> GTFE: Foundations of the Ganainy Temporal Field Equation
Year: 2025
Type: article
Abstract: This work introduces a minimal field-theoretic framework in which time is treated as a dynamical physical quantity. We formulate a scalar temporal field whose excitations possess inertia, propagation speed, and dissipation. From a conservative temporal Lagrangian density, and including a Rayleigh-type dissipation functional, we derive a driven wave equation — the Unified Temporal Field Equation (GTFE). The equation establishes a dynamic degree of freedom associated with time, while remaining compatible with standard relativistic and electromagnetic limits in the absence of temporal distortion. The GTFE predicts measurable corrections to phase and group delay in ultrafast optical regimes, particularly in epsilon-near-zero (ENZ) and attosecond-scale platforms. These predictions arise without modifying the classical electromagnetic description, but by adding a coupled temporal term with its own effective parameters. This work focuses on the theoretical foundation and dimensional consistency of the GTFE. Future studies will address experimental fitting, electromagnetic coupling, temporal geometry, and potential quantized modes.
Author: El-Ganainy, Abdelmonem Abdelrahman
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7115069670
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