Summary of Extended Classical Mechanics: Vol-1 (Rev-2,3)

21 November 2024

This paper explores how classical mechanics can be extended to account for modern scientific concepts like dark matter, dark energy, and negative mass. It focuses on how these concepts affect the understanding of mass and gravitational dynamics.

Key Points:

Equivalence Principle Redefined: The traditional equivalence principle (inertial mass = gravitational mass) is re-examined to include dark matter.

• Matter Mass (Mᴍ): This represents the combined mass of normal (baryonic) matter and dark matter.
• Apparent Mass (Mᵃᵖᵖ): This is a negative mass component introduced to account for situations involving motion and strong gravitational fields. It influences the Effective Mass (Mᵉᶠᶠ), which is the sum of matter mass and negative apparent mass.
• Gravitating Mass (Mɢ): This is the total effective mass of a system, incorporating both matter mass and negative apparent mass. It is equivalent to the mechanical effective mass (Mᵉᶠᶠ).
• Dark Energy and Negative Mass: Dark energy is reinterpreted as a negative apparent mass term, influencing gravitational dynamics.

Modifications to Existing Equations:

• Newton's Second Law is modified to include effective mass and effective acceleration.
• Newton's Law of Universal Gravitation is reinterpreted to account for effective mass.

Methodology:

• Reinterpreting existing concepts in light of extended classical mechanics.
• Developing mathematical models to quantify the relationships between different mass components and their impact on gravitational interactions.
• Analysing how the interplay of mass components affects gravitational forces and dynamics.
• Using simulations to test the models and compare with observational data.

Expected Outcomes:

• Refine the understanding of mass dynamics in extended classical mechanics.
• Explore the implications of negative apparent mass for gravitational theories.
• Gain insights into the role of dark energy and its interaction with matter.

Overall, this research proposes an extended framework for classical mechanics that incorporates modern scientific understanding of mass and gravity.

#ExtendedClassicalMechanics

Discussion:Photon’s Trajectory and Energy Exchange in Gravitational Fields.

ResearchGate Discussion Link here.

Dear Mr. Ilya Boldov,

21 November 2024

Thank you for your thoughtful contributions to our discussion regarding the photon’s trajectory and energy exchange in gravitational fields. While I appreciate your perspective, I maintain several key aspects of the discussion framework deserve more focused consideration.

The discussion centres on a nuanced distinction between intrinsic photon energy (E) and gravitational-interaction energy (Eg), which enables the symmetric energy exchange observed as photons traverse gravitational fields. This framework is grounded in established conservation laws, combining classical mechanics, relativity, and quantum principles. The interpretations align with phenomena such as gravitational redshift and lensing, which are well-documented within relativistic physics.

Your initial dismissal of photon-gravitational interactions as "meaningless" appears to overlook this broader framework. It is widely accepted that photon energy, despite lacking rest mass, possesses an energy equivalent that interacts gravitationally, as evidenced by gravitational redshift and lensing. Your statement that space geometry alone dictates photon paths simplifies these complex interactions and neglects the role of energy conservation in relativistic contexts.

Furthermore, your emphasis on discrete spatial elements and particle geometries in reply2 introduces an interesting but tangential concept that does not directly address the discussion's core argument. While discrete space theory may provide insights into particle motion, it remains unclear how it challenges the proposed framework of E and Eg, which preserves energy conservation in gravitational dynamics. I would welcome a more specific counter or clarification on how this framework conflicts with your perspective.

To advance this discussion constructively, I encourage you to engage directly with the following points:

1. The role of photon energy equivalence in gravitational lensing and redshift phenomena, and how your discrete space model accounts for these relativistic effects.

2. The conservation of energy during photon traversal of gravitational fields, including the distinction between E and Eg, and whether your model preserves or contradicts these principles.

I consider this focused exchange will enhance our understanding and contribute meaningfully to the discourse. I look forward to your response and further exploration of these fascinating topics.

Best regards,

Soumendra Nath Thakur