New Formulation of Physics based on a Complex Terrain Model — III: Relativity of Mass and Gravity Explained as Projection —

In this report, we explain the variation of mass and the generation of gravity from theperspective of “projection,” based on the law of momentum conservation. When a stationaryobject on a geodesic of complex terrain is observed from real space with relative acceleration,the relationship mg = mi sec(2η) is derived between the inertial mass mi and the observedgravitational mass mg , mediated by the projection angle η. It is revealed that even if theinertial mass remains invariant, an increase in the relative acceleration between the complexterrain and real space causes the observation angle η to enlarge, resulting in an increasein the apparent gravitational mass mg . The weak equivalence principle, which is limitedto free fall, asserts mg = mi; this can be explained as a consequence of η = 0 within aconstant-velocity translational environment.When analyzed as a two-body relationship, a Poisson-type equation ∇2mg = ¨mg isobtained, demonstrating that an attractive force appearing to be inversely proportional tothe square of the distance is exerted. Furthermore, by describing the relative motion betweenthe terrain and the real plane as a rotation of the projection angle, we show that singularitiesappear when η → π/2. We also find the relationship between these singularities and theproperties of black holes and light.