Lecture 5 | Quantum Entanglements, Part 1 (Stanford)
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Lecture 5 of Leonard Susskind's course concentrating on Quantum Entanglements (Part 1, Fall 2006). Recorded October 23, 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
Comments
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At times, he seems to be confusing Bell's inequality with Bell's theorem, which is the statement that Bell's inequality is sometimes violated in QM.
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I obtained the result on the Bell's inequality using the
probability of spin of an electron prepared with spin in n direction,
being up in direction m. (1+cos(tmn))/2 (Lecture 4)
A not B on a singlet for the case of A being up B not being 45 deg is then given by
for |u d>= 1. (- 1/sqrt(2)/2 For the case in lecture 5, seems to be - sign
for |d u> =0. (1+1/sqrt(2)/2
Gives the same answer with a simpler way. -
I cannot see a shit on the board. -_-
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they need to re-record this lecture...
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How can sigma_i + tau_i, in the triplet state, have three eigenvalues (0, +/-2) when it's the sum of two 2x2 matrices?
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Regarding the no cloning theorem. As I understand this it is not possible to clone all quantum states for an electron but on the other hand you have quantum superposition as can be observed in the double-slit experiment where you can observe an interference pattern and that is explained as the result of the fact that the electron takes both paths simultaneously and consequently can be in 2 different location at the same time. Does that mean that the electron passing left slit in the double-slit experiment does not shear all the quantum states with the electron passing the right slit but they are still regarded as one and the same electron in quantum superposition?
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QM = cos^2(theta)
Classical HV = 1/2cos^2(theta)+.25
For pi/3, QM predicts 0.25
Classical HV predicts 0.375.........here endeth the lesson! -
beautifully taught
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+Snakebloke you can't let this guy beat your intellectualised meat like that... clearly your grasp is better in this matter
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One of the most important lectures of the series, and the camera man was taking a break, oh well
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In his cloning example, the right came out to be (|u> + |d>)/ sqrt 2. Is the left going to be the same value? If so, what distinguishes it from being right from left.
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Can't read the board, the lecture is very poorly recorded. I thought Stanford was a good school. Why put out such a sloppy result and put your name on it?
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The Bell inequality arises because Bell included an ad-hoc assumption taken from quantum interpretations (that the wave-function represents a complete description of particle alone, and that when interacting with a passive instrument, it behaves like a wave encountering a passive barrier). That assumption is then used to place a constraint on the 'hidden variable' model.
Bell constrained the supposed hidden variable model so that the selection of the outcome is solely on the basis of the disposition of orientation variables (for spin/polarization measurement) internal to the particle, relative to the axis of the of the analyzer. The outcome of the interaction supposedly depends on the orientation of internal properties of the particle alone, the analyzer is required to be a passive marker.
Spatial symmetry means that such a model must operate within the Bell limits, which is essentially a straight-line correlation curve from analyzers aligned to counter-aligned/right-angles (spin/polarization).
In the case of spin/polarization interactions, if the encounter with the instrument spatially distorts the probability distributions along the axes of the analyzer, then there is no surprise that the correlation between one analyzer and another depends on the relative angle of the analyzers. The answer is stunningly simple, and idea that non-locality is required is a fallacy.
This is consistent with the QM prediction that the expectation function for the density of one polarization result when a particle while interacts with a polarization analyzer, is a Cos^2(theta) curve. Note that the probabilities are on average 50-50 because the expectation function of the opposite result is (Sin^2(theta).
Because the spatial orientation of the expectation functions depends on the orientation of the analyzers, the observed correlation between analyzers is then expected.
When this is modelled by discrete hidden variables not mapping onto, but interacting with, a suitable analyzer it is a simple task to build simulation exactly matches the statistical predictions of quantum theory.
Ding dong Bell, the quantum puss's in the well.... -
In the classical "set theory" example , the sets A,B, and C have attributes which are entirely independent of each other -- and this leads on to the inequality statement .
Is it then fair to apply this classical "theorem" to the three sets in the quantum case where we actually start by specifying that the three sets here are not independent , but highly correlated with one another ?
Is it really any wonder that the answer is different from that in the classical case ? -
All these people asking questions about matrixes and vectors etc...how trivial.......the only question that I want answered is ..where has the bottle of booze gone?
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pure academic hubris BS video
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The quality of the video is giving me a headache
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Where do you get that idea? All he is doing is to show that QM doesn't follow the rules of classical set logic.It simply illustrates that the mathematics of QM has a different set of rules. In the same way that complex numbers have a different set of rules from real numbers. The implication is for QM, not classical logic. i.e. you can't apply classical logic to QM - which is sort-of-profound.
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When he says "classical logic" I don't think he means Aristotelian or Boolean or Fregean logic; rather, he's saying that the logic of classical mechanics is different from the logic of quantum mechanics. In CM, a state is a member of a set and two states don't interact, but in QM two states are members of a vector space, and you can add them together.
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Unfortunately in this 5th lecture the camera is not focused in the text on the white board
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