TITLE:
Emergent Gravitation and Quantum Wave Dynamics from a Bounded Vacuum
AUTHORS:
Tanuj Kumar, Vandana
KEYWORDS:
Vacuum, Gravitation, Wave Dynamics, Compton Length, Dispersion
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.4,
April
3,
2026
ABSTRACT: We present a framework in which gravitation, inertia, and wave dynamics emerge from the response of a vacuum endowed with finite potential capacity. The theory is formulated in terms of a scalar vacuum-potential field whose absolute normalization is fixed by relativistic considerations, such that the equilibrium value at infinity equals
c
2
. Static relaxation of localized vacuum-potential deficits reproduces Newtonian gravity in the coarse-grained limit, while time-dependent redistribution generates propagating disturbances governed by a universal wave equation. Finite vacuum capacity implies intrinsic upper bounds on transmissible force and signal speed, yielding
F
max
=
c
4
/G
and
v≤c
without invoking spacetime geometry or independent kinematic postulates. Vacuum microstructure further leads to a universal lattice dispersion relation with Planck-suppressed corrections,
Δv
c
≃−
1
8
(
E
E
P
)
2
, consistent with current astrophysical and gravitational-wave constraints. Gravitational redshift, lensing, horizons, and quantum correlations arise as energetic consequences of bounded vacuum response. The vacuum is modelled as a Dynamical Planck Network (DPN), providing a conservative and internally consistent bridge between relativistic gravitation and quantum wave phenomena.