Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
A new foundation of quantum mechanics for systems symmetric under a compact symmetry group is proposed. This is given by a link to classical statistics and coupled to the concept of a statistical parameter. A vector \phi of parameters is called an inaccessible c-variable if experiments can be provided for each single parameter, but no experiment can be provided for \phi. This is related to the concept of complementarity in quantum mechanics, but more generally to contrafactual parameters.
A significant part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over classical states that can be prepared.
Our universe has a split personality: quantum and relativity. Understanding how the two can coexist, i.e. how our universe can exist, is one of the greatest challenges facing theoretical physicists in the 21st century. The presentation focuses on a simple but mind-bending thought experiment that hints at some fascinating new ways of thinking that may be required to unravel this mystery. Could the world be like a hologram?
Spacetime diagrams, a Doppler shift thought experiment, and introduction to Einstein's two principles.
The quantum equations for bosonic fields may be derived using an 'exact uncertainty' approach [1]. This method of quantization can be applied to fields with Hamiltonian functionals that are quadratic in the momentum density, such as the electromagnetic and gravitational fields. The approach, when applied to gravity [2], may be described as a Hamilton-Jacobi quantization of the gravitational field.
An introduction to the mathematics necessary to fully appreciate the ISSYP relativity and quantum lectures. Binomial theorem, series expansions of common functions, complex numbers, and real and complex waves.
The fact that quantum mechanics admits exact uncertainty relations is used to motivate an ‘exact uncertainty’ approach to obtaining the Schrödinger equation. In this approach it is assumed that an ensemble of classical particles is subject to momentum fluctuations, with the strength of the fluctuations determined by the classical probability density [1]. The approach may be applied to any classical system for which the Hamiltonian is quadratic with respect to the momentum, including all physical particles and fields [2].
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the configuration space is a statistical manifold with a natural information metric. The dynamics then follows from a principle of inference, the method of Maximum Entropy: entropic dynamics is an instance of law without law. The concept of time is introduced as a convenient device to keep track of the accumulation of changes.
What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently moved from interpreting to reconstructing quantum theory. We present a quantum logical derivation based on Rovelli's information-theoretic axioms. Its strengths and weaknesses will be studied in the light of recent developments, focusing on the subsystems rule, continuity assumptions, and the definition of observer.
I will consider physical theories which describe systems with limited information content. This limit is not due observer's ignorance about some “hidden” properties of the system - the view that would have to be confronted with Bell's theorem - but is of fundamental nature. I will show how the mathematical structure of these theories can be reconstructed from a set of reasonable axioms about probabilities for measurement outcomes.