ORCiD: 0000-0003-1871-7803

February 10, 2025

Within Extended Classical Mechanics (ECM), photon dynamics describes dark energy by positing that photons, due to their unique properties within the framework, can exhibit a "negative apparent mass," causing them to effectively repel each other and contribute to the observed accelerating expansion of the universe, which is the primary characteristic of dark energy; this negative mass arises from the complex interaction of photon momentum and energy within the ECM equations, leading to an "effective acceleration" that counteracts gravitational pull.

Photon Dynamics and Dark Energy in the Framework of Extended Classical Mechanics (ECM)

In the framework of Extended Classical Mechanics (ECM), photon dynamics and dark energy are intricately linked through the concepts of effective mass (Mᵉᶠᶠ) and apparent mass (Mᵃᵖᵖ). This framework provides a novel perspective on how gravitational interactions can induce mass in initially massless particles, such as photons, and how these interactions relate to the observed phenomena of dark energy.

Photon Dynamics and Effective Mass

Effective Mass and Apparent Mass:

In ECM, the effective mass (Mᵉᶠᶠ) of a photon is a dynamic property that combines the rest mass (Mᴍ​) and the apparent mass (Mᵃᵖᵖ). For photons, which have zero rest mass, their apparent mass dictates their energy-momentum exchanges and response to forces. This leads to the reformulated force equation:

Fₚₕₒₜₒₙ =−Mᵃᵖᵖ aᵉᶠᶠ

The apparent mass (Mᵃᵖᵖ) can be negative, which is crucial for understanding antigravitational effects and dark energy.

Gravitational Redshift and Photon Energy:

The total energy of a photon is analysed as the sum of its inherent energy (E) and gravitational interaction energy (Eg​). As photons escape a gravitational field, they retain their inherent energy while gradually expending their gravitational energy. This leads to gravitational redshift, where the photon's frequency shifts due to the gravitational potential.

Dark Energy and Negative Effective Mass

Dark Energy as a Gravitational Interaction:

In ECM, dark energy is not treated as a conventional field or particle but as a gravitationally interactive background that influences mass distributions at intergalactic scales. It acts on cosmic scales by modifying the gravitational potential, leading to the observed cosmic acceleration.

Negative Effective Mass and Antigravitational Effects:

The negative effective mass (Mᵉᶠᶠ