This post is on the String-String Duality. In particular, the D=6 string-string duality, which is crucial since it allows interchanging the roles of 4-D spacetime and string-world-sheet loop expansion, and this is mathematically essential for phenomenologically adequate string-compactifications. Here I will prove an equivalence between K3 membrane action and ${T^3} \times {S^1}/{Z^2}$ orbifold action and show how it entails D=6 string-string duality. Working in the bosonic sector, the membrane action is:

where:

Recall I derived, via Clifford algebraic symmetry, the total action:

which is deep since Clifford algebras are a quantization of exterior algebras, and applying to the 'Einstein-Minkowski' tangent bundle, we get via Gaussian matrix elimination, an expansion of ${\not D^{SuSy}}$ via Green-functions, that yields M-Theory's action:

with $k$ the kappa symmetry term. With ${g_{mn}}$ the metric on ${M^{11}}$, and ${x^m}$ the corresponding coordinates with ${B_{mnp}}$ an antisymmetric 3-tensor. The worldvolume ${M^3}$ is:

0

Without getting into the mathematical aspects of the 'quantum mechanics = Bayes theory in the complex-number-system program', I will show that a geometrodynamic derivation of quantum mechanics is possible based on a modified Schrödinger equation whose action-propagator yields an interpretation of 'particle' as curvature in spacetime, and relate it to the conflict I derived between the Lindblad quantum-jump equation:

where:

with ${\rm{d}}{W_\mu }$ the Weiner-quantum-increments, and the collapse-action-functional corresponding to the collapse equation, given by:

where the collapse-action-functional is:

and ${S_{1,2}}\left[ \Gamma \right]$ is given by: