Log for exercise classes (Pedram)
- Exercise 1:
We discussed rotation of vectors in R^3, Galileo transformations, meaning of relativity and
the invariance of the Minkowski length S^2 = x^2+y^2+z^2 - (ct)^2 under Lorentz transformations. We did [RQ] 1,2,4,6 in Chapter 1, [Oe1] 1, [C] 2.1a, 2.6.
- Exercise 2:
We discussed conservation of momentum and energy in classical mechanics,
the relative notion of simultaneity in SR using spacetime diagram, group properties of rotations and Lorentz transformations (boosts) and that partial differential operator (and actually
all covariant vectors) transforms under inverse Lorentz transformations. We did [RQ] 3,7,9 in Chapter 2, [C] 2.1b, 2.3, 2.8
- Exercise 3:
We discussed simultaneity and Lorentz transformations in spacetime diagrams,
time dilation and length contraction, trajectory of a point particle in spacetime parametrized by proper time, and index computation.
We did [RQ] 10,13 in Chapter 2, [MOS] 1.4, 1.8, [Oe1] 2, 3
- Exercise 4:
We discussed scattering of point particles and the relativistic Doppler effect.
The second hour was workshop on problems in Chapter 10. [MOS] 1.16, 1.27, [C] 10.1, 10.7
- Exercise 5:
Midterm test 1. The second hour, we discussed and made a small experiment on
the equivalence principle. We did [RQ] 2 in Chapter 3, [C] 3.1, 3.2.
- Exercise 6:
We recalled the difference between weak and strong equivalence principle.
We reviewed variational calculus, mentioned its use in extremizing paths on curved spaces and discussed the Hamilton principle in classical mechanics.
We did [Oe2] 1, 3.
- Exercise 7:
We discussed the induced metric on embedded surfaces in R^3 and how the metric tensor transforms
under coordinate transformations. We computed the circumference of a circle inside the plane, the sphere and the "pseudo-sphere" and concluded that the classical
result "L=2 pi r" is modified in non-Euclidean geometries. We did [C] 4.1, 4.2, 4.3, 4.9.
- Exercise 8:
We discussed the symmetry of Christoffel symbols, computed the metric in a rotating frame and showed
how length measurements in space using light signals are related to the metric components. We did [RQ] 1, 2 in Chapter 5, [C] 5.2, 5.3, 5.6.
- Exercise 9:
We discussed how to compute the Christoffel symbols directly from the metric (cumbersome!) and by
using the geodesic equation. The second hour was workshop on problems from Chapter 3, 4, 5 and Oe2. We did [Oe2] 6.
- Exercise 10:
Midterm test 2. The second hour, we derived the gravitational angular deflection in Schwarzschild
spacetime. We did [C] 6.1, 6.2.
- Exercise 14:
Midterm test 3. The second hour, we discussed how scaling of the metric by a real number
affects the Christoffel symbols, Riemann tensor, Ricci tensor and Ricci scalar. We concluded that a different sign convention for the metric only affects
the Ricci scalar and the Riemann tensor with all indices down. We mentioned how to compute the Riemann curvature for a spherically symmetric metric in matrix
notation. We did [Oe4] 6a).
Last updated: Jan 24, 2008|