Operational Restrictions on Morphing of Quasi-Geometric 4D Physical Spaces

Abstract

Since a hierarchical notion of dimension is needed to ensure that a virtual, indirect orthogonality of dimensions is maintained in higher-dimensional spatial structures, a generic function for furling and unfurling of the fourth dimension in four-dimensional (4D) spatial structures is proposed. The furling allows three extra dimensions (above the regular three) in a 6D algebraic structure to be represented as a single fourth dimension and thus effectively facilitates morphing of the 4D spacetime into its dual 4D timespace. The effect of the furling of the extra three dimensions resembles that of compactification proposed by Kaluza-Klein theory yet without curling of the furled dimension. The furling supports reexpansion of stringy space into yet another dimension and so enables mapping of radius R (of a closed string being squeezed beyond its minimal radius) into an inverse radius 1/R, which was attributed to string duality, but is shown as due to duality of the 4D spatial structures of spacetime and timespace. Mathematically, it may appear as if further squeezing of the minimal string morphs it into an expanding pointletlike energy bubble so that the stringy spacetime reexpands in a new direction/dimension located within the bubbly dual timespace. So vibrating string is a mirror image of an energy bubblet, both of which do represent the same stringlet. By analogy, particle cast in spacetime could appear mathematically as having a mirror image (or its superpartner) cast in the dual timespace.

Mathematical Gateway to Complementary Hidden Variables in Macrophysics

“…By the same token, by a foreign reference frame (or a foreign vector basis in particular), I mean one in which independent variables cannot be directly measured/expressed, and thus their introduction would likely require indirect representation of some kind of [6].…”

“…(5) (6) which contain the sum of both the active derivative and the other (temporarily made inactive for the duration of the particular partial differentiation performed with respect to the active -for the time being -independent variable) derivative rationalized by the ratio of differentials of the inactive to the active independent variables, respectively.…”

“…Hence, a new synthetic mathematics -as opposed to the old one that is often associated with Poncelet -has the potential to play not only the leading role in operational support of most exact sciences, but also to rectify its own shortcomings in the process. Pure mathematics steadily deteriorated because it propagated tacitly veiled slipups disguised as its legitimate attainments while ignoring some of its proven laws/rules [2] and disregarding even its own inconvenient achievements when the latter dare to challenge its simplistic concepts or its overly simplified methods [5], [6].…”

With Equalized Mass, its Density of Matter can Affect Radial Gravitational Interactions TOO

“…Although 6-dimensional spacetime cannot be applied in the traditional form [25] because one cannot ascertain orthogonality of six dimensions packed together [26], [27], with quantized tuples of dimensions the problem of multiple dimensions of time could be successfully resolved [28], [29].…”

“…The pertinent examples of arbitrary higherInternational Letters of Chemistry, Physics and Astronomy Vol. 54dimensional constructs, which can defy some proven achievements of Abel, Galois and Lagrange, are given in [28], [29].…”