Relativity and Cosmology |
Authors: Tomasz Kobierzycki
This paper proposes an extension of Lorentz spacetime symmetry from the usualconnected domain of an ordinary observer to four orientation sectors defined by one andthe same invariant null boundary. The motivation is that the standard Lorentz groupdescribes all finite boosts available inside a chosen causal sector, but it does not by itselfsupply a real clock—ruler description of the neighbouring non-null domains separated fromthat sector by lightlike directions. The proposed extension completes this local orientationstructure without accelerating ordinary matter through the speed of light and withoutintroducing additional spacetimes. Every observer still has one real time axis and threereal spatial axes. The distinction between sectors is which non-null direction supplies theobserver’s clock and which three directions form its rest space.The local speed of light remains exactly equal to c in every sector. This is not imposedby assigning a different limiting velocity to each description; it follows because all sectorframes share the same null set and their admissible transformations preserve that set.Ordinary Lorentz boosts then describe motion inside any fixed sector, while the sectorextension describes the four possible causal orientations of the complete local frame. Aside sector is therefore not a superluminal state of ordinary matter. It is a Lorentzianframe in which one direction regarded as spatial by an ordinary observer supplies the singlelocal time axis, whereas the inherited ordinary time direction belongs to the side observer’sspatial rest space. Proper time remains real and future-directed, and a change of sectorchanges the clock—ruler decomposition rather than reversing or discontinuously replacingthe physical worldline.The same principle is generalised to curved spacetime by applying the sector structureto local orthonormal coframes and to the proper geometric scales on which a general-relativistic solution depends. When the scale used by one chart reaches its null boundary,the neighbouring sector evaluates the same gravitational field with the reciprocal activescale and with the corresponding sector metric. The purpose is to replace an extrapolationtoward a vanishing, singular scale by a geometrically regular continuation whose curvatureand causal distance can be tested directly. The resulting picture is one spacetime equippedwith a four-sector Lorentz atlas: local causality and the invariant light speed are preserved,while black-hole and cosmological limits can be re-examined as boundaries of sectordescriptions rather than being assumed in advance to be physical singular endpoints
Comments: 41 Pages.
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