This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
I look at the information-processing involved in a quantum computation, in terms of the difference between the Boolean logic underlying a classical computation and the non-Boolean logic represented by the projective geometry of Hilbert space, in which the subspace structure of Hilbert space replaces the set-theoretic structure of classical logic. I show that the original Deutsch XOR algorithm, Simon's algorithm, and Shor's algorithm all involve a similar geometric formulation.
It is shown that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow the existence of vacuum states with non-standard field fluctuations (quantum non-equilibrium). It is shown that such non-equilibrium vacua lead to statistical anomalies, such as a breaking of scale invariance for the primordial power spectrum. The results depend only weakly on the details of the de Broglie-Bohm dynamics.
Up to 90% of matter in the Universe could be composed of heavy particles, which were non-relativistic, or 'cold', when they froze-out from the primordial soup. I will review current searches for these hypothetical particles, both via elastic scattering from nuclei in deep underground detectors, and via the observation of their annihilation products in the Sun, galactic halo and galactic center. The emphasis will be on most recent results, and on comparison with reaches of future particle colliders, such as the LHC and ILC.
The origin of the chemical elements that make up our world is one of the oldest most fundamental scientific questions. The universe after the Big Bang consisted only of hydrogen and helium with traces of lithium. All the other elements, including the carbon in our bodies, the iron, silicon, and oxygen that makes up most of our earth, have been created later by nuclear reactions in stars. However, the origin of many elements beyond iron, including gold and uranium, is still a mystery.
In the standard cosmological model, galaxies and large-scale structure grew by a process of gravitational instability from initial perturbations which were of the simplest statistical form imaginable: a statistically homogeneous and isotropic Gaussian random field. One of the properties of such a field is that its Fourier transform has real and imaginary parts which are independently Gaussian and consequently the phases are uniformly random.
We show that the origin of the dark matter and dark energy problems originates in the assumption of standard Einstein gravity that Newton's constant is fundamental. We discuss an alternate, conformal invariant, metric theory of gravity in which Newton's constant is induced dynamically, with the global induced one which is effective for cosmology being altogether weaker than the local induced one needed for the solar system.
Richard Feynman is said to have said that philosophy of science is of no more use to scientists than ornithology is to birds. I will describe how a sociologist looks at the search for gravitational waves. Is it ornithology to birds?
Preon models enjoyed considerable popularity during the early 1980s, but have seen little progress since then. I will describe a correspondence between one of the more successful preon models and a simple game involving the twisting and braiding of ribbons, subject to straightforward topological conditions. This reproduces the fermions and gauge bosons of the standard model, as well as the electromagnetic, weak and colour interactions. The prospect that such structures may occur naturally within Loop Quantum Gravity will be discussed
The problem of vacuum energy is reviewed. The observational evidence in favor of a non-zero cosmological constant is described. I then discuss several possible explanations for how a theoretically natural huge value of vacuum energy could be adjusted down to the unnaturally tiny but observed value.