Nilpotent Quantum Mechanics: Analogs and Applications

Abstract

The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state) and its environment (vacuum) are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This zero square-root construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on "The 'Logic' of Self-Organizing Systems" [1], in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantum mechanics, will apply.

The universal rewrite system coded

“…It also creates an effect in which any defined system (such as a particle, cell or organism) has a relationship with the rest of the universe in which they act like mirror images of each other, producing a totality zero. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] The closed system is particularly relevant to the natural world, where direct observation determines understanding. We see the same structure of n = 6 in particle physics (in the classification of particles) and in genetics (in the genetic code), where the objects being structured are not intrinsically algebraic, though the algebra produces a useful method of indexing.…”

Quaternion Algebra on 4D Superfluid Quantum Space-Time: Gravitomagnetism

“…here φ is an arbitrary scalar field, having dimensionality of Energy×Length −2 . By combining the algebras of the quaternions [51] with the energy and momentum terms written above we write out the energy-momentum density tensor with added the extra term D T φ:…”