# Some amusements in theoretical physics

#### By Simon Horsley

*"...reality must take precedence over public relations, for Nature cannot be fooled."*

Richard P. Feynman, *Presidential Commission on the Space Shuttle Challenger Accident (1986)*

## Solving problems in wave physics:

This is a postgraduate course designed to help PhD students become mathematically self-sufficient; to be able to solve (or approximately solve) wave propagation problems without the aid of commerical packages. We shall be using pen-and-paper methods alongside simple programs written in python.

### Notes:

Some of these notes contain more detail than will be covered in the lectures. Note - this page is currently being modified.

Lecture 1 - Introduction: the wave equation throughout physics
Lecture 2 - basic complex analysis ( Problems)
Lecture 3 - sources of waves ( Problems)
Lecture 4 - pulses ( Problems)
Lecture 5 - beams of radiation ( Problems, Slides)
Lecture 6 - boundary conditions ( Oliver Heaviside, Slides)
Lecture 7 - scattering from a single obstacle ( Problems, Slides)
Lecture 8 - scattering from an infinite number of obstacles 1 ( Problems, Slides)
Lecture 9 - scattering from an infinite number of obstacles 2 ( Problems, Slides)
Lecture 10 - propagation through inhomogeneous media ( Problems, Your opinion of the course, Slides)

## Two paradoxes:

*"How wonderful that we have met with a paradox. Now we have some hope of making progress."* - Niels Bohr

[As quoted in *Niels Bohr: The Man, His Science, & the World They Changed*, by Ruth Moore (1966)]

I'm interested in the fundamentals of theoretical physics, and I think nothing teaches us new things better than a paradox. It's also fun to observe how different people react to them - denial, anger, depression? This is the place where I'm (very slowly) collecting the paradoxes that I think are interesting. The solutions might find their way here too one day.
- Extracting momentum from a magnet at rest. Does Newton's third law apply to the interaction of charges and magnets?
- Using a gauge transformation to set a magnetic field to zero. The fact that the physics of electromagnetism shouldn't depend on the choice of gauge is
very important to modern physics. However, in some situations the magnetic vector potential can appear as the gradient of a scalar, even though the magnetic field is not zero. What stops us from setting it to zero?

## Not quite physics:

More or Less: The Kate Bush Conjecture: Does Kate Bush's version of pi occur somewhere in the decimal expansion of pi? (Is pi a Normal number?)

The Philosophy of Questions: Lani Watson's project to understand what makes a good question.

Steven Hitchins' Literary Pocket Book: Exploring the relationship between quantum mechanics, geometry, chaos, and modern poetry (amongst other things).