Measuring and tracking the rate of time flow according to the laws of relativity, in form of the analog clock - spacetime clock model

Abstract

This research aims to find a time measurement tool that enables us to track the relative time flow rate according to the variables defined by the theory of relativity. The research problem was the absence of an analog clock that gives a continuous measurement the rate of time flow according to the laws of relativity, and the absence of a law that can be applied to analog clocks so that its indicators give a measurement the rate of time flow according to the variables defined by the theory of relativity. I started the research from the hypothesis that there is a symmetry between the regular circular motion of two objects within the space of classical mechanics, and the rates of time dilation; So that it can be used to measure relative time. I followed the experimental and descriptive method and mathematical proof to test this hypothesis. So I derived the mathematical equations that achieve this symmetry, and employed them to formulate a law that controls the motion of these two objects, and restricts this motion to the values of the variables found in Albert Einstein's theory of relativity. I conducted a laboratory experiment on an analog clock in order to test the validity of this law. I applied the limits of the values of the velocity variable between 10000 km/s and the speed of light in a vacuum. The clock was also tested at large values of the mass variable (the mass of the Sagittarius A* black hole as a model) and at the values of radii that are relatively close to Schwarzschild radius of those blocks. So I got a movement of the parts of the clock in which the time indicators pass over the degrees of measurement at the rate of time flow that an external observer observes at those values.