Physics Summer School Part 2 - Detailed Outline

This page provides a detailed outline of the Physics Summer School – Part Two, showing the themes and topics explored in each session across the four-day course. The programme below explains what students study on each day, from Einstein’s theories of relativity and the foundations of quantum mechanics to cosmology, black holes, and the limits of our current understanding of fundamental physics.

The course is taught through a combination of discussion, mathematical problem-solving, and collaborative investigation. Students are expected not only to engage with challenging conceptual ideas, but also to work with the mathematical frameworks that underpin modern physics, including calculus, complex numbers, and probabilistic models.

View and download the pdf of the outline here.

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Day One – Special and General Relativity
Day Two – Quantum Mechanics
Day Three – Cosmology and Black Holes
Day Four – Unsolved Problems in Physics

Across the course, students explore what happens when the classical framework of physics breaks down and must be replaced by new ways of describing reality. Beginning with relativity, they examine how space and time must be redefined in order to account for the behaviour of light and gravity. The course then develops the mathematical structure of quantum mechanics, in which physical systems are described in terms of wavefunctions and probabilities rather than definite trajectories. These ideas are brought together in cosmology, where students use observational data to infer the large-scale structure and evolution of the universe, and in the study of black holes, where the effects of curved spacetime become extreme. The course concludes by examining the limits of current theory, including the incompatibility between quantum mechanics and general relativity, and the open problems that arise from this tension. Throughout, the emphasis is on combining conceptual understanding with mathematical reasoning, so that students encounter modern physics as a rigorous and evolving framework rather than a collection of isolated topics.

Please note that for some groups, sessions may run in a different order.

10.00 – 1.00 Introduction to Special Relativity

This session introduces students to Einstein’s reformulation of mechanics, beginning with the idea that motion can only be described relative to a frame of reference. Students consider the principle of relativity, the challenge posed by the behaviour of light, and the consequences this has for our understanding of space and time.

The session includes discussion of relative motion, inertial frames, the relativity of simultaneity, and the derivation of time dilation through the light clock thought experiment. It then develops the ideas further through applications and examples, including relativistic energy and momentum. Students work through the reasoning behind these results and apply them quantitatively in physical problems.

1.00 – 2.00 Lunch

2.00 – 3.30 Introduction to General Relativity

The afternoon session develops Einstein’s generalisation of relativity, beginning with the equivalence principle – the idea that gravitational effects are locally indistinguishable from acceleration. Through thought experiments, students explore how this insight leads to the prediction that light should bend in a gravitational field and that gravity cannot be understood simply as a force acting across space.

Building on this, the session introduces the idea that gravity is best understood in terms of the curvature of spacetime. Students examine how motion in a gravitational field can be described as motion along the shortest path in a curved geometry (a geodesic), and are introduced to the mathematical ideas needed to describe curved spaces.

The session then connects these theoretical ideas to observation, including the explanation of the anomalous precession of Mercury’s orbit and the deflection of light by massive bodies, before concluding with applications such as gravitational time dilation and the role of general relativity in modern cosmology.

10.00 – 1.00 Quantum Mechanics Part 1

The day begins by establishing the mathematical framework required for quantum mechanics. Students review key ideas from calculus, including differentiation and the chain rule, and are introduced to complex numbers and Euler’s formula, which are essential for describing wave-like behaviour mathematically.

Building on this foundation, students follow the development of early quantum theory through the work of Niels Bohr. By considering the quantisation of angular momentum, they derive the allowed energy levels of the hydrogen atom and explore how these give rise to discrete emission spectra. These ideas are then connected to real observations, including the use of spectral lines to determine the composition of stars.

The session introduces wave–particle duality and begins to address the limitations of classical models of the atom. Students examine how quantised energy levels can be understood in terms of standing wave patterns, preparing the ground for a more complete mathematical description of quantum systems.

1.00 – 2.00 Lunch

2.00 – 3.30 Quantum Mechanics Part 2

The afternoon session develops the full mathematical framework of quantum mechanics through the introduction and heuristic derivation of the Schrödinger equation. Students explore how physical systems can be described in terms of a wavefunction, and how the square of this function determines the probability of finding a particle in a given state.

They then apply this framework to simple quantum systems, calculating normalisation constants and expectation values, and examining how energy quantisation emerges naturally from bound states.

The session concludes by reflecting on the conceptual implications of quantum mechanics, including the probabilistic nature of physical prediction and the interpretative challenges this creates. This may include discussion of thought experiments such as Schrödinger’s Cat, which highlight the tension between the mathematical formalism and our intuitive understanding of physical reality.

10.00 – 1.00 Introduction to Cosmology

This session brings together ideas from general relativity and quantum mechanics to study the large-scale structure of the universe. Students examine how we can determine the size, age, and evolution of the universe using a combination of observation and physical theory.

Working through key historical and modern methods, students calculate distances to galaxies using Cepheid variables, use redshift data to determine recessional velocities, and apply Hubble’s law to estimate the expansion rate and age of the universe. They also consider the observational evidence underlying modern cosmology, including the relative abundance of elements and the cosmic microwave background radiation.

The emphasis throughout is on how large-scale conclusions about the universe can be inferred from limited data, and on the assumptions and models that make such inferences possible.

1.00 – 2.00 Lunch

2.00 – 3.30 Black Holes

The afternoon session explores one of the most striking predictions of general relativity: the existence of black holes. Students examine how black holes form, how their properties depend on mass and structure, and how their presence can be inferred despite the fact that no light can escape from within the event horizon.

Building on earlier work on curved spacetime, the session considers how gravity behaves in extreme regimes, including the warping of time near a black hole and the structure of the event horizon. Students are introduced to the different types of black holes, from stellar-mass objects to supermassive black holes at the centres of galaxies.

The session concludes by examining the theoretical limits of our current understanding, including Hawking radiation and the question of whether information can be lost in black holes, highlighting the tensions between general relativity and quantum mechanics.

10.00 – 1.00 The Standard Model of Particle Physics

This session draws together ideas from quantum mechanics and field theory to examine the Standard Model of particle physics, the most successful framework currently available for describing the fundamental constituents of matter and their interactions.

Students explore how the Standard Model organises particles and forces within a single theoretical structure, including the unification of the electromagnetic and weak interactions. Particular attention is given to the role of the Higgs boson, whose existence is required for the theory to produce physically meaningful predictions.

The session also considers how such theories are tested in practice, including the role of large-scale experiments such as the Large Hadron Collider in confirming theoretical predictions and extending our understanding of the subatomic world.

1.00 – 2.00 Lunch

2.00 – 3.30 Beyond the Standard Model

The final session turns to the limits of our current understanding. Although the Standard Model and general relativity are each extraordinarily successful within their own domains, they are not mutually compatible, and attempts to apply them simultaneously lead to fundamental difficulties.

Students examine some of the major open problems in modern physics, including the hierarchy problem and the cosmological constant problem, and consider why these challenges suggest that our current theories are incomplete. The session introduces the idea that spacetime itself may not be fundamental, but instead emerges from deeper underlying structures.

The course concludes with a discussion of candidate theories such as string theory, which attempt to unify quantum mechanics and gravity within a single framework, and with a broader reflection on what it means for a physical theory to be complete.

This outline provides a detailed view of the themes and topics explored during the Physics Summer School – Part Two. The programme is designed to introduce students to some of the central ideas and mathematical frameworks of modern physics, while also giving participants the opportunity to apply those ideas through problem-solving, calculation, and discussion.

Students who have not yet studied A-level Mathematics should generally begin with Part One of the course, which focuses on classical physics and is designed to provide the mathematical and conceptual foundation for later work in relativity, quantum mechanics, cosmology, and particle physics.

Return to the main Physics Summer School page for full practical details about the course and how to apply.