# Special Relativity and Probability and Random Processes

## Details

Code 19749

Level of study First Year

Credit value 10

Semester 1

## Module description

The way in which mathematics is used in theoretical physics to describe the physical universe can be beautiful, powerful and take us beyond our intuition. All of these features are illustrated in this module as we investigate Einstein's theory of special relativity and the mathematics of probability which we will use later in quantum mechanics and statistical physics.

One might expect that the combined impact speed of two cars in a head-on collision would be the sum of the two speeds recorded on each car's speedometer just prior to impact. This result (technically called a Galilean transformation) turns out not to be correct - though the error becomes appreciable only as velocities approach the speed of light. In this course we show how the observation that the speed of light is constant leads to the Lorentz transformation: a new set of rules which relate experiments done in moving laboratories. They lead to predictions which have since been verified experimentally such as "moving clocks run slow", "moving rulers shrink" and Einstein's famous equation: E=mc^2. We will also develop the mathematics of dealing with randomness and probability, from discrete outcomes (like the throwing of a dice) to continuous distributions (like heights of adults). Such notions lie at the heart of quantum mechanics, and is the way we deal with complex systems - like the 10^23 atoms in a typical solid. A key concept will be the understanding of probability distribution functions and how they are used to compute averages and variances. We will consider conditional probability and how to combine probabilities ultimately arriving at the central limit theorem.