Triplane Framework: Redefining Space-time Visualization in Special Relativity

Abstract

This research delves into the spatial distribution of speed limits and space-time intervals across various axes within three-dimensional and four-dimensional space-time. A novel theoretical model is proposed based on this distribution, aimed at enhancing the visualization and comprehension of four-dimensional space-time. The primary objective of this study is to offer an intuitive approach to visualizing the spacetime continuum and to present an innovative framework for interpreting four-dimensional space-time. Our investigation revealed that speed limits along different spatial axes may not universally adhere to the speed limit constant, c. Furthermore, we uncovered that the invariant space-time interval can be dissected along these axes, leading to the development of the Triplane Framework. This framework interprets spacetime as three intersecting orthogonal planes rather than four dimensions. Additionally, the study explores the mathematical formalism governing component transformations within this Triplane framework. This research contributes fundamental insights into special relativity by elucidating the distribution of speed limits and space-time intervals within three and four-dimensional space-time. Such insights enrich the interpretation of experimental data in fields like astrophysics and cosmology. Moreover, the proposed Triplane Space-time Framework offers a fresh perspective for visualizing relativistic phenomena, potentially influencing theoretical frameworks in the field.