2017/18 Undergraduate Module Catalogue

MATH2410 Special Relativity

10 creditsClass Size: 70

Module manager: Prof Serguei Komissarov
Email: S.S.Komissarov@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2017/18

Pre-requisite qualifications

MATH1010 or (MATH1050 and MATH1060) or equivalent.

This module is approved as a discovery module

Module summary

In order to explain observed features of the propagation of light and elementary particles, our classical view of space and time has to be replaced by the Special Theory of Relativity. This theory has some surprising consequences - simultaneity of events depends on the speed of observers, moving clocks run slow, an accelerating particle gets heavier as its speed increases, and mass can be converted into energy (and vice versa). The physical theories of fundamental interactions have to comply with the Special Theory of Relativity, which is also essential to the understanding of General Relativity (gravitation, black holes, etc) not covered in this module.

Objectives

The course aims at introducing students to the basic consequences of 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 transformation by the special Lorentz transformation;
(b) apply the theory to various aspects in the study of optics (e.g., the Doppler effect) and particle scattering;
(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

1. Historical survey, the Michelson-Morley experiment. Inertial frames, standard configuration.
2. Einstein's postulates of Special Relativity.
3. Basic consequences of the axioms: lack of simultaneity, time dilation and length contraction.
4. Derivation of the special Lorentz transformation.
5. Consequences of the transformation: inverse transformation, Galilean limit, graphical representation of SLT, length contraction, time dilation, lack of simultaneity, addition of relativistic velocities, acceleration.
6. Optics: the Doppler effect and the aberration of light.
7. Spacetime: the light cone, causality, space-time intervals, the proper Lorentz group.
8. Tensors: notation, 4-vectors and 4-tensors, classification of 4-vectors, scalar product.
9. Mechanics: 4-velocity, 4-acceleration, and 4-force. 4-momentum and its conservation. Rest energy and relativistic kinetic energy. Massive and massless particles.
10. Particle collision and decay.

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	10	1.00	10.00
Lecture	22	1.00	22.00
Private study hours			68.00
Total Contact hours			32.00
Total hours (100hr per 10 credits)			100.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem solving assignments

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Total percentage (Assessment Coursework)		15.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	85.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 26/04/2017

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