9. Gravitational Interaction and General Relativity
Abstract: This chapter primarily discusses concepts such as gravity and general relativity within this model, including a proposed quantum-elastic spacetime solution to the black hole singularity paradox, the specific physical mechanism behind gravitational time dilation in general relativity, the physical interpretation of the inverse-square law of gravity in Newton's law of universal gravitation, and an analysis of corresponding concepts in general relativity such as metric-geodesic-tensor. Additionally, it examines the near-stagnation of entropy-time-space changes within the black hole event horizon.
9.1 Gravitational interaction is modeled as a translational action described by matrices that alter the equilibrium spacing between SEQ. SEQ are interconnected via spring-like bonds in their ground state(Refer to the basic setting in Section 1.6, page2). Gravity modifies this spacing, creating tension with finite potential energy. This system behaves like a loaded spring: under gravitational fields, oscillation frequencies decrease, reducing local spacetime transformation rates and causing time dilation - matching general relativity's predictions while revealing its mechanism. Mass-generated gravity acts as a spherically divergent translation with inverse-square density, curving flat spacetime topologically to produce general relativistic metric changes.
Within this discrete framework, the singularity paradox of black holes is naturally resolved because the tension between SEQ has a upper limit.
Macroscopically, (1)It explains metric variations and gravitational time dilation predicted by general relativity, while remaining compatible with its continuity assumption, (2)The ground-state energy of SEQ can also give a depiction of the cosmological constant in general relativity. (3)At the cosmic edge, adjacent SEQ lack outward coordination sites, creating an expansion tendency from interior with the initial kinetic energy released during the birth of the universe—a potential mechanism for cosmic expansion. In this model, cosmic expansion should gradually decelerate due to the restorative force-the macroscopic manifestation of gravity within the universe generated by the stretched state of SEQ bonds, after reaching zero deceleration-when the initial kinetic energy of cosmic expansion from the Big Bang has been largely converted into the elastic potential energy of spacetime (stored in stretched SEQ bonds), the universe contracts until SEQ spacing returns to equilibrium. This process does not collapse back to the initial birth configuration of universe, nor does it reduce entropy—since the entropic increasing trend remains invariant under expansion or contraction, the homogenization of energy distribution is an irreversible process.
9.2 Consistent with general relativity, high-velocity or accelerated transformations of localized matter compress space, thereby inducing tensile stretching of surrounding space (equivalent gravitational effects). This process not only induces spacetime curvature but also modulates the conduction frequency of waves. In relativity theory, equivalent gravitational fields from velocity/acceleration (1) share the same core mechanism as mass-generated gravity—local SEQ compression (reduced spacing) inducing spacetime stretching, but (2) exhibit vector-directional dependence (anisotropic compression) instead of spherical symmetry, and (3) reflect inertial-SEQ lattice coupling through their non-spherical divergence and preferred orientation alignment in quantum spacetime structure.
9.3 Detailed Correspondence with Newton's law of universal gravitation "The number of SEQ on the surface of a mass source corresponds to the number of gravitational flux lines (i.e., the count of gravitational transmission paths). As the gravitational field diverges spherically, the density of these flux lines becomes inversely proportional to the surface area at any given radius, thus exhibiting an inverse-square relationship with distance. This result directly coincides with Newton's law of universal gravitation."
9.4 Correspondence with Newton's First Law—the Law of Inertia In this framework, the compressed space at the front and the stretched space at the rear—both caused by the object's motion at Constant Velocity—are always the interfacial boundary between the matter wave and the surrounding SEQ. Beyond this boundary, there is no compression or stretching induced by the object's motion at Constant Velocity, only a shift in the harmonic vibration phase of the SEQ , the system reaches equilibrium at Constant Velocity. The work input during acceleration establishes interfacial strain energy in the SEQ network, which then sustains uniform motion through elastic potential equilibration.
9.5 Understanding on General Relativity
9.5.1 Under gravitational and equivalent gravitational interactions, the dynamic deformation of 3D space structural matrix and variation in local SEQ density distribution corresponds to Metric field in General Relativity.
9.5.2 Minimum cumulative conduction count path adjustment along with the cumulative dynamic paths connecting every two-points with the minimal count of adjacent SEQ through spacetime distortion corresponds to geodesic path in general relativity. (Principle of least action)
9.5.3 Global topological homeomorphic transformation in SEQ framework corresponds to Diffeomorphism invariance in General Relativity.
9.5.4 The continuity assumption in general relativity, analogous to the continuum medium framework in fluid mechanics, constitutes a necessary and effective computational framework.
9.5.5 Black hole event horizon: Inside the event horizon of a black hole, due to intense gravitational forces, the spacing between SEQ is compressed to its limit. This extreme compression approximately and locally halts: (1)Energy conduction (2) space transformations (3)Entropy increase step (Neglecting black hole accretion).
9.5.6 Gravitational and Kinematic Time Dilation in GR
All factors that induce metric variation, including mass (gravity), velocity, and acceleration(equivalence principle), compress or stretch spacetime locally, thereby modulating the transformation frequency of related space. This frequency suppression constitutes the fundamental mechanism of time dilation.
