Soumendra Nath Thakur
ORCiD:0000-0003-1871-7803
November, 2024
In the framework of extended classical mechanics, the force equation is expressed as:
F = Mᵉᶠᶠ·aᵉᶠᶠ
where Mᵉᶠᶠ represents the effective mass and aᵉᶠᶠ is the effective acceleration. The term Mᵉᶠᶠ encapsulates the combined contributions of the gravitational mass Mɢ, matter mass Mᴍ, and the negative apparent mass Mᵃᵖᵖ:
Mᵉᶠᶠ = Mɢ = Mᴍ −Mᵃᵖᵖ
Key Components of Mᵉᶠᶠ:
1. Matter Mass (Mᴍ):
The intrinsic mass of the particle or system derived from its rest energy and other inherent properties. For photons, this is zero (Mᴍ=0), emphasizing the absence of rest mass.
2. Negative Apparent Mass (Mᵃᵖᵖ):
A novel concept introduced in this framework, representing the effect of the photon's energy in gravitational interactions. For photons, Mᵃᵖᵖ is directly proportional to their energy, defined as:
Mᵃᵖᵖ = −Mᵉᶠᶠ
3. Gravitational Mass (Mɢ):
In this extended theory, gravitational mass is redefined to include the interplay between matter mass and negative apparent mass, making it an equivalent term for effective mass (Mᵉᶠᶠ).
Role of Mᵉᶠᶠ in the Force Equation:
The force F arises from the interaction between the effective mass (Mᵉᶠᶠ) and the effective acceleration (aᵉᶠᶠ) experienced by a particle or photon in a gravitational and anti-gravitational fields.
For photons, Mᴍ=0, and the effective mass is entirely attributed to the interplay of energy and gravitational potential through Mᵃᵖᵖ. This highlights the unique dynamics of massless particles like photons under gravitational influences.
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