Physics 511A, 2013: Chapter 1, Volume 2. The principle of relativity

From Ilya Nemenman: Theoretical Biophysics @ Emory
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Back to Physics 511A, 2013: Graduate Electrodynamics.

Sections 1-5, 7 will be largely covered in class. Section 6 you will study on your own.

Homework Questions

  1. Problem about uniform relativistic acceleration after Section 7.
  2. Prove that is maximal if taken along a straight world line that connects and .
  3. Derive the formula for length contraction using the Lorentz transform.
  4. Suppose we denote a matrix that performs the Lorentz transformation as . Do Lorentz transformations commute? That is, is equal to ?
  5. Derive the formula for aberration of light when transforming to a new coordinate system.
  6. Prove by direct computation that .