Photon Behaviour Under Negative Apparent Mass in ECM:

Soumendra Nath Thakur

May 11, 2025

In the Extended Classical Mechanics (ECM) framework, the photon—being perpetually in motion—is modelled as a massless particle with a dynamic negative apparent mass (−Mᵃᵖᵖ), distinguishing it fundamentally from ordinary matter. This −Mᵃᵖᵖ accounts for the photon's repulsive interaction with massive bodies and its resistance to gravitational attraction, balanced by an intrinsic energy expenditure.

The effective acceleration (aᵉᶠᶠ) of the photon is state-dependent:

* Upon emission within a gravitationally bound system, the photon exhibits aᵉᶠᶠ = 2c, leading to an effective force of Fₚₕₒₜₒₙ = −2Mᵃᵖᵖ · aᵉᶠᶠ.

* As the photon escapes the gravitational influence of the source, aᵉᶠᶠ reduces to c, and the force becomes Fₚₕₒₜₒₙ = −Mᵃᵖᵖ · aᵉᶠᶠ, reflecting the energetic cost of decoupling from the source's gravitational field.

Although the photon tends toward infinite velocity and frequency due to its −Mᵃᵖᵖ-driven dynamics, this behaviour is constrained by the Planck thresholds:

    f < fₚ ; λ > lₚ and Δt > Tₚ.

These bounds define the photon's maximum frequency and minimum wavelength, stabilizing its propagation speed at c—the maximum permissible speed under ECM, assuming vacuum conditions.

In refractive or reflective media, photons are entirely absorbed and re-emitted by bound electrons. This interaction introduces a time delay between incidence and re-emission, lowering the photon’s effective frequency and causing a transient reduction in speed. Nevertheless, these effects are environmental and do not contradict the constancy of photon speed in free space.

Thus, under ECM, the photon's behaviour—including its effective acceleration, energy dissipation, and Planck-limited oscillation—is a direct consequence of its negative apparent mass (−Mᵃᵖᵖ) and the fundamental constraints of the vacuum medium.