Physics 511A, 2014: Chapter 1, Volume 2. The principle of relativity

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Back to Physics 511A, 2014: Graduate Electrodynamics.

Sections 1-5, 7 will be largely covered in class. Much of section 6 will be your own responsibility.

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? Do they add? That is, is $L({\vec {v_{1}}})L({\vec {v_{2}}})$ equal to $L({\vec {v_{1}}}+{\vec {v_{2}}})$? Verify this by direct construction.
5. Derive the formula for aberration of light when transforming to a new coordinate system.
6. Prove by direct computation that $u_{i}w^{i}=0$.