Unified Energy-Mass-Frequency Equation:
Mᵉᶠᶠ⋅c² = h⋅f = E
This equation bridges extended classical mechanics and quantum theory, presenting a cohesive framework to describe the energy-mass-frequency relationship. It establishes the equivalence of a photon’s relativistic energy, its effective mass-energy, and its quantum electromagnetic energy.
1. Effective Mass (Mᵉᶠᶠ) in Photon Dynamics
From extended classical mechanics, the effective mass Mᵉᶠᶠ plays a central role in the dynamics of massless particles, including photons. It is defined as:
Mᵉᶠᶠ = Mɢ = Mᴍ −Mᵃᵖᵖ
Where:
The force equation encapsulates this relationship:
Fₚₕₒₜₒₙ = Mᵉᶠᶠ·aᵉᶠᶠ
This underscores that the photon's behaviour in gravitational fields is dictated by its energy-driven effective mass Mᵉᶠᶠ, not rest mass.
2. The Term Mᵉᶠᶠ⋅c²:
This term represents the effective mass-energy of a photon in extended classical mechanics. While photons lack rest mass (M₀=0), their effective mass Mᵉᶠᶠ emerges from their intrinsic energy (E):
Mᵉᶠᶠ = E/c² = (h⋅f)/c²
By incorporating Mᵉᶠᶠ into the energy equation, we establish that the photon's energy (E) governs mass-like behaviour in gravitational interactions, enabling the photon to exchange momentum and energy dynamically.
3. Quantum Energy: E=h⋅f
This represents the photon's quantum electromagnetic energy, where h is Planck's constant, and f is the frequency.
4. Relativistic Energy:
E=Mᵉᶠᶠ⋅c²
This term extends Einstein's equation (E=mc²) to photons by substituting the effective mass (Mᵉᶠᶠ) for rest mass.
• Even without rest mass, photons possess energy equivalent to a mass-like quantity due to their motion and frequency, emphasizing the role of effective mass in photon dynamics.
5. Unified Representation
The equation Mᵉᶠᶠ⋅c² = h⋅f = E provides a unified perspective:
This unified representation aligns classical mechanics with quantum principles, emphasizing the photon’s dual nature as both a quantum particle and a relativistic entity.
6. Significance in Photon Dynamics
• Energy-Mass Interplay:
The inclusion of Mᵉᶠᶠ emphasizes its pivotal role in gravitational interactions. Despite photons lacking rest mass, their effective mass enables them to interact gravitationally.
• Observable Phenomena:
Gravitational lensing, redshift, and energy exchanges are explained through momentum transfer facilitated by Mᵉᶠᶠ.
• Force Dynamics:
The force equation Fₚₕₒₜₒₙ = Mᵉᶠᶠ·aᵉᶠᶠ represents the negative force generated by the photon’s total energy, which includes both its gravitational interaction energy (Eg) and its intrinsic energy (E). This negative force is responsible for:
Escape from the Gravitational Well:
Facilitating the photon’s ability to escape the gravitational pull of the source well by expending energy associated with its gravitational interaction (Eg).
Maintenance of Constant Speed (c):
Sustaining the photon’s constant speed by utilizing the negative force generated from its inherent energy (E), which is not expended unless there is cosmic recession.
By expressing E as both Mᵉᶠᶠ and h⋅f, this framework integrates the principles of classical mechanics and quantum mechanics, providing a unified model for photon behaviour in gravitational fields. Rather than relying on geometric spacetime curvature, this approach introduces quantifiable energy-mass-frequency relationships, advancing the understanding of photon dynamics.
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1 comment:
de Broglie's conditions published in the 1930s, which require a localized photon to obey Maxwell's equations by being self-propelling and self-guiding in a straight line by default, provides robust theoretical support to my framework. The concept that the photon's self-propelling nature arises from half of its energy propelling the other half is a profound insight that aligns well with the dynamics described in my extended classical mechanics approach.
In particular, this point reinforces the interpretation of the negative force in my equation Fₚₕₒₜₒₙ = Mᵉᶠᶠ·aᵉᶠᶠ, where the photon's total energy (inclusive of its gravitational interaction energy Eg and intrinsic energy E) generates a negative force. This force is critical for the photon's:
Escape from the Gravitational Well: Enabling the photon to overcome the gravitational pull and propagate outward.
Maintenance of Constant Speed (c): Allowing the photon to self-propel and maintain its characteristic speed irrespective of external influences.
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