PHYM006	Relativity and Cosmology	2013-14
	Dr T.J. Harries
Delivery Weeks:	T2:01-11
Level:	7 (NQF)
Credits:	15 NICATS / 7.5 ECTS
Enrolment:	28 students (approx)

Description

This module is an introduction to the special and general theories of relativity. Although the course avoids the use of advanced mathematical topics and emphasises the concepts behind the theory, students will require a good level level of mathematical fluency and intuition in order to engage with material.

Module Aims

The module aims to develop an understanding of Einstein's Special Theory of Relativity. The General Theory will also be introduced and applied to the standard cosmological model and to the three historical tests of the theory: the precession of the perihelion of mercury, the bending of light passing close to the sun and the gravitational red shift.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. give coherent explanations of the principles associated with: special relativity, general relativity, and cosmology;
  2. interpret observational data in terms of the Standard Model of the evolution of the universe;
  3. describe experiments and observational evidence to test the general theory of relativity, explain how these support the general theory and can be used to criticise and rule-out alternative possibilities;
  4. apply tensors to the description of curved spaces;
  5. solve problems by applying the principles of relativity;
  6. deduce the Friedmann equations describing the evolution of the Universe.
  7. explain what is meant by: intrinsic and extrinsic curvatures, the curvature of space, local inertial reference frame, and Riemannian coordinates/geometry.
  8. describe world lines of particles and photons in a curved space-time;
  9. describe the Cosmological Principle and the Robertson-Walker metric;
• Discipline Specific Skills and Knowledge:
  10. explain to non-specialists the basis of one of the corner-stones of 20th century Physics;
• Personal and Key Transferable / Employment Skills and Knowledge:
  11. locate, retrieve and evaluate relevant information from the WWW.
  12. meet deadlines for completion of work to be discussed in class by developing appropriate time-management strategies.

Syllabus Plan

1. Introduction
2. Key aspects of special relativity
   1. Galilean and Lorentz transformations
   2. Length contraction and time dilation
   3. Doppler effect
   4. Relativistic mechanics
3. Accelerated reference frames
   1. The person in the lift
   2. Inertial forces
   3. Tidal forces
4. Curved spaces
   1. Euclidean spaces
   2. Curvature in one and two dimensions
   3. Intrinsic and extrinsic curvature
   4. Riemannian curvature
   5. Introduction to tensors
5. Application to space-time physics
   1. The equivalence principle
   2. Tidal forces and local inertial frames
   3. Equations for world lines of free particles and photons
   4. Schwarzschild metric
   5. Black holes
6. Experimental tests of general relativity
   1. Advance of perihelion of mercury
   2. Bending of light
   3. Gravitational red shift
7. Cosmology
   1. The cosmological principle
   2. Robertson-Walker metric
   3. Red-shift distance relation
   4. The Friedmann equations
   5. Cosmic microwave background
   6. Helium production
8. Additional Topics
   1. Eotvos experiments
   2. Observational tests of GR
   3. Gravitational waves
   4. Gravitational lensing
   5. Derivation of the Friedmann equations from the Robertson-Walker metric

Learning and Teaching

Learning Activities and Teaching Methods

Description	Study time	KIS type
20×1-hour lectures	20 hours	SLT
2×1-hour problems/revision classes	2 hours	SLT
5×6-hour self-study packages	30 hours	GIS
4×4-hour problem sets	16 hours	GIS
Reading, private study and revision	82 hours	GIS

Assessment

Weight	Form	Size	When	ILOS assessed	Feedback
0%	Guided self-study	5×6-hour packages	Fortnightly	1-12	Discussion in class
0%	4 × Problems sets	4 hours per set	Fortnightly	1-12	Solutions discussed in problems classes.
100%	Final Examination	2 hours 30 minutes	May/June	1-12	Mark via MyExeter, collective feedback via ELE and solutions.

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Lambourne R. (2010), Relativity, Gravitation and Cosmology, Cambridge, ISBN 9-7805-2113-1384 (UL: 530.11 LAM/X)

Supplementary texts:

• Hartle J.B. (2003), Gravity: An Introduction to Einstein's General Relativity, Addison-Wesley, ISBN 9-7808-0538-6622 (UL: 530.11 HAR)
• Kenyon I. (1990), General Relativity, Oxford University Press (UL: 530.11 KEN)

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phym006

Further Information

Prior Knowledge Requirements

Pre-requisite Modules	Vector Mechanics (PHY1021), Introduction to Astrophysics (PHY1022) and Mathematics with Physical Applications (PHY2025)
Co-requisite Modules	none

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Original form of assessment	Form of re-assessment	ILOs re-assessed	Time scale for re-assessment
Whole module	Written examination (100%)	1-12	August/September assessment period

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods SLT - scheduled learning & teaching activities 22 hrs GIS - guided independent study 128 hrs PLS - placement/study abroad 0 hrs Total 150 hrs

Summative assessment Coursework 0% Written exams 100% Practical exams 0% Total 100%

Miscellaneous

IoP Accreditation Checklist	N/A this is an optional module
Availability	MPhys and PGRS only
Distance learning	NO
Keywords	Physics; Theory; Spaces; Curvature; Time; Curves; General theory; Shifts; Cosmological; Equation; Inertial frame.
Created	01-Oct-10
Revised	N/A