• [deleted]

  • Post #62

Has anyone noticed that Feynman did for complex arithmetic what Hamilton did for quaternion arithmetic. Complex arithmetic is more difficult to make sense of because it makes no spatial sense. But both Feynman and Hamilton suffer from an overloading problem. If you use the quaternion division algebra then you are stuck with polar and axial conventions or rules, which should be made explicit by using complex quaternions. Complex arithmetic needs complex octonions to make explicit what is crammed into the imaginary unit, which can be expressed as

any permutation or association of o(a(bc)) . So in his "QED strange theory" he shows how to generalize the Principle of Least Time by analyzing a mirror by considering possible paths and doing complex arithmetic - now connected to the best tested theory in Physics. It should extend to complex octonions, which should have direct physical meaning.

Maybe physicists have been making Octonionic Sense all along without explicitly noticing it, and that octonions are so ordinary that we just take it for granted.

4 days later

  • [deleted]

  • Post #63

Given that the 'unreasonable effectiveness of math in physics' seems

to depend on the good behavior of algebra, somehow, is it possible to

decide whether Alternativity is a criterion of good behavior ? Would

it imply, say, an inability to get Classical Mechanics from Quantum Mechanics ?

Or would a lack of alternativity not be a problem for the system as a whole ?

a year later

The core Idea we postulate it is that the nature has same fundamentals. In this scientific article we

will explore the broad area in physical science in different aspect and compare to existing known

scientific theories. There are no remarkable contradictions with accepted theories, instead

integrates and interprets to a better Unified theory.

Gravity is the basic interaction and the Photon is the ultimate elementary particle that every

thing is made of. Sphere is dominating shape of the Nature. Multi-Dimensions are important

issue for sphere Geometry. Dark matter which has two faces is also another face of the

universe's matter.

We focus particle theory in both astrophysical and subatomic particles including WIMPs MACHOs,

Quarks, and Leptons. The Natures Elementary charge's characteristic is significant in the charged

subatomic particles , such as Proton, Electrons, while it is trivial in the other Neutral particles, such

as Neutron, Neutrino, and Neutron star, this phenomena is seemingly based on quantum of what

may called ultimate elementary particles. It is about ODD and EVEN numbers, DISORDERED and

ORDERED systems. Our conclusion of particle system hierarchy is that there are two main

categories due to quantity of Photons

dimensions and the shape seems to be a key of understanding of the natures fundamentals

4 years later

  • [deleted]

  • Post #66

2^0 = Q (Real), 2^1 = C(Complex)I, 2^2 = H(quaternions)IJK, 2^3 = O(octonions )

Is there a next level?

2^4 = Hextonian? 16 dimensions? ijklmnopqrstuvw

15-Point Projective Space?

http://demonstrations.wolfram.com/15PointProjectiveSpace/