Abstract

The Theory of Space (TS) proposes that gravity is a pulsed, quantized flow of space toward massive bodies, rather than a smooth classical field. This paper examines that proposal against an already independently established result in general relativity: the Painlevé–Gullstrand “river model,” in which space falls inward at the Newtonian escape velocity, reproducing the Schwarzschild geometry exactly. We show that TS's proposal reduces to this river model in the appropriate continuum limit, and go further: starting from a quantized, Planck-like construction of spatial, temporal, mass, and energy scales built from TS's own fermionic action quantum, we give an explicit, if heuristic, derivation of the classical river-model velocity itself, recovered via the standard energy-conservation argument relating a Newtonian potential to an escape velocity, and use this same velocity relation to locate the horizon and derive the corresponding quantized area. This connects TS's discrete construction to the continuous result by an explicit derivation, not merely by separate consistency with known physics. We then identify the constraint — the extraordinarily precise confirmation of the equivalence principle by the MICROSCOPE mission — that any pulsed, quantized extension of this kind must respect, and show it is satisfied if the pulsation is understood as the decohered average of an astronomical number of microscopic constituents rather than a coherent property of the source mass as a whole. We connect TS's resulting quantization of area to the independently developed Bekenstein–Mukhanov proposal for black hole horizon quantization, note that the two research programs are not in numerical agreement and that the wider literature itself lacks consensus on this point, identify a structural connection between TS's zitterbewegung radius and the Planck length, and extend the construction to rotating sources, showing that the exact Kerr irreducible-mass relation corresponds to a clean split of the quantized action budget between horizon area and rotation. We give an explicit order-of-magnitude estimate, via the Mathisson–Papapetrou–Dixon equations, of the size of any TS-specific correction to the geodetic precession measured by Gravity Probe B, and show it to be safely undetectable. We identify the quantum-gravity-induced-entanglement (QGEM) protocols as the closest existing experimental proposal to a genuine falsification test of TS's central gravitational claim, while being explicit about the regime in which TS currently makes no prediction distinct from semiclassical gravity. Finally, we outline two exploratory cosmological directions — whether a maximum-density initial condition could substitute for the inflationary epoch, and whether TS's own energy accounting bears on the long-standing question of the universe's total energy — identifying, in each case, the specific dynamical result still required and stating plainly that neither is yet established.

Keywords: Theory of Space; river model; Painlevé–Gullstrand; quantized black hole; equivalence principle; black hole entropy; Bekenstein–Mukhanov; Mathisson–Papapetrou–Dixon; quantum gravity phenomenology; gravitationally induced entanglement; cosmology