Physics at small scales and high speeds

This course will introduce the two pillars of Modern Physics: Quantum Mechanics and Einstein’s theory of relativity. Whilst classical physics (which includes Newtonian mechanics, and the wave theory of light) describes most phenomenon we encounter in everyday life, its predictions break down when describing more extreme situations. In particular, when describing the laws of physics on small (subatomic scales ) we enter the “Quantum” world, where the postulates of Quantum theory force us to abandon the idea that we can completely determine the state of a particle and its evolution in time and instead adopt a probabilistic approach and accept that there are quantum limitations on the accuracy with which we can determine certain observables. Similarly, when modelling objects moving at speeds that are an appreciable fraction of the speed of light we must use Einstein’s theory of Special Relativity rather than the concepts of Newtonian mechanics. This forces us to abandon the concept of absolute time and 3D space and instead consider objects moving in a 4-dimensional space time.

We will explore both the key concepts underpinning these theories and how they can be used to mathematically solve problems. Each session will open with a short introduction to the topics being discussed but the remaining time will be devoted to working in groups and with the lecturer to solve problems and further explore the physical consequences of the theories. This course will boost your confidence in solving problems in physics and mathematics and enable you to describe phenomenon that cannot be modelled using the laws of classical physics. 

Learning outcomes

The learning outcomes for this course are:

• To understand where the laws of classical physics break down and how key experiments contributed to the development of Quantum theory and Special relativity.  
• To understand the consequences of the laws of Special relativity and apply them in physical situations.  
• To understand the postulates of Quantum Mechanics and apply them in physical situations.  
• Gain confidence in using mathematics to solve problems in physics 

Classes

1. Key experiments/observations that highlighted failures of classical physics  
2. Physics at small scales: the postulates of Quantum Mechanics  
3. Solutions to the Schrodinger equation: potential wells, Quantum Tunnelling and beyond  
4. Physics at high speeds: the postulates of special relativity and their consequences  
5. Case study: CERN as a laboratory for physics at small scales and high speeds 

Required reading

Before commencing the required reading for the course, you may want to re-familiarise yourself with the following topics typically taught in high-school physics and mathematics: Newton’s laws, conservation of momentum and energy in collisions (1D and 2D), waves and their properties (including interference and diffraction), calculus and differential equations. The following resources may be useful in doing this: 

• https://openstax.org : this online initiative provides free textbooks across numerous subjects. “Physics (high school)” Digital version ISBN-13: 978-1951693213 provides coverage of all of the physics topics listed above and introductory chapters on Quantum Theory and Special Relativity. 

• https://isaacphysics.org : an online learning platform that provides support and activities in physics problem solving for teachers/students from GCSE-level upwards towards university physics. Isaac also contains practice mathematics questions, that will provide good preparation for this course. 

1. A Cavendish Quantum Mechanics Primer (The first chapter which covers some preliminaries, including some required mathematics, is available for free online), Warner & Cheung, Periphyseos Press (2nd Edition)

2.  Relativity: A Very Short Introduction, Russell Stannard, OUP Oxford; 1st ed. edition, ISBN-10: 0199236224

3. University Physics, Volume 3 (Specifically unit 2: Modern physics, chapters 5-7 and chapter 11), Ling, Sanny and Moebs, OpenStax; 1st edition digital version, ISBN-10: 01947172220

Typical week: Monday to Friday

For each week of study you select a morning (Am) and an afternoon (Pm) course, each course has five sessions, one each day Monday to Friday. The maximum class size is 25 students. Your weekly courses are complemented by a series of two daily plenary lectures, exploring new ideas in a wide range of disciplines. To add to the learning experience, we are also planning additional evening talks and events.

Evaluation and Academic Credit 

If you are seeking to enhance your own study experience, or earn academic credit from your Cambridge Summer Programme studies at your home institution, you can submit written work for assessment for one or more of your courses. 

Essay questions are set and assessed against the University of Cambridge standard by your Course Director, a list of essay questions can be found in the Course Materials. Essays are submitted two weeks after the end of each course, so those studying for multiple weeks need to plan their time accordingly. There is an evaluation fee of £65 per essay.

For more information about writing essays see Evaluation and Academic Credit.

Certificate of attendance

A certificate of attendance will be sent to you electronically within a week of your courses finishing.