Help us caption and translate this video on Amara.org: www.amara.org/en/v/mQo/ Professor Susskind opens the lecture by examining entanglement and density matrices in more detail.  He shows that no action on one part of an entangled system can affect the statistics of the other part.  This is the principle of locality and is directly connected to the requirement that systems evolve over time only through unitary operators.  Violating locality implies non-local hidden variables which are equivalent to wires that transmit information instantaneously.  These would allow true "spooky action at a distance," but they don't exist. Professor Susskind then discusses the simplest possible continuous system of a particle moving in one dimension.  He presents the wave function for such a system, and discusses its Hermitian operators and observables including the operators corresponding to position, momentum, and energy.  The energy operator is the Hamiltonian, and generates the time evolution of a system.  Finally, he presents the difference between the Hamiltonian for a relativistic particle moving with a constant velocity in any reference frame (e.g. a photon or neutrino), and a non-relativistic particle (i.e. one with mass). Topics:  - Is entanglement reversible? - Continuous systems - A particle moving in one dimension - Position, momentum, and energy operators - Hamiltonian operator generates the time evolution of a system Recorded on February 27, 2012.

1. Introduction to Quantum Mechanics
2. The Basic Logic of Quantum Mechanics
3. Vector Spaces and Operators
4. Time Evolution of a Quantum System
5. Heisenberg Uncertainty Principle & The Schrödinger Equation
6. Entanglement: Entangled, Singlet, & Triplet States
7. Entanglement and the Nature of Reality
8. Particles Moving in One Dimension and their Operators
9. Fourier Analysis applied to Quantum Mechanics
10. The Uncertainty Principle and Classical Analogs

Quantum theory governs the universe at its most basic level. In the first half of the 20th century physics was turned on its head by the radical discoveries of Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, and Erwin Schroedinger. An entire new logical and mathematical foundation—quantum mechanics—eventually replaced classical physics. We will explore the quantum world, including the particle theory of light, the Heisenberg Uncertainty Principle, and the Schrödinger Equation. This course is second-part of a six course sequence given by Prof. Leonard Susskind that explores the theoretical foundations of modern physics - the Theoretical Minimum. Topics in the series include classical mechanics, quantum mechanics, theories of relativity, electromagnetism, cosmology, and black holes.