It is shown that 100-year-old, conflicting ideas on the positive or negative energy of the gravity field collide with the principle of local conservation of energy. A scrutiny of the Schwarzschild metric, carried out with a different method than that applied by E. Schrödinger but completed with a similar result, reconfirms that the gravity field holds no energy at all, with that recognition being tacitly acknowledged by Misner, Thorne, and Wheeler in 1973. Given that it does not hold any energy, it cannot, by definition, be qualified as a force-field. Given that it is not a force-field, it is capable of being completely transformed away even in the rigid reference-frame of a distant observer outside of the field. Contrary to what (early) Einstein believed, this can (and must) be achieved... by the concept of “flowing spaces” that was introduced by elder Einstein himself in 1952. It is shown that this concept leads to empirical consequences. Moreover, the energy of the gravity field is necessarily replaced by an inexhaustible “dark energy,” which flows into any massive object (including Newton’s apple) whenever, after a free fall, it is being decelerated. Thereby Schrödinger’s vision of “new foundations” of the energy conservation principle (as a consequence of his recognition that the gravity field holds no energy) is coming true. Because of the absence of any gravitational field lines that originate from that energy, the (main) seat of this dark energy cannot be in three-dimensional space, but must sit at a location separated from ordinary space by a short distance in a direction perpendicular to all three ordinary spatial directions.