Exam questions (theory), Special relativity

1. Show that Maxwell equations without sources are invariant for boosts.
2. Enunciate the postulates of special relativity, and derive boosts and rotations from them.
3. Derive the expression of the Lorentz-Fitzgerald contraction and explain its consequences for the Michelson-Morley experiment.
4. Derive the expression of time dilation from Lorentz transformations.
5. Explain how 4-momentum must be defined, and derive [math]\displaystyle{ E=mc^2 }[/math].
6. How do velocity and acceleration vary under boosts?
7. Define 4-vectors and give three examples. What does one mean by the terms covariant and contravariant? Define 4-tensors and give two examples.
8. Explain what are the properties of Minkowski space-time, and how 4-vectors can be characterised. Give the various canonical forms and the corresponding properties.
9. Define the concept of 4-force. What does Newton's second law become in special relativity?
10. Show how Maxwell's equations can be rewritten in covariant form. Define the 4-current density.
11. Define the field tensor of electromagnetism, and show how the electric and magnetic fields transform under a boost. What are the Lorentz invariants one can build from them?
12. What is the electromagnetic field of a moving charge?