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.
The starting point of the reconstruction process is a very simple quantum logical structure on which probability measures (states) and conditional probabilities are defined. This is a generalization of Kolmogorov's measure-theoretic approach to probability theory. In the general framework, the conditional probabilities need neither exist nor be uniquely determined if they exist. Postulating their existence and uniqueness becomes the major step in the reconstruction process.
In our approach, rather than aiming to recover the 'Hilbert space model' which underpins the orthodox quantum mechanical formalism, we start from a general `pre-operational' framework, and verify how much additional structure we need to be able to describe a range of quantum phenomena. This also enables us to investigate which mathematical models, including more abstract categorical ones, enable one to model quantum theory. Till now, all of our axioms only refer to the particular nature of how compound quantum systems interact, rather that to the particular structure of state-spaces.
It will be shown that the conventional (i.e. real or complex Hilbert space) model of quantum mechanics can be deduced from the indistinguishability of the simplest types of statistical mixtures. The result does not have the low dimension exclusion of the quantum logic approach.
In a quantum-Bayesian delineation of quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. (A quantum system has potentially as many quantum states as there are agents considering it.) But what then is the role of the rule? In this paper, we argue that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, we show how to view the Born Rule as a normative rule in addition to usual Dutch-book coherence.
I will discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. These require that systems appear completely classical as restricted to a single measurement, that different measurements, and likewise different pure states, be equivalent up to the action of a compact group of symmetries, and that every state be the marginal of a bipartite state perfectly correlating two measurements.
We review situations under which standard quantum adiabatic conditions fail. We reformulate the problem of adiabatic evolution as the problem of Hamiltonian eigenpath traversal, and give cost bounds in terms of the length of the eigenpath and the minimum energy gap of the Hamiltonians. We introduce a randomized evolution method that can be used to traverse the eigenpath and show that a standard adiabatic condition is recovered. We then describe more efficient methods for the same task and show that their implementation complexity is close to optimal.
Clock synchronization, relativity of simultaneity, nature of space, and how a universal speed limit can make sense.
Dr. Smolin is a faculty member at Perimeter Institute for Theoretical Physics and author of several books including most recently “The Trouble with Physics”. He is known for devising several different approaches to quantum gravity, in particular, loop quantum gravity. His research interests include cosmology, elementary particle theory, the foundations of quantum mechanics, and theoretical biology. This information Chalk and Talk will explore in special topics in Quantum Gravity.
Heisenberg Uncertainty Principle, Feynman sum over paths interpretation of quantum mechanics, and the harmonic oscillator: introduction to tunnelling, QFT (what is a photon?), and zero point energy.