"Abstraction" tab added - 16th February/2017
Abstraction: This page has been added to communicate and translate some less technical pieces, loose thoughts and some random musings. Sometimes it just better to be a little indirect. To borrow the tools of the poet and to stimulate thought and discussion.
Who's afraid of the Unit Quaternion ? - 11th November/2016
Article: Quantum Mechanics is a physical theory riddled with problems. At the core of these problems is the fact that the Quantum theory has not recognised that the qubit is a quaternion. Rather the qubit is thought of as a 2-level Quantum system, and the remaining degrees of freedom are ignored - giving rise to the probabilistic interpretation and indeterminism.
Parallel Transport and the Geometric Phase - 15th October/2016
Video: An animated derivation of the geometric phase of the spinor. It is shown how to derive the geometric phase of the spinor by solving the equation of parallel transport for a tangent vector moving along a path on the surface of the Bloch sphere.
Meditation: The hidden variables of Quantum and Classical Mechanics are found in the parameter space of the quaternion. The quaternion is a 4-dimensional vector which describes rotations in 3 and 4 dimensions in full generality. Applied to the fundamental particles, the quaternion describes the orientation and precession of the magnetic moment of the fundamental particles. Conventionally thought of as a 3-dimensional vector the magnetic moment is in fact 4-dimensional, and the intrinsic spin of the fundamental particles, as measured in the Stern-Gerlach experiment, is understood as the 4th-dimensional shadow of the quaternion when viewed from a 3-dimensional perspective.
Vectors, Spinors and Galilean Frames - 14th December/2015
Article: The Law of the Spinor states that the global phase is the sum of the geometric phase and the dynamic phase. These are the intrinsic parameters of the unit spinor and are presented here in their analytic form for the first time. These parameters are the 4th-dimensional shadow of the spinor as seen from a 3-dimensional perspective.
Parallel Transport, Quaternions and The Bloch Sphere - 28th August/2015
Article: Curious about parallel transport, quaternions, the qubit, geometric and global phases - then this article is for you. Living in an age where quantum computing technologies are promised to be right around the corner - ready to hit the market at any moment - or so we are lead to believe, ... you would not be alone thinking - '"surely we have mastered the basics" - au contraire!! This article is an account of what is known and what still remains elusive about that most fundamental piece of quantum information - the Qubit.
New Logo Design - 20th August/2015.
New logo design courtesy of barryosullivan.ca. Reminiscent of the Celtic trinity, the icon is a Möbius strip of the second kind, where it takes four complete revolutions to return to the initial point.
The Geometric Phase of the Qubit - 24th July/2014
Article: One possible way to bridge the gap between the Quantum Mechanics and General Relativity is to utilize the mathematical language of General Relativity within the Quantum Theory itself. Differential Geometry - which is the mathematical language of General Relativity - is here used to define the geometric phase of the Qubit. The geometric phase of the Qubit is defined by solving the equation of parallel transport for all paths generated by the unit Quaternion on the Bloch sphere.