### Modern Physics Video Lecture Courses

General Relativity (Physics 514, McGill University)

Course topics:

Course by Professor Alex Maloney. Introduction. Gravitation and Curvature, a brief review of special relativity. Differential Geometry I: Metrics, Manifolds and Tensors. Differential Geometry II: Curvature, Geodesics. General Relativity. Einstein's Equation. The Stress Tensor. Linearized Gravity. Newtonian Solutions. Gravity Waves. The Schwarzschild Black Hole. Tests of GR. Cosmology, FRW universes. General Black Holes.

Special Relativity (Stanford, by Leonard Susskind)

Course topics:

Space and time of Newtonian mechanics. The old ether theory. The new special theory. Postulates of special relativity. Comparisons of meter sticks and clocks; setting of clocks. Lorentz transformation. Four-dimensional space-time of Minkowski. Einstein's velocity addition law. Aberration. Doppler Effect. Particle dynamics. Longitudinal and transverse mass. Association of momentum with motion of energy. Motion of charged particles in E and B fields. Transitions, collisions, reactions. Light pressure. Matrices in four-space. Time-like, space-like, and singular intervals. Proper time, proper length. The principle of covariance. Character of tensor equations. Geodesics. Tensor analysis for special relativity. Tensor algebra; contraction. Discussion of four-vectors; position, velocity, acceleration, momentum, force. Electrodynamics in four-space. Lorentz four-potential. Maxwell stress tensor. Electromagnetic field tensor, dual tensor. Collisions and Reactions Momentum space. Radiation from accelerated charges. Jacobian determinants. Dynamics of a system of particles. Radiated power; Larmor's formula. Multipole radiation.

Einstein's Theory (Stanford, by Leonard Susskind)

Course topics:

The equivalence principle. Paths of particles and light rays. Gravitational red shift. Twin paradox. Clocks on a rotating platform. Tensor analysis for general relativity. Transformations of tensors; algebra of tensors. Christoffel symbols. Covariant derivatives. Riemann-Christoffel tensor. Ricci tensor. Equation for a geodesic. Principle of Covariance. Einstein's field equations Gravitational field in free space. Weak-field approximation to Einstein's field equations. Discussion of the Schwarzschild solution. Gravitational shift of spectral lines Black holes. Gravitational Waves. Cosmology.

Quantum Mechanics (Stanford)

Course topics:

Randomness in quantum mechanics. The two slit experiment. Interference. Observables. Reversible and irreversible processes. Heisenberg's uncertainty principle. Wavepackets. Relativistic particles. Complex numbers and Hilbert space. Complex functions. Complex vectors. Inner product. Bra. Ket. Operators. Linear operators. Hermit operators. Eigenvalues and eigenvectors. The postulates of quantum mechanics. Observables. States. Entangled staes. Bell states. Coherent states. Schrodinger equation. Time dependent and time independent schroedinger equations. Scattering theory. Partial waves. Hamiltionians.

Quantum Entanglements (Stanford, Fall 2006)

Quantum Entanglements (Stanford, Spring 2007)

Course topics:

Quantum Mechanics review. Observables. Spin. States. Density matrices. Hidden variables. Bell's inequality. EPR paradox. Projective Hilbert space. Fubini-Study metric. QM Copenhagen interpretation. QM Bohm interpretation. Wavefunction collapse. Quantum information channels. Quantum teleportation. No-communication theorem. Entropy. Entanglement.

Cosmology (Stanford)

Course topics:

Early Scientific Cosmology. Cartesian and Newtonian World Systems. Cosmology After Newton and Before Einstein. Stars. Galaxies. Location and the Cosmic Center. Containment and the Cosmic Edge. Space and Time. Curved Space. Special Relativity. General Relativity. Black Holes. Expansion of the Universe. Redshifts. Newtonian Cosmology. The Cosmic Box. The Many Universes. Observational Cosmology. The Early Universe. Horizons in the Universe. Inflation. The Cosmic Numbers. Darkness at Night. Creation of the Universe. The Golden Age of Cosmology

Carl Sagan Explains 4th Dimension

Lecture outline:

Physicists say "Space is curved. Universe is finite but unbounded.", what do they mean? Carl Sagan takes you to a flat universe where he shows how a 3D world would look for 2D creatures. From this explanation you can understand how difficult it would be for us to understand four dimensions.

Why Physicists Need the Large Hadron Collider

Video lecture outline:

The LHC is the biggest (27 kilometers around) scientific instrument ever built and it is now ramping up to start taking data. It smashes together protons at enormous energy in order to create new forms of matter. Physicists hope to find the Higgs Boson which is the missing link in our current theory. Hopefully unanticipated discoveries will be made. I will explain why physicists need this expensive tool in order to understand nature at the smallest distance scales.

Why did the LHC break down last year?

LCD video outline:

A report on the causes of the September 19th incident that brought down the LHC. The main reason was an electrical part overheating and no longer being superconducing. As a result, huge force crashed the magnets together.

Air on the Dirac Strings

Video description:

"Air on the Dirac Strings" explores the rotation of objects connected by a belt or by strings to a fixed background. Such an object plus its connections to the background will be entangled by a 360 degree rotation, yet returned fully to its original configuration after a 720 degree rotation. This combination of topology and geometry has applications to the physics of an electron.

The geometry/topology of the Dirac string trick is intimately connected with the quaternions. The patterns of rotation of an object that is connected to a background are described directly by the quaternion algebra. The quaternions are also useful for representing rotations in the usual sense, and they were used in this way to program the graphics in this movie.

This motion has been incorporated into the Philippine wine dance where a dancer rotates a wine glass 720 degrees without spilling a drop.

Bonus: Graduate Classical Mechanics (Physics 451, McGill University)

Course topics:

Lagrangian Mechanics. Degrees of freedom and equations of motion. Conservation of

Energy and Momentum. The Calculus of Variations. Euler-Lagrange equations. Constrained Systems and Lagrange multipliers. Oscillators. Small ď¬‚uctuations. Damped, forced and anharmonic. One dimensional systems. Motion in a central field. Kepler's laws. Symmetries and Conservation laws. Noether's theorem. Gallilean relativity. Rotation. Euler's equations. Rigid Bodies. Theory of small fluctuations. Molecules. Hamiltonian Mechanics. Phase space. Poisson brackets. Canonical Transformations. Symmetries. Noether's theorem. Time Permitting: Liouville's theorem & Poincar'e recurrence. Hamilton-Jacobi theory. Integrable systems. Chaos. Quantization. Field Theory.

Bonus 2: Classical Mechanics (Stanford University)

Course topics:

Lagrangian formulation of mechanics. Variational principles and least action principles, Lagrangian equations of motion, constraints and configuration manifolds, conjugate variables and phase space, and symmetries and conservation laws. Hamiltonian formulation of mechanics. Hamilton's equations, canonical transformations, Poisson brackets, Liouville's theorem, invariants, Hamilton-Jacobi equation, action-angle variables, and adiabatic damping. We will also introduce the symplectic approach to canonical transformations using Lie transformation and Lie Algebra. Rigid body motion. Inertia tensors. Euler angles. Rotation matrices. Small oscillations. Normal modes, ordinary resonance, parametric resonances. Central force problems (the Kepler problem and scattering).

Bonus 3:Lee Smolin about Universe

Video outline:

What is space and what is time? This is what the problem of quantum gravity is about. In general relativity, Einstein gave us not only a theory of gravity but a theory of what space and time are - a theory that overthrew the previous Newtonian conception of space and time. The problem of quantum gravity is how to combine the understanding of space and time we have from relativity theory with the quantum theory, which also tells us something essential and deep about nature.

Have fun guys! Till next month!

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