In the Newtonian limit:
U = m phi
g = – del phi
phi = – MG / r
so
g = – MG / r squared
and Newton defined:
F = mg = -mMG / r squared
Newton simply assumed this equivalence principle without proof, but it has been derived in ECE and now in ECE2. Newton assumed that the mass m in F = mg is the same as the mass m in F = – mMG / r squared. The reason for this is now known to be geometry from ECE and ECE2 theories. So this verifies teh antisymmetry laws of ECE and ECE2 to many orders of magnitude, because the equivalence principle has been verified experimentally to many orders of magnitude, starting with Galileo (two different masses reach the ground at the same time). The reason for this is that the acceleration g of the earth is defined by the mass M of the earth and is independent of the masses of the test particles (or two stones of diffferent mass dropped to the ground). Apparently Galileo used inclined planes and did not drop stones from the leaning tower of Pisa. Teh antusymmetry laws of ECE and ECE2 completely change dynamics and electrodynamics and were introduced in UFT132 ff. by Eckardt, Lindstrom and myself.
So U is the potential energy of gravitational attraction in joules. The total energy is the hamiltonian:
H = E + U
In ECE theory there is a new minimal prescription:
p = mQ
which is the equivalent of the electrodynamical
p = eA
ECE2 is a theory of general relativity in which both torsion and curvature are correctly non zero. The Newtonain acceleration due to gravity g is augmented to:
g = – (2/m) (del U + partial p / partial t)
and equated to spin connection terms by antisymmetry. This gives rise to non Newtonian effects which can no longer be attributed to the incorrect Einsteinian theory. ECE2 gives the conditions for counter gravitation and counter gravitational devices have already been designed by AIAS / UPITEC in cooperation with Alex Hill (www.et3m.net, www.upitec.org, www.aias.us). Note 319(2) is the simplest theory to date of counter gravitation. The antisymmetry laws of ECE were introduced in UFT131 ff. and completely change electrodynamics and dynamics. They can be used to derive the Newtonian equivalence principle:
F = mg = – mMG / r squared
from geometry. They explain why m is the same in the two left hand sides of the above equation, which has been verified experimentally to many orders of magnitude, starting with Galileo.