Quantized Spacetime from First Principles: A Unified Framework for Quantum Fields and Gravity

We investigate the consequences of postulating that space and time are fundamentally quantized, defined
by minimum units ℓP and tP, without introducing new particles, symmetries, or dimensions. Starting
from three foundational assumptions—validity of quantum mechanics, validity of general relativity, and
quantized spacetime—we construct a unified framework that spans quantum theory, gauge fields, gravity,
and discrete spacetime dynamics.

Quantum mechanics is reformulated on a time lattice, where unitary evolution, wavefunction collapse, and
non-Markovian memory emerge naturally from finite-step causal dynamics. We develop a discrete Quan-
tum Field Theory (QFT) incorporating gauge invariance for scalar, Abelian (U(1)), and non-Abelian
(SU(2), SU(3)) fields. Interaction strengths and ranges arise from the activation geometry of discrete
Planck-scale cells.

Gravitational dynamics emerge from the collective behavior of a scalar phase field ϕ(x). We derive a fully
tensorial metric gμν (ϕ) constructed from local phase gradients, and demonstrate that it generates the
Levi-Civita connection, Ricci curvature, and the full Einstein field equations. This construction provides
a spin-2 gravitational sector without assuming a fundamental metric. Topological entropy in discrete net-
works is shown to encode internal quantum states, and its internal degrees of freedom match the minimal
Hilbert space structure of Standard Model fermions.

Finally, the framework leads to falsifiable predictions: a correction to orbital dynamics at high resolution
(tested on Mercury and LEO satellites), a decoherence threshold for entangled photons, and a mechanism
for short gamma-ray bursts arising from quantum disruption events in black hole interiors.
This work demonstrates that a consistent and predictive unification of quantum theory and gravity may
arise from a minimal change in perspective: treating spacetime as fundamentally quantized.