» S.V. Vaseghi - Digital Processing and Noise Reduction
S.V. Vaseghi - Digital Processing and Noise Reduction
||Digital Processing and Noise Reduction
||An experimentalist collects events about a physical system. A theorists builds a model to describe what patterns of events within a system might generate the experimentalist's data set. With hard work and luck, the two will agree!
Events are handled mathematically as 4-vectors. They can be added or subtracted from another, or multiplied by a scalar. Nothing else can be done. A theorist can import very powerful tools to generate patterns, like metrics and group theory. Theorists in physics have been able to construct the most accurate models of nature in all of science.
I hope to bring the full power of mathematics down to the level of the events themselves. This may be done by representing events as the mathematical field of quaternions. All the standard tools for creating mathematical patterns - multiplication, trigonometric functions, transcendental functions, infinite series, the special functions of physics -should be available for quaternions. Now a theorist can create patterns of events with events. This may lead to a better unification between the work of a theorist and the work of an experimentalist.
An Overview of Doing Physics with Quaternions
It has been said that one reason physics succeeds is because all the terms in an equation are tensors of the same rank. This work challenges that assumption, proposing instead an integrated set of equations which are all based on the same 4-dimensional mathematical field of quaternions. Mostly this document shows in cookbook style how quaternion equations are equivalent to approaches already in use. As Feynman pointed out, "whatever we are allowed to imagine in science must be consistent with everything else we know." Fresh perspectives arise because, in essence, tensors of different rank can mix within the same equation. The four Maxwell equations become one nonhomogeneous quaternion wave equation, and the Klein-Gordon equation is part of a quaternion simple harmonic oscillator. There is hope of integrating general relativity with the rest of physics because the affine parameter naturally arises when thinking about lengths of intervals where the origin moves. Since all of the tools used are woven from the same mathematical fabric, the interrelationships become more clear to my eye. Hope you enjoy.