June 08, 2023
Sizeless points, physical points, spacetime continuum, physical space, intrinsic deformation of space, gravitational waves, expansion of space, Theorem of Formal Dependence, gravity in CALMs.
This paper proves in formal terms a quality of all points of the continuum geometrical space that is often explicitly or implicitly assumed: points have neither size nor shape. It also highlights the contradiction of, on the one hand, denying the reality of a physical space, which continues to be (together with time and spacetime) just an illusion for most contemporary physicists, and, on the other hand, accepting that this unreal space is continuously undergoing intrinsic deformations, accelerated intrinsic expansions, and propagation of its own deformations (gravitational waves), as if something that is not real, that is just an illusion, had the actual physical ability to warp, expand, vibrate and transmit its own vibrations. If, on the contrary, the physical reality of space (together with time and spacetime) is assumed, almost insoluble problems arise related to the modeling of spacetime through a four-dimensional infinitist continuum of points without size or shape or duration. As a counterpoint, this work considers the structure and functioning of CALMs, where, apart from being free of the inconsistencies related to infinity proved in the papers 3, 4 and 5, none of these problems arise, and where it is possible to envisage a theory of gravity in which spacetime warps are unnecessary.
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