Classical Optics and Special Relativity (361-0-1)

Instructors

Carl Dahl

Meeting Info

Technological Institute A110: Mon, Wed, Fri 11:00AM - 11:50AM

Overview of class

Special relativity is at the heart of our most foundational understanding of the universe. The very nature of what particles can exist is entirely constrained by quantum mechanics and the representations of the Lorentz group. How can special relativity, which allows space and time to rotate into each other, be consistent with the quantum mechanics of Bohr, Planck, Heisenberg, and Schrodinger which treat time on a very special footing? Our path to the answer of relativistic quantum field theory begins by understanding our first relativistic classical field theory: Classical Electrodynamics. This course will introduce us to the modern language of Lorentz invariant field theory, highlighting universal principles.


Part 1: Review of Special Relativity phenomena, including time dilation, length contraction, and problems with simultaneity. Why do these phenomena follow from a universal speed of light, and how can they be described using the language of space-time events and space-time diagrams?


Part 2a: Foundations and Symmetries (Classical Mechanics): How do symmetry groups (2-D and 3-D rotations) constrain the nature physical laws in classical mechanics? Review of geometric objects (scalars, vectors, tensors) as the natural language for rotationally invariant laws.

Part 2b: Foundations and Symmetries (Special Relativity): Introducing Lorentz transformations (boosts) as rotations in space-time, and the corresponding new geometric objects (4-scalars, 4-vectors, 4-tensors).

Part 2c: Relativistic dynamics: Relativistic 4-momentum conservation.
4-forces and 4-acceleration. How to describe the phenomena from Part 1 in accelerating reference frames.


Part 3a: Review of classical field theory (E&M): Electromagnetism in
one frame of reference. Maxwell's equations, conservation laws and the
Poynting vector, Scalar and vector potentials and their E&M gauge
transformations.

Part 3b: Relativistic field theory (E&M): Manifestly Lorentz-invariant
forms for Maxwell's Equations, with 4-currents, 4-potentials, and the
field tensor. Relativistic conservation laws in E&M. Lorentz
transformations and invariants of electromagnetic fields.

Part 3c: Action principles. The electromagnetic field interacting with
a point particle. Conservation laws from symmetry via Noether.
Connection to quantum field theory.


Part 4a: Classical optics, linear media. Review of wave solutions to
Maxwell's equations in vacuum and in dielectrics. Anisotropic media and
bi-refringence.

Part 4b: Classical optics, non-linear media. Phase matching and
resulting phenomena (frequency doubling, spontaneous down-conversion).
Connection to quantum optics.

Teaching Method

The course will be lecture driven with weekly homework and take-home final.

Class Materials (Required)

We will reference the following texts, available online at no charge to
Northwestern students:


Griffiths, "Introduction to Electrodynamics", 5th Edition.

https://www.cambridge.org/highereducation/books/introduction-to-electrodynamics/FD23E188E2BDCDB40199CFE3386EC08F#contents



Blandford and Thorne, "Applications of Classical Physics",
http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/