Effective Acceleration of Photon Extended Classical Mechanics (ECM)

Effective Acceleration of Photon at Emission (ECM Framework)

Photon Propagation and Effective Constants in ECM

Using the kinematic relation:

\[\Delta d = v_0\,\Delta t + \tfrac{1}{2}\,a^{\mathrm{eff}}\,(\Delta t)^2\]

Given \(\Delta d = 3\times10^{8}\,\mathrm{m},\; v_0 = 0,\; \Delta t = 1\,\mathrm{s}\),

\[\Rightarrow\quad a^{\mathrm{eff}} = 6\times10^{8}\;\mathrm{m\,s^{-2}}\]

At high \(a^{\mathrm{eff}}\) (for example, 2c/s), photons maintain \(v=c\) due to the compensatory rise of the apparent mass \(-M^{\mathrm{app}}\) as energy reduces:

\[\Delta h f \downarrow \;\Rightarrow\; \Delta M_m \downarrow \;\Rightarrow\; -M^{\mathrm{app}} \uparrow\]

At escape: \(-M^{\mathrm{app}} \rightarrow -M^{\mathrm{app}},\; \Delta M_m \rightarrow 0\Rightarrow v = c\).

Effective Acceleration of Photon at Emission (ECM Framework)

In Extended Classical Mechanics (ECM), a photon’s mass-frequency state is governed by the manifestation principle:

\[\Delta PE_{\text{ecm}} \leftrightarrow \Delta KE_{\text{ecm}} \leftrightarrow \Delta M_m, \quad M^{\mathrm{app}} \equiv -\Delta PE_{\text{ecm}}\]

The effective acceleration at emission, \(a^{\mathrm{eff}}_{\text{photon}}\), is a variable, context-dependent parameter that describes the photon’s kinematic emergence over a chosen time interval. The effective acceleration varies inversely with the apparent mass according to the formal bookkeeping relation:

\[(-M^{\mathrm{app}})\;a^{\mathrm{eff}}_{\text{photon}} \sim \text{constant}\quad\text{(formal force-like bookkeeping)}\]

This relation is analogous to the frequency–wavelength law:

\[c = f_{\text{photon}}\;\lambda_{\text{photon}}\]

and remains dimensionally consistent when the mass–energy mapping is made explicit:

\[\Delta M_m = \frac{\Delta E}{c^2}\quad\text{(with }\Delta E=\Delta PE_{\text{ecm}}=\Delta KE_{\text{ecm}}\text{)}\]

The corresponding force-like quantity is defined as:

\[F_{\text{photon}} = (-M^{\mathrm{app}})\;a^{\mathrm{eff}}_{\text{photon}}\]

In ECM this \(F_{\text{photon}}\) is self-generated by the photon (not an external force) and manifests as a repulsive effect directed away from the source.

As \(a^{\mathrm{eff}}_{\text{photon}}\) decreases, \(-M^{\mathrm{app}}\) increases, and vice versa.
Photon frequency \((f_{\text{photon}})\) and wavelength \((\lambda_{\text{photon}})\) adjust to maintain \(c = f_{\text{photon}}\,\lambda_{\text{photon}}\).
The manifestation principle ensures all relations are dimensionally and physically consistent.

This unified ECM framework explains the autonomous acceleration of photons at emission, linking apparent mass, effective acceleration, photon frequency, wavelength, and intrinsic repulsive force in a single internally consistent formalism.