Inroad to understanding general relativityRoger Luebeck © 2025The preprint of my journal article is at this link: preprint.special_relativity.pdf Also see my tutorial for computing non-kinematical and kinematical time-keeping dilation, with commentary on the Hafele-Keating study of circumnavigating jets: time-dilation.pdf Begin: The inroad to understanding general relativity lies outside the comprehension of the monumentally complex mathematics of the geometrical spacetime model, which, not incidentally, utilizes terms that ensure it reduces to Newton's law of gravity in flat space. Rather, one needs to understand that Newton's law of gravity -- which involves comparitively simple mathematics -- in conjunction with the simple intuitive concept of the equivalence principle and the easy-to-understand (and easy to mathematize) absolute approach to special relativity (which necessarily involves the absolute nature of light) -- will yield the precise non-kinematical clock-slowing as we find in the spacetime model pertaining to true gravitational force. (See: spacetime curvature for a discussion of the distinction between gravitational force and gravitational effect.) In fact, none of the phenomena described by Einstein's spacetime model that goes beyond the above-mentioned non-kinematical clock-slowing need be unique to that model. The differences in predictions between Einstein's spacetime and Newton's law can all be accounted for by considering that Newton did not allow for gravitational fields (or any other phenomena) being established at the speed of light, and that there was no allowance for the presence of dark matter. Adding the just-mentioned considerations to Newton's law (along with a consistent application of the equivalence principle) would of course make the mathematics of Newtonian gravity every bit as complex as the mathematics of the spacetime model, assuming one could even find a way to mathematically incorporate such considerations outside the spacetime model. The true -- and easily visualizable -- picture of reality is that which maintains space and time as completely separate entities -- as is the case in the Newtonian view. Spacetime is a geometrical model in which space and time are not completely separate, and which thus affords no visualization of the universe. In the Newtonian "space and time" (as opposed to "spacetime") picture of the universe, objects are slowed and follow curved paths through space alone due to gravity -- a very simple and completely familiar picture. Neither within the Newtonian picture nor within the spacetime model should we think of an individual photon being slowed. Any object that enters a gravitational field must give up energy to the field. A photon would not be a photon if it gave up energy. Rather, it is absorbed. Gravitational fields certainly involve quantum interference, especially prominent in understanding the case of a light-ray passing through. There is absorption and emission of photons in the field. It is in the same broad category as intentional quantum interference in a condensate ("slow light") and the slowing and bending of light in water. In the spacetime model, the slowing and bending is of course modeled as a curving of spacetime. See slow light for further discussion about slowing light and for a brief discussion about causality in the context of emergence. Roger Luebeck © 2025 Updated 12/13/2025 site map |