Physics 511A, 2011: Chapter 1, Volume 2. The principle of relativity

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Back to Physics 511A, 2012: Graduate Electrodynamics.

Sections 1-5, 7 were 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 $\int _{a}^{b}ds$ is maximal if taken along a straight world line that connects $a$ and $b$.
3. Derive the formula for length contraction using the Lorentz transform.
4. Suppose we denote a matrix that performs the Lorentz transformation as $L({\vec {v}})$. Do Lorentz transformations commute? That is, is $L({\vec {v_{1}}})L({\vec {v_{2}}})$ equal to $L({\vec {v_{1}}}+{\vec {v_{2}}})$?
5. Derive the formula for aberration of light when transforming to a new coordinate system.
6. Prove by direct computation that $u_{i}w^{i}=0$.