The quantum Hall states at filling factors $ u=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. For the first time we report experimental evidence for the non-Abelian nature of excit
ations at $ u=7/2$ and examine the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles, by measuring resistance oscillations as a function of magnetic field in Fabry-Perot interferometers using new high purity heterostructures. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near $ u=5/2$ and $7/2$, indicating stability of the fermion parity. When phase fluctuations are observed, they are predominantly $pi$ phase flips, consistent with fermion parity change. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.
We discuss the key role that Hamiltonian notions play in physics. Five examples are given that illustrate the versatility and generality of Hamiltonian notions. The given examples concern the interconnection between quantum mechanics, special relativ
ity and electromagnetism. We demonstrate that a derivation of these core concepts of modern physics requires little more than a proper formulation in terms of classical Hamiltonian theory.
An attempt is made to avoid the difficulty of the infinite reaction of the electron on itself, which occurs in quantum electrodynamics, by introducing difference equations instead of differential equations. This vision allows the difficulty of the re
lativistic wave equation emphasised by Klein, for example, to be essentially eliminated.
The goal of this paper is to explain how the views of Albert Einstein, John Bell and others, about nonlocality and the conceptual issues raised by quantum mechanics, have been rather systematically misunderstood by the majority of physicists.