Lecture 6 | The Theoretical Minimum

(February 13, 2012) Leonard Susskind starts the class by answering a question that arose in the last lecture about photons and the energy at different states and then continues with the topic of entanglement.

[josella]

This lecture corresponds to the following paragraphs in the Quantum Mechanics - The Theoretical Minimum (2014) book:
0:00:00 Question from last week
0:10:38 4.14 Collapse
0:14:44 6.1 Tensor Products
0:25:00 6.4 Two Spins
0:35:36 6.5 Product States
0:41:50 6.8 Observables
1:02:00 6.7 Entangled States
1:27:30 6.9 Composite States
1:33:52 Questions

[qwadratix]

Actually, I rather love the way he doesn't let inconsequential mathematical niceties get in the way of the Physics.
He really doesn't care if a factor of '-1', or 'h' or 'i' get lost, much less whether it's a right or left hand frame. People accuse him of being slapdash but I've no doubt he's fully capable of paying attention to the detail when he feels it matters.
Wonderful entertaining stuff.

[kai-xuanyao]

Don't you guys wonder where the first 20 mins went? In the beginning of this video there are already stuff on the blackboard and they're not from the last lecture. And at about 10', Lenny said that half an hour had passed. I am sure there's 20 more mins before this video.

[badlydrawnturtle]

The student questions make me feel so smart.

[asgeirnilsen]

I just want to thank for sharing these lectures for free. I recommend starting with "Classical mechanic" and then these lectures, then you just can go on.

[MrEzystreet]

Beautiful! He explains everything in such a great manner.

[patriciaheil]

about 53:20 the audio drops by 50%, right after a beep. is that beep something about battery power? I had to turn on captions to keep following. 1 hour 10 the audio is almost completely gone.

[DIOGYKD]

Can't thank you enough, this is treasure.

[vman]

I'd like to try to clarify the response to the question the person from the audience asks at 50:00. The electron we're considering is in the up state. The direction in which we're measuring is along the x-axis. The question is, why, intuitively, does the electron get flipped from up to down when a measurement is taken in this direction? I believe the point, which is not explicitly stated, is that measurement and the action of a spin operator are different. The action of the sigma-x spin operator on a state vector is to change that state vector (in this case, the state happens to be an eigenvector of sigma-z and it gets flipped to another eigenstate of sigma-z). Measurement would actually collapse the state onto either right or left, in this case with equal probability since the state down (into which the action of the sigma-x spin operator transitions the up state electron) can be expressed as a superposition of the eigenvectors of sigma-x where the coefficients alpha_r and alpha_l are both 1/sqrt(2).

My follow-up question is, how do you know whether an apparatus that is interacting with an electron is acting as a spin operator or as a measurement device?

[columbiafermi]

Aside from the Physics, I try to identify what he is eating.

[omerkzlkanat]

Where is the guy that posted timestamps?

[BankingBrad]

Thanks for giving us these great videos

[vman]

What a wonderful lecture series!

Automatic closed caption needs some work... see for example 9:46... :)

[peterwan]

So, can a product space basis be made of ur, ul, dr, dl?

[TheRamlaw]

Merlin had magic, Susskind has physics, Times change the wizards remain.

[enisten]

8:28 Doesn't the spread in the energy levels consist of the two eigenvalues we were already considering here? Is there some other spread? How come the spread in the energy levels is inversely proportional to the spread in the lifetimes of the states for a free spin-1/2 particle in a magnetic field, for which there are only two energy levels and therefore only one possible transition between them (i.e. one lifetime)? Does this mean the photon's energy actually needs to match the difference in energies of the two states EXACTLY, unlike what the prof implied? How can one even construct a continuum of energy eigenvalues for a free spin-1/2 partcile in a magnetic field? I think he confused the situation with that of an electron inside an atom, for which there are an infinite number of discrete energy levels. So I'm still confused like the student about the actual possibility of an infinite precision match of frequencies. This should be impossible unless you're using a photon emitted from the same kind of atom making the same transition. What am I missing?

[Metallurgist]

At 43, Susskind applies the Sigma (x) matrix to the (up) state spin and gets a (down) spin  -- which is fine from the matrix maths point of view .
However, in an earlier lecture  he had shown that if an (up) state spin is "measured " on an ( x) orientated detector there would be a 50 % chance of getting either (right) or (left) spins --- isn't this more or less the same thing ?
I'm confused by the conflict between the two circumstances?     

[NikitaEvseev]

would you please give me the link to that so popular video ;)

[davidwilkie]

Perfectly good lecture, parallels in Logical Duality and Logarithmic Time AM-FM Timing-spacing Communication requires re-cognition reiteration (?).

In the Holographic Principle Imagery projection-drawing composed of Electron-photon-phonon-Proton Resonance Bonding Superposition-point Quantum Operator Logic Fields Modulation Mechanism Condensation Chemistry.., the continuous cause-effect connection bond is reciprocal-reversible recirculating @.dt zero-infinity instantaneous reflection in ratios of 0-1-2-3-4 superimposed proportioning recognised in "pumping" Lasers and LIDAR position mapping methods. "Near" nodal vibrational timing is emitting and "distant" positioning is reflected, (what is the REAL circumstance of e-Pi-i sync-duration Inflation-Gravitation?), such that the superimposed positioning Imagery of QM-TIME Holography is created by what appears to be e-Pi-i sync-duration resonance, condensed matter bonding via Temporal Singularity, the Reciproction Apature here-now-forever, ie at continuous creation cause-effect Origin.

(Everyone has a different orientation to any understanding, and Holography is the ultimate test of doodle-drawing relationships, maybe the Wheeler timing-phase-> Feynman Diagrams-> Susskind's modified and reintegrated GR Black-body Singularity composite story for String Theoretical Vibration, projection-drawing analysis of Quantum-field pictures works..)

The old "Tired Light" Theory of Red-shifted or expanded Universe idea, requires reiteration, old => distant pulse-evolution differentiates "ride the wave" of UHF ->ULF holographic positioning projected probability phase-locked coherence-cohesion sync-duration resonances, so image inversion via the Apature of entangled Singularity Reciproction Act-uality => AM-FM Timing-spacing coordination Communication. (Just saying)

[davidwilkie]

This far along in an education, the details overwhelm the basic concepts used at an origin story of terms and behaviours that the students expect to represent the subject of discussion, except, for the QM explanation, there never is a "setup" of fixed points from which to develop understanding. Eg Chemistry used quantized measurement to analyze the amorphous blob of the world of metaphysics into the table of chemical elements, but that word "elements" came from geometric connection thousands of years before, and in turn, was first revealed from basic Astronomical Time and Illustrated Space of mythology. (in that order)

The original non-comprehension of existence, but clear observations of simple causes and effects, (becoming measurable mathematically), has continued in parallel to the development of "the science of measurement", and there's still no absolute confirmation of the motivation, of cause/effect duality.

The causality connection is real and mostly invisible change without a definitive hypothesis, or it's one that is acceptable in purely mathematical analysis, but not in explanatory context. It is what it is, time eternal. Word-definition has both functional and topical meaning, as an identification (of conceptual behaviour) in context.

A glossary of geometric elements in congruence with the chemical/crystal elements is suggested in context by the occurrence of a connecting pivot-point origin at .dt, ..then the subset element-axial-line of connection between now and a "lineal" sum of +/- elements of eternity in the instant .dt, ..that progresses in that lineal-instant interval to divide continuously in every possible ratio of infinity and .dt, ..in the quantized progression of the resonant natural numbers. Ie temporal singularity is the amorphous "numberness" of a continuous eternal existence derived from the superposition now, and oscillating/uncertain in the interval - in Qantum Number dominant progression quanta familiar to musicians and Quantum Chemistry.

Information density at the limits is equivalent to the probability of stated existence of an element approaching one. It's concentrated/focused on an original meaning.
Something vaguely intuitive like the "sound of one hand clapping", but visually indefinite like the concept of reflection that is implied by the infinite limit of continuous existence in dualistic +/- 1, is connection to zero. Something resonant floating in nothing.