Definitions of Apparent Mass and Effective Mass

Soumendra Nath Thakur

04-09-2024

Apparent Mass

Definition: Apparent mass refers to the situation where the effective mass of an object or system appears to be reduced due to the influence of a negative effective mass term. This concept arises under specific conditions, such as objects in motion or within strong gravitational fields, where the negative effective mass term significantly impacts the system's dynamics. Apparent mass is not exclusively intensive but can manifest under particular circumstances where the negative effective mass plays a prominent role.

Characteristics:

• Negative Effective Mass: Apparent mass is characterized by a negative value when the negative effective mass term is significant. This situation arises in contexts involving mechanical and gravitational dynamics, as well as in phenomena such as dark energy, where the negative contribution influences the system's overall behaviour.

• Conditions for Negative Apparent Mass: Apparent mass becomes negative when the negative effective mass term dominates the system’s overall effective mass. This typically occurs in scenarios involving objects in motion or within strong gravitational fields, especially under extreme gravitational potentials.

Effective Mass

Definition: Effective mass is a composite term that includes both the matter mass and the negative effective mass. It represents the total mass affecting the system's response to applied forces or gravitational influences.

Characteristics:

• Positive or Negative Effective Mass: The effective mass can be either positive or negative depending on the relative magnitudes of the matter mass and the negative effective mass.

• Positive Effective Mass: When the matter mass is greater than the negative effective mass, the effective mass is positive.

• Negative Effective Mass: When the negative effective mass term is significant, or in extreme conditions such as high velocity or strong gravitational fields, the effective mass can become negative.

• Implications: The effective mass determines how an object or system responds to forces or gravitational influences. In classical mechanics, this is reflected in the equation  F = (Mᴍ + Mᵉᶠᶠ)aᵉᶠᶠ, where Mᵉᶠᶠ may include a negative component from apparent mass, which is characterized as negative effective mass.

Example in Context:

• In Motion: When force is applied and acceleration increases, the effective mass can include a negative term, leading to a reduction in the apparent mass. This is captured by the formula F = (Mᴍ + Mᵉᶠᶠ)aᵉᶠᶠ, where Mᵉᶠᶠ may be negative due to the negative effective mass contribution.

• In Gravitational Potential: In gravitational contexts, if the negative effective mass is significant, the effective mass can become negative, affecting the gravitational dynamics. This is described by Mɢ = Mᴍ + (-Mᵉᶠᶠ), where Mᵉᶠᶠ includes the negative apparent mass term.

Summary:

• Apparent Mass: Always represents the negative effective mass term in a system where this negative contribution is significant.

• Effective Mass: A combination of matter mass and negative effective mass, which can be positive or negative depending on the system's conditions.

Apparent Mass Summary:

Definition:

• Apparent Mass refers to the concept of negative effective mass in specific conditions.

Characteristics: 

•It is always negative when the negative effective mass term is dominant, such as in scenarios involving dark energy or extreme gravitational fields.

Effective Mass Summary:

Definition:

• Effective Mass combines matter mass and negative effective mass.

Characteristics:

• Can be positive when matter mass exceeds the magnitude of the negative effective mass.

• Can be negative when the negative effective mass term is significant or in extreme conditions.

Summary

• Apparent Mass: Represents the negative effective mass term.

• Effective Mass: The overall mass affecting the system, including both matter mass and any negative effective mass components.

Summary of "Dark Energy and the Structure of the Coma Cluster of Galaxies" by A. D. Chernin et al.

Soumendra Nath Thakur

04-09-2024

Three Types of Masses:

Matter Mass (Mᴍ): Total mass of both dark matter and baryonic matter within the cluster, contributing to its gravitational binding.

Dark Energy Effective Mass (Mᴅᴇ): Conceptual mass representing dark energy's effect, characterized by negative pressure, which creates a negative mass (Mᴅᴇ < 0) that opposes gravitational attraction.

Gravitating Mass (Mɢ): Net mass causing gravitational attraction, combining the effects of matter mass and dark energy:

Mɢ = Mᴍ + Mᴅᴇ

Matter Density (ρᴍ) in the Cluster:

Definition: Total mass per unit volume, including dark and baryonic matter.

Formula: ρᴍ =Mₜₒₜₐₗ/V

Components:

Dark Matter Density (ρᴅᴍ): Dominant component (~80-90%).

Baryonic Matter Density (ρᴏʀᴅ): Visible matter (~10-20%).

Density Relationships:

Matter Density (ρᴍ): Density of all matter components.

Dark Energy Density (ρᴅᴇ): Constant, uniform density (ρᴅᴇ ≈ 0.71 × 10⁻²⁹ g/cm³).

Gravitating Mass Density (ρɢ): Combined density including matter and dark energy:

ρɢ = ρᴍ + ρᴅᴇ

Matter Density of the Coma Cluster:

The average matter density (ρᴍ) in the core of the Coma Cluster is about ρm ≈ 10⁻²⁶ kg/m³, with dark matter constituting 85-90% of this total.

Uniformity of Average Matter Density (ρᴍ) in the Universe:

The average matter density across the universe is roughly uniform on very large scales, in accordance with the cosmological principle. Local variations exist due to structures, but these average out over larger distances.

Effective Mass and Negative Effective Mass:

Effective Mass: Includes both matter and dark energy effects, representing the net gravitational influence.

Negative Effective Mass: Arises from dark energy's negative pressure, contributing to antigravitational forces.

Comparison with Classical Mechanics:

Classical mechanics equates "mass" and "gravitational mass," assuming gravitational forces are always attractive. The study suggests extending classical mechanics to include dark energy's effects to account for observed antigravitational forces.

Keywords: Dark Energy, Gravitating Mass, Matter Density, Coma Cluster, Antigravitational Force,

#ExtendedClassicalMechanics #DarkEnergy, #GravitatingMass, #MatterDensity, #ComaCluster, #AntigravitationalForce, #EffectiveMass, #UniversalForce, #NegativeEffectiveMass, #GravitationalDynamics,

Negative Effective Mass: Insights from Universal Force and Acceleration Dynamics

Expanded Insights - Dark Energy as a By-Product of ...

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

01-09-2024

The universal force Fᴜₙᵢᵥ is defined by the product of the effective acceleration aᵉᶠᶠᴜₙᵢᵥ and the combined inverse contributions of two types of mass: the variable effective mass Mᵉᶠᶠᴜₙᵢᵥ and the constant matter mass Mᴍᴜₙᵢᵥ. This relationship emphasizes that the universal force depends not only on acceleration but also on the dynamic interplay between these masses. The effective mass reflects the system’s response to dynamic factors such as motion and gravitational interactions, and it can differ from the constant matter mass by varying according to system conditions.

The universal force and acceleration increase or decrease proportionally with the combined reciprocal masses, where variations in the effective mass directly influence acceleration and the resulting universal force. As the effective mass decreases, acceleration increases, and vice versa. This relationship aligns with the interpretation of "negative effective mass," where changes in the dynamic state of the universe alter gravitational interactions.

The concept of "negative effective mass" arises from this interpretation of effective mass. When extended to dark energy's influence on gravitational dynamics, it captures the idea that the effective mass may exhibit properties akin to a negative effective density, leading to repulsive gravitational effects. In this context, "negative effective mass" describes how the dynamic properties of dark energy counteract gravitational attraction, contrasting with the attractive behaviour of conventional matter.

The effective mass Mᵉᶠᶠᴜₙᵢᵥ reflects the apparent mass loss or gain relative to the constant matter mass Mᴍᴜₙᵢᵥ. When there is an apparent mass loss, the effective mass increases to maintain balance within the system’s dynamics, suggesting that under certain conditions, the effective mass could be perceived as "negative." This negative value provides a framework for understanding inverse gravitational effects observed with dark energy, where repulsive dynamics challenge traditional gravitational interactions.

Additionally, when the universal force Fᴜₙᵢᵥ increases, the effective acceleration aᵉᶠᶠᴜₙᵢᵥ also increases. Initially, the effective mass Mᵉᶠᶠᴜₙᵢᵥ is equivalent to the matter mass Mᴍᴜₙᵢᵥ. However, as force or acceleration continues to increase, the effective mass can exceed the matter mass, thereby potentially dominating the gravitating mass Mɢᴜₙᵢᵥ. This implies that the effective mass plays a crucial role in determining the overall gravitational behaviour, supporting the idea of "negative effective mass" in scenarios where dark energy exerts a repulsive force.

By incorporating the concept of "negative effective mass" into the extended framework of classical mechanics, we develop a more comprehensive understanding of the gravitational dynamics, allowing us to account for the repulsive effects of dark energy on the universe's expansion. This refined interpretation bridges the abstract notion of dynamic mass variations with observable cosmological phenomena, providing insight into the complex interplay between mass, force, and acceleration in the universe.

Dark energy's influence on the universe's expansion can be understood in terms of the effective mass (Mᵉᶠᶠᴜₙᵢᵥ) exhibiting properties that suggest a negative effective density. When the effective mass exceeds the matter mass (Mᴍᴜₙᵢᵥ), it contributes to gravitational dynamics that may resemble those associated with a negative gravitating mass (Mɢᴜₙᵢᵥ), leading to the repulsive effects observed in the universe.

Mathematical Framework:

The mathematical framework establishes a relationship between potential energy, effective mass, and universal force, providing insight into the universe's expansion and the concept of "negative effective mass." The potential energy of the universe (PEᴛₒₜᴜₙᵢᵥ) is directly proportional to the effective mass (Mᵉᶠᶠᴜₙᵢᵥ), indicating that the effective mass plays a crucial role in defining the universe's dynamics.

The equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ describes the universal force as directly proportional to effective acceleration (aᵉᶠᶠᴜₙᵢᵥ) and inversely proportional to effective mass (Mᵉᶠᶠᴜₙᵢᵥ). An increase in acceleration leads to an increase in the universal force and a corresponding decrease in effective mass, which can lead to the formation of matter. Over time, potential energy becomes dependent on both the matter mass (Mᴍᴜₙᵢᵥ) and the present effective mass, shaping the gravitational dynamics.

By linking these parameters, this framework explains how variations in effective mass, particularly when perceived as negative, contribute to the repulsive effects associated with dark energy, providing a comprehensive view of the complex interplay between mass, force, and acceleration in the universe.

The Equations:

PEᴛₒₜᴜₙᵢᵥ ∝ Mᵉᶠᶠᴜₙᵢᵥ,

This expression, establishes a direct relationship between the universe's potential energy and its effective mass. In the early universe, effective mass played a critical role in determining the potential energy. The universal force was necessary to convert this potential energy into kinetic energy, facilitating the rapid expansion of the universe. As the effective mass decreased, acceleration increased, reflecting the dynamics of this early rapid expansion.

The equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ

describes that the universal force is directly proportional to effective acceleration, and effective acceleration is inversely proportional to effective mass. This relationship suggests that in the early universe, the universal force was the product of the effective mass and the effective acceleration.

Since acceleration is inversely proportional to mass, an increase in effective acceleration leads to a corresponding increase in the universal force, which, in turn, causes a decrease in the effective mass as the acceleration increases, and so corresponding increase in matter mass through formation. As acceleration increase, the effective mass decrease, forming matter mass.

Later, the potential energy became dependent on both the matter mass (Mᴍᴜₙᵢᵥ) and the present effective mass.

The force is influenced by the interaction between the matter mass and the effective mass, where the effective acceleration (aᵉᶠᶠᴜₙᵢᵥ) is inversely related to the total mass, comprising both matter and effective mass, represented by the equation:

Fᴜₙᵢᵥ = (Mᴍᴜₙᵢᵥ+Mᵉᶠᶠᴘᵣₑₛₑₙₜ) · aᵉᶠᶠᴜₙᵢᵥ

As the effective acceleration increases, the apparent matter mass decreases, corresponding increase in present effective mass, which is negative, within this combined mass. Thus, the emergence of dark energy from negative effective mass and its dominant role in gravitational dynamics can be explained by the relationship between effective mass and gravitational effects. As acceleration increased, the apparent matter mass decreased, generating effective mass.

Dark energy's influence on the universe's expansion can be understood in terms of the effective mass (Mᵉᶠᶠᴜₙᵢᵥ) exhibiting properties that suggest a negative effective density. When the effective mass exceeds the matter mass (Mᴍᴜₙᵢᵥ), it contributes to gravitational dynamics that may resemble those associated with a negative gravitating mass (Mɢᴜₙᵢᵥ), leading to the repulsive effects observed in the universe. As provided under, "Negative Effective Mass: Insights from Universal Force and Acceleration Dynamics".

#EffectiveMass, #UniversalForce, #NegativeEffectiveMass, #GravitationalDynamics, #DarkEnergy,

Dark Energy as a By-Product of Negative Effective Mass: Discussion.

Soumendra Nath Thakur

31-08-2024

Effective dark energy is interpreted as a manifestation of negative effective mass, a concept rooted in extended classical mechanics and involving the dynamics of potential, kinetic, and gravitational forces. This phenomenon emerges from the apparent reduction in invariant matter mass and its resulting influence on the universe's overall dynamics. ResearchGate Discussion Link Here!

Note: Matter mass Mᴍ is understood as the combined mass of normal matter (such as baryonic matter) and dark matter.

Summary:

Effective dark energy, considered a by-product of negative effective mass, arises from the intricate interplay of potential, kinetic, and gravitational dynamics in the universe. This concept challenges traditional views by suggesting that dark energy is not a separate entity but rather a consequence of negative effective mass. The fundamental equation, PEᴛₒₜᴜₙᵢᵥ ∝ Mᵉᶠᶠᴜₙᵢᵥ, establishes a direct relationship between the universe's potential energy and its effective mass, highlighting their intrinsic connection.

In the early universe, effective mass played a critical role in determining the potential energy. The universal force was necessary to convert this potential energy into kinetic energy, facilitating the rapid expansion of the universe. As the effective mass decreased, acceleration increased, reflecting the dynamics of this early rapid expansion, as described by the equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ. This equation illustrates that the universal force is directly proportional to effective acceleration, offering key insights into the universe's expansion dynamics.

As the universe continued to evolve, its potential energy became influenced by both matter mass and effective mass, including contributions from dark energy and other effective masses. Later, the universal force was shaped by both matter and effective mass, with effective acceleration inversely related to the combined mass. The ongoing generation of dark energy and its dominance in gravitational dynamics are thus explained by the relationship between effective mass and gravitational effects, suggesting a repulsive gravitational force that significantly influences the universe's structure and evolution.

Effective dark energy can thus be seen as a by-product of negative effective mass, arising from the complex interrelations of potential, kinetic, and gravitational forces, and reflecting the apparent reduction in invariant matter mass over time.

Reference: Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781 

UPDATE 01-09-2024: Expanded Insights on Negative Effective Mass and Dark Energy Dynamics

Negative Effective Mass: Insights from Universal Force and Acceleration Dynamics

The universal force Fᴜₙᵢᵥ is defined by the product of the effective acceleration aᵉᶠᶠᴜₙᵢᵥ and the combined inverse contributions of two types of mass: the variable effective mass Mᵉᶠᶠᴜₙᵢᵥ and the constant matter mass Mᴍᴜₙᵢᵥ. This relationship emphasizes that the universal force depends not only on acceleration but also on the dynamic interplay between these masses. The effective mass reflects the system’s response to dynamic factors such as motion and gravitational interactions, and it can differ from the constant matter mass by varying according to system conditions.

The universal force and acceleration increase or decrease proportionally with the combined reciprocal masses, where variations in the effective mass directly influence acceleration and the resulting universal force. As the effective mass decreases, acceleration increases, and vice versa. This relationship aligns with the interpretation of "negative effective mass," where changes in the dynamic state of the universe alter gravitational interactions.

The concept of "negative effective mass" arises from this interpretation of effective mass. When extended to dark energy's influence on gravitational dynamics, it captures the idea that the effective mass may exhibit properties akin to a negative effective density, leading to repulsive gravitational effects. In this context, "negative effective mass" describes how the dynamic properties of dark energy counteract gravitational attraction, contrasting with the attractive behaviour of conventional matter.

The effective mass Mᵉᶠᶠᴜₙᵢᵥ reflects the apparent mass loss or gain relative to the constant matter mass Mᴍᴜₙᵢᵥ. When there is an apparent mass loss, the effective mass increases to maintain balance within the system’s dynamics, suggesting that under certain conditions, the effective mass could be perceived as "negative." This negative value provides a framework for understanding inverse gravitational effects observed with dark energy, where repulsive dynamics challenge traditional gravitational interactions.

Additionally, when the universal force Fᴜₙᵢᵥ increases, the effective acceleration aᵉᶠᶠᴜₙᵢᵥ also increases. Initially, the effective mass Mᵉᶠᶠᴜₙᵢᵥ is equivalent to the matter mass Mᴍᴜₙᵢᵥ. However, as force or acceleration continues to increase, the effective mass can exceed the matter mass, thereby potentially dominating the gravitating mass Mɢᴜₙᵢᵥ. This implies that the effective mass plays a crucial role in determining the overall gravitational behaviour, supporting the idea of "negative effective mass" in scenarios where dark energy exerts a repulsive force.

By incorporating the concept of "negative effective mass" into the extended framework of classical mechanics, we develop a more comprehensive understanding of the gravitational dynamics, allowing us to account for the repulsive effects of dark energy on the universe's expansion. This refined interpretation bridges the abstract notion of dynamic mass variations with observable cosmological phenomena, providing insight into the complex interplay between mass, force, and acceleration in the universe.

Dark energy's influence on the universe's expansion can be understood in terms of the effective mass (Mᵉᶠᶠᴜₙᵢᵥ) exhibiting properties that suggest a negative effective density. When the effective mass exceeds the matter mass (Mᴍᴜₙᵢᵥ), it contributes to gravitational dynamics that may resemble those associated with a negative gravitating mass (Mɢᴜₙᵢᵥ), leading to the repulsive effects observed in the universe.

Mathematical Framework:

The mathematical framework establishes a relationship between potential energy, effective mass, and universal force, providing insight into the universe's expansion and the concept of "negative effective mass." The potential energy of the universe (PEᴛₒₜᴜₙᵢᵥ) is directly proportional to the effective mass (Mᵉᶠᶠᴜₙᵢᵥ), indicating that the effective mass plays a crucial role in defining the universe's dynamics.

The equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ describes the universal force as directly proportional to effective acceleration (aᵉᶠᶠᴜₙᵢᵥ) and inversely proportional to effective mass (Mᵉᶠᶠᴜₙᵢᵥ). An increase in acceleration leads to an increase in the universal force and a corresponding decrease in effective mass, which can lead to the formation of matter. Over time, potential energy becomes dependent on both the matter mass (Mᴍᴜₙᵢᵥ) and the present effective mass, shaping the gravitational dynamics.

By linking these parameters, this framework explains how variations in effective mass, particularly when perceived as negative, contribute to the repulsive effects associated with dark energy, providing a comprehensive view of the complex interplay between mass, force, and acceleration in the universe.

The Equations:

PEᴛₒₜᴜₙᵢᵥ ∝ Mᵉᶠᶠᴜₙᵢᵥ,

This expression, establishes a direct relationship between the universe's potential energy and its effective mass. In the early universe, effective mass played a critical role in determining the potential energy. The universal force was necessary to convert this potential energy into kinetic energy, facilitating the rapid expansion of the universe. As the effective mass decreased, acceleration increased, reflecting the dynamics of this early rapid expansion.

The equation Fᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ · aᵉᶠᶠᴜₙᵢᵥ

describes that the universal force is directly proportional to effective acceleration, and effective acceleration is inversely proportional to effective mass. This relationship suggests that in the early universe, the universal force was the product of the effective mass and the effective acceleration.

Since acceleration is inversely proportional to mass, an increase in effective acceleration leads to a corresponding increase in the universal force, which, in turn, causes a decrease in the effective mass as the acceleration increases, and so corresponding increase in matter mass through formation. As acceleration increase, the effective mass decrease, forming matter mass.

Later, the potential energy became dependent on both the matter mass (Mᴍᴜₙᵢᵥ) and the present effective mass.

The force is influenced by the interaction between the matter mass and the effective mass, where the effective acceleration (aᵉᶠᶠᴜₙᵢᵥ) is inversely related to the total mass, comprising both matter and effective mass, represented by the equation:

Fᴜₙᵢᵥ = (Mᴍᴜₙᵢᵥ+Mᵉᶠᶠᴘᵣₑₛₑₙₜ) · aᵉᶠᶠᴜₙᵢᵥ

As the effective acceleration increases, the apparent matter mass decreases, corresponding increase in present effective mass, which is negative, within this combined mass. Thus, the emergence of dark energy from negative effective mass and its dominant role in gravitational dynamics can be explained by the relationship between effective mass and gravitational effects. As acceleration increased, the apparent matter mass decreased, generating effective mass.

Dark energy's influence on the universe's expansion can be understood in terms of the effective mass (Mᵉᶠᶠᴜₙᵢᵥ) exhibiting properties that suggest a negative effective density. When the effective mass exceeds the matter mass (Mᴍᴜₙᵢᵥ), it contributes to gravitational dynamics that may resemble those associated with a negative gravitating mass (Mɢᴜₙᵢᵥ), leading to the repulsive effects observed in the universe. As provided under, "Negative Effective Mass: Insights from Universal Force and Acceleration Dynamics.

The Role of Effective Mass in Gravitational Dynamics:

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
30 August 2024

Introduction

The study "Generation of Dark Energy in the Universe: Dominance in Gravitational Dynamics" presents a novel framework for understanding the gravitational dynamics of the universe, incorporating the concept of effective mass. This literature review will delve into the key findings of the study, its implications for cosmology, and potential areas for future research.

Key Findings

Effective Mass and Gravitational Mass: 

The study introduces the equation

Mɢᴜₙᵢᵥ = Mᵉᶠᶠᴜₙᵢᵥ = Mᴍᴜₙᵢᵥ + Mᵉᶠᶠᴘᵣₑₛₑₙₜ, 

which relates the gravitational mass of the universe (Mɢᴜₙᵢᵥ) to its matter mass (Mᴍᴜₙᵢᵥ) and present effective mass (Mᵉᶠᶠᴘᵣₑₛₑₙₜ).

Negative Gravitating Mass: 

When the effective mass exceeds matter mass, negative gravitating mass arises, leading to repulsive gravitational effects.

Potential Energy: 

The potential energy of the universe is linked to the effective mass and matter mass, evolving over time.

Force and Acceleration: 

The study derives equations relating universal force, effective mass, and effective acceleration, providing insights into the dynamics of the universe.

Implications for Cosmology

Accelerated Expansion: The dominance of negative gravitating mass contributes significantly to the observed accelerated expansion of the universe.

Dark Matter and Dark Energy: 

The study offers a new perspective on the role of dark matter and dark energy in shaping cosmic dynamics.

Quantum Gravity: 

The concepts introduced in the study may have implications for quantum gravity theories, providing potential avenues for further exploration.

Conclusion

The study "Generation of Dark Energy in the Universe: Dominance in Gravitational Dynamics" offers a valuable contribution to our understanding of the universe's gravitational dynamics. By introducing the concept of negative gravitating mass and its relationship to effective mass and matter mass, the study provides new insights into the drivers of cosmic expansion and the interplay between different forms of energy and matter. Future research can delve deeper into these concepts, exploring their implications for quantum gravity and potential experimental verification.