Quantum Foundations

In recent decades, there has been a renaissance of interest in foundational issues in quantum theory,
particularly in relation to quantum information science, cosmology and quantum gravity. This course
provides an introduction to modern research on quantum foundations.

The first part of the course covers central cornerstones of quantum mechanics: quantum entanglement,
the measurement problem, the Einstein-Podolsky-Rosen argument, Bell's theorem and quantum nonlocality,
experimental tests of quantum non-locality and the failure of local hidden variable theories, and
the delicate "peaceful co-existence" between quantum theory and the no-signalling principle in special
relativity. It is followed by detailed account of the theory of quantum measurement, including the von
Neumann's measurement paradigm, state-verification measurements and generalized measurements. We
then further develop the connection between quantum theory and relativity: we discuss the restrictions
posed by special relativity on instantaneous measurements of non-local variables - properties of composite
systems with space-like separated parts - and explore some recent developments in this subject.

In the second part of the course we review major foundational perspectives on quantum theory, starting
with the "orthodox" standard Copenhagen theory, followed up by an early attempt at an alternative to
standard quantum theory, de Broglie-Bohm theory, and some of its problems. Then we go on to consider
the physics of decoherence, some simple models of decoherence, and estimates of decoherence rates. This
brings us to a more recent class of attempts at alternatives to quantum theory, the so-called 'dynamical
collapse models' proposed by Ghirardi-Rimini-Weber, Pearle and others; we describe these models and
review some of their problems. Finally, we discuss many-worlds quantum theory and the problem of
making sense of probability in many-worlds theory. We will develop some of the above topics in more
depth, while briey touching the others.

Examples sheets and examples classes will complement the course.

Desirable Previous Knowledge

A good understanding of undergraduate level quantum theory is required. (Cambridge 1B Quantum
Mechanics course is a good starting point.)

Optional Introductory Reading

1. Benjamin Schumacher and Michael Westmoreland, Quantum Processes Systems, and Information,
Cambridge University Press, Chapters 1-8. This is a good starter for those students who wish to review
the core aspects of quantum theory in the context of quantum information. One might also find
useful Benjamin Schumacher’s lectures on Quantum Theory, video archived at http://pirsa.org/C10028/.

Optional reading to complement course material

1. John Bell, “Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, 2nd
edition, Chapters 1,2 and 22.
2. Robert Spekkens, lectures on Foundations of Quantum Mechanics given to Perimeter Scholars International
(2009). Video archived at pirsa.org, beginning with the first lecture at http://pirsa.org/09110168/
3. Yakir Aharonov and Daniel Rohrlich, "Quantum Paradoxes: Quantum Theory for the Perplexed",
WILEY-VCH Verlag, Chapters 3, 7 and 14.
4. “Many Worlds? Everett, Quantum Theory, and Reality", Simon Saunders, Jonathan Barrett, Adrian
Kent and David Wallace (eds.) (Oxford University Press, 2010), Chapter 8 (available at arXiv:0906.2718)
and Chapter 10 (available at arXiv:0905.0624).

Example Classes

There will be three example sheets in total.
Provisionally, two example classes will take place in Lent term and one in Easter term.

The first two example classes will take place in a row on the 5th of March, 2-4pm, in MR3.

The third example class will take place on Friday 10th of May, 2-4 pm, MR15.

The revision class will take place on Friday 24th of May, 10am-12pm, MR14.