Division Algebras:: Octonions Quaternions Complex Numbers by Geoffrey M. Dixon

By Geoffrey M. Dixon

I do not comprehend who Gigerenzer is, yet he wrote whatever very shrewdpermanent that I observed quoted in a favored sleek journal: "Evolution has tuned the best way we predict to frequencies of co-occurances, as with the hunter who recollects the realm the place he has had the main good fortune killing game." This sanguine proposal explains my obsession with the department algebras. each attempt i've got ever made to attach them to physics - to the layout of truth - has succeeded, with my expectancies frequently exceeded. no doubt this robust assertion is coloured by way of a selective reminiscence, however the type of online game I sought, and nonetheless search, turns out to frowst approximately this actual watering gap in droves. I settled down there a few years in the past and feature by no means feIt like Ieaving. This e-book is ready the beasts I chosen for cognizance (if you are going to, to ren­ der this metaphor politically right, as an instance i used to be a nature photographer), and the type of instruments I needed to strengthen to get the type of pictures Iwanted (the instruments that i discovered there have been for my style overly summary and theoretical). 1/2 thisbook is set those instruments, and a few purposes thereof that are meant to show their strength. the remainder is dedicated to an illustration of the intimate connection among the maths of the department algebras and the traditional version of quarks and leptons with U(l) x SU(2) x SU(3) gauge fields, and the relationship of this version to lO-dimensional spacetime implied by way of the math

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Extra info for Division Algebras:: Octonions Quaternions Complex Numbers and the Algebraic Design of Physics

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41] because the lack of source implies the impossibility of importing into the theory the basic Newtonian potential. Under these conditions the representation of the Newtonian contribution is reduced to a religious belief, rather than a serious scientific statement. For these and numerous additional inconsistencies of Einstein’s gravitation or general relativity at large we refer the reader to Yilmaz [47], Wilhelm [48], Santilli [53], Alfv´en [49,50], Fock [51], Nordensen [52], and large literature quoted therein.

On the contrary, the assumption of hadronic constituents that can be fully defined in our spacetime directly implies new clean energies. 1 The Negative Impact of General Relativity on Antimatter An important requirement of any consistent classical theory of antimatter is the existence of antigravity defined as a gravitational repulsion experienced by antimatter in the field of matter, and vice-versa. As we shall see in detail in Chapter 4, this is essentially due to the achievement in the classical treatment of antimatter of a full dynamical equivalence between electromagnetic and gravitational interactions, thus including the existence of both attraction and repulsion, which classical equivalence is generally lost when antimatter is solely treated in second quantization owing to the notorious absence of a consistent gravitational theory for that level of study.

A more rigorous definition of these two tensors will be given shortly. It should be indicated that, for a possible solution of Eq. 6), various explicit forms of the electromagnetic fields as well as of the short range fields originating the energy-momentum tensors are given in Ref. [41]. Since both sources tensors are positive-definite, Ref. 7) with consequential general law mInert. ≥ mGrav. 8) where the equality solely applies for the electron. Finally, Ref. 1 for the exterior gravitational problem of a neutral massive body, such as a star, by showing that the situation is essentially the same as that for the π ◦ .

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