EECS 395/495 - Special Relativity in Optics
CATALOG DESCRIPTION: This course will introduce students to Special Relativity (SR), illustrate the relation between SR and Maxwell’s Equations, and explain the origin of magentic fields and forces. In addition, it will describe quantitatively how modern optical devices and systems such as Sagnac interferometers, gyroscopes, accelerometers, clocks and the global positioning system must take into account the effects of SR.
REQUIRED TEXTS: None
- Primary: “Special Relativity,” A.P. French, W.W. Norton, New York, London (MIT Introductory Physics Series); Available from Amazon.com
- Secondary: “Classical Electrodynamics,” J.D. Jackson, Third Edition, Wiley, New York.; Available from Amazon.com
COURSE GOALS: This course will introduce students to Special Relativity (SR), with an emphasis on the role SR plays in the field of optics. After taking this course, a student would: be familiar with the experimental foundation behind SR, understand the origin of magnetic fields and forces, and be able to anlayze quantitatively the effect of SR on the behavior of modern optical devices and systems.
PREREQUISITES: EECS 224 or equivalent.
PREREQUISITES BY TOPIC:
- Maxwell’s Equations in Vector Form
- Elementary Differential Equations
DETAILED COURSE TOPICS
- Experimental Foundation behind Special Relativity
- Lorentz Transformation of Coordinates
- Addition of Velocities
- Time Dilation and Lorentz Contraction; Proper Time.
- Forward Time Travel and Resolution of the Twin Paradox.
- Lorentz Transformation of Electric and Magnetic Fields.
- Second Order Doppler Effect.
- Origin of Magnetic Fields and Forces.
- Lorentz Invariant Representation of Maxwell’s Equations.
- Maxwell Stress-Energy Tensor.
- SR in accelerated frames; Sagnac Effect; Fresnel Drag for Electromagnetic Waves in Moving Media.
- Relevance of SR to modern devices: Optical Gyroscopes, Global Positioning Systems, Atomic Clocks, Optical Accelerometers.
- 1Outlook for Further Studies: Connection between SR and General Relativity; Connection Between SR and Electron Spin.
COMPUTER USAGE: Matlab based exercises.
LABORATORY PROJECTS: Not Applicable
- Homeworks (80%)
- Final Examination (20%)
COURSE OUTCOMES: When a student completes this course, s/he would:
- be familiar with the experimental foundation behind Special Relativity (SR),
- understand the origin of magnetic fields and forces,
- understand the behavior of modern optical devices and systems where SR play practical and important roles, and
- calculate the effect of SR under most circumstances relevant to the field of optics
ABET CONTENT CATEGORY: 100% Engineering.