Reduced action
The reduced Planck constant, used as the primitive action quantum per radian of phase.
The framework / An introduction
From a single tick
to a connected framework.
The Quantum Lattice Model explores how a common set of phase-action rules can organize Planck-scale quantities, relativistic motion, gravitational routing, and quantum wave dynamics.
The starting point
Three primitives.
QLM takes reduced action, a spatial increment, and a temporal increment as its base layer. Planck-sector quantities are then expressed in this shared notation.
Spatial increment
The Planck length, used as the primitive spatial increment in the lattice description.
Temporal increment
The Planck time, used as the primitive proper-time interval for one lattice tick.
STEP 01
Start with reduced action
dS = ℏ dθ
QLM treats the reduced Planck constant ℏ as the action quantum per radian. A change in physical phase therefore carries a corresponding amount of action. This is the framework’s primitive phase–action relation.
The spatial and temporal primitives, ℓP and tP, supply the lattice increment and proper-time tick. The starting set is {ℏ, ℓP, tP}.
Continue in QLM ISTEP 02
Relate energy to phase flow
E = ℏ dθ/dτ
Energy is expressed as reduced-action throughput per unit proper time. Here θ is phase and τ is proper time along a worldline; the rate at which phase advances determines the associated energy.
For the saturated update used in the foundational paper, one tick advances one radian in one Planck proper-time interval. This fixes ΔS = ℏ and EP = ℏ/tP.
Continue in QLM ISTEP 03
Establish the transport scale
c = ℓP/tP
The ratio of the lattice’s spatial and temporal increments sets the invariant transport speed. QLM III develops relativistic kinematics through this transport rule, proper-tick accumulation, and synchronization.
The kinematic sector examines interval structure, Lorentz transformations, and the energy–momentum relation using the same lattice variables.
Continue in QLM IIISTEP 04
Develop the density and routing sectors
uP = ℏ/(ℓP³tP)
QLM II extends the saturated throughput scale to a proposed local energy-density cap and uses it to construct a finite saturated-core model for collapse.
QLM IV develops the exterior routing sector separately. It describes gravitational throttling through routing availability Y(r) and its connection to Schwarzschild redshift.
Continue in QLM IV Density cap in QLM IISTEP 05
Connect coherent transport to wave dynamics
E = ℏω
QLM V develops the quantum dynamical sector by organizing coherent phase-action flow into continuum wave descriptions, including the Schrödinger, Klein–Gordon, and Dirac equations.
The paper connects lattice transport amplitudes, relativistic fields, and the nonrelativistic envelope while keeping the phase–action relation as a common starting point.
Continue in QLM VBeyond the core sequence
Focused questions.
Companion papers.
The Planck energy identity
A short, focused note isolates EP = mPc² = ℏ/tP as saturated one-tick reduced-action throughput.
Read the identity noteTemporal-spatial phase closure
The closure extension examines rest mass as the inertial response of confined phase-action flow, developing the relation m = ℏτ/r² under the transport condition r = cτ.
Read the closure extensionReading the research
Assumptions and status
belong in the open.
QLM is presented as an independent theoretical framework. Its primitive choices, proposed bounds, and derivations should be evaluated in the context of the individual papers.
The archive preserves each paper’s stated status, including foundational work, compatible extensions, dynamics, and focused notes. These labels describe the work’s place within the QLM research program.
For a first reading, begin with QLM I. For a specific topic, use the archive summaries and core identities to choose the relevant paper.