Lecture 4 | Quantum Entanglements, Part 1 (Stanford)
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Lecture 4 of Leonard Susskind's course concentrating on Quantum Entanglements (Part 1, Fall 2006). Recorded October 16, 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: http://www.youtube.com/view_play_list?p=A27CEA1B8B27EB67 Stanford Continuing Studies: http://continuingstudies.stanford.edu/ About Leonard Susskind: http://www.stanford.edu/dept/physics/people/faculty/sussk... Stanford University channel on YouTube: http://www.youtube.com/stanford
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I've asked this before but hoping that new people looking at this video may be able to answer - how does he get 6 states for the two electron system. I see uu, ud, du, dd, but I don't see where the math plops out two more states. I realize my problem is I'm probably still thinking about this classically, but this has always been my hangup in these lectures.
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You'd think with Stanford's endowment, they could film this in something better than PotatoCam.
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Susskind "Let's just get the cookie out of the way that's the most important thing..." He's the Groucho Marx of Physics.
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I AM DYINGGGG..
Please helpp...
How did he count 6 variables at 01:22 ? Why we remove 2 variables and which ones do we talking about? -
fascinating , finally I understand something
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Electrons nailed to the black board ... Cool
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21:15 Sussmann: it took me about 15 minutes to figure it out, but I used a lot of tricks. If you try this without tricks you will be much faster ... LOL
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There is more humour in this video than in any other Susskind lecture.
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Why do I feel so f**** stupid.....?
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At 1.08 he suddenly produces a table ,which shows the action of the different sigma operators on the spin state of an electron.
Mathematically the action of these matrices on the relevant vectors is correct -- but I don't remember him previously showing the validity of doing this in relation to changing the specific spin state .
Anyone care to explain ? -
When he starts the calculations at 1:29:00. Should he not actually had used 1/sqrt(2){|ud> - |du>} to make the calculations of the mean value to be zero for all of the <σ1>, <σ2>, <σ3> matrices? At the end of the calculations at 1:47:20 he change the + sign to a - sign. When using the + sign the calculations of the mean value does not end up equal to zero or do they?
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I have follow this introduction in quantum entanglement from Lecture 1 and to this point where I have hit a brick wall and don't understand what he is saying. From 1:20:20 and forward in this video he says..."The gentleman over here remarked before about the number of variables that it takes to specify the states of an electron and the answer was 2. The answer was 2 independent real variables that are important in specifying the state of an electron. How many do you think it takes to specify 2 electrons? Lets go to the counting. There's a 4-dimensional vector space |uu>, |ud>, |du>, |dd>. What states can you build? You can multiply each of these with a complex number and ad them all together. That's the most general state of 2 electrons that you can write down. The linear combination with arbitrary coefficients, subject to the constraint thet the soms of the squares are equal to 1 and that the phase doesn't matter. Now how many are they? " What does he mean by the "phase" and exactly how is the counting done? I have try to find some information that I have missed from previous Lecture 2 and to this point but cant find anything that helps me to understand this. If I ad a different complex number to each of the 4 vectors and ad them all together I end up with .................... [a+c+i(b+d), e+g+i(b+f), a+e+i(b+f), c+g+i(d+h)]. How does he come to the conclusion that you should remove 2 variables and end up with 6 variables? Which variables are supposed to "go away" and why?
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It is a pity that this masterful lectures are only viewable in such a low video quality. It is true that they are so well read that one can follow them even without looking at the video, at most by playing with the formulas with paper and pencil. But the fact that we get constantly tons of high quality video crap shoved up our minds (e.g. the frontpage of this site), and that this treasure that teaches such beautiful and deep ideas, is only viewable at 240p, makes a very distinctive and sad statement about the world we are living in and our culture.
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Susskind's statement : "commuting matrices have the same set of eigenvectors" is clearly false : the diagonal matrices diag (1,2) and diag (1,1) commute , but <1,1> is an eigenvector of only diag(1,1), not of diag (1,2).. A weaker statement does hold :
If AB = BA and A has a basis of eigenvectors whose eigenvalues are all different , then A and B have the same set of eigenvectors. -
Broken shoulder?? :(
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Wow, santa Claus is pretty good at physics!
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Quantum Entanglement is pervasively known as The God Effect, it’s the synchronicity between spatially separated particles on an infinitesimally subatomic scale regardless of their distance. When entanglement occurs, there’s a correlation between their momentum, velocity and spin in their state of entanglement, and their speed in which information propagates between particles seem instantaneous, regardless of their fluctuation in space. An inseparable relationship first introduced by Erwin Schrodinger in 1935.
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It's much better to browse these courses and lectures on his website "The Theoretical Minimum." They summarize each lecture so you know what you're about to watch.
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Is there is a limited distance between the two entangled electrons?
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