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2005/06 Undergraduate Module Catalogue

MATH2410 Special Relativity

10 creditsClass Size: 200

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2005/06

Pre-requisites

(MATH1011 or 1060 or 1740) and (MATH1050) and (MATH1410), or equivalent.

This module is approved as an Elective

Objectives

To introduce students to the concept of the relativity of motion and to the physical and mathematical principles of the Special theory of Relativity. On completion of this module, students should be able to: (a) present the physical basis of light-speed invariance and the replacement of Galilean transformations by special Lorentz transformations; (b) apply the theory to various aspects in the study of optics, for example, the Doppler effect; (c) manipulate the mathematical relation between mass and energy and the physical meanings of this relationship; (d) present example sheets to test his or her ability to apply reasoning based on relativistic ideas rather than an ability to apply set formulae.

Syllabus

To explain observed features of the propagation of light, our classical view of space and time has to be replaced by the special theory of relativity. This theory has some surprising consequences - moving clocks run slow and the mass of a particle increases with speed. The energy - mass relation is derived using relatively simple calculations. Special relativity is essential to the understanding of general relativity (gravitation, black holes, etc.) not covered in the course. Topics covered include: 1. Historical survey, the Michelson-Morley experiment Inertial frames, standard configuration. 2. Derivation of Special Lorentz transformations (SLT). 3. Consequences of the transformation: inverse transformation, Galilean limit, graphical representation of SLT, length contraction, time dilation, the twin 'paradox', lack of simultaneity, velocity transformation, lack of rigidity. 4. Optics: the transformation of plane waves, the Doppler effect, aberration, reflection at a moving mirror, speed of light in a moving medium. 5. Spacetime: the light cone, causality, group properties of the Lorentz transformation. 6. Tensors: notation, 4-tensors, raising and lowering indices, products. 7. Mechanics: the 4-velocity, 4-acceleration, and 4-force. Velocity-mass relation, 4-momentum. The 4-force and energy equation consequences. 8. Particle scattering and decay.

Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures (22 hours) and examples classes (11 hours).

Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

2 hour written examination at end of semester (85%), coursework (15%).

Reading list

The reading list is available from the Library website

Last updated: 13/05/2005

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