GRT?s ?Flat Spot?
Keywords: Gravitational Potential, GRT, Atomic Clock
In classical physics, a potential is an entity whose physical effects are revealed by its derivatives. For example, the gradient of Newtonian gravitational potential is gravitational force per unit mass responding, the gradient of Coulomb potential is an electric field, the time derivative of Ampere vector potential augments that electric field, and the curl of that vector potential is the magnetic field. In quantum physics, the vector potential can produce an effect directly: a phase shift. This is, perhaps, an example of a potential producing a physical effect without any differentiation. Likewise in GRT, the gravitational potential can produce physical effects directly: it can slow clocks, redden light emitted, or bend light passing by, and contribute to orbit precessions. All this is very confounding. We might, perhaps, be well advised to create a different word for ?potentials? that require no differentiation to cause a physical effect. On the other hand, it could be that the physical effects observed ought to be attributed, not to potentials per se, but rather to appropriate second derivatives thereof. This paper discusses candidate second order expressions to account for the GRT effects. The new second-order expressions work in the scenarios for which we presently have data (primarily GPS scenarios), but could be discriminated from GRT in a new, but available, scenario: we need to document how an atomic clock runs at the saddle-point of the gravitational potential between two source masses, such as Earth and Moon.