19 February 2022

# Relativity and Beyond

online courseThe aim of this Enrichment Workshop is to, as much as possible, follow the approach and arguments used by Albert Einstein in his ground-breaking 1905 Paper: On the Electrodynamics of Moving Bodies, that introduced SPECIAL RELATIVITY to the world. Specifically, we focus on Part I of the Paper, in which Einstein delineates the main mathematical theory. Our approach is to make complementary use of space-time pictures, animations and algebraic formulation. To make the course accessible to pre-University students we focus on core mathematical relationships that are sufficient for understanding the physical significance of the theory, rather than treating the most general transformations which require a knowledge of more convoluted mathematics.

This workshop is broken down into the following sections:

SECTION 1: POSTULATES AND MODEL BUILDING

SECTION 2: SIMULTANEITY AND THE RELATIVITY OF LENGTHS AND TIME

SECTION 3: LORENTZ TRANSFORMATION

SECTION 4: PHYSICAL MEANING OF THE EQUATIONS

SECTION 1: POSTULATES AND MODEL BUILDING

In this opening section we establish the mathematical model for the theory of special relativity and outline Einstein’s two postulates upon which he was able to construct the theory. In so doing we will take time to reflect on the significance and brilliance of Einstein’s ‘thought experiment’ approach.

SECTION 2: SIMULTANEITY AND THE RELATIVITY OF LENGTHS AND TIME

In this section we will reproduce Einstein’s original construction (that he developed in section 1 and 2 of his 1905 Paper) in which he used the two principles of relativity to develop a non-Newtonian concept of simultaneity. We then use this model to compute relativistic measures for length and time and to show that we cannot attach any absolute agreement to the concept of simultaneity.

SECTION 3: LORENTZ TRANSFORMATION

In this third section we formally define the concept of an inertial frame of reference and our task will be to find the system of equations connecting the transformation of co-ordinates and times of these two frames of reference. What is known as the Lorentz Transformation.

SECTION 4: PHYSICAL MEANING OF THE EQUATIONS

In this final section we will use our results previously established in the Workshop to derive the equations for length contraction and time dilation. And this session will culminate in a consideration of the Twin Paradox (1911). Another of Einstein’s thought experiments, that arose beyond the content of his 1905 Paper, and which demonstrated that in special relativity time is a route-dependent quantity.

### Course leader

Ian Tame is a Master postgraduate in Mathematics (with specialism stochastic processes). He has published mathematics articles (in English and German), possesses a postgraduate teaching qualification, and has over 25 years’ experience in education.

### Target group

Students studying, or about to study mathematics, physics or philosophy at A-level or International Baccalaureate Diploma and other pre-university courses - especially those who aspire to study mathematics, science, computing or engineering-based disciplines at university; and current Undergraduate students studying Mathematics.

### Course aim

By the end of the course students will have gained a thorough understanding of Part I of Einstein’s seminal 1905 Paper in which he delineated the mathematical theory of special relativity. Specifically, students will learn how to use the concept of non-Newtonian simultaneity to derive the equations (with examples) that describe the counter-intuitive phenomena of length contraction and time dilation.

### Fee info

EUR 99: plus 19% VAT