UNIVERSITY | PHYSICS |

Deciding which course to study at university can be a daunting challenge, further complicated by the fact that often studying a subject at university level bears little resemblance to studying that subject at secondary school. In this series of posts we ask subject-specialist tutors about the practicalities of studying their subjects at university, the key differences in those subjects between university and school, and the best ways a student can prepare in order to hit the ground running when they arrive at university.

At school Physics can largely be a combination of rote learning and applied mathematics. Students are taught some formulae and then asked to apply them in various scenarios in their exams. This is certainly an essential skillset for going on to do Physics in higher education but it does not give the student an introduction to the practicalities of studying the subject at university and beyond. As such it can be a daunting prospect to commit to three years or longer in a subject which is so different to study at this higher level, so here I will give an overview of how a Physicist learns to think and approach the various physical theories which they must tackle at degree level.

At university, a Physics course will be divided into several modules, with each traditionally being a physical theory. In their first year, students may have modules in Classical Mechanics, Wave Dynamics, Electromagnetism and so on, before moving on to theories such as Quantum Mechanics, Relativity, Information Theory and more in years two, three and maybe four, often with the option to specialise in those theories in which the student is most interested.

The difference with school, however, is that each physical theory you learn at university is built, as it were, from the ground up. Rather than starting with the formulae in that theory and then just applying them, students are first taught what are known as the “axioms” of the theory, i.e. those statements which are most fundamental within the theory, and then by using nothing but logic and mathematics the student is taught how to travel from these axioms to the higher, more complex forms of the theory. In short: the student is shown how we arrive at the formulae, and this understanding is what is typically scrutinised in a university Physics exam. A student may have to arrive for example at a modified form of a key formula in the theory, by specifying certain conditions which change the nature of the formula in a specific question.

Furthermore, concepts which are passed over without a second thought in secondary school Physics, such as mass, space and time to pick a few, are shown to be much deeper and woollier than we would think at first. The student at university learns that these concepts cannot be taken for granted but have specific applications, applications which differ (sometimes very greatly) between physical theories. For example, the concept of mass is very different in Classical Mechanics compared to General Relativity, and this is before we even get to Quantum Mechanics which changes things in even more exotic ways.

This difference gets to the heart of what Physics is as a discipline: each physical theory is in essence its own world, with its own terms, assumptions and way of thinking. When we talk about mass in Quantum Mechanics we do not mean the same thing as when we talk about mass in Relativity. These meanings across theories can have correspondences, but the correspondence is not complete and indeed cannot be since at the moment we do not have what Physicists call a Grand Unified Theory – a theory which is applicable in all occasions, at all scales of the universe. This is the ultimate goal of Physics, but in the meantime we have to make do with our individual physical theories, each with its own domain of applicability and description of the world.

This is the main point: when learning a physical theory at university, the student must learn a new and unique way of thinking. Being aware when concepts can be reasonably carried over from other physical theories but also knowing when a new way of thinking about a concept is required. This conceptual level of studying Physics is often entirely missed at school, and students can be shocked when unpicking conceptual ideas form a major component of their study at university. If this sounds like the most intriguing aspect of Physics to you than it may also be worth considering a course in Physics & Philosophy where these types of issues are burrowed into in much more depth (the downside however is that for a joint degree like Physics & Philosophy you necessarily cover less Physics than in a pure Physics degree).

I would advise picking up a few books at university level in an area of physics which the student has studied at school, and then to follow along some “proofs” in the book. For example, the student may pick up a book in Classical Mechanics for Undergraduates and look at how we arrive at the formula for the Centre of Mass of an extended body or system of point particles. The student will see how, by starting from simple axioms and then using logical steps and mathematical reasoning we arrive at a general and utilisable formula. It is a beautiful thing to see and a rewarding process when you follow along, work through difficulties, and arrive at the conclusion yourself.

Once you start going through a few proofs and derivations you will eventually and inevitably arrive at a proof you cannot follow and do not understand. Do not panic! This will happen frequently during your time at university, so now you will really feel like a physicist! This is the opportunity for real development and each student will find their own ways of handling such an impasse. The first step is normally to go to a library and find several textbooks on the same topic with derivations of the same concept. Each author will describe the situation differently, and by piecing together these different explanations you may find one which “clicks” with you. This does not always help however, and when it does not is when you will really get to the heart of your understanding of the theory, and in these cases I find it useful to write as clearly and succinctly as possible the different areas of difficulty I am having in understanding the derivation in question. By reducing the issues to their most minimal form, you can often identify which concepts you will need to look up to understand the background of the derivation better, or failing this, you will at least be able to ask your teachers specific questions which are more likely to yield the answers you need to develop your understanding.

Physics at university is a big step-up and students are thrown into a world of self-study where they are left to their own devices in finding the answers to conceptual or technical problems. Aside from diving into textbooks, the best preparation is to practise answering the types of questions you will have to do during your course and work on problem-solving. A book full of such questions is ‘The Flying Circus of Physics', which also contains solutions. For general inspiration, the Feynman Lectures on Physics provide a classic (if highly personal) take on Physics. Note, however, that these do not contain problems. As the saying goes, you will no more become a physicist without solving problems than become a musician without practising. Lastly, the more Mathematics you have, the better prepared you will be for the Physics course. If you have not done two full A-levels in mathematics, or have done so with a lot of focus on Decision Maths/Statistics, time spent over the summer learning more Mechanics or Further Pure will not go unrewarded and vice versa.

Written by William Brooke, Director of Witherow Brooke

WILLIAM BROOKE STUDIED PHYSICS AT CHRIST CHURCH, OXFORD, GOING ON TO STUDY HIS MASTER’S IN THEORETICAL & PARTICLE PHYSICS.