The Q-Field Flamework Temporal Coherence, Emergent Spacetime, and the Structure of the Present

ABSTRACT We introduce a scalar field framework in which physical time is described as a dynamical quantity through a field Q(x,t), with logarithmic variable ϕ = ln Q . This formulation allows the definition of temporal structure as a field with its own dynamics, governed by a consistent Lagrangian description. From this construction, we derive a field equation for ϕ and an associated effective spacetime metric, enabling a geometric interpretation of dynamics. In this picture, gravitational phenomena emerge from spatial variations of the temporal field rather than from a fundamental force. The model reproduces the Newtonian limit in weak-field regimes and provides a unified framework linking temporal evolution, geometry, and effective gravitational dynamics. Potential observational consequences and extensions are briefly discussed.