Gravitational Time Dilation Derived from Special Relativity and Newtonian Gravitational Potential

Abstract

Einstein was known for often presenting "gedanken" or thought experiments (Miller, 1999). This paper is such an exercise. Time dilation in Special Relativity is based on the derived value of γ (a scalar value) (Einstein, 1905). γ will be calculated as a function of relativistic kinetic energy, allowing time dilation to become a function of relativistic kinetic energy. With the new methodology constructed, a "gedanken” experiment is considered. Can a time dilation function be derived, using Newtonian gravitational potential energy in the same manor kinetic energy was used in Special Relativity? This paper carries out the derivation and compares the results with General Relativity's Schwarzschild solution. The what if thought experiment provides a first order accuracy to GR's Schwarzschild solution.