10C's : C4, C5

C4:
    [See lectures, class web pages, HWs & solutions, and Math Insight S2.3, on p. 446 of TB1.]
    Two principles of special relativity:
        A. The speed of light, c, is the same for all observers moving with any constant velocity;
        B. Laws of nature are the same for all observers moving with any constant velocity.
    Consequences:
        (For equations of the following three items, see the first three equaions (and only the first three, not the rest) of Math Insight S2.2.)
        * E = m c^2,  and relation of the mass, m, to the rest mass, M;
        * Time dilation (which is independent of direction of the motion of a moving clock); For the equations, see Math Insight S2.1.
        * Length contraction (only in the direction of the motion of an object).

C5
     [See lectures, class web pages, HWs & solutions, and S4 of TB1; see also Chapter 3 of TB2 ]
Einstein's general relativity: the warping of the Minkowski  (3+1)-dimensional (flat) spacetime.  

* Equivalence principle: The effects of gravity are exactly equivalent to the effects of acceleration.
    ** Thus the principle of special relativity (the democracy among observers moving with constant velocity with respect to each other) is generalized to the principle of general relativity (the democracy among observers moving with acceleration with respect to each other due to gravity).
* Einstein's general relativity relates mass/energy to the warping of the Minkowski spacetime, like Riemann's warping (in the 19th century) of the Euclidean (flat) space. However, Einstein's relating geometry of spacetime to mass/energy was revolutionary, which Riemann did not have. Also Riemann geometry does not involve time.
* In curved (or warped) space, geodesics ("straight lines" in curved space) replace straight lines in Euclidean (flat) space.
* Observational verifications of general relativity
        1. Precession of the perihelion of Mercury.
        2. Bending of light in gravitational field, gravitational lensing.
        3. Gravitational time dilation and redshift of light .
        4. Observation of the decrease of orbital period of binary star system (by Hulse and Taylor), consistent with the consequence from gravitational  wave emission..

Culture:
    * We watched the discussion of general relativity from PBS "Einstein Reveals", edited by Chau.
    * Hermann Minkowski was a professor of Einstein when Einstein was a undergrad at ETH, Zurich, Switzerland.
    * Euclid of Alexandria lived from about 325 BC to 265 BC.
    * Georg Friedrich Behard Riemann lived from 1826 to 1866.
    * See link to the 1993 Nobel prize of Hulse and Taylor.