Programme And Module Handbook
 
Course Details in 2023/24 Session


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Module Title LC Special Relativity and Probability and Random Processes
SchoolPhysics and Astronomy
Department Physics & Astronomy
Module Code 03 19749
Module Lead Dr Dimitri Gangardt & Dr Richard Mason
Level Certificate Level
Credits 10
Semester Semester 1
Pre-requisites
Co-requisites
Restrictions Available to MSci Physics w Theo Physics students only
Contact Hours Lecture-20 hours
Practical Classes and workshops-8 hours
Guided independent study-72 hours
Total: 100 hours
Exclusions
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.
Learning Outcomes

By the end of the module the student should be able to:

  • use the Lorentz transformations to translate events between inertial frames;
  • calculate time dilation and Lorentz contractions;
  • use the energy momentum invariant to solve simple problems relativistic kinematics;
  • deduce when non-relativistic transformations can be used;
  • convert a description of a probability problem into a space of possible outcomes and their probabilities and use this information to calculate conditional probabilities;
  • recognise problems that represent binomial probability or Poisson distributions and be able to calculate probabilities from such distributions;
  • use a probability distribution function of a continuous variable and to be able to compute probabilities, averages and variances of such distributions
Assessment 19749-01 : Exam : Exam (Centrally Timetabled) - Written Unseen (80%)
19749-02 : Assessed problems : Coursework (20%)
Assessment Methods & Exceptions Coursework (20%); 1.5 hour Examination (80%)
Other None
Reading List