Authors: Carlos Castro
We extend the construction of Born's Reciprocal Phase Space Relativity to the case of Clifford Spaces which involve the use of $polyvectors$ and a $lower/upper$ length scale. We present the generalized polyvector-valued velocity and acceleration/force boosts in Clifford Phase Spaces and find an $explicit$ Clifford algebraic realization of the velocity and acceleration/force boosts. Finally, we provide a Clifford Phase-Space Gravitational Theory based in gauging the generalization of the Quaplectic group and invoking Born's reciprocity principle between coordinates and momenta (maximal speed of light velocity and maximal force). The generalized gravitational vacuum field equations are explicitly displayed. We conclude with a brief discussion on the role of higher-order Finsler geometry in the construction of extended relativity theories with an upper and lower bound to the higher order accelerations (associated with the higher order tangent and cotangent spaces). We explain how to find the procedure that will allow us to find the $n$-ary analog of the Quaplectic group transformations which will now mix the $X, P, Q, .......$ coordinates of the higher order tangent (cotangent) spaces in this extended relativity theory based on Born's reciprocal gravity and $n$-ary algebraic structures.
Comments: 30 Pages. Submitted to Foundations of Physics. It is explained how to construct n-ary extensions of Born's reciprocal relativity based on n-ary algebras.
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[v1] 2013-02-16 04:58:54
[v2] 2013-04-20 20:42:51
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