# SPECIAL RELATIVITY - 2023/4

Module code: PHY3038

## Module Overview

An FHEQ Level 6 course on Einstein’s theory of Special Relativity in a rigorous four vector and tensor approach. Postulates and principles are reviewed. The course then develops relativistic dynamics of point-particles and waves and the relativistic treatment of electromagnetic and electrodynamics phenomena

### Module provider

Mathematics & Physics

STEVENSON Paul (Maths & Phys)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 117

Lecture Hours: 22

Tutorial Hours: 11

Semester 1

None.

## Module content

• Fundamentals The necessity for special relativity, the postulates, review of definitions, including inertial frames, clocks, spacetime, events and coordinates, spacetime intervals, proper time.

• Mathematical Notation Four-vectors, covariant and contravariant quantities and transformation rules, Lorentz boosts, invariants, tensors. Minkowski spacetime

• Relativistic Mechanics Transformation of four-vectors.  Lorentz contraction. Time dilation.  Use of proper time, transformation of velocities.  The four-velocity, and four-momentum and related invariants.  Forces and acceleration. Equations of motion.

• Electrodynamics Waves; The relativistic invariance of the Maxwell equations.  Representation of E and B fields in relativistic form.  The current four-vector.  The Lorentz force.  The electromagnetic potentials A and ɸ

• Gauges;  The Coulomb gauge;  retarded and advanced potentials

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COURSEWORK ASSIGNMENT 30
Examination End of Semester Examination (2 hours) 70

None.

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

• understanding of the concepts of Special Relativity;  the ability to apply these concepts to problems in the physics of particle and wave mechanics; an understanding of the links between Special Relativity and Electromagnetism; the ability to tackle problems linking these two areas.

Thus, the summative assessment for this module consists of:

• Coursework; a written report on a conceptual aspect of Special Relativity; 30%, 1000 words (addresses learning outcome 4)

• 2-hour closed-book examination at the end of the semester (70%), with a section A of compulsory questions and a section B with 2 questions chosen from 3.  In Part A answer all questions; In Part B answer two questions out of three. If all three questions in Part B are attempted only the best two will be counted. (addresses learning outcomes 1, 2, 3, and 4)

Formative assessment

Problem sets are issued during the course.  Some of the class time will be devoted to problem-solving tutorials.

Feedback

Students will receive detailed feedback on the coursework assignment;  oral feedback is given in tutorial sessions on the problem sets.

## Module aims

• develop the theory and conceptual understanding of special relativity and space-time from first principles, using four-vector and tensor notations, providing applications of the theory from the dynamics of point particles through to electrodynamic phenomena.

## Learning outcomes

 Attributes Developed 001 Define and use four-vectors and the accompanying mathematical machinery that accompany them, including deriving invariants and using tensors. K 002 Apply the principles of Special Relativity to an extended range of problems involving particle dynamics and wave-like phenomena. C 003 Understand how electromagnetism and electrodynamics are developed from a relativistic point of view, and be able to manipulate the Maxwell Equations in four-space, and understand the use of retarded and advanced potentials KC 004 Describe and explain concepts relating to the consequences of Special Relativity, the nature of space-time and related observables KPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Enable students to understand the physics concepts involved in Special Relativity, how they interlink with Electromagnetism, and to equip students with the formal methods necessary to enable them to tackle a wide range of applications and problems in Special Relativity and guide further study.

The learning and teaching methods include:

1. Complete set of self-contained lecture notes for self-study and from which live lectures are presented

2. Captured content based on live lecture-based material

3. Tutorial classes in which problems are worked through with the assistance of teaching staff

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: PHY3038

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics with Astronomy BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Technologies BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Nuclear Astrophysics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics MSc 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Nuclear Astrophysics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Astronomy MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Physics with Quantum Technologies MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Physics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2023/4 academic year.