A layman's description: The Source of Energy and Its Relationship to Vibration in ECM.

Soumendra Nath Thakur 

March 27, 2025

The fundamental source of energy in the universe is existence itself. Existence manifests as vibration, and the relationship between energy and vibration is quantitatively expressed by Planck’s equation:  

E = hf

• where (f) represents the frequency of vibration and (h) is Planck’s constant.  

Energy possesses the ability to perform work, which occurs when a force displaces an object. The work done (W) is given by:  

W = Fd

• when the applied force (F) is aligned with the direction of displacement.

According to Newton’s second law, force is related to mass and acceleration as: 

 

F = ma

This equation implies that an applied force (F) causes an inertial object of mass (m) to accelerate in the same direction, provided the force is sufficient to overcome resistance.  

Extension in ECM: Incorporating Negative Apparent Mass.

In the Extended Classical Mechanics (ECM) framework, Newton’s force equation is extended by introducing 'negative apparent mass' (-Mᵃᵖᵖ), which emerges dynamically when matter is in motion. The ECM force equation is:  

F = (Mᴍ + (-Mᵃᵖᵖ))aᵉᶠᶠ

where:  

• Mᴍ represents matter mass, including both ordinary matter and dark matter.  
• -Mᵃᵖᵖ denotes the negative apparent mass generated from M during motion.  

Mass-Energy Conversion and Effective Mass in ECM:

Mass does not retain the same structural form when converted into kinetic energy. While mass and energy are interconvertible, their physical structures differ. When mass transforms into kinetic energy, the energy itself acquires a 'negative apparent mass', leading to a reversal in its gravitational properties—gravity transitions to antigravity.  

According to ECM principles, the effective mass of kinetic energy is defined as:  

Mᵉᶠᶠ = Mᴍ - Mᵃᵖᵖ

Since |Mᵃᵖᵖ| > Mᴍ, it follows that:  

Mᵉᶠᶠ <0 

indicating that kinetic energy has a negative effective mass.  

Implications for Dark Energy and Dark Matter:  

Dark energy, existing beyond our perception, likely possesses a negative effective mass because its frequency is beyond our perceptible range. In ECM, dark matter is incorporated within M (matter mass), while the distinction between dark matter and dark energy arises from their respective 'negative apparent mass' and 'negative effective mass' properties:  

• Dark matter retains a positive effective mass and gravitates.  
• Dark energy has a negative effective mass, leading to antigravitational effects.  

This perspective offers a structured explanation of how ECM accounts for the fundamental nature of energy, mass, dark matter, and dark energy, extending classical mechanics beyond conventional interpretations.