted upon
Small modification in 1:03:3 correct proof =>
* = λb * then we conjucate all => = λb* as Lambda is real (eigen value of Hermitian Matrix) then there is no difference then = λb then we subtract from first equation
This is really good ! Hope he is still teaching and we could attend his lecture. Just a wish !
Would be nice if a higher quality video was uploaded, the blackboard looks more like a bunch of black blocks then that you can see the formula's o.o
Suprisingly, he makes a real mess of the orthogonality proof at 1:04:50.
When he reverses 'a' and 'b' in the second equation, he's already conjugated, so he should have: (blMla)=B*(bla)
and not
(blMla)*=B*(bla)*,
the B here standing for the eigenvalue, I can't type lamda.
Then all he needs to do is show that B*=B as B is real.
I hope this helps for anyone as confused as I was!
What an incredible find. There is no way in the world to match the quality or value of the material being presented here - if you actually want to be conversant in quantum mechanics without spending your life. Given all that, does anyonw know which of these lectures actually gets into a discussion, definition, manipulation of entangled particles?
Hi, I have an MPhil degree in Physics. I have taken six courses of Prof. Susskind which are "Classical Mechanics," "Quantum Entanglements Part 1," "Special Theory of Relativity," "General Theory of Relativity," "Cosmology," and "Statistical Mechanics". I have also taken handwritten notes of him in all the details and currently I'm typing his notes on Latex. Kindly let me know in the comments which lectures of him do you want the notes of and I will make them for you on Latex. Cheers!!
@4kx I wish I knew what could (reliably) make people happy. But, yes, I think this is a better question than "what job is waiting for me?".
@4kx I can't tell you what job would be waiting for you; but I can tell you that - if that's the question you want to ask - you should stick with engineering. If you're going to change, do it because you love the subject, not because you can sell yourself at a higher price.
Now I have to learn Trigonometry. I either forgot or did not learn anything either about the numbers, be it complex or imaginary. This is exactly the kind of course I wanted in which I can go back and learn what did not learn before and then apply that learning to learn something absolutely mindboggling.
Frankly, it still does not appear to me to be science. It is more like a science fiction written in Mathematics, rather than written in English. Sometimes I feel I must be crazy to go through this ordeal, where much isn't visual. But there is a carrot down the rabbit hole.
I can totally see that
This lecture series is great, but I can't watch this one.
An error occured, please try again!
Somebody fix it, please!
hello
Hey
I like how ive heard for years that no one understands quantum mechanics yet susskind just says "its calculus but for probabilities" LOL
In those types of calculus, though simple, there is a best way to drive them (with maximum security, maximum generality, keeping as long as possible a useful "helicopter view" without loosing information during the mathematical operations), and minimizing the mistakes... This way is the following :
It seems to me , the reason the electrons at 90deg, half emit photons is that only half of them line up when you prepare them. The other half continues the precession indefinitely being before the photon emission state threshold. The kinetic energy of the precession must exceed the photon energy. However the mathematics still works the same.
Good luck to you with your probability calculations, if you can prepare electrons always half of the cases, regardless the variables depending on the magnetic field, for instance..
@Boepyne you are correct
I am loving these lectures. But I have a question. He's using "pointer" to distinguish a vector in physical space for pedagogical purposes from a "vector", a vector in the vector space of states. Wouldn't it be less confusing to talk of state vectors, state spaces, orthogonal state vectors, etc. versus vectors, space, orthogonal/perpendicular etc.?
It would be less confusing if people who couldn't use abstract vector spaces didn't take courses too hard for them.
1:09:00 The measurement will only tell you what the state is if you know beforehand that exactly one of the two states is realised.
Two important lessons: "When you multiply matrices, the order counts. The order counts when you multiply matrices" 1:41:33
Absolutely consistent.
glad i took linear algebra
i know. its sooo hard to wrap my head round this maths. especially because there are so many names to learn.
@ 7:50 He talks about the set of numbers such that x^2 + y^2 = 1. But wouldn't it have made more sense to say that the complex conjugate is essentially the inverse? Z1*Z2 = 1 is an inverse relationship.
Just responding for people in the future. The answer is no because not every complex number has the property (z*)z = 1. Only those of unit magnitude. So it is not true that the complex conjugate is the inverse in general. This is why in one of these lectures he talks about "unitary complex numbers." Unitarity is the property which means the complex, or hermitian conjugate of an operator is equal to its inverse. He's being somewhat flippant because this is a property you'd normally associate with a matrix or general operator but in some senses you can think of complex numbers as being a matrix with one entry.
Wikipedia gives the general formula for dotting the sigma vector with an arbitrary unit-length vector in threespace. I don't know whether the following is particularly beautiful or interesting, but here's what I got when I expanded the elements in that general formula to their respective 2x2 representations of complex numbers as matrices of real numbers:
a3 0 a1 a2
0 a3 -a2 a1
a1 -a2 -a3 0
a2 a1 0 -a3
I observe that:
- All the a3s are on the main diagonal, and the main diagonal is a3, a3, -a3, -a3.
- All the a2s are on the counterdiagonal as a2, -a2, -a2, a2.
- The remaining elements are 0, 0, 0, 0, a1, a1, a1, a1.
So I got that the bra vector is the state of the system and the M matrix is the observables but what is the ket vector? the state of the system after you measure to find out what the observables are? and if the bra and ket are the same vector does that mean that the gazintas are the same as the gazoutas? (as we called them at one place I worked)
As a graduate in mathematics from Cambridge, I find the method-explaining parts to be irritatingly slow (but necessary for the intended audience - I don't dispute that). Even so, I'm still glad to see such an enjoyable series of lectures available for free.
Agreed, it's odd to even attempt this stuff without getting at least to Abstract Vector spaces and natural comfort with operations in euclidean spaces.
What's your favorite Area, I only have a BS from a state school but was a passionate student (mental disorders and superpowers are like electricity and magnetism) Topology was a favorite for sure. I love linear algebra, but studied so much on my own (and my Community College had the best math In Plato's dodecahedron imo) I was always way ahead of those classes. Topology with graduate students was not too different actually.
I'm just getting into this stuff but I think I'm understanding
It still amazes me that someone looked at the strange properties of the spin of an electron and realized that this totally abstract idea of vector spaces and the properties of Hermitian matrices described the results perfectly.
Yes, right? But it was an accident, so many bright people were searching, someone was bound to discover it. But in fact they sort of got it wrong. You do not need matrix algebra for QM, it can be formulated in the real Clifford algebra of spinors. This was revealed by David Hestenes in the 1960's, too late to catch on..
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Mind Blown I did not know a conjugate can Equal , in Matrix ....
I love it that doing the matrix math is the analog of running an experiment. I found a website that forced me to realize that you can't get an answer out of matrix math just by inspection with rare exceptions, you have to run the math step by step. i.e. you can't tell bow an experiment will turn out until you run it. All the more so in quantum mechanics where the values don't even exist until you run the experiment -- that thing that Einstein mistakenly conceived as "hidden values" that always existed and that the experiment revealed.
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They're quaternions that play the role of observables.
I'll have to get up to snuff on vector analysis and review matrix operations and watch this again. That would be my advice to anyone. Be up to speed on those topics before watching this.
@SuperWorldwide23 Well, I'm no expert, but to give you the gist of it; a quantum value, like spin, only obtains a particular value in the very act of measurement - so the rather abitary value that falls out when measuring one particle will be instantaneouly reflected in the other. Sorry I've not responded 'til now, I forgot all about this until my attention was drawn back by another response.
I understand Matrix expectation value and eigen values
not sure why we are surprised that we force spin to be along one direction the answer will be one way or the other way? Is there another way of thinking about this?
simplicity is the fpundation of all knowledge
...so ypu can stuff paying attention to detail.
@alecbrady since I was a kid, I loved know how things works, how machines, electronics, toys works - very often I crashed them to see what is inside. The universe is the most complicated toy we can imagine, understanding how IT works probably is the most beautiful thing in it. However, does physicist are happy? Dealing with numbers, models make them happy trough whole live?
A rather faster paced (more concise) exposition of qm (including entanglement) is given by DrPhysicsA. Though even there he also labours the arithmetic and algebra.
but when we convert a bra vector ket (or cet, I don't know the spelling) we do the same, transform the columns to rows, and then complex conjugate..
Great help (as thumbed up) - but why in the world would you call lambda 'B'???
I think L would have been a better choice ;-)
Ha! I just noticed that the corrected proof has appeared on the whiteboard after the break; someone must have pointed it out over coffee.
i loved the ending of this video
HD PLEASE???
when you normal complex conjugate a matrix, you not only complex conjugate the numbers, but also interchange the rows and columns.
When you multiply the vector by its complex conjugate, what is the resulting number a probability of, photon emission or not emitting a photon?
There is always one who either asks stupid questions to try to look smart or repeats what was already said so they can feel smart
Read The Feynman Lectures on Physics, Vol III.
Thanks Suss
I had to replay this to get this key lesson straight: when we prepare the electron by putting it in a magnetic field, the way to find the quantum state we're putting it in is first, take the dot product of the direction cosines of the direction of our magnetic field with the vector of "sigma" matrices (elsewhere identified as Pauli matrices), and consider the result as an operator for hypothetically turning on the magnetic field again without changing the direction of the magnet and looking for whether the electron emits a photon. We know very well that if we did that, it wouldn't. We associate that result (no photon) with one of the eigenvalues of the operator. The associated eigenvector is the state we are putting the electron into. End of procedure.
I had to replay it cos my brain kept filling up and spilling out my ears...
exp(iθ), it's just a phase.
59:00:00
dif bw eigen state and any other state is that eigen state is measurable?
Ya. He had it right initially, but then the students confused him.
I checked out your videos/profile as we share a common interest in science and music. Very impressive sir. You have truly mastered your art. Also kudos for thinking for yourself and trying to understand the universe scientifically, instead of taking the easy way out and following the religious heard.
It seems to me the proof at 1:04:00 is wrong. The third line is wrong: * =/= lambda_b* *. lambda_b* should be lambda_a* there, and the proof doesn't go through. He should have written e.g.: = lambda_a ; = lambda_b ; * = = lambda_b* = lambda_b , as lambda_b* = lambda_b, for it is real. Hence lambda_a = lambda_b . Since lambda_a =/= lambda_b, = 0.
No, he was right, except he haven't to complex conjugated lambda_b.
* =
= lambda_b = lambda_b *
So * = lambda_b *
and = lambda_b .
Matúš Frisík Sorry, I must insist that the third line at 1:04:26 is wrong, for * = = lambda_b =/= lambda_b* .
He corrected himself, he wrote * = lambda_b* *. Which is correct, since lambda_b* = lambda_b, so the result is same, but you're right there were no need to complex conjugate lambda_b.
Oh, and * =/= lambda_b* , so your way wasn't correct either. Correct equation is * = lambda_a .
Matúš Frisík = lambda_b . Then how do you complex conjugate lambda_b ?
I am still reading part I, can't wait to get to part III. I am struggling a bit to understand it. But I think I will be allright knowing that I am not a native English speaker, and at school they are still teaching me what a force is and how to calculate a momentum.
0:35:47: i think Steven Hawking is auditing this course xD
You won't understand it without the math, you can't just jump halfway through it will all be jibberish. If you don't want to "spend your life" then watch these lectures rather than going to University. If you want to be conversant go listen to Michio Kaku or Brian Cox.
Without this highschool math, that is :)
Andrei Andrei. It took over a hundred years before mathematicians routinely accepted "i". -and before that, over a thousand years before they accepted negative numbers!. Complex numbers are indespensible to maths - and since Nature is mathematical, indespesible to physics,too. Complex numbers complete the number system - in the sense of wanting to solve all (polynomial) equations. Learn to love them. I promise that with a little familiarisation, you will.
Okay but when I was first presented negative number I don't remember having trouble accepting them. Complex numbers still don't make sense.
If you accepted negative numbers so easily, you probably thought of the numbers as some kind of arrows on the number line. Well, complex numbers are no different ! They're just arrow on the number 'plane' ! We call that plane the complex plane, or the Argand plane. What you thought about the number line (the arrows) still apply, and it actually is a good way to see that complex numbers are as natural as the reals.
Then when you hear the word 'complex' substitute with 'orthogonal'. If you can cope with orthogonality and can accept that the complex parts of complex numbers behave orthogonaly to the real part then you can see why they are good for representing orthogonal parameters of a thing. Compare with complex numbers to represent the amplitude and phase of sinusoids in electronics though complex exponentials. It works just fine. Two parameters, two parts to the number.
Do anyone have any idea regarding how to find observables or hermition operator along the x,y,z axis ?
36:42
I don't get the idea of HERMITIAN CONJUGATION...I mean, the simple complex conjugate of each matrix is the same as that, so why do we use a special term like "hermitian conjugation" ?
Just in case of Hermitian matrices, they are equal to their complex conjugate..
Thought the same;)
Could me some one tell me, what job is waiting for me, if I change my studies to theoretical physic? I'm now on mechanical engineering, is it worth to change the studies?
Sitting on the street with cardboard sheet with text asking money and food.
Good gravy!....lol @ the guy around 00:58 who has to explain to the whole
class that he knows the geometric interpretation......
With some editing, most of the repetitions and empty times could be eliminated
around 58:00 for about 1 whole minute, is this guy serious?
I thought it was silly too
Hermitian conjugate isn't the same as complex conjugating it.
I hope he never gets pulled over with his electron visible to the cop on the back aeat.
that would be the entangled youtube video, floating on the other side of the galaxy
Where we are if the Thing begin reduce h? 😂 I think h/ you didnt how funny that All is
0=nix 🤣 # aha²? 🤣
I don't understand at all what you are trying to ask. What Thing?
+Snakebloke your genius intellect is needed here! please provide some intellectualised geniusness to this subject
I was never taught any of this elementary trig in highschool...
That's programming for ya.
at 1:18:32 b is current state and a is predicted or future state
15:21 " chocolate chip " :)
00:34 the guy asking a question sounds like Stephen Hawking. :)
Stephen Hawking in the lecture? 35:45
+DerMacDuff LOL...I know that accent,...there was a mathematics professor here in RUclips long ago,..he was from Norweigh..he spoke like that..He even replied my messages...I dont see him here anymore...I had fun in youtube long ago..
xD
Unless you write in an appropriate basis.
another interesting toy is our brain i would add :D
i guess the logo s at the starting is for susskind truly😂
too many questions from people who wants to show off how smart they are
Or maybe they simply want confirmation that they aren't misinterpreting his presentation. Questions are vital for true learning, as I see it at least.
haha, it's funny you say that, I always think the same thing too whenever students try to ask sophisticated questions, maybe I'm not being so cynical after all.
Miister Cloud You can tell when the questions are genuine and when they are for showing off. Plus there are also the fake laughs to remove any doubt.
Haha, I used to do that in my first year comp sci classes :P
people also tend to use comment sections to show off how smart they are :P
Pointer!....pointer!!
What?
@@srinikethvelivela9877 He wants us to let him know when he mistakenly uses "vector" when he means "pointer". (He uses "pointer" for a spacial vector, and "vector" for a more abstract, non-spacial, concept/vector, as in bras and kets.)
😉
@@deecampbell.rva-2 thanks dude
Clark Ronald Jones Deborah Robinson Matthew
@Boepyne He makes the mess because he's influenced by the audience. If you're next to a blackboard (or whiteboard ;-) ) you lose the overview. I don't like it if people try to correct you who don't know what they're talkin' about. About the proof. I think you're not done after B*=B. What you really have to assume is that a/b is equal to b/a. This is true for real numbers. And than you are at the same point where he makes the fault. Maybe it's possible to show it for complex numbers too.
1:16:57
just refresh
if b isnt eigen state of sys,how do we know it exists
hmm, tried.
Dont' work!
how is z=x+iy ???? that's only if you are adding vectors ???? Anybody knows ?
It's just the way a complex number is usually conceived. i is assumed to belong to the number system and to have the property that i^2 = -1 (which no real number would satisfy).
you can work on Wall Street and make the big bucks doing statistical and info/systems theory for JP Morgan.
Boepyne is perfectly correct for orthogonality proof at 1:04:50; 2 mistakes have been made on the same equation. One mistake from Susskind by making 2 operations at the same time but only noting one on the board; the second mistake is induced by the student intervention... Happy enough they are "fairly lucky". But they end nevertheless proving the theorem by means of a wrong proof !!! Pity! History of science gives lots of historic false proofs of right theorems!...
complex and modified. hard to absorb.
im so confused....fuck i wanna learn more math!!! i dont think im dumb but im not a genius i guess either.
Ooh, Ooh, teacher pick me! I'm oh so smart! Mummy and Daddy tell me so every day! Freakin' Stanford geeks.