Talks

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.

In a 1960 paper, E. C. G. Stueckelberg showed how one can obtain the familiar complex-vector-space structure of quantum mechanics by starting with a real-vector-space theory and imposing a superselection rule. In this talk I interpret Stueckelberg’s construction in terms of a single auxiliary real-vector-space binary object—a universal rebit, or “ubit." The superselection rule appears as a limitation on our ability to measure the ubit or to use it in state transformations. This interpretation raises the following questions: (i) What is the ubit? (ii) Could the superselection rule emerge naturally as a result of decoherence? (iii) If so, could one hope to see experimentally any effects of imperfect decoherence? Background reading: E. C. G. Stueckelberg, "Quantum Theory in Real Hilbert Space," Helv. Phys. Acta 33, 727 (1960). P. Goyal, "From Information Geometry to Quantum Theory," arXiv:0805.2770. C. M. Caves, C. A. Fuchs, and P. Rungta, "Entanglement of Formation of an Arbitrary State of Two Rebits," arXiv:quant-ph/0009063.

Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. We show that it is possible to derive the complex nature of the quantum formalism directly from the assumption that a pair of real numbers is associated to each sequence of measurement outcomes, and that the probability of this sequence is a real-valued function of this number pair. By making use of elementary symmetry and consistency conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes. Reference: arXiv:0907.0909 (http://arxiv.org/abs/0907.0909)

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. Using these concepts and some weak assumptions, the Hilbert space of quantum mechanics is constructed. The complete set of axioms for time-independent quantum mechanics is provided by proving Born`s formula under weak assumptions. 1. Helland, I.S. (2006) Extended statistical modeling under symmetry: the link towards quantum mechanics. Ann. Statistics 34, 1, 42-77. 2. Helland, I.S. (2008) Quantum Mechanics from Focusing and Symmetry. Found. Phys. 38, 818-842. Reference: arXiv 0801.2026. (http://arxiv.org/abs/0801.2026)

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? The half hour multimedia presentation provides refreshing insight into how science works – how theoretical physicists search for the ultimate nature of reality, and is followed by a half hour question and answer session with PI researcher Sean Gryb.