Abstracts Details

We present here two extremely simple derivations of h and of the complete self energy of the electron. This is based, however, on an extensive set of ideas consisting of a dual fluid plenum which retains relativistic invariance. These ideas have been presented extensively elsewhere and so for those not familiar with these ideas an extensive bibliography is appended to this paper. The most recent summary of these ideas will appear shortly for those who wish to see a capsule summary.

Even so, a few words must be said about this fluidic approach relevant to h and to the fluid models for the electron and for electromagnetic dipole waves. The basic concept involves replacing the QM paradigm with a realistic dual fluid phenum consisting of continuous positive and negative fluids. These give a neutral vacuum space and give fluid models of the canonical particles and electromagnetic waves (mainly dipole waves which form the basis for all electromagnetic waves). Relativistic invariance is retained, at least on an empirical and realistic basis and this is explained extensively in the bibliography (see at least a-d in the bibliography).

This^{ }paper is an overview of the conditions necessary to replace^{ }the basic tenets of quantum mechanics.

*A ^{ }presentation is made showing how imaginary numbers, exponentials, and transfinite^{ }ordinals can be given logical meanings that are applicable to^{ }the definitions for the axioms of quantum mechanics (QM). This^{ }is based on a proposed logical definition for axioms that^{ }includes an axiom statement and its negation as parts of^{ }an undecidable statement that is forced to the tautological truth^{ }value ?true.? The logical algebraic expression for this is shown^{ }to be isomorphic to the algebraic expression defining the imaginary^{ }numbers* ?i().

*This supports a progressive and Hegelian view of*

^{ }theory development This means that thesis and antithesis axioms in^{ }the QM theory structure, which should be carried along at^{ }present, could later on be replaced by a synthesis to^{ }a deeper theory prompted by subsequently discovered new experimental facts^{ }and concepts. This process could repeat at a later time,^{ }since the synthesis theory axioms would then be considered as^{ }a new set of thesis statements from which their paired^{ }antithesis axiom statements would be derived. The present epistemological methods^{ }of QM, therefore, are considered to be a good way^{ }of temporarily leapfrogging defects in our conceptual and experimental knowledge^{ }until a deeper determinate theory is found. These considerations bring^{ }logical meaning to exponential forms such as the psi and^{ }wave functions. This is derived from the set theoretic meaning^{ }for simple forms such as 2

^{A}, which is known to^{ }be the set of all subsets of the (discrete) set^{ }A.

*The equal symbol in equations that are axioms, and*e

^{ }all its other symbols, can be mapped to a transfinite^{ }ordinal Imaginary exponential forms (such as^{i}

*) can be shown*.

^{ }to stand for the (continuous) set of all subsets or^{ }the set of all experimental situations (which thus includes arbitrary^{ }sets of experimental situations) which are based on the axiom^{ }, a transfinite ordinalA vortex ring model of the photon, sustained by a two fluid ZPE model, expands at the speed of light and has implications for nonlocal connectivity.