Quantum Lattice Model: Invariant Transport and Lorentz Kinematics from Proper Ticks

This paper reconstructs the inertial kinematic structure of special relativity within the Quantum Lattice Model (QLM) using only the reduced-action Planck primitives ℏ, ℓP, and tP. Starting from the invariant lattice transport identity c = ℓP/tP, the analysis shows that Lorentz symmetry emerges as a structural consequence of invariant phase-action transport rather than as an independently imposed geometric postulate. The derivation proceeds in three steps. First, action transport per lattice tick and per lattice spacing yields the invariant null bridge E/p = c for massless propagation. Second, proper time is defined operationally as invariant tick accumulation along worldlines. Radar synchronization, together with preservation of the null update bound, determines the Lorentz boost and the invariant spacetime interval. Finally, invariance of the corresponding quadratic form in frequency space, combined with the QLM phase-gradient relations E = ℏω and p = ℏk, yields the rest-phase invariant E² − (pc)² = E₀². The rest-phase energy E₀ is then connected to inertial mass through the low-velocity boost response of the closed rest-phase inventory, giving E₀ = mc² and therefore the standard relativistic energy-momentum form E² − (pc)² = (mc²)². No preferred global lattice slicing is assumed, and no spacetime geometry is imposed a priori. The invariant interval instead arises as the macroscopic expression of a microscopic per-tick action-transport constraint. Special relativity therefore appears as the coordinate structure compatible with invariant phase-action propagation on the lattice.