Assisting Acceleration (aᵉᶠᶠ): Definition

Soumendra Nath Thakur
24-08-2024

Assisting Acceleration (aᵉᶠᶠ), also known as, effective Acceleration, refers to the acceleration that arises in a system when a negative effective mass (Mᵉᶠᶠ, mᵉᶠᶠ) is present. In traditional physics, mass resists acceleration according to Newton's second law of motion. However, when negative effective mass is introduced, it counteracts this resistance, effectively "assisting" the original acceleration of the system. As the magnitude of the negative effective mass increases (i.e., as Mᵉᶠᶠ becomes more negative), the system experiences an increase in kinetic energy, leading to an enhanced or assisted acceleration. This acceleration, denoted as aᵉᶠᶠ, occurs alongside the original acceleration and can be seen as a direct consequence of the negative effective mass's influence, making the object move more freely with less resistance and thus requiring less force to achieve the same or greater acceleration.

Expression: aᵉᶠᶠᵉᶜᵗᶦᵛᵉ = a + |aᵉᶠᶠ|

#assistingacceleration

Power of negative effective mass:

- Soumendra Nath Thakur

Negative effective mass accelerates distant galaxies and influences the Universe's large-scale structure and local mechanical matter. It aids the acceleration associated with the inverse-square law of gravity in extended classical mechanics. Negative effective mass can exist anywhere, including mass, motion, and gravity, and is also the source of dark energy. This new perspective on gravitational dynamics provides a new dimension to cosmic and mechanical phenomena.

External info: ... In some cases, negative effective mass can cause an object to accelerate backward when pushed forward, which is contrary to everyday experience.

#negativeeffectivemass #darkenergy

Acceleration Boosted by Negative Effective Mass behind the Inverse-Square Law of Gravity:

23 August 2024

This scenario examines the interplay between the inverse-square law of gravity and the concept of negative effective mass, focusing on how these factors collectively influence an object's motion.

According to the inverse-square law of gravity, as an object moves away from Earth's surface, the gravitational force exerted on it decreases with the square of the distance. In this context, the concept of negative effective mass becomes pivotal. Negative effective mass introduces an 'assisting acceleration' (aᵉᶠᶠ) or 'acceleration boost' by effectively reducing the object's resistance to gravitational force.

The reduction in gravitational influence due to negative effective mass arises because this mass type is not a static property but is generated as a result of the object's motion or elevation. As the object moves or is elevated, the negative effective mass begins to play a significant role, diminishing the overall gravitational pull on the object. This effect enables the object to accelerate more readily, even as it travels farther from the Earth.

General description of negative effective mass in motion and its empirical support:

23 August 2024

1. Motion and Acceleration:

• When an object with a certain matter mass is put into motion with a particular velocity, it experiences acceleration due to the application of a force. According to Newton's second law of motion, this force is directly proportional to the product of the object's mass and its acceleration.

2. Invariant Matter Mass and Effective Mass:

• As the object accelerates, its intrinsic matter mass appears to be reduced because of the generation of an effective mass. This effective mass acts to assist the object's acceleration, thereby altering the dynamics of its motion.
• Describing a scenario where the inverse-square law of gravity and the concept of negative effective mass work together to influence an object's motion. 
• As an object moves away from the Earth's surface, the inverse-square law of gravity dictates that the gravitational force decreases with distance. This decrease in gravitational pull is where the concept of negative effective mass comes into play, assisting the object's acceleration. The negative effective mass effectively reduces the overall gravitational influence on the object, making it lighter and allowing it to accelerate more easily. As a result, an object with invariant mass can experience increased acceleration due to the combined effects of the inverse-square law of gravity and the negative effective mass assisting its motion.

3. Creation of Negative Effective Mass:

• The concept of effective mass is derived from the difference between the matter mass and the gravitating mass of the object. When the gravitating mass is significant relative to the matter mass, the effective mass can turn out to be negative. This negative effective mass results from the reduction of the object's apparent matter mass as described by the equation.

4. Empirical Support:

• This theoretical framework, which suggests that negative effective mass emerges due to the decrease in the invariant matter mass, is supported by empirical research. Specifically, the study titled "Dark Energy and the Structure of the Coma Cluster of Galaxies" by A. D. Chernin and colleagues provides evidence that aligns with the notion of negative effective mass. This research, particularly in the context of dark energy, corroborates the theoretical understanding of how effective mass interacts with gravitational and mechanical systems.

Summary: The described phenomenon illustrates how an object's apparent matter mass decreases due to the generation of an effective mass that resists acceleration. This results in a negative effective mass, consistent with the findings from empirical research that validate this theoretical concept. The integration of this idea offers a deeper understanding of how negative effective mass influences gravitational and mechanical dynamics.

" When an object with mass Mᴍ sets into motion (v), it accelerates (a) due to the force (F) = Mᴍ·a, and its invariant mass decreases due to the creation of effective mass that assists its acceleration, in turn, creates a negative effective mass (Mᵉᶠᶠ) due to the apparent loss of gravitational mass represented in the equation (Mᵉᶠᶠ = Mᴍ − Mɢ), an equation supported by intercontinental studies on Dark Energy and the Structure of the Coma Cluster of Galaxies" by A. D. Chernin et al. which aligns well with Soumendra Nath Thakur’s concept of negative effective mass.  "

Key Equations and Their Significance in Analysing Negative Effective Mass: ℝ

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

23-08-2024

• Mᵉᶠᶠ = Mɢ − Mᴍ

This fundamental equation directly relates effective mass to gravitating mass and matter mass.
Analysis: This equation relates the effective mass Mᵉᶠᶠ to the gravitating mass Mɢ and matter mass Mᴍ. It implies that the effective mass is the difference between the total gravitating mass and the matter mass.

Consistency: Mathematically consistent. It aligns with the concept that effective mass can incorporate additional factors (like dark energy) affecting gravitational dynamics. This equation is foundational and coherent with the concept of effective mass.

• KE = 1/2·|Mᵉᶠᶠ|·v²

This equation shows how kinetic energy can be positive despite a negative effective mass.

Analysis: This shows kinetic energy KE for a system with negative effective mass. The magnitude of effective mass is used to ensure kinetic energy remains positive.

Consistency: Physically and mathematically consistent. Kinetic energy is positive as it depends on the magnitude of mass and velocity squared, regardless of the sign of the effective mass.

• F = G·(Mᴍ₁ + Mᴍ₁ᵉᶠᶠ)·(Mᴍ₂ + Mᴍ₂ᵉᶠᶠ)/r²

This equation incorporates both matter mass and negative effective mass into gravitational force calculations.

Analysis: This extends the classical gravitational force equation to include negative effective mass.

Consistency: Mathematically consistent with classical mechanics, but physically unconventional. Incorporating negative effective mass introduces repulsive gravitational effects, aligning with some theoretical models but deviating from traditional positive mass assumptions.

• Fʀₑₚ =  −G·Mᵉᶠᶠ·Mᴏₜₕₑᵣ/r²

This equation represents the repulsive force associated with negative effective mass.

Analysis: This represents the repulsive force due to negative effective mass.

Consistency: Mathematically consistent. It reflects the potential for negative effective mass to create repulsive forces, similar to dark energy effects. Physically, it aligns with the hypothesis of repulsive gravity due to negative effective mass.

• Eᴛₒₜ = (PEᴍₘ + PEᴍₘᵉᶠᶠ) + KE

This provides the total energy expression, including potential and kinetic energies.

Analysis: This equation expresses total energy as the sum of potential and kinetic energies.

Consistency: Mathematically and physically consistent. It correctly includes both potential and kinetic energy components and aligns with energy conservation principles.

• PE = Eᴛₒₜ - KE, PE = PEᴍₘ + PEᴍₘᵉᶠᶠ

This equation helps understand potential energy in relation to total energy and kinetic energy.

Analysis: This decomposes potential energy from the total energy minus kinetic energy and accounts for potential energy contributions from both matter and effective masses.

Consistency: Mathematically and physically consistent. It is a correct representation of potential energy, adhering to the total energy equation.

• KE = 1/2 Mᴍv²

This classical equation for kinetic energy is important for understanding how kinetic energy depends on matter mass and velocity.

Analysis: This is the classical equation for kinetic energy based on matter mass and velocity.

Consistency: Mathematically consistent. It is a standard formula for kinetic energy and is consistent with the principles of classical mechanics.

• Mᵉᶠᶠ ∝ −1/Mᴍ

This equation highlights the inverse relationship between effective mass and matter mass.

Analysis: This equation indicates an inverse proportional relationship between effective mass and matter mass.

Consistency: Mathematically consistent. It reflects the concept that as matter mass increases, effective mass decreases (negatively). This is a valid relationship given the context of negative effective mass.

• aᵉᶠᶠ = a−1/a

This equation describes how effective acceleration relates to acceleration in the presence of negative effective mass.

Analysis: This describes the effective acceleration in relation to the conventional acceleration in the presence of negative effective mass.

Consistency: Physically unconventional. It introduces a reciprocal relationship, which may not be intuitive. Careful interpretation is required to ensure this aligns with physical behaviour under negative effective mass conditions.

• F = Mᴍ·a

This classical force equation is crucial for understanding the relationship between force, matter mass, and acceleration.

Analysis: This is the classical force equation, showing force as the product of matter mass and acceleration.

Consistency: Mathematically consistent. It is a fundamental equation in classical mechanics and is relevant for understanding force in the context of matter mass.

• Summary of Consistency:

Mathematically: The equations are generally consistent with the principles of classical mechanics, with modifications to incorporate negative effective mass. They adhere to the laws of energy, force, and acceleration.

Physically: The introduction of negative effective mass leads to unconventional results such as repulsive forces and non-intuitive energy relationships. These results are consistent with theoretical models involving dark energy and negative mass but require careful physical interpretation to align with observed phenomena and established principles.

Overall, while the equations are mathematically consistent, physical interpretation requires careful consideration of how negative effective mass affects conventional mechanics.

#equations