1 Mass is variable

It is assumed that, for particles having rest mass, mass is equivalent to kinetic energy with coupling constant c 2. This paper examines the consequences for Newtonian gravity, in flat spacetime, when mass changes according to speed and gravity. It is assumed that gravitational mass is the same as inertial mass. The inertial mass increase with speed is: m = γm 0 = m 0 / 1 − β 2 (1) where m 0 is the rest mass and β = v/c. Some physicists dislike this interpretation , preferring to regard rest mass as a constant and refusing to interpret " m " as mass. It is a matter of taste. Upon accepting (1), it is clear that different observers will report different masses for a given object, according to their relative velocities. Gravity leads to changes in γ, throughout an orbital motion. In the conventional description of a conservative gravitational system, kinetic energy T is gained at the expense of gravitational potential energy U and the sum of these energies is constant. Thus, when the reference point at which U = 0 is at r = ∞, gravitational attraction leads to a hyperbolic orbit. 1/α ≡ 1 + GM/rc 2 (2) T = (γ − 1)m 0 c 2 (3) U = (1 − 1/α)m 0 c 2 (4) and so, γ = 1/α. In a closed orbit, where the kinetic energy is insufficient to permit escape, the potential reference point is some value of r less than infinity, R. The SR gamma boost is modified in that case γ = 1/α R (5) 1/α R ≡ 1 + GM/rc 2 − GM/Rc 2 (6) In addition to the effect of gravity on speed, which affects the mass, it is postulated that gravitational potential directly affects rest mass. The Pound-Rebka (ref 1) Mossbauer experiment shows that a falling photon, in a gravitational field, " g " , appears to gain energy: hν ⋆ = hν(1 + gh/c 2) (7) The source is at the upper level and the absorber is at the lower level, separated vertically by " h ". It was found necessary to decrease the relative energy of the source by gh/c 2 in order to achieve resonance at the absorber. Now, consider a gedanken annihilation experiment. A thermalized (low kinetic energy) positron-electron pair of total rest mass m 0 annihilates at the upper level, and produces …